Working together, Sarah and Heidi can clean the garage in 2 hours. If they work alone, it takes Heidi 3 hours longer than it takes Sarah. How long would it take Heidi to clean the garage alone?

Working Together, Sarah And Heidi Can Clean The Garage In 2 Hours. If They Work Alone, It Takes Heidi

Answers

Answer 1

Given the rates:

[tex]\begin{gathered} \frac{1}{t}=Sarah^{\prime}s\text{ }Rate \\ \\ \frac{1}{t+3}=Heidi^{\prime}s\text{ }Rate \\ \\ \frac{1}{2}=Rate\text{ }working\text{ }together \end{gathered}[/tex]

Add their rates of cleaning to get rate working together:

[tex]\frac{1}{t}+\frac{1}{t+3}=\frac{1}{2}[/tex]

Solving for t:

[tex]\begin{gathered} \frac{2(t+3)+2t-t(t+3)}{2t(t+3)}=0 \\ \\ \frac{2t+6+2t-t^2-3t}{2t(t+3)}=0 \\ \\ \frac{t+6-t^2}{2t(t+3)}=0 \\ \\ -t^2+t+6=0 \\ \\ (t+2)(t-3)=0 \end{gathered}[/tex]

Hence:

t = -2

t = 3

Time can't be negative; then:

Heidi's time: t + 3

3 + 3 = 9

ANSWER

It will take Heidi 9 hrs to clean garage working alone


Related Questions

What is the slope? y= x+2

Answers

The given equation is

[tex]y=x+2[/tex]

It is important to know that the slope is the coefficient of x when it's expressed in slope-intercept form like this case.

Hence, the slope is 1.

-3 (2x + 4) - (2x + 4) < -4(2x +3)

Answers

-3 (2x + 4) - (2x + 4) < -4(2x +3)​

expand

-6x - 12 - 2x - 4 < -8x - 12

Collect like terms

-6x + 8x - 2x < 12 + 4 -12

The is no solution

4) Identify the LIKE terms: 7y + 5r-4r + 2w 7y and 2w 7y and 5 O -4r and 2w 51 and 41

Answers

Problem Statement

We are asked to identify the like terms from the following expression:

[tex]7y+5r-4r+2w[/tex]

Concept

When we are asked to identify like terms, the question is asking us to find which terms have the same variables with the same power.

For example:

[tex]\begin{gathered} \text{Given the expression:} \\ x^2+2x+y+yx+y^3+y^2+2y+3x^2 \\ \\ 3x^2\text{ and }x^2\text{ are like terms because they have the same variable (x) and both have a power of 2.} \\ y\text{ and 2y are like terms because they have the same variable (y) and both have a power of 1.} \\ \\ \text{Those are the only like terms in the expression} \end{gathered}[/tex]

With the above information, we can solve the question.

Implementation

By the explanation given above, the like terms from the given expression are:

[tex]5r\text{ and }-4r[/tex]

Write a rule for the nth term of the sequence, then find a_20. 7, 12, 17, 22, ...

Answers

Problem

To find the 20th term of the sequence: 7, 12, 17, 22.

The rule for the nth term of the sequence is addding 5 to the term before to get the next term.

Concept

This is an arithmetic sequence since there is a common difference between each term. In this case .

Common ratio = 5

The term to term rule of a sequence describes how to get from one term to the next.

Final answer

The first term is 7. The term to term rule is 'add 5'.

myself and my daughter is having issues with this problem. we keep coming up 11.96 and rounding it to 12 but it saying it is wrong

Answers

using trigonometric ratio

[tex]\tan 23^{\circ}=\frac{13}{y}[/tex][tex]\begin{gathered} y=\frac{13}{\tan 23^{\circ}} \\ y=\frac{13}{0.42447481621} \\ y=30.6260807557 \\ y\approx30.6 \end{gathered}[/tex]

Note

tan 23 = opposite/adjacent

36. Let f(x) = x 4 x - 6 and g(x) = x - 2x – 15. Findf(x)•g(x)

Answers

f(x) = x^2 + x - 6

g(x) = x^2 - 2x - 15

Process

factor both functions

f(x) = (x + 3)(x - 2)

g(x) = (x - 5)(x + 3)

Divide them:

f(x) / g(x) = [(x + 3)(x - 2)] / [x - 5)(x + 3)]

Simplify like terms

f(x) / g(x) = (x - 2)/ (x - 5)

25 mice were involved in a biology experiment involving exposure to chemicals found in ciggarette smoke. developed at least tumor, 9 suffered re[iratory failure, and 4 suffered from tumors and had respiratory failure. A) how many only got tumors? B) how many didn't get a tumor? C) how many suffered from at least one of these effects?

