ahmad bought 2 books for 120 at a book fair. Another time he bought 4 books for 280 .wwrite an equation in standard form that represents. Ahmad spending with respect to the number of books purchased.

Answers

Answer 1

An equation in standard form is written as y = 80x - 40

How to write equation for books ahmad bought

Let the cost of books Ahmad bought be represented by m

let the flat cost by c (c reduction at the fair)

Information given in the question is interperted as

ahmad bought 2 books for 120 at a book fair

2m + c = 120

Another time he bought 4 books for 280

4m + c = 480

The required equation leads to 2 simultaneous equation with 2 unknown

2m + c = 120

4x + c = 480

solving the 2 equations gives

m = 80 and y = -40

representing the equation as 1 we have

y = mx + c

Definition of variables to suit the problem to be solved

y = Total cost

m = cost per book

x = number of books

c = flat cost

writing the equation

y = 80x - 40

Learn more about linear functions for costing at:

https://brainly.com/question/29213643

#SPJ1


Related Questions

What are the coordinates of point (1, 5) after dilating by 1/3 about (4,2)?
(2, 1)
(-1,-5)
(3, 2)
(3, 3)

Answers

The coordinates of point (1,5) after dilation is (3,3). Therefore, 4th option is correct.

It is given to us that -

The coordinates of the original point is (1,5)

=> [tex](x_{o},y_{o} )=(1,5)[/tex] ---- (1)

The dilating factor is 1/3

=> [tex]s=\frac{1}{3}[/tex] (say) ---- (2)

And, the center of dilation is at the point (4,2)

=> [tex](x_{cod},y_{cod})=(4,2)[/tex] ---- (3)

We have to find out the coordinates of point (1,5) after dilation.

Using the formula for dilation coordinates from original to image, we have

[tex][(x_{cod}+s(x_{o}-x_{cod}),y_{cod}+s(y_{o}-y_{cod})]\\=[4+\frac{1}{3}(1-4),2+\frac{1}{3}(5-2)]\\=[(4-1),(2+1)]\\=(3,3)[/tex]

Thus, the coordinates of point (1,5) after dilation is (3,3). Therefore, 4th option is correct.

To learn more about dilation visit

https://brainly.com/question/13176891

#SPJ1

Jack is 2 years older than Bob. What was the difference between their ages one year ago?
Need Help ASAP!

Answers

The difference between their ages one year ago was 2 years.

What is difference?

Difference in maths, the result of one of the important mathematical operations, which is obtained by subtracting two numbers.

Given that, Jack is 2 years older than Bob,

Let Bob's age be x then, Jack's age will be (x+2)

Their ages before 1 year was =

Bob's = x-1

Jack's = (x+1)

Difference = x + 1 - x + 1 = 2

Hence, The difference between their ages one year ago was 2 years.

For more references on differences, click;

https://brainly.com/question/2432925

#SPJ1

Two angles in triangle PQR are congruent, ∠P and ∠Q; ∠R measures 26.35°. What is the measure of ∠P?

Answers

The required measure of ∠P would be 76.825° in the given triangle PQR.

Given that two angles in triangle PQR are congruent, ∠P and ∠Q;

∠R measures 26.35°.

Let the measure of ∠P would be x

∠P = x = ∠Q

We know that the sum of interior angles is always 180 degrees in the triangle.

⇒ ∠P + ∠Q + ∠R = 180°

⇒ x + x  + 26.35° = 180°

⇒ 2x  + 26.35° = 180°

⇒ 2x = 180° - 26.35°

⇒ 2x = 153.65

⇒ x = 153.65/2

⇒ x = 76.825°.

Therefore, the required measure of ∠P would be 76.825° in the given triangle PQR.

Learn more about the triangles here:

https://brainly.com/question/17997149

#SPJ1

Michelle is selling blueberries and raspberries at a farmers' market. She makes $1.75 for each pint (pt) of blueberries she sells and $2.40 for each pint of raspberries. At the end of the day, she has made exactly $116.65 by selling a total of 57 pt of fruit.
How many pints of blueberries did she sell?

Answers

The number of the blueberries is 31.

How many pints of blueberries did she sell?

In this case,  the only way that we can be able to obtain the number of the pints of the blueberries that she sold is by the use of a simultaneous equation.

Let the number of  the blueberries be x and the number of the raspberries be y.

