Simplify: (A + C)(AD + AD) + AC + C

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

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.

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Answer:

Each gets 14 cards.

Step-by-step explanation:

7*8=56

56 Is the total amount of cards

56/4 equals 14

We divide 56 by 4 since 4 is the total number of friends.

a = F/m

because F = ma

Answer:

295

Step-by-step explanation:

he has 379 less apples now so you have to subtract 379 from 674

674 - 379 = 295

The coordinate pairs that could represent the equation 3x - 2y = 12 are

( x₁ , y₁ ) = ( 2 , -3 )

( x₂ , y₂ ) = ( 4 , 0 )

( x₃ , y₃ ) = ( 0 , -6 )

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be A

3x - 2y = 12

Now , Substituting the values of x and y in the above equation , we get

a)

The coordinate pair ( 2 , -3 )

So , the equation becomes

3 ( 2 ) - 2 ( -3 ) = 12

6 + 6 = 12

12 = 12

Therefore , the coordinate pair satisfies the given equation

b)

The coordinate pair ( 4 , 0 )

So , the equation becomes

3 ( 4 ) - 2 ( 0 ) = 12

12 = 12

Therefore , the coordinate pair satisfies the given equation

c)

The coordinate pair ( 0 , -6 )

So , the equation becomes

3 ( 0 ) - 2 ( -6 ) = 12

12 = 12

Therefore , the coordinate pair satisfies the given equation

Hence , the coordinate pairs that satisfies the the equation 3x - 2y = 12 are

( 2 , -3 ) , ( 4 , 0 ) and ( 0 , -6 )

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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

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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.

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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.

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Answer:

He would have detailed 16 cars.

Step-by-step explanation:

912/57=16

" I hoped I helped you matey : - ) "

           [ 9(a + h) - 3 - 9a + 3]/h =

          9h /h = 9

Answer:

[tex]\textsf{(d)} \quad \boxed{9a+9h-3}[/tex]

[tex]\textsf{(e)} \quad \boxed{9a+9h-6}[/tex]

[tex]\textsf{(f)} \quad \boxed{9}[/tex]

Step-by-step explanation:

Given function:

[tex]f(x) = 9x - 3[/tex]

Part (d)

To find f(a + h), substitute x = a + h into the function:

[tex]\begin{aligned}\implies f(a+h)&=9(a+h)-3\\&=9a+9h-3\end{aligned}[/tex]

Part (e)

Find f(a) by substituting x = a into the function:

[tex]\implies f(a)=9a-3[/tex]

Find f(h) by substituting x = h into the function:

[tex]\implies f(h)=9h-3[/tex]

Therefore:

[tex]\begin{aligned}\implies f(a)+f(h)&=(9a-3)+(9h-3)\\&=9a-3+9h-3\\&=9a+9h-6\end{aligned}[/tex]

Part (f)

[tex]\begin{aligned}\implies \dfrac{f(a+h)-f(a)}{h}&=\dfrac{(9(a+h)-3)-(9a-3)}{h}\\\\&=\dfrac{9a+9h-3-9a+3}{h}\\\\&=\dfrac{9h}{h}\\\\&=9\end{aligned}[/tex]

After 10 years students in both schools are same.

Algebra is a branch of mathematics that uses mathematical expressions to represent problems. To form a meaningful mathematical expression, variables such as x, y, and z are combined with mathematical operations such as addition, subtraction, multiplication, and division. It teaches you how to solve a problem by following a logical path. As a result, you will have a better understanding of how numbers function and interact in an equation. You will be able to do any type of math better if you have a better understanding of numbers.

There are two high schools in a small town.

High school A has currently 900 students and is projects to grow by 30 students each year

Similarly

High school B has currently 750 students and is projected to grow by 45 students each year.

To find the equation for each situation in terms of t years.

also in how many years t' the number of students in both high schools would be same?

Given

The initial strength of school A = 900

the increasing rate of students = 30 students per year

i.e students in 1 year = 30

students in t years = 30t

Total students of school A after 't' years = 900+ 30t

⇒ A = 600+ 65t

The initial strength of school B = 750

increasing rate of students = 45 per year

i.e. student in 1 year = 45

⇒ student in 't' years = 45t

Total students of school B in 't' years = 950 + 30t

=> B=950+30t

Now to find no. of years 't' when students in both schools are the same i.e. A =B

⇒ 900+ 30t = 750 + 45t

⇒ 45t-30t = 900-750

⇒ 15t = 150

⇒t= 150 /15

⇒t=10

Therefore after 10 years, students in both schools are the same.

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Answer:

$1701.75

Step-by-step explanation:

34535-500=34035

34035/20=$1701.75 per year

The resulting equation after the first step in the solution is: 2v + 4 = 8.

In Mathematics, an equation is sometimes referred to as an expression and it can be defined as a mathematical expression which shows that two (2) or more thing are equal.