Answers

Explanation:

The total number of mice for the experiment is

[tex]Universalset=25[/tex]

How to know how many mice didn't have a tumor?

Identify the total mice who did not have any effects or the effects did not include a tumor.

The number of mice that had respiratory failur is

[tex]n(R)=9[/tex]

Based on this, it can be concluded 9 mice did not have a tumor,

Hence,

The number of mice that didnt have a tumor is 9

To figure out the number that got only tutmor, we will consider the number that has both tumors and respiratory failure

[tex]n(T\cap R)=4[/tex]

The number that developed tumors is given below as

[tex]n(T)=15[/tex]

Hence,

The number that got

The vertices of ABC are A(2,-5), B(-3, - 1), and C(3,2). For the translation below, give the vertices of AA'B'C'. T * - 1) (ABC) The vertices of AA'B'C' are A'B', and c'| (Simplify your answers. Type ordered pairs.)

Answers

In order to calculate the translation of <-4, -1> to the triangle ABC, we just need to add these coordinates to all vertices of the triangle, that is, add -4 to the x-coordinate and -1 to the y-coordinate. So we have that:

[tex]\begin{gathered} A(2,-5)\to A^{\prime}(2-4,-5-1)=A^{\prime}(-2,-6) \\ B(-3,-1)\to B^{\prime}(-3-4,-1-1)=B^{\prime}(-7,-2) \\ C(3,2)\to C^{\prime}(3-4,2-1)=C^{\prime}(-1,1) \end{gathered}[/tex]

So the vertices after the translation are A'(-2, -6), B'(-7, -2) and C'(-1, 1).

Examine the following graph, where the exponential function P(x) undergoes a transformation.The preimage of the transformation is labeled P(x), and the image is labeled I(x).

Answers

Explanation

For the function P(x), the value of x in the function is halved to get the values of x in the image.

This can be seen in the graphs below.

The red line represents the preimage and the blue line represents the image.

Answer: Option 4

Find the product of (x+3)^2

Answers

Find the product of (x+3)^2​

Remember that

(x+a)^2=x^2+2xa+a^2

therefore

(x+3)^2=x^2+6x+9

answer is

x^2+6x+9

True Or False? the y intercept for the line of the best fit for this scatterplot is 5

Answers

From the graph of the line we notice that if we prolong the line to the y-axis it will intercept it at approximately 4.5.

Therefore, the stament is False.

A rectangle is placed around a semicircle as shown below. The width of the rectangle is 8 yd. Find the area of the shaded regiorUse the value 3.14 for 1, and do not round your answer. Be sure to include the correct unit in your answer.

Answers

It is given that,

[tex]\begin{gathered} Radius\text{ of semicircle = width of rectangle = 8 yd} \\ Diameter\text{ of semicircle = length of rectangle = 16 yd} \\ \pi\text{ = 3.14} \end{gathered}[/tex]

The area of the semicircle is calculated as,

[tex]\begin{gathered} Area\text{ = }\pi\times r^2 \\ Area\text{ = 3.14 }\times\text{ 8 }\times\text{ 8/2} \\ Area\text{ = 100.48 yd}^2 \end{gathered}[/tex]

The area of the rectangle is calculated as,

[tex]\begin{gathered} Area\text{ = Length }\times\text{ Breadth} \\ Area\text{ = 16 yd }\times\text{ 8 yd} \\ Area\text{ = 128 yd}^2 \end{gathered}[/tex]

The area of the shaded region is calculated as,

[tex]\begin{gathered} Area\text{ of shaded region = Area of rectangle - Area of semicircle} \\ Area\text{ of shaded region = 128 yd}^2\text{ - 100.48 yd}^2 \\ Area\text{ of shaded region = 27.52 yd} \end{gathered}[/tex]