We have

x + y = 57 ------ (1)

1.75x + 2.40y = 116.65 ------- (2)

x = 57 - y ------ (3)

Then we have;

1.75(57 - y) + 2.40y = 116.65

99.75 - 1.75y + 2.40y = 116.65

Collecting like terms;

- 1.75y + 2.40y = 116.65 - 99.75

0.65y = 16.9

y = 16.9/0.65

y = 26

To obtain the number of blueberries

x + 26 = 57

x = 57 - 26

x = 31

Learn more about simultaneous equations:https://brainly.com/question/16763389

#SPJ1

x³ ÷ 3 = y; use x = 3, and y = 1

Answers

Step-by-step explanation:

If x = 3 :

x³ ÷ 3 = y

3³ ÷ 3 = y

27 ÷ 3 = y

y = 27 ÷ 3 = 9

Please help me I am a poor person and I’m not able for a reason but please

Answers

Answer:

d /c

Step-by-step explanation:

if its rotated at an 270 angle then its d or c cause they are the same

Find the slope of the graph using points 1,2 and 5,10

Answers

(y^2 - y^1)/ (x^2 - x^1) = slope

10-2 / 5-1 = 8/4 = 2

The slope of the line is 2

Answer:

2

Step-by-step explanation:

The slope of a line is defined by the formula:

[tex]m=\dfrac{\Delta \, y}{\Delta \, x} = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]

In this problem, we are given two points in the form [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex].

So, we can define the x's and y's as:

[tex]x_1 = 1[/tex], [tex]y_1 = 2[/tex], [tex]x_2 = 5[/tex], [tex]y_2 = 10[/tex].

Hence, the slope of the line can be solved for.

[tex]m = \dfrac{10-2}{5-1}[/tex]

[tex]m = \dfrac{8}{4}[/tex]

[tex]m = 2[/tex]

The slope of the line with points (1, 2) and (5, 10) is 2.

18. A random sample of n = 16 scores is obtained from a
population with a mean of μ = 45. After a treatment
is administered to the individuals in the sample, the
sample mean is found to be M = 49.2.
a. Assuming that the sample standard deviation is
s = 8, computer and the estimated Cohen's d to
measure the size of the treatment effect.
b. Assuming that the sample standard deviation is
s = 20, computer and the estimated Cohen's d to
measure the size of the treatment effect.
c. Comparing your answers from parts a and b, how
does the variability of the scores in the sample
influence the measures of effect size?

Answers

Through reporting statistical results, we found that  [tex]r^{2}[/tex] is 0.22 and Cohen's [tex]d[/tex] is 0.52 when s = 8, and  [tex]r^{2}[/tex] is 0.04 and Cohen's [tex]d[/tex] is 0.21 when s = 20. It is also observed that when the variability of the scores in the sample, [tex]r^{2}[/tex] decreases, there is simultaneous decrease in the measures of effect size, Cohen's [tex]d[/tex] as well.

It is given to us that -

A random sample of n = 16 scores

Population with a mean of μ = 45

Sample mean is found to be M = 49.2

In Reporting Statistical results, there are two different effect sizes, namely eta-squared [tex]r^{2}[/tex] and Cohen's [tex]d[/tex].

Eta-square, [tex]r^{2} = \frac{t^{2} }{t^{2}+df }[/tex]

where, [tex]df = n-1[/tex]

[tex]SEM = \frac{s}{\sqrt{n} }[/tex]

and, [tex]t=\frac{x_{2} -x_{1} }{SEM}[/tex]

Cohen's [tex]d=\frac{x_{2} -x_{1} }{s}[/tex]

a) Given that the sample standard deviation is s=8

We have n = 16

So, [tex]df = n-1 = 16-1 = 15[/tex]

[tex]SEM = \frac{s}{\sqrt{n} } = \frac{8}{\sqrt{16} } = \frac{8}{4} = 2[/tex]

We also have μ = 45 and M = 49.2. This implies

[tex]t=\frac{x_{2} -x_{1} }{SEM} = \frac{49.2-45}{2} = \frac{4.2}{2} =2.1[/tex]

Now,

[tex]r^{2} = \frac{t^{2} }{t^{2}+df } = \frac{(2.1)^{2} }{(2.1)^{2}+ 15 }= \frac{4.41}{4.41+15} \\= \frac{4.41}{19.41} = 0.22[/tex]

Cohen's [tex]d=\frac{x_{2} -x_{1} }{s} = \frac{49.2-45}{8} = \frac{4.2}{8} = 0.52[/tex]

b) Given that the sample standard deviation is s=20

We have n = 16

So, [tex]df = n-1 = 16-1 = 15[/tex]

[tex]SEM = \frac{s}{\sqrt{n} } = \frac{20}{\sqrt{16} } = \frac{20}{4} = 5[/tex]

We also have μ = 45 and M = 49.2. This implies

[tex]t=\frac{x_{2} -x_{1} }{SEM} = \frac{49.2-45}{5} = \frac{4.2}{5} =0.84[/tex]

Now,

[tex]r^{2} = \frac{t^{2} }{t^{2}+df } = \frac{(0.84)^{2} }{(0.84)^{2}+ 15 }= \frac{0.706}{0.706+15} \\= \frac{0.706}{15.706} = 0.04[/tex]

Cohen's [tex]d=\frac{x_{2} -x_{1} }{s} = \frac{49.2-45}{20} = \frac{4.2}{20} = 0.21[/tex]

c) Comparing a and b, we see that the variability of the scores in the sample, [tex]r^{2}[/tex] is 0.22 when s = 8 and [tex]r^{2}[/tex] is 0.04 when s = 20. Similarly, Cohen's [tex]d[/tex] is 0.52 when s = 8 and [tex]d[/tex] is 0.21 when s = 20.