In this exercise, you're required to describe the steps that should be taken to find a solution to the given equation by solving for v. Therefore, the appropriate and required steps that should be used include the following:

Step 1: Rearrange the equation by collecting like terms.

(v + v) + 4 = 8

Step 2: Add the like terms together.

2v + 4 = 8

Step 3: Subtract 4 from both sides of the equation.

2v + 4 - 4 = 8 - 4

2v = 4

Step 4: Divide both sides of the equation by 2.

v = 4/2

v = 2.

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Complete Question:

Consider the equation v + 4 + v = 8. What is the resulting equation after the first step in the solution?

v +4 = 8 – v

v +4 = 8

4 + v = 8 – v

2v + 4 = 8

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.

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If the chef follows the recipe proportions, then the true statement is;

A: The chef uses 3/16 cup of flour for every cup of water because 1/8 ÷ 2/3 = 3/16

Fractions can be presented in the form of word problems just like algebraic word problems.

Now, we are told that the chef uses 2/3 cup of flour for every 1/8 cup of water in a dough recipe.

This means that;

2/3 cup of flour = 1/8 cup of water

Thus;

1 cup of flour = (1 * 1/8)/(2/3) = 3/16 cups of flour for every cup of water

Looking at the given options, we can conclude that the only correct one based on our answer is Option A.

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The number of the blueberries is 31.

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

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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.

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Answer:

d /c

Step-by-step explanation:

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

The value of 2,850,000,000 in scientific notation is 2.85*[tex]10^{9}[/tex], so option A is correct.

Given:

= 2,850,000,000

= 2850,000 * [tex]10^{3}[/tex]

= 2850 * [tex]10^{3}[/tex] * [tex]10^{3}[/tex]

= 2850 * [tex]10^{6}[/tex]

= 285*[tex]10^{7}[/tex]

= 28.5*[tex]10^{8}[/tex]

= 2.85*[tex]10^{9}[/tex]

Therefore the value of 2,850,000,000 in scientific notation is  2.85*[tex]10^{9}[/tex], so option A is correct.

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

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

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The equation that represents the difference in seed yield between beans without treatment and beans with treatment is (seed yield with treatments-seed yield without treatment) whose value will be 340.

According to the question,

We have the following information:

We have a diagram where seed yield is given.

Now, the required equation represents the difference in seed yield between beans without treatment and beans with treatment will be:

(seed yield with treatments-seed yield without treatment)

(300+310-270)

(610-270)

340

Hence, the equation that represents the difference in seed yield between beans without treatment and beans with treatment is (seed yield with treatments-seed yield without treatment) whose value will be 340.

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When 15 milliliters of pure drug are in 500 mL of solution, the percent strength of the solution is

information from the problem

15 milliliters of pure drug are in 500 mL of solution

the percent strength of the solution = ?

The question is a percentage problem, percentage deals with a fraction hundred and used as follows

= volume of pure drug / volume of solution * 100

= 15 milliliters / 500 milliliters  * 100

= 0.03

= 3%

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The quantity of first brand is 102 gallons and quantity of second brand is 68 gallons

Given,

The first brand of antifreeze = 70% pure antifreeze

The second brand of antifreeze =  95% pure antifreeze

The quantity of mixture = 170 gallons contains 80% pure antifreeze

We have to find the quantity of each brand of antifreeze must be used;

Now,

The quantity of first brand = x gallons

The quantity of second brand = y gallons

Then,

x + y = 170

x = 170 - y ....(1)

70x / 100 + 95y / 100 = (80 × 170) / 100

70x + 95y = 13600

Now, putting the value of x from equation 1:

70 (170 - y) + 95y = 13600

11900 - 70y + 95y = 13600

11900 + 25y = 13600

25y = 13600 - 11900

25y = 1700

y = 1700/25

y = 68

Now, putting this value of y in equation 1:

x = 170 - 68

x = 102

Therefore,

The quantity of first brand is 102 gallons and quantity of second brand is 68 gallons

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Answer:

1,296 miles

Step-by-step explanation:

to answer this question, we have to apply the next formula:  

Distance = Speed rate x time

speed rate = 54 miles per hour

time = 24 hours

Replacing with the values given and solving for D (distance)

D = 54 mph x 24 h = 1,296 m

The car traveled 1,296 miles

Hope this helped! :)

The equation of the given straight line is y = 3x.

We are given a graph. The graph shows a straight line. Several points are marked on the line in the graph. The coordinates of two such points are (1, 3) and (2, 6). We need to find the equation of the straight line.

The equation of the straight line can be found using the two-point form of a line. The equation is solved below.

(y - y1) = [(y2 - y1)/(x2 - x1)]×(x - x1)

(y - 3) = [(6 - 3)/(2 - 1)]×(x - 1)

y - 3 = 3(x - 1)

y = 3x - 3 + 3

y = 3x

Hence, the equation of the line shown in the graph is y = 3x.

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

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).

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The trigonometric measures for the given angle are as follows:

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]

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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

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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).