The following data are an example of what type of regression?
x
1
2
4
6
8
10
12
OA. Exponential
OB. Quadratic
O C. Linear
OD. None of the above
Y
1.2
1.4
2.1
3.1
4.3
5.6
7.2

Answers

The given data is an example of Option C Linear regression equation,

y = 0.5438x + 0.2169

Given,

The data;

x ; 1 2 4 6 8 10 12

y ; 1.2 1.4 2.1 3.1 4.3 5.6 7.2

We have to find the type of regression of the given data;

Regression equation;

In statistics, a regression equation is used to determine whether or not there is a link between two sets of data.

Lets find regression equation first;

There are 7 number of pairs

The regression equation is;

y = 0.5438x + 0.2169

That is,

The given data is an example of Option C Linear regression equation,

y = 0.5438x + 0.2169

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The food service manager at a large hospital is concerned about maintaining reasonable food costs. The following table lists the cost per serving, in cents, for items on four menu's. On particular day, a dietician orders 68 meals from menu 1, 43 meals from menu 2, 97 meals from menu 3, and 55 meals from menu 4.Part AWrite the information in the table as a 4x5 matrix M. Maintain the ordering of foods and menu's from the table.M=[__]Part BWrite a row matrix N that represents the number of meals ordered from each menu. Maintain the ordering of menu's from the tableN=[___]Part CFind the product NMNM=[___]1st blank options (average or total)2nd blank (each food, food, or each menu)

Answers

Answer and step by step:

a) To write the information in the table as a 4x5 matrix:

b) Write a row matrix N that represents the number of meals ordered from each menu.

c) Find the product NM:

To find the product of two matrices, the matrices have to be the same number of columns and rows. Then it cannot be solved.

Which of the following sequences represents an arithmetic sequence with a common difference d = –4? 768, 192, 48, 12, 3 35, 31, 27, 23, 19 24, 20, 16, 4, 0 5, –20, 80, –320, 1,280

Answers

The general formula of an arithmetic sequence is:

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

Where d is known as the common difference and it represents the distance between consecutive terms of the sequence. So we can calculate this distance for each of the four options:

[tex]\begin{gathered} 768,192,48,12,3 \\ 768-192=576 \\ 192-48=144 \end{gathered}[/tex]

So in the first sequence the difference between terms is not even constant so this is not the correct option.

[tex]\begin{gathered} 31-35=-4 \\ 27-31=-4 \\ 23-27=-4 \\ 19-23=-4 \end{gathered}[/tex]

In the second sequence the distance is -4 so this is a possible answer.

[tex]\begin{gathered} 20-24=-4 \\ 16-20=-4 \\ 4-16=-12 \\ 0-4=-4 \end{gathered}[/tex]

In the third sequence the distance is not always the same so we can discard this option.

[tex]\begin{gathered} -20-5=-25 \\ 80-(-20)=100 \end{gathered}[/tex]

Here the distance isn't constant so the fourth option can also be discarded.

Then the only sequence with a distance d=-4 is the second option.

I am supposed to give the reasons why these triangles are equal.

Answers

Statements Reasons.

1. NL bisects angles KNM and KLM. 1. Given.

2. KNL = MNL 2. Definition of angle bisector

KLN = MLN

3. NKL = NML 3. Parallelogram theorem.

4. Triangles NKL and NML are congruent. 4. AAA postulate.

The parallelogram theorem mentioned states that opposite interior angles are congruent.

The AAA postulate of congruence states that two triangles are congruent if all three interior angles are congruent correspondingly.

At its first meeting, the math club had 16 students attend. At its second meeting, 25 students attended. What was the percent of increase?

Answers

First, subtract 16 to 25:

25 - 16 = 9

next, calculate the associated percentage of 9 to 16, as follow:

(9/16)(100) = 56.25

Hence, the increase was of 56.25%

Write the translation of point P(2, -9) to point P'(0, -12). [A] (x, y) =(x-3, y – 2) [B] (x, y) = (x+3, y +2) [C] (x, y) = (x+ 2, y + 3) [D] (x, y) = (x-2, y-3)

Answers

Applying the transformation (x, y) → (x - 2, y - 3) to point P, we get:

P(2, -9) → (2 - 2, -9 - 3) → P'(0, -12)

A professor decided he was only going to grade 8 out of 10 HW problems he assigned. How many different groupings of HW problems could he grade?

