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baherus [9]
3 years ago
13

Solve for x. A) 10.5 B) 10 C) 6√3 D) 20

Mathematics
1 answer:
faltersainse [42]3 years ago
8 0
There are three right triangles in this figure.  Set up Pythagorean theorem for each of them.
Let y be the altitude of the largest triangle.
Let z be the left side.
We have for large triangle:
x² + z² = (9+3)²
For left sub-triangle:
y² + 3² = z²
For right sub-triangle:
y² + 81 = x²

So the three equations are
x² + z² = 144
y² + 9 = z²
y² + 81 = x²

Solve last equation for y², plug into second equation, solve that for z² in terms of x², and lastly plug z² into the first equation to find
x² + x² - 72 = 144
2x² = 216
x² = 108
x = √108 = √(36·3) = 6√3

The answer is C) 6√3
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The distance between the parallel lines x – 2y = 3 and 2x – 4y = 12 is
Svetradugi [14.3K]

Given :

Parallel lines are

x – 2y = 3 and 2x – 4y = 12

Step-by-step explanation:

Lets write the given lines in slope intercept form y=mx+b

x -2y = 3  \\-2y=-x+3\\Divide \; both \; sides \; by -2\\y=\frac{x}{2} -\frac{3}{2}

From the above equation , y intercept of first line is \frac{-3}{2}

Solve the second equation for y and find out y intercept

2x-4y=12\\-4y=-2x+12\\Divide \; by \; -4\\y=\frac{1}{2} x-3

y intercept of second line is -3

To find the distance between parallel lines, we subtract the y intercepts

\frac{-3}{2} -(-3)=\frac{-3}{2} +\frac{6}{2} =\frac{3}{2} =1.5

Answer:

The distance between the parallel lines = 1.5

Reference:

brainly.com/question/24145911

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Combine like terms to create an equivalent expression.<br> 3.26d+9.75d-2.65
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Find the surface area
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Answer:

Step-by-step explanation:

area of top=7×6=42 yd²

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