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3 years ago

A right triangle's hypotenuse has length 5. If one leg has length 3, what is the length of the other leg?

Mathematics

2 answers:

Paraphin [41]3 years ago

8 0

Answer:

a^2 + b^2 = c^2
3^2 + b^2 = 5^2
9 + b^2 = 25
b = _/16
b = 4

Explanation:

Pythagorean Theorem

n200080 [17]3 years ago

6 0

Answer:

The length of the other leg will be = 4

Step-by-step explanation:

You have to use your Pythagoras theorem to determine the length of the other leg.

Hypotenuse^2=a^2+b^2

since you are given the length of the hypotenuse and one leg you can change the formula to:

b^2 = h^2 - a^2

b = √h^2-a^2

b=√5^2-3^2

b=√25-9

b=√16

b=4

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Z varies directly with x and inversely with y. When x=6 and y=2, .z=15. Write function that models variation. Then, find z when

tester [92]

$\bf \begin{array}{cccccclllll}
\textit{direct proportional variation}\\\\\textit{something}&&\textit{varies directly to}&&\textit{something else}\\ \quad \\
\textit{something}&=&{{ \textit{some value}}}&\cdot &\textit{something else}\\ \quad \\
y&=&{{ k}}&\cdot&x
\\
&& y={{ k }}x
\end{array}\\ \quad \\$

$\bf \textit{inverse proportional variation}\\\\
\begin{array}{llllll}
\textit{something}&&\textit{varies inversely to}&\textit{something else}\\ \quad \\
\textit{something}&=&\cfrac{{{\textit{some value}}}}{}&\cfrac{}{\textit{something else}}\\ \quad \\
y&=&\cfrac{{{\textit{k}}}}{}&\cfrac{}{x}
\\
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\end{array}$

$\bf \\\\
-------------------------------\\\\
\textit{z varies directly with x}\implies z=kx
\\\\
\textit{and inversely with y}\implies z=\cfrac{kx}{y}
\\\\\\
\textit{we also know that}\quad 
\begin{cases}
x=6\\
y=2\\
z=15
\end{cases}\implies 15=\cfrac{k\cdot 6}{2}\implies 30=6k$

$\bf \cfrac{30}{6}=k\implies \boxed{5=k}\impliedby \textit{constant of variation}
\\\\\\
thus\implies z=\cfrac{5x}{y}\\\\
-------------------------------\\\\
\textit{what's "z" when }
\begin{cases}
x=4\\
y=9
\end{cases}\implies z=\cfrac{5\cdot 4}{9}$

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4 years ago

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11111nata11111 [884]

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3 years ago

Stephanie needs to cover her yard with 4103/4ft2 of soil she has enough for 125 ft2 in one bag and 65 ft 2 in another bag how mu

Evgen [1.6K]

Answer:

Stephanie requires 835.75 square feet more amount of soil to cover her yard.

Step-by-step explanation:

Given:

Total square feet of yard she need to cover with soil = $\frac{4103}{4}\ ft^2$

$\frac{4103}{4}\ ft^2$ can be rewritten as 1025.75 square feet.

Total square feet of yard she need to cover with soil = $1025.75\ ft^2$

Amount of soil in one bag = $125\ ft^2$

Amount of soil in other bag = $65\ ft^2$

Total Amount of soil she has is equal to sum of Amount of soil in one bag and Amount of soil in other bag.

Framing the equation we get;

Total Amount of soil she has= $125+65 = 190\ ft^2$

Now We need to find the Amount of soil she required more to cover the yard.

Amount of soil she required more is equal to difference of Total Amount of soil she has and Total square feet of yard she need to cover with soil.

Framing the equation we get;

Amount of soil she required more = $1025.75-190= 835.75\ ft^2$

Hence Stephanie requires 835.75 square feet more amount of soil to cover her yard.

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