When using the quotient rule of exponents, you must _____
coefficients and _____
the exponents.

Answer:

(r o q)(-1) = 20

(q o r)(-1) = -11

Step-by-step explanation:

Given

[tex]q(x) = -2x + 1[/tex]

[tex]r(x) = 2x^2 + 2[/tex]

Solving (a): (r o q)(-1)

In function:

(r o q)(x) = r(q(x))

So, first we calculate q(-1)

[tex]q(x) = -2x + 1[/tex]

[tex]q(-1) = -2(-1) + 1[/tex]

[tex]q(-1) = 2 + 1[/tex]

[tex]q(-1) = 3[/tex]

Next, we calculate r(q(-1))

Substitute 3 for q(-1)in r(q(-1))

r(q(-1)) = r(3)

This gives:

[tex]r(x) = 2x^2 + 2[/tex]

[tex]r(3) = 2(3)^2 + 2[/tex]

[tex]r(-1) = 2*9 + 2[/tex]

[tex]r(-1) = 20[/tex]

Hence:

(r o q)(-1) = 20

Solving (b): (q o r)(-1)

So, first we calculate r(-1)

[tex]r(x) = 2x^2 + 2[/tex]

[tex]r(-1) = 2(-1)^2 + 2[/tex]

[tex]r(-1) = 2*1 + 2[/tex]

[tex]r(-1) = 6\\[/tex]

Next, we calculate r(q(-1))

Substitute 6 for r(-1)in q(r(-1))

q(r(-1)) = q(6)

[tex]q(x) = -2x + 1[/tex]

[tex]q(6) = -2(6) + 1[/tex]

[tex]q(6) =- 12 + 1[/tex]

[tex]q(6) = -11[/tex]

Hence:

(q o r)(-1) = -11

Answer:

A. 3(2x - 12) = 2(3 + 2x - 12)

B. Length = 6, width = 3

Step-by-step explanation:

l = 2x - 12

w = 3

Area = 3(2x - 12)

Perimeter = 2(3 + 2x - 12)

if A = P

3(2x - 12) = 2(3 + 2x - 12)

6x - 36 = 6 + 4x - 24

6x - 4x = 6 - 24 + 36

2x = 18

x = 9

Length = 2x - 12 = 2(9) - 12 = 18 - 12 = 6

Answer:

(25a2c - 15a2d - 10cb + 6db)

Step-by-step explanation:

Equation at the end of step 1: (((75•(a2))•c)-((32•5a2)•d))-30cb)+18db

STEP 2:Equation at the end of step2:  ((((3•52a2) • c) -  (32•5a2d)) -  30cb) +  18db

STEP3:

STEP 4:Pulling out like terms

4.1     Pull out like factors :

  75a2c - 45a2d - 30cb + 18db  =

 3 • (25a2c - 15a2d - 10cb + 6db)

Answer:

Cells come from pre-existing cells.

Answer:

(A) Living things can only come from living things.

(B) Cells come from pre-existing cells.

Step-by-step explanation:

i just answered this on e d g e n u i t y.

hope this helps <3

Answer:

12 ft

Step-by-step explanation:

it's either 12 or 18, I have no idea  :/

The maximum revenue obtained for the given revenue function is 43340.

Maxima and minima are the highest and lowest values of a function within a given set of ranges.

Now, as per the given question;

The given revenue function is;  R(x) = 395x − 0.9x²

Differentiate the given function with respect to x.

dR/dx = 395 − 2×0.9x

dR/dx = 395 - 1.8x

Put the given equation equal to zero and find the critical point for which the function will become maximum.

395 - 1.8x = 0

x = 219.44

x ≈≈ 220.

Substitute the obtained value of x in the revenue function to find its maximum value.

R(x) = 395x − 0.9x²

R(220) = 395×220 − 0.9(220)²

R(220) = 86900 - 43560

R(220) = 43340.

Therefore, the maximum revenue calculated for the given revenue function is 43340.

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The distance between X(-9,2) and Y(5,-4) is 15.23 units.

