Using the completing-the-square method, find the vertex of the function f(x)=-2x^2+12x+5 and indicate whether it is a minimum or a maximum and at what point.

Answer: C

Step-by-step explanation:

2944 distinct 5-letter strings can be created using the letters a, b, c, d, and e if repetition is allowed but the letter a appears at most twice

Given that

form 5-letter distinct strings can be created using the letters a,b,c,d, and e, and repetitions are allowed but the letter a appears at most twice

let's consider that letter a is not there in the string

each letter is repetitive then it is [tex]4^{5}[/tex]

now letter a is considered once

5c1 ×[tex]4^{4}[/tex]

now letter a is repetitive twice

5c2 × [tex]4^{3}[/tex]

[tex]4^{5}[/tex] + 5c1 × [tex]4^{4}[/tex] + 5c2 × [tex]4^{3}[/tex]

1024+ 1280 + 640 = 2944

2944 distinct 5-letter strings can be created using the letters a, b, c, d, and e if repetition is allowed but the letter a appears at most twice

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Check the picture below.

[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ A(\stackrel{x_1}{-7}~,~\stackrel{y_1}{2})\qquad B(\stackrel{x_2}{3}~,~\stackrel{y_2}{-8}) ~\hfill AB=\sqrt{(~~ 3- (-7)~~)^2 + (~~ -8- 2~~)^2} \\\\\\ ~\hfill AB=\sqrt{( 10)^2 + ( -10)^2} \implies \boxed{AB=\sqrt{ 200 }}[/tex]

[tex]B(\stackrel{x_1}{3}~,~\stackrel{y_1}{-8})\qquad C(\stackrel{x_2}{-4}~,~\stackrel{y_2}{-9}) ~\hfill BC=\sqrt{(~~ -4- 3~~)^2 + (~~ -9- (-8)~~)^2} \\\\\\ ~\hfill BC=\sqrt{( -7)^2 + ( -1)^2} \implies \boxed{BC=\sqrt{ 50 }} \\\\\\ C(\stackrel{x_1}{-4}~,~\stackrel{y_1}{-9})\qquad A(\stackrel{x_2}{-7}~,~\stackrel{y_2}{2}) ~\hfill CA=\sqrt{(~~ -7- (-4)~~)^2 + (~~ 2- (-9)~~)^2} \\\\\\ ~\hfill CA=\sqrt{( -3)^2 + (11)^2} \implies \boxed{CA=\sqrt{ 130 }} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{\LARGE perimeter}}{\sqrt{200}~~ + ~~\sqrt{50}~~ + ~~\sqrt{130}} ~~ \approx ~~ \text{\LARGE 32.61}[/tex]

Answer:

The registration fee is $28

Step-by-step explanation:

5,600/100=56 which is 1% of 5,600.

56/2=28 which is 0.5% of 5,600.

;)

Answer: $28

Step-by-step explanation:

you calculate what 0.5 percent is of 5,600  :)

The variable y varies directly with x and the variation equation is (b) y = -1/2x

The graph represents the given parameter

On the graph, we can see that:

The values of x are divided by -2 to get y

This means that the graph represents a direct variation

Recall that we stated that:

The values of x are divided by -2 to get y

This means that the constant of variation is -1/2

The direct variation equation is represented as:

y = kx

Where k represents the constant of variation i.e. k = -1/2

Substitute the known values in the above equation So, we have the following equation

y = -1/2x

Hence, the equation of variation is y = -1/2x

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A situation which could be represented by this graph is: A student walks 1.5 km to a friend’s house in 20 minutes. The two students then walk another 1.5 km to school in 40 minutes.

In Mathematics, a graph can be defined as a type of chart that is typically used to graphically represent data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate and y-coordinate respectively such as time (min) and distance (km).

In this scenario, the time (in minutes) was plotted on the x-axis of the graph while the distance covered (in kilometers) was plotted on the y-axis of the graph.

By critically observing the graph (see attachment), we can reasonably and logically deduce that the first student walked a distance of 1.5 kilometer to his or her friend’s house in 20 minutes, then, they both walked at a constant speed for 5 seconds before increasing their speed, covering another distance of 1.5 kilometer to their school within 40 minutes (60 - 20 minutes).

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Complete Question:

The graph below shows distance over time. Which of these situations could be represented by this graph?

answer choices

A student walks 1.5 km to a friend’s house in 40 minutes. The two students then walk another 1.5 km to school in 20 minutes.

A student walks 1.5 km to a friend’s house in 20 minutes. The two students then walk another 1.5 km to school in 40 minutes.