Answers

Answer:

The number of groupings is 45

Explanation:

Given that the professor decided he was only going to grade 8 out of 10 HW problems he assigned.

We want to calculate the number of ways the professor can grade the HW.

Which is a conbination;

[tex]10C8[/tex]

Solving we have;

[tex]\begin{gathered} n=10C8=\frac{10!}{8!(10-8)!} \\ n=45 \end{gathered}[/tex]

Therefore, the number of groupings is 45

Two airplanes leave the same airport. One heads north, and the other heads east. After some time, the northbound airplane has traveled 15 miles. If the two airplanes are 39 miles apart, the eastbound airplane has traveled __ miles.

Answers

Answer:

36 miles

Explanation:

Let's go ahead sketch the given problem as shown below;

From the above diagram, we can go ahead and determine x, which is the distance the eastbound plane has traveled, using the Pythagorean theorem;

[tex]\begin{gathered} 39^2=x^2+15^2 \\ 1521=x^2+225 \\ x^2=1521-225 \\ x=\sqrt[]{1296} \\ x=36\text{miles} \end{gathered}[/tex]

Agrocery store bought milk for $2.20 perhalf gallon and stored it in two refrigerators. During the night one refrigerator malfunctioned and ruined 13 half gallons. If the remaining milk is sold for $3.96 per half gallon, how many half gallons did the store buy if they made a profit of $121.00

Answers

Answer

The store bought 98 half gallon milks

Explanation

Let the number of half gallon nilks they bought be x

They bought each half gallon milk at a rate of 2.2 dollars each

13 half gallons got spoilt.

They then sold the rest of the half gallone (x - 13) gallons at 3.96 dollars per half gallon

Profit = Revenue - Cost

Revenue = (Amount of half gallons sold) × (Price of each one)

Revenue = (x - 13) × 3.96

Revenue = (3.96x - 51.48)

Cost = (Amount of half gallons bought) × (Price of each one)

Cost = x × 2.20

Cost = 2.20x

Profit = 121 dollars

Profit = Revenue - Cost

121 = (3.96x - 51.48) - 2.20x

121 = 3.96x - 51.48 - 2.20x

121 = 1.76x - 51.48

1.76x - 51.48 = 121

1.76x = 121 + 51.48

1.76x = 172.48

Divide both sides by 1.76

(1.76x/1.76) = (172.48/1.76)

x = 98 half gallon milks

Hope this Helps!!!

can you please help me with the both of them?

Answers

The values of x and angle in triangle STU are 11 and 123, 65, and the values of x and angle in triangle BCD is 3 and 70, 50

The inner of two angles are formed where two sides of a polygon meet are called the interior angle

Given that in two triangles

S = 58, T= 5x + 10 and U = 11x +2

B = 22x + 4, C = 15x + 5 and D =120

In the Triangle STU Formula to find out the value of x is

Sum of interior angles = exterior angle

= 5x + 10 + 58 = 11x +2

= 5x + 68 = 11x + 2

11x -5x = 68 -2

6x = 66

X = 11

Now substitute x value in T & U

T = 5(11) +10                     U = 11(11) + 2

T= 55 +10                          U = 121 + 2

U = 123                              T = 65

In the Triangle BCD Formula to find out the value of x is

Sum of interior angles = exterior angle

22x + 4 + 15x + 5 = 120

37x + 9 = 120

37x = 111

X = 3

Now substitute x value in B & C

B = 22(3) +4                     U = 15(3) + 5

T= 66 +4                          U = 45 + 5

U = 70                             T = 50

Therefore the values of x and angle in triangle STU are 11 and 123, 65, and the values of x and angle in triangle BCD are 3 and 70, 50

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The barrel of a rifle has a length of 0.983m. A bullet leaves the
muzzle of a rifle with a speed of 602m/s. What is the
acceleration of the bullet while in the barrel? A bullet in a rifle
barrel does not have constant acceleration, but constant
acceleration is to be assumed for this problem.
Answer in units of m/s^2

Answers

The acceleration of the bullet while in the barrel is 184335.7 m/s^2.