The distance formula states that if there are 2 points A(x1, y1) and B(x2, y2), then the distance between the two points is given by the formula-

[tex]\sqrt{(x1-x2)^{2} + (y1-y2)^{2} }[/tex]

Here, we are given that there are 2 points- X(-9, 2) and Y(5, -4)

So here we can say that,

x1 = -9, y1 = 2

and x2 = 5, y2 = -4

Now, plugging in the values given above in the distance formula we will find XY as follows-

XY = [tex]\sqrt{(-9-5)^{2} + (5+4)^{2} }[/tex]

XY = [tex]\sqrt{(-14)^{2} + (9)^{2} }[/tex]

XY = [tex]\sqrt{196+ 81 }[/tex]

XY = [tex]\sqrt{277 }[/tex]

The square root of 277 is approximately 15.23.

Thus, XY = 15.23

Therefore the value of XY to the nearest hundredth is 15.23 units.

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Answer:8

Step-by-step explanation:

It has the same number of edges, planes, and vertices as a cuboid. Therefore, there are 12 edges in the shape.

A rectangular prism is a three-dimensional shape that has two at the top and bottom and four are lateral faces.

A rectangular prism has 12 edges.

It has the same number of edges, planes, and vertices as a cuboid.

The shape can be a rectangular prism or cuboid.

Therefore, there are 12 edges in the shape.

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y=1/2x-3

The graph shows that the line moves up 1 and right 2, up 1 and right 3, etc., and that b is the y intercept. It denotes a positive 1/2 slope.

The y intercept is -3 because the line crosses the y axis at -3. The shaded region has to be below the line. Our response is the second graph in the first row.

so

y= 1/2x -3

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Answer:

An equation of the line that passes through the point (6, − 2) and is perpendicular to the line will be:

Step-by-step explanation:

We know that the slope-intercept form of the line equation is

y=mx+b

where m is the slope and b is the y-intercept.

Given the line

6x+y=2

Simplifying the equation to write into the  slope-intercept form

y = -6x+2

So, the slope = -6

As we know that the slope of the perpendicular line is basically the negative reciprocal of the slope of the line.

Thus, the slope of the perpendicular line will be: -1/-6 = 1/6

Therefore, an equation of the line that passes through the point (6, − 2) and is perpendicular to the line will be

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

substituting the values m = 1/6 and the point (6, -2)

[tex]y-\left(-2\right)=\frac{1}{6}\left(x-6\right)[/tex]

[tex]y+2=\frac{1}{6}\left(x-6\right)[/tex]

subtract 2 from both sides

[tex]y+2-2=\frac{1}{6}\left(x-6\right)-2[/tex]

[tex]y=\frac{1}{6}x-3[/tex]

Therefore, an equation of the line that passes through the point (6, − 2) and is perpendicular to the line will be:

Answer: he probably didn't pay attention to the - sign on -5.4

Answer:

The second coupon

Step-by-step explanation:

Answer:

First coupon ($250.00)

Step-by-step explanation:

Figure out the new price with first coupon:

Figure out the new price with second coupon:

I hope this helps!

Answer:

12

Half of 24 is 12

I hope this helps C:

Answer:

23.5

Step-by-step explanation:

i hope this is helpful :)

Answer: 7 8 9 7 6 12 2 0

Step-by-step explanation:

Answer:

1) -8m +4+p

2) 10-3t

3)im not sure for the rest

Step-by-step explanation:

Answer:

Step-by-step explanation:

so the equation will be: y = 5 + 3.50x. y is the total cost, and x is the number of hours. To solve for 6 hours, just plug 6 into the equation so: y = 5 + 3.50(6) = 26. So the answer is: it costs $26.00 to rent a drill for 6 hours.

Answer:

a. Probability = 0.15

b. Probability = 0.3

Step-by-step explanation:

Given

[tex]P(Bedroom) = 0.4[/tex]

[tex]P(Kitchen) = 0.1[/tex]

[tex]P(Bathroom) = 0.2[/tex]

[tex]P(Living\ room) = 0.15[/tex]

Solving (a): Probability of being somewhere else

This is calculated by subtracting the sum of given probabilities from 1.