A student walks 1.5 km to a friend’s house in 30 minutes. The two students then walk another 1.5 km to school in 30 minutes.

A student walks 1.5 km to a friend’s house in 20 minutes. The two students then walk another 1.5 km to school in 60 minutes.

Answer:

a) 1:25 b) 2:06 c) 5:00 d) 4:10

Step-by-step explanation:

Answer: anna worked 4.33repeating hours washing cars and 3.25 hours landscaping

Step-by-step explanation:

i personally used a guess and check method.

i multiplied 9(hourly wage for washing cars) and 4.33repeating(number of hours) = 39

i multiplied 12(hourly wage landscaping) and 3.25(number of hours) = 39

39 + 39 = $78

The y-intercept of the graph of the function g(n) represents the height of the flower.

We are given:

A researcher is following the growth of a particular type of flower. She writes the given equation to show the height of the flower g(n), in inches, after n days.

g(n) = 10(1.02)^n

which is an exponential function.

We need to find what the y-intercept of the graph of the function g(n) represents.

We have the exponential function;

g(n) = 10(1.02)^n

where,

x-coordinate of the graph represents the number of days.

y-coordinate of the graph represents the height of the flower.

Thus, the y-intercept of the graph of the function g(n) represents the height of the flower.

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The value of x will be 24.

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

For a given right triangle, the expression is,

⇒ sin (3x - 7) = cos (x + 1)

Now,

Solve for x as;

The expression is,

⇒ sin (3x - 7) = cos (x + 1)

Since, sin x= cos (90 - x)

So, We get;

⇒ sin (3x - 7) = cos (x + 1)

⇒ cos (90 - (3x - 7)) = cos (x + 1)

⇒ 90 - (3x - 7) =  (x + 1)

⇒ 90 - 3x + 7 = x + 1

⇒ 97 - 3x = x + 1

⇒ 97 - 1 = x + 3x

⇒ 96 = 4x

⇒ 4x = 96

⇒ x = 96/4

⇒ x = 24

Thus, The value of x will be 24.

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anwser: she has 34 cookies left

If a - b = -5 and ab = 0 then the value of the expression a³-b³ is -125.

In the question ,

it is given that ,

the value of a - b = -5 and ab = 0

we need to find the value of the expression (a³-b³) ,

we know the identity that a³-b³ = (a - b)(a² + b² + ab)

we first need the value of a² + b² .

given that a - b = -5

squaring both the sides , we get

(a - b)² = 25

a² + b² - 2ab = 25

given ab = 0, so a² + b² = 25

Substituting a² + b² = 25 in the identity a³-b³ = (a - b)(a² + b² + ab) ,

we get ,

a³-b³ = (-5)(25 + 0)

a³-b³ = -5 × 25

a³-b³ = -125

the answer is -125 .

Therefore , If a - b = -5 and ab=0 then the value of the expression a³-b³ is -125.

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Answer:

second number = (x + 7.5)

Since the product of the two numbers is double of their sum,

             x(x + 7.5) = 2(x + x + 7.5)

             x² + 7.5x = 2(2x + 7.5)

             x² + 7.5x = 4x + 15

x² + 7.5x - 4x - 15 = 0

      x² + 3.5x - 15 = 0

                      ∴ x = -6 or 2.5

∴ second number

= -6 + 7.5 or 2.5 + 7.5

= 1.5 or 10

∴ The two numbers that I am thinking of are either -6 and 1.5 or 2.5 and 10.

Answer:   A) 0.05%

Step-by-step explanation:  Converting the shaded area of the hundredths grid to a fraction would be 5/100 (or 1/20 simplified). Then convert 5/100 to a percentage by calculating 5 ÷ 100, which is 0.005%, therefor the answer is A.

The two coordinates on the segment AB due to internal division are (5,0) and (-3,-4).

What is internal division?

When a point P divides the line joining the two points and the potint P lies in between the two coordinates then the division is internal division. If the point lies outside of the given coordinates then the division is known as external division.

The division is internally because point P lies on the line as given in the question.

The formula for the internal division is as follows:

[tex]X=\frac{mx_1+nx_2}{m+n}\\Y=\frac{my_1+ny_2}{m+n}[/tex]

Since points are A(-5,-5) and B(7,1) hence, [tex]x_1=-5,x_2=7,y_1=-5,y_2=1[/tex] and ratio is 1:5 then [tex]m=1,n=5[/tex].

Substute all value to obtain the coordinates.