First, let us understand the acceleration:

Any action where the velocity changes are said to it as acceleration. There are only two ways to accelerate: altering your speed or altering your direction, or altering both. This happens because velocity is both a speed and a direction.

We are given;

The length of the barrel of the rifle is 0.983 m.

The speed of the bullet is 602m/s.

From the third equation of motion, we know that,

v^2 = u^2+ 2aS

Initial velocity, u=0

Final velocity, v = 602m/s.

Distance, S = 0.983 m.

Substitute the given values in the above formula,

v^2 = u^2 + 2aS

(602)^2 = 0 + 2 * a * 0.983

1.966a = 362404

a = 362404/1.966

a =  184335.7 m/s^2.

Thus, the acceleration of the bullet while in the barrel is 184335.7 m/s^2.

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Find the third side in simplest radical form: 3 789

Answers

Apply the Pythagorean theorem:

c^2 = a^2 + b^2

Where:

c = hypotenuse (longest side )

a & b = the other 2 legs of the triangle

Replacing:

c^2 = 3^2 + (√89)^2

c^2 = 9 + 89

c ^2 = 98

c = √98 = √(49x2) = √49 √2 = 7 √2

Third side = 7 √2

The perimeter of rhombus EFGH is 48 cm and the measure of

Answers

Given data

Perimeter = 48cm

perimeter of a rhombus is the sum of all length of the outer boundary.

A rhombus has equal length

Perimeter = 4L

4L = 48

L = 48/4

L = 12cm

a) GH = 12cm

b)

c)

To find

Opposite = 6 side facing the given angle

Hypotenuse = 12 side facing right angle

[tex]\begin{gathered} \text{Apply trigonometry ratio formula} \\ \sin \theta\text{ = }\frac{Opposite}{\text{Hypotenuse}} \\ \sin \theta\text{ = }\frac{6}{12} \\ \sin \theta\text{ = 0.5} \\ \theta\text{ = }\sin ^{-1}0.5 \\ \theta\text{ = 30} \end{gathered}[/tex]

Therefore,

Angle

y = 2x - 9 y = -1/2x + 1Graph both equations to find the solutionfor this system.

Answers

To answer this question, we can graph both lines equations using the intercepts of both lines. The intercepts are the x- and the y-intercepts for both lines.

The x-intercept is the point where the line passes through the x-axis. At this point, y = 0. Likewise, the y-intercept is the point where the line passes through the y-axis. At this point, x = 0.

Therefore, we can proceed as follows:

1. Graphing the line y = 2x - 9

First, we can find the x-intercept. For this, y = 0.

[tex]\begin{gathered} y=2x-9\Rightarrow y=0 \\ 0=2x-9 \\ 9=2x \\ \frac{9}{2}=\frac{2}{2}x \\ \frac{9}{2}=x\Rightarrow x=\frac{9}{2}=4.5 \end{gathered}[/tex]

Therefore, the x-intercept is (4.5, 0).

The y-intercept is:

[tex]y=2(0)-9\Rightarrow y=-9[/tex]

Therefore, the y-intercept is (0, -9).

With these two points (4.5, 0) and (0, -9) we can graph the line y = 2x - 9.

2. Graphing the line y = -(1/2)x +1

We can proceed similarly here.

Finding the x-intercept:

[tex]\begin{gathered} 0=-\frac{1}{2}x+1 \\ \frac{1}{2}x=1 \\ 2\cdot\frac{1}{2}x=2\cdot1 \\ \frac{2}{2}x=2\Rightarrow x=2 \end{gathered}[/tex]

Therefore, the x-intercept is (2, 0).

Finding the y-intercept:

[tex]\begin{gathered} y=-\frac{1}{2}(0)+1 \\ y=1 \end{gathered}[/tex]

Then the y-intercept is (0, 1).

Now we can graph this line by using the points (2, 0) and (0, 1).

Graphing both lines

To graph the line y = 2x - 9, we have the following coordinates (4.5, 0) and (0, -9) ---> Red line.

To graph the line y = -(1/2)x + 1, we have the coordinates (2, 0) and (0, 1) ---> Blue line.

