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2 years ago

Find the area of the smallest side of the right triangle. Show your work. Box your answer.

Mathematics

1 answer:

lawyer [7]2 years ago

4 0

Answer:

25 ft²

Step-by-step explanation:

The hypotenuse = $\sqrt{169}$ = 13 ft

the side with area 144 ft² = $\sqrt{144}$ = 12 ft

Using Pythagoras' identity to find the third side x ( smallest )

x² + 12² = 13²

x² + 144 = 169 ( subtract 144 from both sides )

x² = 25 ( take the square root of both sides )

x = $\sqrt{25}$ = 5

Thus area of smallest side = 5² = 25 ft²

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Help with Algebra 2: 1. <img src="https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%5B7%5D%7Bx%5E5%7D%20%7D%7B%5Csqrt%5B4%5D%7Bx%5E2%7D%

Mars2501 [29]

Answer:

See explanation

Step-by-step explanation:

1. Given the expression

$\dfrac{\sqrt[7]{x^5} }{\sqrt[4]{x^2} }$

Note that

$\sqrt[7]{x^5}=x^{\frac{5}{7}} \\ \\\sqrt[4]{x^2}=x^{\frac{2}{4}}=x^{\frac{1}{2}}$

When dividing $\sqrt[7]{x^5}$ by $\sqrt[4]{x^2},$ we have to subtract powers (we cannot subtract 4 from 7, because then we get another expression), so

$\dfrac{5}{7}-\dfrac{2}{4}=\dfrac{5}{7}-\dfrac{1}{2}=\dfrac{5\cdot 2-1\cdot 7}{14}=\dfrac{3}{14}$

and the result is $x^{\frac{3}{14}}=\sqrt[14]{x^3}$

2. Given equation $3\sqrt[4]{(x-2)^3} -4=20$

Add 4:

$3\sqrt[4]{(x-2)^3} -4+4=20+4\\ \\3\sqrt[4]{(x-2)^3}=24$

Divide by 3:

$\sqrt[4]{(x-2)^3} =8$

Rewrite the equation as:

$(x-2)^{\frac{3}{4}}=8\\ \\(x-2)^{\frac{3}{4}}=2^3$

Hence,

$\left((x-2)^{\frac{3}{4}}\right)^{\frac{4}{3}}=(2^3)^{\frac{4}{3}}\\ \\x-2=2^{3\cdot \frac{4}{3}}\\ \\x-2=2^4\\ \\x-2=16\\ \\x-2+2=16+2\\ \\x=18$

3 0

2 years ago

Max was on vacation twice as long as Jerrad and half as long as Wesley. The boys were on vacation a total three weeks. How long

mote1985 [20]

3 weeks = 21 days
Let Jerrad's vacation be X then Max's be 2X and Wesley's 4X
X+2X+4X=21
7X=21 devide by 7
X=3 so Jerrad had 3 days vacation
2*3= 6 Max had 6 days
4*3=12 Wesley had 12 days vacation

5 0

2 years ago

Solve for x. −3(x 5)=−9 Enter your answer in the box.

GaryK [48]

x=8

Step-by-step explanation:

Divide both sides by the numeric factor on the left side, then solve.

5 0

1 year ago

Will give Brainliest! A rectangle on the coordinate plane has vertices at (0, 0), (4, 0), (4, 2) and (0, 2). A dilation of the r

alisha [4.7K]

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Step-by-step explanation:

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2 years ago

Find the slope <br> (-19,-6) (15,16)

Alex Ar [27]

Answer:

11/17

Step-by-step explanation:

slope between two points: slope = (y2 - y1) / (x2 - x1)

(x1, y1) = (-19, -6), (x2, y2) = (15, 16)

m = (16 - ( - 6)) / (15 - ( - 19))

refine

m = 11/17

sorry it is hard to follow... i am on my phone rn :/

5 0

3 years ago