[tex]X_1=\frac{1(-5)+5(7)}{1+5}\\X_1=5\\Y_1=\frac{1(-5)+5(1)}{1+5}\\Y_1=0[/tex]

Hence, the first cordinate is (5,0).

As given in the question that the ratio in not necessarily in the order of 1:5 so, consider the ratio is 5:1.

Now, m=5 and n=1.

Again substitute all values in to find the new coordinate.

[tex]X_2=\frac{5(-5)+1(7)}{5+1}\\X_2=-3\\Y_2=\frac{5(-5)+1(1)}{5+1}\\Y_2=-4[/tex]

Hence, another coordinate is (-3,-4).

Hence, the two coordinates on the segment AB due to internal division are (5,0) and (-3,-4).

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The quadratic equation whose sum of two real roots is 31 and product is 210 will be [tex]x^{2} -31x+210 = 0[/tex].

According to the question,

We have the following information:

The sum of roots of a quadratic equation = 31

The product of roots of a quadratic equation = 210

We know that the standard form of the quadratic equation is given as follows:

[tex]ax^{2} +bx+c = 0[/tex]

Now, the sum of roots is -b/a and the product of roots is c/a.

So, we have the following expressions:

-b/a = 31

b = -31 and a = 1

c/a = 210

c = 210 and a = 1

So, the equation will be:

[tex]x^{2} -31x+210 = 0[/tex]

Hence, the quadratic equation whose sum of two real roots is 31 and product is 210 will be [tex]x^{2} -31x+210 = 0[/tex].

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The value of the exponent 3.6 x 10^7 + 2.1 x 10.^7 is D. None of the above.

The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.

In this case, the value of 3.6 x 10^7 + 2.1 x 10^7 will be:

= 3.6 x 10^7 + 2.1 x 10.^7

= 5.7 × 10^7

Therefore, the correct option is D.

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Answer:

Below

Step-by-step explanation:

a(x-p)(x-q)        p = -2    q = 5

a ( x- - 2)(x - 5)         sub in the values of the point given (3,6) to calculate 'a'

6  = a (3+2)(3-5)

a = -6 /10 = - 3/5

y = -3/5 (x+2)(x-5)  

Answer:

[tex]\textsf{Intercept form}: \quad y=-\dfrac{3}{5}(x+2)(x-5)[/tex]

[tex]\textsf{Standard form}: \quad y=-\dfrac{3}{5}x^2+\dfrac{9}{5}x+6[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6 cm}\underline{Intercept form of a quadratic equation}\\\\$y=a(x-p)(x-q)$\\\\where:\\ \phantom{ww}$\bullet$ $p$ and $q$ are the $x$-intercepts. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}[/tex]

If the x-intercepts are (-2, 0) and (5, 0) then:

Substitute the values of p and q into the formula:

[tex]\implies y=a(x-(-2))(x-5)[/tex]

[tex]\implies y=a(x+2)(x-5)[/tex]

To find a, substitute the given point on the curve P (3, 6) into the equation:

[tex]\implies 6=a(3+2)(3-5)[/tex]

[tex]\implies 6=a(5)(-2)[/tex]

[tex]\implies 6=-10a[/tex]

[tex]\implies a=\dfrac{6}{-10}[/tex]

[tex]\implies a=-\dfrac{3}{5}[/tex]

Substitute the found value of a into the equation:

[tex]\implies y=-\dfrac{3}{5}(x+2)(x-5)[/tex]

Expand to write the equation in standard form:

[tex]\implies y=-\dfrac{3}{5}(x^2-3x-10)[/tex]

[tex]\implies y=-\dfrac{3}{5}x^2+\dfrac{9}{5}x+6[/tex]

Answer:

$134.86

Step-by-step explanation:

Let the original price before tax be x.

A whole amount is 100% of the amount, so x is 100% of the original price without tax.

The tax rate is 6%, so the tax on x is 6% of x. Add 6% of x to 100% of x, and you have 106% of x. The item plus tax cost 106% of x.

106% of x = $142.95

106/100 × x = 142.95

1.06x = 142.95

x = 142.95/1.06

x = $134.86

Answer: $134.86

The line equation passing through the given points and parallel to the given lines are:

Line 1: y=-4x+13...(i)

Line 2: y=2x-12...(ii)

Line 1

The first line is passing through point (1,9) and parallel to the y=4x+2 line.

Since line 1 would be parallel to line y=4x+2, hence both lines would have the same value of slope (m).