We graph both lines, and the point where the two lines intersect will be the solution of the system:

We can see that the point where the two lines intersect is the point (4, -1). Therefore, the solution for this system is (4, -1).

We can check this if we substitute the solution into the original equations as follows:

[tex]\begin{gathered} y=2x-9 \\ -2x+y=-9\Rightarrow x=4,y=-1 \\ -2(4)+(-1)=-9 \\ -8-1=-9 \\ -9=-9\Rightarrow This\text{ is True.} \end{gathered}[/tex]

And

[tex]\begin{gathered} y=-\frac{1}{2}x+1 \\ \frac{1}{2}x+y=1\Rightarrow x=4,y=-1 \\ \frac{1}{2}(4)+(-1)=1 \\ 2-1=1 \\ 1=1\Rightarrow This\text{ is True.} \end{gathered}[/tex]

In summary, we found the solution of the system:

[tex]\begin{gathered} \begin{cases}y=2x-9 \\ y=-\frac{1}{2}x+1\end{cases} \\ \end{gathered}[/tex]

Using the intercepts of the lines, graphing the lines, and the point where the two lines intersect is the solution for the system. In this case, the solution is (4, -1) or x = 4, and y = -1.

What is the zero of function f?f(x)=3 square root of x+3 -6

Answers

Solution:

Given:

[tex]f(x)=3\sqrt{x+3}-6[/tex]

The zeros of a function are the values of x when f(x) is equal to 0.

Hence,

[tex]\begin{gathered} 0=3\sqrt{x+3}-6 \\ \\ Collecting\text{ the like terms,} \\ 0+6=3\sqrt{x+3} \\ 6=3\sqrt{x+3} \\ \\ Divide\text{ both sides by 3;} \\ \frac{6}{3}=\sqrt{x+3} \\ 2=\sqrt{x+3} \\ \\ Taking\text{ the square of both sides;} \\ 2^2=x+3 \\ 4=x+3 \\ \\ Collecting\text{ the like terms;} \\ 4-3=x \\ 1=x \\ x=1 \end{gathered}[/tex]

Therefore, x = 1

The correct answer is OPTION A.

Point Q is shown on the coordinate grid belowWhich statement correctly describes the relationship between the point (-3,2) and point G

Answers

The coordinate of Q is (-3,-2)

The relationship between (-3, -2) and (-3, 2)

(x,y) changes into (x,-y) which is the reflection along x axis

The point (-3, 2) is a reflection of point Q across the x-axis

Answer : The point (-3, 2) is a reflection of point Q across the x-axis

3 373,Consider the complex number z =+22What is 23?Hint: z has a modulus of 3 and an argument of 120°.Choose 1 answer:А-2727-13.5 +23.41-13.5 - 23.41

Answers

To answer this question, we can proceed as follows:

[tex]z=-\frac{3}{2}+\frac{3\sqrt[]{3}}{2}i^{}\Rightarrow z^3=(-\frac{3}{2}+\frac{3\sqrt[]{3}}{2}i)^3[/tex][tex](-\frac{3}{2}+\frac{3\sqrt[]{3}i}{2})^3=(\frac{-3+3\sqrt[]{3}i}{2})^3=\frac{(-3+3\sqrt[]{3}i)^3}{2^3}[/tex]

We applied the exponent rule:

[tex](\frac{a}{b})^c=\frac{a^c}{b^c}[/tex]

Then, we have:

[tex]\frac{(-3+3\sqrt[]{3}i)^3}{2^3}=\frac{(-3+3\sqrt[]{3}i)^3}{8}[/tex]

Solving the numerator, we have:

[tex](a+b)^3=a^3+b^3+3ab(a+b)[/tex]

[tex](-3+3\sqrt[]{3}i)^3=(-3)^3+(3\sqrt[]{3}i)^3+3(-3)(3\sqrt[]{3}i)(-3+3\sqrt[]{3}i)[/tex][tex]-27+81\sqrt[]{3}i^3-27\sqrt[]{3}i(-3+3\sqrt[]{3}i)[/tex][tex]-27+81\sqrt[]{3}i^3+81\sqrt[]{3}i-27\cdot3\cdot(\sqrt[]{3})^2\cdot i^2[/tex][tex]-27+81\sqrt[]{3}i^2\cdot i+81\sqrt[]{3}i-81\cdot3\cdot(-1)[/tex][tex]-27+81\sqrt[]{3}(-1)\cdot i+81\sqrt[]{3}i+243[/tex][tex]-27-81\sqrt[]{3}i+81\sqrt[]{3}i+243[/tex][tex]-27+243=216[/tex]