Thus, we can see that when the variability of the scores in the sample, [tex]r^{2}[/tex] decreases, there is simultaneous decrease in the measures of effect size, Cohen's [tex]d[/tex] as well.

Therefore, through reporting statistical results, we found that  [tex]r^{2}[/tex] is 0.22 and Cohen's [tex]d[/tex] is 0.52 when s = 8, and  [tex]r^{2}[/tex] is 0.04 and Cohen's [tex]d[/tex] is 0.21 when s = 20. It is also observed that when the variability of the scores in the sample, [tex]r^{2}[/tex] decreases, there is simultaneous decrease in the measures of effect size, Cohen's [tex]d[/tex] as well.

To learn more about Cohen's visit https://brainly.com/question/19281754

#SPJ1

If LK = MK, LK = 7x-10, KN = x + 3, MN = 9x-11, and KJ = 28, find LJ

Answers

LJ = 46 is the value when  LK  congruent MK .

What do you mean by congruent?

It is claimed that two figures are "congruent" if they can be positioned exactly over one another. Both of the bread slices are the same size and shape when stacked one on top of the other. Congruent refers to having precisely the same shape and size.

By given figure ,

        MK = MN - KN

               = 9x - 11 - ( x + 3 )

               = 8x - 14

now given LK ≅ MK

           LK = MK

8x - 14 = 7x - 10

8x - 7x = 14 - 10

 x = 4

length of LJ = LK + KJ

                    = 7x - 10 + 28

                    = 7(4) + 18

                    = 28 + 18  ⇒ 46

Learn more about congruent

brainly.com/question/12413243

#SPJ1

Sample space(3,4,5,6,7,8,9,10,11,12,13,14) event F(6,7,8,9,10) event G(10,11,12,13) outcomes are equally likely find P(ForG)

Answers

The probability of the sets P(F or G) is; P(F or G)  = 0.67

How to Interpret Union of sets?

We are given the following;

Sample Space; S = {3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}

Set F = {6, 7, 8, 9, 10}

Set G = {10, 11, 12, 13}

Now, F or G, simple means; F ∪ G

Thus;

F or G = {6, 7, 8, 9, 10, 11, 12, 13}

Number of terms is (F or G) = 8

Number of terms is Sample space = 12

Thus;

P(F or G) = 8/12 = 2/3 = 0.67

Read more about Union of sets at; https://brainly.com/question/20561161

#SPJ1

Which figure is shaded to represent an equivalent fraction?

Answers

Answer: the one on the top left corner

Answer: the third one (bottom left) but also the second one (top right)

Step-by-step explanation: 2. there are 8 total parts to the figure and four of those parts are shaded. 4/8

3. There are four total parts to the figure but only 2 are shaded. 2/4

2/4 and 4/8 are both EQUIVALENT to 1/2. Therefore, that is the correct answer.

Illustrative Mathematics

An albatross is a large bird that can fly 400 kilometers in 8 hours at a constant speed. Using for distance in kilometers and for number of hours, an equation that represents this situation is .

What are two constants of proportionality for the relationship between distance in kilometers and number of hours? What is the relationship between these two values?

Write another equation that relates and in this context.

Answers

1. Two constants of proportionality representing the proportional relationship between distance in kilometers and number of hours are 400 km and 8 hours.

2. The relationship (ratio) between the two values is 50 km per hour or the equation, d = 50t.

3. Another equation that relates distance and time in this context is t = d/50 or 400/50.

What is the constant of proportionality?

The constant of proportionality is the ratio relating two given values in a proportional relationship.

Other names for the constant of proportionality include:

Constant rateUnit rateConstant ratioRate of changeConstant of variation.

Distance, d = 400 km

Constant speed, t = 8 hours

d = 400/8

d = 50t

Constant of proportionality = 50.

t = d/s

Where d, distance = 400 km and s, speed = 50 km/h

= 400/50

= 8 hours

Learn more about the constant of proportionality at https://brainly.com/question/10159347

#SPJ1

Which equation defines the distance, d, between points (-3,3) and
(a,b)? Select all that apply.
d=√(a-3)² + (b+3)²
d √(-3-a)² + (3 — b)²
d=√(a+b)² + (−3 − 3)²
d=√(a+3)² + (b − 3)²
-

Answers

The distance is d = √(-3 - a)² + (3 - b)²

What is Distance between two points ?

Distance between two points is the length of the line segment that connects the two points in a plane.