[tex]Probability = 1 - (0.4 + 0.1 + 0.2 + 0.15)[/tex]

[tex]Probability = 1 - 0.85[/tex]

[tex]Probability = 0.15[/tex]

Solving (b): Probability of being in bedroom or kitchen

This is calculated as:

[tex]Probability = P(Bedroom) + P(Kitchen)[/tex]

[tex]Probability = 0.2 + 0.1[/tex]

[tex]Probability = 0.3[/tex]

Round 6193 to 6000

Round 48 to 40

6000/50 = 120

The answer is B. 120

Answer:

The answer is "[tex]8\pi[/tex]"

Step-by-step explanation:

[tex]\to r(v,u) =(4 \cos v, 4 \sin v,u) \\\\0\leq v \leq 2\pi, \ \ 4\leq u\leq 5\\\\\to r_v= (-4 \sin v, 4 \cos v, 0)\\\\\to r_u=(0,0,1)[/tex]

[tex]\to r_v\times r_u = \left|\begin{array}{ccc}\hat{i}&\hat{j}&\hat{k}\\-4 \sin v& 4 \cos v& 0\\0&0&1\end{array}\right| \\\\[/tex]

                [tex]= (4 \cos v, -4 \sin v, 0)[/tex]

[tex]|r_v \times r_u| = \sqrt{16 \cos^2 v +16 \sin^2 v}\\\\[/tex]

             [tex]= \sqrt{16( \cos^2 v + \sin^2 v)}\\\\= \sqrt{16(1)}\\\\= \sqrt{4^2}\\\\=4[/tex]

Calculating the surface area:

[tex]=\int^{2\pi}_{0} \int^{5}_{4} 4 \ du \ dv \\\\=\int^{2\pi}_{0} 4[4]^{5}_{4} \ dv \\\\=\int^{2\pi}_{0} 4[5-4] \ dv \\\\=\int^{2\pi}_{0} 4 \ dv \\\\=4 [v]^{2\pi}_{0}\\\\= 4 \times 2\pi\\\\= 8\pi[/tex]

This question is based on the parametrization. Therefore, 8[tex]\pi[/tex] is the surface area as a double integral by using parametrization.

Given:

The portion of the cylinder [tex]x^{2} +y^{2} = 16[/tex] between the planes z=4 and z=5.

Let u=z and v=θ and use cylindrical coordinates to parameterize the surface.

We need to express the area of the surface as a double integral.by using parametrization.

According to the question,

It is given that u=z and v=[tex]\theta[/tex],

Therefore, r(v,u) = (4 Cos v,4 Sin v, u)

Range of v : 0 [tex]\leq[/tex] v [tex]\leq[/tex] 2[tex]\pi[/tex]

Range of u : 4 [tex]\leq[/tex] u [tex]\leq[/tex] 5

[tex]\rightarrow r_v= (-4 \;sin\; v,4\;cos\; v,0)\\\rightarrow r_u=(0,0,1)[/tex]

[tex]\rightarrow r_u \times r_v =\begin{bmatrix} \hat{i}& \hat{j} & \hat{k}\\ -4\; sin\;v & 4\; cos\; v & 0 \\ 0 & 0 & 1\end{bmatrix}\\\\=(4 cos v,\;-4 sin v ,0)\\\\\left | r_v \times r_u \right | = \sqrt{16cos^{2}v+16sin^2v } \\\\= \sqrt{16(cos^{2}v+sin^2v) }\\\\=\sqrt{16}\\\\=4[/tex]

Now calculating the surface area,

[tex]=\int\limits^{2\pi}_0\int\limits^5_4 4 du\; dv\\\\=\int\limits^{2\pi}_0 4[u]^5_4 dv\\\\=\int\limits^{2\pi}_0 4[5-4] dv\\\\\\=\int\limits^{2\pi}_0 4dv\\\\\\=4[v]^{2\pi}_0 = 4(2\pi-0)= 8\pi[/tex]

Therefore, 8[tex]\pi[/tex] is the surface area as a double integral by using parametrization.

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Answer: 1. a) 0 b) -4 2. a) 3 b) -9 3. a) -80 b) -339 c) -14 4. a) 110 b) -87

Step-by-step explanation: This took forever

Answer:

I think its (6,8) if im wrong i will write the correct answer here or i will right it in the comments

Step-by-step explanation:

The answer is K^2 = 711.6Y on solving the given equation.