Then, the numerator is equal to 216. The complete expression is:

[tex]=\frac{(-3+3\sqrt[]{3}i)^3}{8}=\frac{216}{8}=27[/tex]

Therefore, we have that:

[tex]z^3=(-\frac{3}{2}+\frac{3\sqrt[]{3}}{2}i)^3=27[/tex]

In summary, therefore, the value for z³ = 27 (option B).

Find f (-9) if f (x) = (20+x)/5

Answers

The given function is expressed as

f(x) = (20 + x)/5

We want to find f(- 9). To do this, we would substitute x = - 9 into the function. It becomes

f(- 9) = (20 + - 9)/5 = (20 - 9)/5

f(- 9) = 11/5

Other Questions
find the perimeter and area It is Nadines birthday, and she is making walnut brownies for her sleepover. She invited eight of her friends to her party. The recipe that she is using makes twenty-four brownies, but she only wants to make eight. The recipe for twenty-four calls for \large 4\frac{1}{2} cups of walnuts. How many cups of walnuts will she need for eight people? hXL for School: Practice & Problem Solving 5.2.PS-19 Question Help Equivalent ratios can be found by extending pairs of rows or columns in a multiplication table. Write 3 3 ratios equivalent to using the multiplication table. 5 Click the icon to view the multiplication table. 3 Find three ratios that are equivalent to 5 12 6 4 IA. B. OC. 20 10 6 15 15 9 OD OE. F. 9 30 15 Click to select your answer(s) and then click Check Answer. All parts showing Clear All Check Answer Review progress Question 7 of 12 Back Next > A food truck caters an event attended by 100 guests. Every guest orders one of two possible dishes: a salad or a turkey plate. The price of each meal decreases as more of that particular type are ordered. The price of a salad is $10.00 minus $0.06 for each salad ordered. The price of a turkey plate is $12.00 minus $0.02multiplied by the square of the number of turkey plates ordered. Guests pay for their meal only after everyone has placed their order.Using differentiation, find the maximum revenue for the food truck.Remember that the number of meals is a positive integer. Round revenue to the nearest cent. Based on the audio, what may the villagers do after the natural disaster? Graph the linear function g(x) = -4+7xGraph the linear function G (x equals negative 4 + 7x If there are three black, four white, two blue, and four gray socks in a drawer, what would be the probability of picking a blue sock? Round your answer to the nearest tenth.15.4%25%22%15.38% In the image below LMOP. Given the lines are parallel, LMNPON because and that LNMONP by the , you can conclude the triangles are similar by the AA Similarity Theorem. If NP = 20, MN = x+ 6, NO = 15, and LN = 2x - 3 then x = . 76) In bacteria, the unit of DNA that contains multiple genes under the control of a single promoter is called ____ this unit is referred to as _____ mRNAa. an operator, a polycistronicd. an operon, a monocistronicb. a template, a structurale. a template, a monocistronicc. an operon, a polycistronic z divided by 13=28 i need the answers this is hard for me The graph shows a relationship between two quantities.200018001600140012001000800600400200Od-8 -6 4-2 0 2 4Which equation best represents the relationship between the variables? Find the reference angle for a rotation of 129. are there two types of addiction, psychologicaland physical. How do you figure out what the order pairs are in this equation? 2x-2=y Determine the smallest integer value of x in the solution of the following inequality.3x + 4> -18 Every rational number is also an integer.TrueorFalse Put the following equation of a line into slope-intercept form, simplifying allfractions.12y-2x = 108 a cannon sitting on top of a 40 m mound shoots a projectile with an initial velocity of 4.47 m/s parallel to ground. how far away did it land? How many possible triangles can be created if measure of angle B equals pi over 6 comma a = 20, and b = 10? what does 1,58025=I know the answer, I need to show how I got it.