The formula is d =√(x₁ - x₂)² + (y₁ - y₂)²

Points are (-3, 3) and (a, b)

We know, the distance formula is

d =√(x₁ - x₂)² + (y₁ - y₂)²

Let, (x₁, y₁) = (-3, 3)

(x₂,  y₂) = (a, b)

Now, plug in the values in given formula

d = √(-3 - a)² + (3 - b)²

Hence, the distance is d = √(-3 - a)² + (3 - b)²

To read more about Distance between two points.

https://brainly.com/question/7243416

#SPJ9

Drag drop the core in order from least to greatest on the number line -10 1 -31/3 0 8 1/4 9/8 -9/8

Answers

An arrangement of the order the numbers would appear on a number line from least to greatest is: -31/3, -10, -9/8, 0, 1, 1/4, 9/8, 8.

What is a number line?

In Mathematics, a number line can be defined as a type of graph with a graduated straight line which is composed of both positive and negative numbers that are placed at equal intervals along its length.

Generally speaking, a number line typically increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).

In order to arrange the given numbers in order from least to greatest, we would convert them into a decimal number as follows:

-31/3 = -10.33 -10 = -10.0-9/8 = -1.12501/4 = 0.251 = 1.09/8 = 1.1258 = 8.0

Read more on number line here: brainly.com/question/28032137

#SPJ1

Given f(x) = 2x^2 - 4x - 4, find the equation of the tangent line of f at the point
where x = -3.

Answers

The equation of the tangent line of f at the point x = -3 will be y = -16x-48.

According to the question,

We have the following information:

f(x) = [tex]2x^{2} -4x-4[/tex]

Now, we will first find the derivation of this function with respect to x:

Let's take its derivation to be f'(x).

f'(x) = 4x-4

Now, finding the slope of the equation when x = -3:

f'(-3) = 4*(-3)-4

f'(-3) = -12-4

f(-3) = -16

Now, we know that following formula is used to find the equation of a line:

(y-y') = m(x-x')

y-0 = -16{x-(-3)}

y = -16(x+3)

y = -16x-48

Hence, the equation of the tangent line of f at the point x = -3 will be y = -16x-48.

To know more about equation of the tangent line here

https://brainly.com/question/26704591

#SPJ1

f(x)= 0.6x5-2x4+8x Describe the end behaviour of the polynomial function








Answers

Step-by-step explanation:

if I understand your typing correctly, and there is nothing missing, we have

f(x) = 0.6x⁵ - 2x⁴ + 8x

the "end behavior" means the general tendency of the result values for very large or very low values of x (going to +infinity and -infinity).

the higher (or lower in the negative direction) x gets, the more the highest exponent will dominate the result values.

it does not matter, that it has a diminishing factor (or coefficient) like 0.6.

the much stronger progression of x⁵ vs. smaller exponents like x⁴ or x will easily compensate for that with sufficiently large x.

so, ultimately, the term with the highest exponent (in our case 0.6x⁵) defines the end behavior.

with x going to +infinity, so does the function result (+infinity).

with x going to -infinity, so does the function result (-infinity, because an odd exponent number like 5 will maintain the sign of the argument).

if the ( n+4)th terms of an A.P is 4n + 17 then find a. S10 b. An +1 c. Sn d. An​

Answers

The measures of the arithmetic sequence are given as follows:

a. [tex]S_{10} = 350[/tex]

b. [tex]A_{n + 1} = 17 + 4n[/tex]

c. [tex]S_n = \frac{n(30 + 4n)}{2}[/tex]

d. [tex]A_n = 17 + 4(n - 1)[/tex]

What is an arithmetic sequence?

An arithmetic sequence is a sequence of values in which the difference between consecutive terms is constant and is called common difference d.

The nth term of an arithmetic sequence is given by the rule shown below:

[tex]a_n = a_1 + (n - 1)d[/tex]

In which [tex]a_1[/tex] is the first term of the sequence.

The sum of the first n terms is given by the rule shown below:

[tex]S_n = \frac{n(a_1 + a_n)}{2}[/tex]

The equation given for this problem is:

[tex]a_{n + 4} = 4n + 17[/tex]

Hence the sequence can be written as follows:

17, 21, 25, 29, 33.

Then the first term and the common ratio are given as follows:

[tex]a_1 = 17, d = 4[/tex]

Then the nth term is of:

[tex]A_n = 17 + 4(n - 1)[/tex]

The (n + 1)th term is of:

[tex]A_{n + 1} = 17 + 4(n + 1 - 1)[/tex]

[tex]A_{n + 1} = 17 + 4n[/tex]

The sum of the first n terms is of:

[tex]S_n = \frac{n(a_1 + a_n)}{2}[/tex]

[tex]S_n = \frac{n(17 + 17 + 4(n - 1))}{2}[/tex]

[tex]S_n = \frac{n(30 + 4n)}{2}[/tex]

The sum of the first ten terms is of:

[tex]S_{10} = \frac{10(30 + 4(10))}{2} = 350[/tex]

More can be learned about arithmetic sequences at https://brainly.com/question/6561461

