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Katyanochek1 [597]
3 years ago
9

Find the value of x using the diagram below. Round to the nearest whole number.

Mathematics
1 answer:
nikitadnepr [17]3 years ago
6 0
<u>Answer:</u>
<span>C. 32
</span>
<u>Explanation:</u>
Base of larger triangle 
= Hypotenuse of smaller triangle
= √(14^2+14^2)
= 14√2

So,
x 
= Hypotenuse of larger triangle 
= √(25^2+(14√2)^2) 
= √(625+392)
= √1017
= √(9 * 113)
= 3 √113
= 31.89 
= 32 approximately

So the correct answer is C. 32
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Bond [772]

Given the system of equations:

\begin{gathered} 2x+9y=27 \\ x-3y=-24 \end{gathered}

To solve it by substitution, follow the steps below.

Step 1: Solve one linear equation for x in terms of y.

Let's choose the second equation. To solve it for x, add 3y to each side of the equations.

\begin{gathered} x-3y=-24 \\ x-3y+3y=-24+3y \\ x=-24+3y \end{gathered}

Step 2: Substitute the expression found for x in the first equation.

\begin{gathered} 2x+9y=27 \\ 2\cdot(-24+3y)+9y=27 \\ -48+6y+9y=27 \\ -48+15y=27 \end{gathered}

Step 3: Isolate y in the equation found in step 2.

To do it, first, add 48 to both sides.

\begin{gathered} -48+15y=27 \\ -48+15y+48=27+48 \\ 15y=75 \end{gathered}

Then, divide both sides by 15.

\begin{gathered} \frac{15y}{15}=\frac{75}{15} \\ y=5 \end{gathered}

Step 4: Substitute y by 5 in the relation found in step 1 to find x.

\begin{gathered} x=-24+3y \\ x=-24+3\cdot5 \\ x=-24+15 \\ x=-9 \end{gathered}

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x = -9

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Also, you can graph the lines by choosing two points from each equation, according to the picture below.

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Step-by-step explanation:

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