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2 years ago

You earn $102 for doing 12 hours of yard work. Your friend earns $120 working at a store for 15 hours.

Mathematics

1 answer:

krek1111 [17]2 years ago

3 0

Answer:

You earn more per hour and you would get $127.50

Step-by-step explanation:

You can find how much money you get per hour by dividing! 102 divided by 12 is 8.5 and 120 divided by 15 is 8 so you get more!

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Which is equivalent to RootIndex 3 StartRoot 8 EndRoot Superscript one-fourth x?

Nat2105 [25]

<h3>Answer: Choice C</h3>

RootIndex 12 StartRoot 8 EndRoot Superscript x

12th root of 8^x = (12th root of 8)^x

$\sqrt[12]{8^{x}} = \left(\sqrt[12]{8}\right)^{x}$

=========================================

Explanation:

The general rule is

$\sqrt[n]{x} = x^{1/n}$

so any nth root is the same as having a fractional exponent 1/n.

Using that rule we can say the cube root of 8 is equivalent to 8^(1/3)

$\sqrt[3]{8} = 8^{1/3}$

-----

Raising this to the power of (1/4)x will have us multiply the exponents of 1/3 and (1/4)x like so

(1/3)*(1/4)x = (1/12)x

In other words,

$\left(8^{1/3}\right)^{(1/4)x} = 8^{(1/3)*(1/4)x}$

$\left(8^{1/3}\right)^{(1/4)x} = 8^{(1/12)x}$

-----

From here, we rewrite the fractional exponent 1/12 as a 12th root. which leads us to this

$8^{(1/12)x} = \sqrt[12]{8^{x}}$

$8^{(1/12)x} = \left(\sqrt[12]{8}\right)^{x}$

4 0

2 years ago

Read 2 more answers

In the after school Dena, Shawn, and Amanda knit scarfs that are the same size with yellow, white, and blue yarn. Denas scarf is

jenyasd209 [6]

Answer:

$\frac{8}{20}$

Step-by-step explanation:

We have been given that in the after school Dena, Shawn, and Amanda knit scarfs that are the same size with yellow, white, and blue yarn. Denas scarf is 2/5 yellow, Shawn's scarf is 3/5 , and Amanda's scarf is 3/4 yellow.

To make Amanda's argument true, let us compare each fraction by making a common denominator.

We can see that least common denominator of each fraction would be 20.

$\text{Dena's scarf}=\frac{2}{5}\Rightarrow\frac{2*4}{5*4}=\frac{8}{20}$

$\text{Shawn's scarf}=\frac{3}{5}\Rightarrow\frac{3*4}{5*4}=\frac{12}{20}$

$\text{Amanda's scarf}=\frac{3}{4}\Rightarrow\frac{3*5}{4*5}=\frac{15}{20}$

Since $\frac{8}{20}$ , therefore, Amanda's scarf has the most yellow.

8 0

2 years ago

Find the measure of angle A. This is for my math class, and I’ve been stuck on this for a while. Please help!

Kruka [31]

Answer:

20°

Step-by-step explanation:

The sum of angles in a ∆ = 180°

Therefore, $(17x - 1) + (3x - 4) + 25 = 180$

Use this expression to find the value of x, then find the measure of angle A.

$17x - 1 + 3x - 4 + 25 = 180$

$17x + 3x - 1 - 4 + 25 = 180$

$20x + 20 = 180$

Subtract 20 from both sides

$20x + 20 - 20 = 180 - 20$

$20x = 160$

Divide both sides by 20

$\frac{20x} = \frac{160}{20}$

$x = 8$

Find measure of angle A.

Angle A is given as $3x - 4$

Plug in the value of x and solve

$A = 3(8) - 4 = 24 - 4 = 20$

8 0

3 years ago

Consider the points A(5, 3t+2, 2), B(1, 3t, 2), and C(1, 4t, 3). Find the angle ∠ABC given that the dot product of the vectors B

Vilka [71]

Answer:

66.42°

Step-by-step explanation:

<u>Given:</u>

A(5, 3t+2, 2)

B(1, 3t, 2)

C(1, 4t, 3)

BA • BC = 4

Step 1: Find t.

First we have to find vectors BA and BC. We do that by subtracting the coordinates of the initial point from the coordinates of the terminal point.

In vector BA B is the initial point and A is the terminal point.

BA = OA - OB = (5-1, 3t+2-3t, 2-2) = (4, 2, 0)

BC = OC - OB = (1-1, 4t-3t, 3-2) = (0, t, 1)

Now we can find t because we know that BA • BC = 4

BA • BC = 4

To find dot product we calculate the sum of the produts of the corresponding components.

BA • BC = (4)(0) + (2)(t) + (0)(1)

4 = (4)(0) + (2)(t) + (0)(1)

4 = 0 + 2t + 0

4 = 2t

2 = t

t = 2

Now we know that:

BA = (4, 2, 0)

BC = (0, 2, 1)

Step 2: Find the angle ∠ABC.

Dot product: a • b = |a| |b| cos(angle)

BA • BC = 4

|BA| |BC| cos(angle) = 4

To get magnitudes we square each compoment of the vector and sum them together. Then square root.

$|BA| = \sqrt{4^2 + 2^2 + 0^2} = \sqrt{20} = 2\sqrt{5}$

$|BC| = \sqrt{0^2 + 2^2 + 1^2} = \sqrt{5}$

$2\sqrt{5}\sqrt{5}\cos{(m\angle{ABC})} = 4$

$10\cos{(m\angle{ABC})} = 4$

$\cos(m\angle{ABC}) = \frac{4}{10}=\frac{2}{5}$

$m\angle{ABC} = cos^{-1}{(\frac{2}{5})}$

$m\angle{ABC} = 66.4218^{\circ}$

Rounded to two decimal places:

$m\angle{ABC} = 66.42^\circ$

3 0

1 year ago

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Leviafan [203]

I’m sorry??? What????

8 0

3 years ago