#SPJ1

2. Write the correct equation that you would use to solve for side x.
Z
X
520
y = 13cm
Z
Y

Answers

The correct equation that could be used to solve for side x is x = sin52° × (Hypotenuse)

Trigonometry: Determining the correct equation to solve for side x

From the question, we are to determine the correct equation that could be used to solve for side x

From the given diagram, we observe that

Side x is the Opposite

Side z is the Adjacent

Side y is the Hypotenuse

Using SOH CAH TOA, we can write that

sin (angle) = Opposite / Hypotenuse

From the diagram,

Given angle = 52°

Hypotenuse = y = 13

Thus,

sin 52° = x/13

x = sin 52° × 13

OR

x = sin52° × (Hypotenuse)

Hence, the equation is x = sin52° × (Hypotenuse)

Learn more on Trigonometry here: https://brainly.com/question/27220508

#SPJ1

when he shoots a free throw he makes a basket 20% of the time Jai shoots 120 free throws in Use benchmarkercents of 1% and 10% to help you determine the answer​

Answers

Benchmark percentage of 1% = 9.6 & 10% = 24.

What is Free Throw Percentage?

Free throw percentage (FT%) puts a player’s successful free throws in perspective to their total attempts.

In basketball, a free throw (or foul shot) is awarded to a player who has been fouled by the other team. The number of free throws depends on where on the court the player was while being fouled.

To find 1% of a number, we can move the decimal point of the number two places to the left.

Therefore, 1% of 120 is 1.2

To find 10% of a number, we can move the decimal point of the number one place to the left.

Therefore, 10% of 120 is 12

Since 10% of 120 is 12 and

20% = 2 x 10%

then 20% of 120 = 2 x 10% of 120

= 2 x 12 = 24

Since 1% of 120 is 1.2 and

8% = 8 x 1%

then 8% of 120 = 8 x 1%  of 120

= 8 x 1.2 = 9.6

Hence the answer is, Benchmark percentage of 1% = 9.6 & 10% = 24.

To learn more about benchmark percentages click here https://brainly.com/question/1201714

#SPJ9

A pole that is 2.5 m tall casts a shadow that is 1.65 m long. At the same time, a nearby building casts a shadow that is 50.25 m long. How tall is the building?
Round your answer to the nearest meter.

Answers

The building is  76.545 m tall.

Given:

A pole that is 2.5 m tall casts a shadow that is 1.65 m long. At the same time, a nearby building casts a shadow that is 50.25 m long.

Let x be the height of the building.

2.5/1.65 = x/50.25

2.5*50.25 = x * 1.65

25/10*5025/100 = x*165/100

25*5025/10 = 165x

25*5025 = 1650x

126300 = 1650x

x = 126300/1650

x = 76.545 m.

Therefore the building is  76.545 m tall.

Learn more about the building and shadow here:

https://brainly.com/question/26277943

#SPJ1

The population of a specific species of nocturnal mammal is decreasing at a rate of 3.5%/year. The graph models the number of mammals x years after they were originally counted.

Identify and interpret the key features of the exponential function modeled in terms of this situation.

Select each correct answer.

The y-intercept represents the number of mammals when they were originally counted.

The line y = 0 is an asymptote of the graph.

The y-intercept.is 75.

The y-intercept is 120.

The asymptote indicates that the number of mammals counted when the study began was 120.

The asymptote indicates that as years pass, the number of mammals will approach 0.

The line x = 0 is an asymptote of the graph.

Answers

Answer:

The y-intercept represents the number of mammals when they were originally counted.

The line y = 0 is an asymptote of the graph.

The y-intercept is 120.

The asymptote indicates that as years pass, the number of mammals will approach 0.

the difference of x and 5 is at least -25

Answers

Answer: x - 5 is less than or equal to -25

Step-by-step explanation:

Translate the phrase into a math expression. Twelve more than the quotient of six divided by three. Responses (6÷3)+12 eft parenthesis 6 divided by 3 right parenthesis plus 12 6÷(3+12) 6 divided by left parenthesis 3 plus 12 right parenthesis (3÷6)+12 left parenthesis 3 divided by 6 right parenthesis plus 12 3÷(6+12) 3 divided by left parenthesis 6 plus 12 right parenthesis

Answers

The given phrase on translation to math expression is (6 ÷ 3) + 12 , the correct option is (a) .

In the question ,

an mathematical phrase is given , that is "Twelve more than the quotient of six divided by three" .

we have to translate it into mathematical expression ,

So , the term quotient of six divided by three is written as 6 ÷ 3 .

and phrase " more " is represented by " + " ,

Hence the given phrase,  "Twelve more than the quotient of six divided by three" is  (6 ÷ 3) [tex]+[/tex] 12 .

Therefore , The given phrase on translation to math expression is (6 ÷ 3) + 12 , the correct option is (a) .

The given question is incomplete , the complete question is

Translate the phrase into a math expression , "Twelve more than the quotient of six divided by three" .

