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3 years ago

Which pairs of angles are alternate exterior angles? Choose all answers that are correct.

Mathematics

2 answers:

Maksim231197 [3]3 years ago

6 0

A and D are the correct answers. They are on opposite sides of the transversal and are on the outside of the parallel lines.<span />

tekilochka [14]3 years ago

6 0

It would be A and H , B and G
this is because they are completely opposite each other as you can see in the diagram.<span />

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You invest $2,500 in an account that grows 5% each year. what will be your investment amount after 6 years?

lesantik [10]

Answer: b. $3,374.65

Step-by-step explanation:

The exponential equation of growth (continuously) is given by :-

$y=Ae^{rx}$ , where A is the initial amount, r is the rate of growth ( in decimal) and x is the time period.

Given : You invest $2,500 in an account that grows 5% each year.

i.e. A= $2,500 and r= 5%=0.05

Then, the equation model this situation will be :-

$y=2500e^{0.05x}=2500(1.05)^x$

Now, At x= 6

$y=2500e^{0.05\times6}\\\\\Rightarrow\ y=2500e^{0.3}=3374.64701894\approx3374.65$

Hence, the investment amount after 6 years will be $3,374.65.

4 0

3 years ago

Find the 11th term 64,-32,16,-8

NeTakaya

Answer:

Step-by-step explanation:

mmmmmmmmmk idk b

3 0

4 years ago

If ab = 10 ft, ac = 14 ft, and bc = 20 ft, what is rs? 10 ft 14 ft 20 ft 24 ft

Fiesta28 [93]

The side |rs| is congruent to side |ac| which is 14 ft.

<h3>What are congruent triangles?</h3>

Congruent triangles are two similar triangles that have corresponding sides and angles and they are of equal measure.

The figures from the textbook illustrate that following rotation, the two triangles are congruent.

This signifies that the angles and sides of the first triangle are equal to the angles and sides of the other triangle.

Therefore:

ab = tr = 10 ft
ac = rs = 14 ft
bd = ts = 20 ft

Learn more about congruent triangles here:

brainly.com/question/1675117

#SPJ1

5 0

2 years ago

Veronica works each day and earns more money per hour the longer she works. Write a function to represent a starting pay of $20

MArishka [77]

<u>Answer:</u>

The range of the amount Veronica makes each hour if she can only work a total of 8 hours is 20 ≤ x ≤ 29.55

<u>Solution: </u>

Let us assume that Veronica worked x hours

The starting pay is $\$20$

Each hour increase is $5\%$

So the function is $f(x)=20(1.05)^{x}$

Now if she works 8 hours, she will earn, $= 20(1.05)^8$

$\Rightarrow 20\times1.477 = 29.55$

So, the range will be 20 ≤ x ≤ 29.55

4 0

4 years ago

The polynomial -x^3-x^2+12x represents the volume of a rectangular aquatic tank in Cubic feet. The length of the tank is (x+4).

Sliva [168]

Answer:

A. x(x +4)(3 -x) . . . . a cubic will have 3 linear factors

B. The dimensions are x, x+4, 3 -x, or 1.694 ft, 5.694 ft, 1.306 ft

C. x = (√37 -1)/3 ≈ 1.694254 ft

D. Maximum volume: ≈ 12.597 ft³

Step-by-step explanation:

A. The first attachment shows the synthetic division of the given polynomial by x+4. The result is -x^2 +3x = x(3 -x). Hence the factored polynomial is ...

x(3-x)(x+4) . . . . . . shown as positive

Since the polynomial is a cubic, we know there will be 3 roots. For this problem, that means we expect 3 factors.

B. We are apparently to assume that the dimensions of the tank correspond to the three factors:

For the maximum size tank (see part C), the corresponding measurements in feet are

1.694 ft
1.306 ft
5.694 ft

C. Tank volume will be maximized when the derivative of volume with respect to x is zero. The derivative polynomial is ...

dV/dx = -3x^2 -2x +12

Solving this by the usual methods, we find the positive value of x to be ...

x = (-1 +√37)/3 ≈ 1.694254 . . . . feet

D. Evaluating the polynomial for this value of x gives ...

volume ≈ 12.5972 . . . cubic feet

6 0

3 years ago