Given that, 1 = 711.6Y/K^2 and we have to solve it for the value of K^2. For this we simply have to solve the given equation steps wise. So, let's proceed to solve the equation.

1 = 711.6Y/K^2

Now, multiply K^2 with 1, we get

K^2 = 711.6Y

So, the value of k^2 will be equal to Y times 711.6 and further we can solve it for the various value of Y.

Let us suppose, we have to solve the above equation for the specific value of Y.

So, put Y = 1

On solving, we get

K^2 = 711.6x1

K^2 = 711.6

K = (711.6)^(1/2)

K = 26.67

∴ K^2 = 711.6Y is the equation we will get on solving the equation given to us in the question.

Hence, K^2 = 711.6Y is the required answer.

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Answer: 24

I am bad at explaining so i wouldn't help there

Answer:

24

Step-by-step explanation:

75% is also 3/4. 3/4 out of 32 can be 3 x 32/4 which is 3 x 8, or 24.

Answer:

Shifts 4 units down ---> [tex]g(x)=2x-10[/tex]

Stretches f(x) by a factor of 4 away from x-axis--->[tex]g(x)=8x-6[/tex]

Shifts f(x) 4 units right---> [tex]g(x)=2x-14[/tex]

Compress f(x) by a factor of 1/4 toward the y-axis ---> [tex]g(x)=1/2x-3/2[/tex]

Step-by-step explanation:

We are given [tex]f(x)=2x-6[/tex]

We need to match the transformations.

1) shifts f(x) 4 units down.

When function f(x) shifts k units down the new function becomes f(x)-k

In our case

[tex]g(x)=2x-6-4\\g(x)=2x-10[/tex]

So, Shifts 4 units down ---> [tex]g(x)=2x-10[/tex]

2) Stretches f(x) by a factor of 4 away from x-axis

When function f(x) is stretched by a factor of b away from x-axis the new function becomes f(bx)

[tex]g(x)=2(4x)-6\\g(x)=8x-6[/tex]

So, Stretches f(x) by a factor of 4 away from x-axis--->[tex]g(x)=8x-6[/tex]

3) Shifts f(x) 4 units right

When function f(x) shifts h units right the new function becomes f(x-h)

[tex]g(x)=2(x-4)-6\\g(x)=2x-8-6\\g(x)=2x-14[/tex]

So,  Shifts f(x) 4 units right---> [tex]g(x)=2x-14[/tex]

4) Compress f(x) by a factor of 1/4 toward the y-axis

When function f(x) is compressed by h factor of a toward the y-axis the new function becomes h.f(x)

[tex]g(x)=1/4(2x-6)\\g(x)=1/2x-3/2[/tex]

Compress f(x) by a factor of 1/4 toward the y-axis ---> [tex]g(x)=1/2x-3/2[/tex]

(Option Not given)

(If we compress f(x) by a factor of 4 towards y-axis we get g(x)=8x-24)

Answer:

[tex]z - 0.05z = 236.60[/tex]

Step-by-step explanation:

Given

[tex]Discount = 5\%[/tex]

[tex]Total\ Cost = 236.60[/tex]

Represent the cost of goods bought with z

When the coupon is applied, the discount becomes

[tex]Discount = 5\% * z[/tex]

This gives:

[tex]Discount = 0.05 * z[/tex]

[tex]Discount = 0.05z[/tex]

The discount subtracted from the cost of good will gives the total amount paid.

So, we have:

[tex]Cost\ of\ Goods - Discount = Total\ Cost[/tex]

This gives:

[tex]z - 0.05z = 236.60[/tex]

Hence, option (a) is correct

Answer:

4 1/2  and 7 1/4

Step-by-step explanation:

Answer:D

Step-by-step explanation:

just took it on edge

Answer:

The answer is d

Step-by-step explanation:

A (i think)

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

14-8=6

10-4=6

14-8=10-4

14-8=10-???

    6=10-???

    6=10-4

    6=6

???=-4