(a) (6÷3)+12

(b) 6÷(3+12)

(c) (3÷6)+12

(d) 3÷(6+12)

Learn more about Expressions here

https://brainly.com/question/7360128

#SPJ1

Describe the features of the function that can be easily seen when a quadratic function is given
in the form: y=ax^2+Bx+C and how they can be identified from the equation. How can this
form be used to find the other features of the graph?
Please help

Answers

When a quadratic equation is given in the form y = ax^2 + Bx + C the easily seen features are

the opening of the curve in the axis - open upwardthe x - coordinate of the vertex, v(h, k) h = -b/2a the axis of the parabola - y axisthe discriminant given by (b² - 4ac)

How this form can be used to find other features

Equation of a parabola is the equation used to trace the path of a parabola. this equation is a quadratic equation

The formula for the roots of the quadratic equation is derived from the equation of the form y = ax^2 + Bx + C to be

-b ± √{(b² - 4ac)2a)

the y intercepts is gotten by equating x = 0

The axis of symmetry refers to the axis where the parabolic curve can be bisected. this is in the y axis

"a" shows if the curve opens upwards or downwards.

negative means the parabola opens downwardspositive the parabola opens upwards

Learn more about other forms of quadratic equation here:

brainly.com/question/29339843

#SPJ1

NO LINKS!! Please help me with this problem. Find a formula that expresses the fact that an arbitrary point P(x, y) is on the perpendicular bisector l of segment AB.​

Answers

Given points

A(-5, 4), B(9, - 6)

Find the midpoint of AB

M = ((- 5 + 9)/2, (4 - 6)/2) = (2, -1)

Find the slope of AB

m = (-6 - 4)/(9 + 5) = - 10 / 14 = - 5/7

The point P is on the perpendicular line to AB that passes through its midpoint.

We know perpendicular lines have opposite-reciprocal slopes.

So the line we are looking for has a slope of 7/5.

Use the point-slope equation to find the line:

y - y₁ = m(x - x₁)y - (-1) = 7/5(x - 2)y + 1 = 7/5(x - 2)                    Point- slope formy = 7/5x - 19/5                        Slope- intercept form5y = 7x - 197x - 5y = 19                             Standard form

Choose any form above of the same line.

Answer:

[tex]\textsf{Slope-intercept form}: \quad y=\dfrac{7}{5}x-\dfrac{19}{5}[/tex]

[tex]\textsf{Standard form}: \quad 7x-5y=19[/tex]

Step-by-step explanation:

A perpendicular bisector is a line that intersects another line segment at 90°, dividing it into two equal parts.

To find the perpendicular bisector of segment AB, find the slope of AB and the midpoint of AB.

Define the points:

Let (x₁, y₁) = A(-5, 4)Let (x₂, y₂) = B(9, -6)

Slope of AB

[tex]\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-6-4}{9-(-5)}=\dfrac{-10}{14}=-\dfrac{5}{7}[/tex]

Midpoint of AB

[tex]\textsf{Midpoint}=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)=\left(\dfrac{9+(-5)}{2},\dfrac{-6+4}{2}\right)=(2,-1)[/tex]

If two lines are perpendicular to each other, their slopes are negative reciprocals.

Therefore, the slope of the line that is perpendicular to line segment AB is ⁷/₅.

Substitute the found perpendicular slope and the midpoint of AB into the point-slope formula to create an equation for the line that is the perpendicular bisector of line segment AB:

[tex]\implies y-y_1=m(x-x_1)[/tex]

[tex]\implies y-(-1)=\dfrac{7}{5}(x-2)[/tex]

[tex]\implies y+1=\dfrac{7}{5}x-\dfrac{14}{5}[/tex]

[tex]\implies y=\dfrac{7}{5}x-\dfrac{14}{5}-1[/tex]

[tex]\implies y=\dfrac{7}{5}x-\dfrac{19}{5}[/tex]

Therefore, the formula that expresses the fact that an arbitrary point P(x, y) is on the perpendicular bisector of segment AB is:

[tex]\textsf{Slope-intercept form}: \quad y=\dfrac{7}{5}x-\dfrac{19}{5}[/tex]

[tex]\textsf{Standard form}: \quad 7x-5y=19[/tex]

If a=-5xa=−5x and b=3x-4ib=3x−4i, then find the value of the a^{3}ba
3
b in fully simplified form.

Answers

The value of expression a³b will be;

⇒ - 75x⁴ + 100x³i

What is substitution method?

To find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.