Using the standard formula of line equation, we could identify that line y=4x+2 has:

ay = bx + c, m= -b/a

y=4x+2, m=-4

We could use the line equation formula, where:

y-y1 = m (x-x1)

we use the given point (1,9) and the slope value (m=-4) to get the line equation passing through the point:

y-9 = -4(x-1)

y-9=-4x+4

y=-4x+13...(i)

Line 2

The first line is passing through point (5,2) and parallel to the y=-2x+7 line.

Since line 2 would be parallel to line y=-2x+7, hence both lines would have the same value of slope (m).

Using the standard formula of line equation, we could identify that line y=-2x+7 has:

ay = bx + c, m= -b/a

y=-2x+7, m=-2

We could use the line equation formula, where:

y-y2 = m (x-x2)

we use the given point (5,2) and the slope value (m=2) to get the line equation passing through the point:

y-2 = 2(x-5)

y-2 = 2x-10

y=2x-12...(ii)

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Answer:

125 in simplest form is 1/8.

Step-by-step explanation:

The number of coins that the pirates collect is A. 10.

From the information, the pirate ship found a treasure chest that contained 127 gold coins and 253 silver coins and there are 38 pirates on the ship.

The number of coins that way person will get will be:

=>Total coins / Number of pirates

= (253 + 127) / 38

= 380 / 38

= 10

Each person gets 10 coins.

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The translation made from f(x) → f(x) + 6 is sliding it up

A translation is a geometric change in Euclidean geometry that involves moving each point in a figure, shape, or space by the same amount in one direction.

A translation can also be thought of as moving the origin of the coordinate system or as adding a constant vector to each point.

Any translation in a Euclidean space is an isometry.

the translation made from f(x) → f(x) + 6 involves moving the graph up 6 units

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Answer:

Hi

Step-by-step explanation:

so the question is asking what is 2/5  of  150

if 150 is able to evenly be split up into 5 even parts we can the add two of those parts to get our answer.  

does 150 split up into 5 even parts??

hmmm  you probably are thinking,  15 does divide by 5 evenly into 3 parts, so we now know that 150 also splits up into 5 even parts of 30  :)

2 time 30 = 60

so there is how to figure out the answer and , the answer 60 :)

Answer:

43446

Step-by-step explanation:

52 weeks in an year

835.5 × 52 = 43446

Considering the definition of an inequality, the number of folders Jan would need to buy for the Supply Guys to be the cheaper option is more than 18.

An inequality is the existing inequality between two algebraic expressions, connected through the signs:

An inequality contains one or more unknown values ​ in addition to certain known data.

Solving an inequality consists of finding all the values ​​of the unknown for which the inequality is true.

In this case, you know that:

Being "x" the number of folders, the inequality that expresses the previous relationship is

45 + 0.45x > 50.40 + 0.15x

Solving:

0.45x - 0.15x > 50.40 -45

0.30x> 5.4

x> 5.4÷ 0.3

x> 18

Finally, the number of folders Jan would need to buy is more than 18.

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The domain of the function A(m) = 184 - 8m representing the bank charges on monthly fees is m ≤ 23

The equation is linear equation in the slope intercept form as

y = mx + c

where

m = slope = -8

c = intercept = 184

x = input variables = m

y = output variables = A(m)

The domain refers to all possible values of m, generally the equation has no restriction for m however for the problem being discussed y should not be negative. hence we solve for m when y = 0

0 = 184 - 8m

8m = 184

m = 23

The maximum value of m is 23 hence the domain is m ≤ 23

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The number of candy bar that she bought is 6

The total amount that she spend for soda and candy= $12

The cost of one soda = $3

The cost of one candy bar = $1.50

Number of soda that she bought = 1

Consider the number of candy bar that she bought as x

Then the equation will be

3×1 + 1.50 × x = 12
Multiply the terms

3 + 1.50x = 12

Move 3 to right hand side of the equation

1.50x = 12 - 3

1.50x = 9

Move 1.50 to the right hand side of the equation

x = 9 / 1.50

x = 6

Hence, the number of candy bar that she bought is 6

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La cinta de Mario tiene una longitud que es 0.75 veces la longitud de la cinta de Beatriz.

Sabemos que la longitud de la cinta de Mario tiene una longitud de 6 metros, mientras que su amiga Beatriz tiene una cinta de longitud de 8 metros.

Para saber cuantas veces es la longitud de la cinta de mario comparada con la longitud de la cinta de beatriz, tenemos que tomar el cociente entre ambas longitudes, obtendremos:

6m/8m = 0.75

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