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3 years ago

Which expression is equivalent to (125^2/125^4/3)

1 answer:

6 0

$\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{125^2}{125^{\frac{4}{3}}}\implies \cfrac{(5^3)^2}{(5^3)^{\frac{4}{3}}}\implies \cfrac{5^{3\cdot 2}}{5^{3\cdot \frac{4}{3}}}\implies \cfrac{5^6}{5^4}\\\\\\ 5^6\cdot 5^{-4}\implies 5^{6-4}\implies 5^2\implies 25$

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A rectangle has an area of 12 square feet and a length of 5 feet.What is its width?

MrMuchimi

Answer:

width = 2.4

Step-by-step explanation:

so we know that the formula to get an area of a square/rectangle is A=lw, where A is the area, l is the length, and w is the width.

we already have the area and the length, so all we need now is the width.

to find the width, simply plug in the area and the length into the formula, which will give you:

A = lw -given formula

12 = 5(w) -plug in known variables

12/5 = 5w/5 -divide both sides by 5 to get x by itself

2.4 = w -turn the fraction into decimal if you prefer it that way

possible answers: w = 2.4, w = 12/5, or w = 2 2/5

4 0

3 years ago

[need math help] Study buddies part #2

rosijanka [135]

Answer:

Part A) The distance between Whitney's house and Anh's house is 6.5 miles.

Part B) The total distance traveled by Whitney during the trip was 9.5 miles.

Step-by-step explanation:

Part A)

Notice that during Whitney's journey to Anh's house, her velocity was negative for some time. So, Whitney was travelling backwards. Hence, the total distance Whitney traveled will be greater than the actual distance from Whitney's house to Anh's.

So, instead, we can calculate Whitney's total displacement. Total displacement is given by:

$\displaystyle \text{Displacement}=\int_a^bv(t)\, dt$

Where v(t) is the velocity function.

So, the displacement of Whitney when she traveled from her house to Anh's house will be:

$\displaystyle \text{Displacement}=\int_0^{24}v(t)\, dt$

To calculate the integral, we can split it off at t = 11, t = 16, and t = 24.

The three regions represent three geometric figures, which we can use to calculate the area and then find the integral. Rewriting:

$\displaystyle \text{Displacement}=\int_0^{11}v(t)\, dt+\int_{11}^{16}v(t)\, dt+\int_{16}^{24}v(t)\, dt$

Now, we can calculate the area of each figure.

The first figure is a trapezoid with a height of 0.8 and two bases of 11 and 3. So, its area is:

$\displaystyle A_1=\frac{1}{2}(0.8)(11+3)=5.6\text{ miles}$

The second figure is a triangle with a height of 0.6 and a base of 5. So, its area is:

$\displaystyle A_2=\frac{1}{2}(0.6)(5)=1.5\text{ miles}$

Lastly, the third figure is another triangle will a height of 0.6 and a base of 8. So, its area is:

$\displaystyle A_3=\frac{1}{2}(0.6)(8)=2.4\text{ miles}$

However, notice that the second figure is below the x-axis. During that interval, Whitney was traveling backwards. Hence, we will subtract the second area from the rest of the areas.

Then the displacement will be:

$\displaystyle \text{Displacement}=5.6-1.5+2.4=6.5\text{ miles}$

So, the distance between Whitney's house and Anh's house is 6.5 miles.

Part B)

The total distance differs from displacement in that it includes all the distances in both directions. It is given by:

$\displaystyle \text{Distance}=\int_a^b|v(t)|\, dt$

In other words, all of our values are now positive. We will utilize the same strategy:

$\displaystyle \text{Distance}=\int_0^{11}|v(t)|\, dt+\int_{11}^{16}|v(t)|\, dt+\int_{16}^{24}|v(t)|\, dt$

Substitute. The only difference is that we will add 1.5 instead of subtracting it. So:

$\displaystyle \text{Distance} =5.6+1.5+2.4=9.5$

Therefore, in this instance, Whitney traveled a total of 9.5 miles to get to Anh's house.

6 0

3 years ago

At a sale this week, a desk is being sold for $133 . This is 35% of the original price.

slega [8]

Answer:

392.35

Step-by-step explanation:

35% + 35% is 70 % so 133 +133 is 70 % witch is 269.

next we need to figure out 30 percent and they give us 35 % so. you add to zeros to 30 because percentage is out of 100 and there are 2 zeros in 100. so it look like this

3000 ÷ 133 = 22.56 is 30% of 133

70% + 30% = 100%

269 + 22.56= 291.56 is your answer

4 0

3 years ago

Iam really lost on this one please need help

mafiozo [28]

I would say -13 because y = - 10 - 3 would mean that what ever -10 minus 3 equals is what y equals and -10 - 3 is -13

3 0

4 years ago

Please, help with this question!

tester [92]

Answer:

arc AM = 114°

Step-by-step explanation:

the measure of a tangent- chord angle is half the measure of its intercepted arc, that is

∠ MAC = $\frac{1}{2}$ (AM )

57° = $\frac{1}{2}$ AM ( multiply both sides by 2 to clear the fraction )

114° = AM

5 0

2 years ago

Which expression is equivalent to (125^2/125^4/3)​

Which expression is equivalent to (125^2/125^4/3)