Given that;

The expression is,

⇒ a³b

The values are;

a = - 5x

b = 3x - 4i

Now,

Substitute the value of a and b, we get;

The expression is,

⇒ a³b

⇒ (-5x)³ × (3x - 4i)

⇒ - 25x³ (3x - 4i)

⇒ - 75x⁴ + 100x³i

Thus, The value of expression a³b will be;

⇒ - 75x⁴ + 100x³i

Learn more about the substitution method visit:

https://brainly.com/question/26094713

#SPJ1

Find sin x/2, cos x/2, tan x/2. from the given information. tan x = [tex]\sqrt{2}[/tex]. 0° < x < 90°

Answers

The trigonometric measures for the given angle are as follows:

[tex]\sin{\left(\frac{x}{2}\right)} = \sqrt{\frac{3 - \sqrt{3}}{6}}[/tex][tex]\cos{\left(\frac{x}{2}\right)} = \sqrt{\frac{3 + \sqrt{3}}{6}}[/tex][tex]\tan{\left(\frac{x}{2}\right)} = \sqrt{\frac{3 - \sqrt{3}}{3 + \sqrt{3}}}[/tex]

How to obtain the trigonometric measures?

We are given the measure of the sine for the angle and we need to find the three measures, sine, cosine and tangent for half the angle.

These measures are dependent on the cosine of the function, hence we apply the definition of the tangent as follows:

[tex]\tan{x} = \frac{\sin{x}}{\cos{x}}[/tex]

Hence:

[tex]\sqrt{2} = \frac{\sin{x}}{\cos{x}}[/tex]

[tex]\sin{x} = \sqrt{2}\cos{x}[/tex]

The exact value of the cosine can be found applying the identity as follows:

sin²(x) + cos²(x) = 1.

Then, from the equation of the sine as a function of the cosine from the tangent relation, we have that:

[tex](\sqrt{2}\cos{x})^2 + \cos^2{x} = 1[/tex]

[tex]2^\cos^2{x} + \cos^2{x} = 1[/tex]

[tex]\cos^2{x} = \frac{1}{3}[/tex]

[tex]\cos{x} = \pm \sqrt{\frac{1}{3}}[/tex]

The angle is of the first quadrant, as 0° < x < 90°, hence the cosine is positive, thus:

[tex]\cos{x} = \frac{1}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{\sqrt{3}}{3}[/tex]

The identity that gives the sine for half the angle is:

[tex]\sin{\left(\frac{x}{2}\right)} = \sqrt{\frac{1 - \cos{x}}{2}}[/tex]

Hence:

[tex]\sin{\left(\frac{x}{2}\right)} = \sqrt{\frac{1 - \frac{\sqrt{3}}{3}}{2}}[/tex]

[tex]\sin{\left(\frac{x}{2}\right)} = \sqrt{\frac{3 - \sqrt{3}}{6}}[/tex]

The identity for the cosine is almost the same, just there is a plus instead of a minus, hence:

[tex]\cos{\left(\frac{x}{2}\right)} = \sqrt{\frac{1 + \cos{x}}{2}}[/tex]

[tex]\cos{\left(\frac{x}{2}\right)} = \sqrt{\frac{1 + \frac{\sqrt{3}}{3}}{2}}[/tex]

[tex]\cos{\left(\frac{x}{2}\right)} = \sqrt{\frac{3 + \sqrt{3}}{6}}[/tex]

The tangent is the sine divided by the cosine, hence the inserting the entire division and the same square root and simplify the common denominator, thus:

[tex]\tan{\left(\frac{x}{2}\right)} = \sqrt{\frac{3 - \sqrt{3}}{3 + \sqrt{3}}}[/tex]

More can be learned about trigonometric measures at brainly.com/question/24349828

#SPJ1

point r is located at (-5,-2), Point T is located at (2,5) the ratio of RS/ST is 2/5 Plot point S on RT to make the ratio true

Answers

The point S of line segment RT such that RS / ST = 2 / 5 is equal to (- 3, 0).

How to determine the coordinates of the point within a line point

Herein we find a line segment whose endpoints are known (R(x, y) = (- 5, - 2), T(x, y) = (2, 5)) and in which we must determine the coordinates of a point S within line segment RT such that the partition ratio is observed:

RS / ST = 2 / 5

[tex]\overrightarrow{RS} = \frac{2}{5} \cdot \overrightarrow {ST}[/tex]

S(x, y) - R(x, y) = (2 / 5) · [T(x, y) - S(x, y)]

(7 / 5) · S(x, y) = (2 / 5) · T(x, y) + R(x, y)

S(x, y) = (2 / 7) · T(x, y) + (5 / 7) · R(x, y)

Now we determine the location of point S:

S(x, y) = (2 / 7) · (2, 5) + (5 / 7) · (- 5, - 2)

S(x, y) = (4 / 7, 10 / 7) + (- 25 / 7, - 10 / 7)

S(x, y) = (- 21 / 7, 0)

S(x, y) = (- 3, 0)

The location of point S is (- 3, 0). A representation of the geometric system is shown in the image attached below.

To learn more on partitioning line segments: https://brainly.com/question/20411716

#SPJ1

Customer: "If I purchase this product for $79.99 and two accessories for $9.99 and $7.00, how much would I owe after the 8.75% tax is applied?"
Employee: "Your total would be __________."

Answers

The answer is $105.46

Determine the vertex of the graph of the following parabola. f(x)=−(x−2)2−3

Answers

The vertex of the Parabola is (2, -3)

What is a vertex?

The vertex of a parabola is the point where the parabola crosses its axis of symmetry.  If the coefficient of the x2 term is positive, the vertex will be the lowest point on the graph, the point at the bottom of the “ U ”-shape.  If the coefficient of the x2 term is negative, the vertex will be the highest point on the graph, the point at the top of the “ U ”-shape.

From  the function f(x) =[tex]-(x-2)^{2}[/tex] - 3

The equation of parabola in vertex form is

y=[tex]a(x-h)^{2}[/tex]+k

where h and k are the coordinates of the vertex

comparing the two equations

h = 2, k = -3

The coordinates of the vertex is (2, -3)

In conclusion, the vertex is (2, -3).

Learn more about vertex: https://brainly.com/question/525947

#SPJ1

Other Questions
Mr. Townsend needs to make 13 pairs of butterfly wings for costumes for a play. Each pair of wings is made with 3/4 yard of fabric. The fabric costs $8 per yard.You'll apply properties of multiplication in the following steps to find the total cost of the fabric.1. Use multiplication to write an expression for the amount of fabric needed to make 13 pairs of wings.2. Multiply the amount of fabric by the price per yard to find an expression for the total cost.3. Use the associative and commutative properties to rearrange the terms in the expression to make it easier to calculate. Explain why the rearranged expression is easier to work with.4. Simplify your expression to find the total cost. Show your work. What is the most likely reason Wangari Muta Maatthai encouraged East African women to plant 20 million trees? 1. Nationalist groups in the Balkans in the late 1800s believed they had the right to___________or the ability to choose their own government. The Missing PatentWilbur and Orville Wright's official patent for their "flying machine," submitted in 1903, is an important slice of American history. The patent was supposed to be stored in the National Archives, where historical treasures are housed. However, in 2000, officials discovered that it seemed to have vanished. Researchers looked through storage vaults, filing cabinets, and archives around the country, to no avail. Some wondered whether the document had been stolen. Finally, Chris Abraham, newly assigned to the National Archives' document recovery program, volunteered to solve the puzzle. Abraham suspected that the patent might have been mistakenly sent to a huge storage facility in Kansas where other, less important patent documents were kept. Abraham was right: after searching through boxes and boxes of documents, he found the patent on March 22, 2016.What is the main idea of the passage? The wholesale price for a pair of shoes is $4.50. A certain department store marks up the wholesale price by 50%. Find the price of the pair of shoes in thedepartment store.Round your answer to the nearest cent, as necessary. Why can you not selectively epoxidize an alkene with mcpba in the presence of a ketone?. Find the y-intercept of the line. If needed use "/" for a fraction. b= y=10+4x .. If the president, vice president, and leaders of congress were all unable to hold office, who would assume the office of president?. 1.5 devided by 2.5 rounded to the nearest tenth Sanjay's class was studying the water cycle. Their teacher asked them: "Where in the room will the most evaporation take place?" In small groups the children collected the following materials: ~zip lock bag ~soil ~water in a spray bottle ~tape Each group added soil to fill the bottom 1/4 of the bag. Next they sprayed the soil with water. They sealed the bags and taped them in a sunny window. The next day, at 11:00 am, the students checked their bags. Here is a photograph of one of the bags; the student models all looked similar. Is this a fair test? Explain. A) No. The students did know if any evaporation took place. B) Yes. All of the students followed the same steps when setting up their model. C) No. The students should tape bags in different places to get different temperatures. D) Yes. The students could see that the water in the soil evaporated and then condensed on the bag. which selection best explains how hitler was able to take over the western europe ? Judy has been suffering from depression for several years. Medication worked at first, but it has not been effective for the last two years, even though judy has tried several different drugs. Judy is willing to try a different type of biological treatment, but she does not want any part of her brain physically altered. What treatment might her psychiatrist recommend?. A family has two cars. The first car has a fuel efficiency of 40 miles per gallon of gas and the second has a fuel efficiency of 20 miles per gallon of gas. During one particular week, the two cars went a combined total of 1700 miles, for a total gas consumption of 55 gallons. How many gallons were consumed by each of the two cars that week? Christine knits 22 centimeters of scarf each night. Write an equation that shows the relationship between the nights xx and the length knitted y. What is the name given to the process by which a parent cell becomes two identical daughter cells?. Why were the Caribbean islands not as united as the mainland colonies you are purchasing a used car and will make 5 annual payments of $3,500 starting one year from today. if your funds could be invested at 9%, what is the present value of the care? (round answer to nearest dollar) $20,946 $13,614 $14,839 $17,500 When a commercial bank receives a deposit, it must keep part of the deposit as cash reserves to satisfy itsA) securities and loans.B) required reserves.C) excess reserves.D) interbank loans.E) loan requirements. A person demonstrates ________ when he or she thinks imaginatively, solves problems, visualizes situations, learns new information, and thinks logically.