Hey there!
Here are the steps involved in answering this question:
1. Write 12 out of 32 as a fraction which is
2. Turn the fraction into a decimal. To do this, divide the numerator by the denominator. The numerator is the top part of the fraction while the denominator is the bottom part of the fraction.

= 0.375
3.<span> You get 0.375. Now, turn this into a percent. Move the decimal, 2 places to the right or just multiply the decimal by 100.</span>
0.375 = 37.5%
The final answer is 37.5%.
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Answer:
x = - 
Step-by-step explanation:
Given
-
=
x
Multiply through by 6 to clear the fractions
2x - (3 - 2x) = 15x ← distribute and simplify left side
2x - 3 + 2x = 15x
4x - 3 = 15x ( subtract 4x from both sides )
- 3 = 11x ( divide both sides by 11 )
-
= x
Answer:
x = 12
, y = -3
Step-by-step explanation:
Solve the following system:
{2 x + 7 y = 3 | (equation 1)
x = -4 y | (equation 2)
Express the system in standard form:
{2 x + 7 y = 3 | (equation 1)
x + 4 y = 0 | (equation 2)
Subtract 1/2 × (equation 1) from equation 2:
{2 x + 7 y = 3 | (equation 1)
0 x+y/2 = -3/2 | (equation 2)
Multiply equation 2 by 2:
{2 x + 7 y = 3 | (equation 1)
0 x+y = -3 | (equation 2)
Subtract 7 × (equation 2) from equation 1:
{2 x+0 y = 24 | (equation 1)
0 x+y = -3 | (equation 2)
Divide equation 1 by 2:
{x+0 y = 12 | (equation 1)
0 x+y = -3 | (equation 2)
Collect results:
Answer: {x = 12
, y = -3
You basically plug in the x values with the given function so the y values are -5,-10,-15,-20
Answer:
The answer is below
Step-by-step explanation:
Let x be the diameter of the semicircle. radius = x/2
The window is a combination of a rectangle and semicircle.
Width of window = diameter = x, let length of the window = y.
Perimeter of semicircle = πr = πx/2
Perimeter of window = x + y + y + πx/2
20 = x + 2y + πx/2
2y + x + πx/2 = 20
2y = 20 - x(1 - π/2)
y = 10 - x(1 - π/2)/2
Area of semicircle = (1/2)πr² = (1/2)π(x/2)²
Area of window = xy + (1/2)π(x/2)²
A = x(10 - x(1 - π/2)/2) + πx²/8
A = 10x - x² - πx²/4 + πx²/8
A = 10x - x² - πx²/8
The maximum area is at dA / dx = 0
dA / dx = 10 - 2x - 2πx/8
0 = 10 - 2x - πx / 4
2x + πx / 4 = 10
2.785x = 10
x = 3.59 feet
Maximum area = 10x - x² - πx²/8 = 10(3.59) - 3.59² - π(3.59²) / 8
Maximum area = 17.95 feet²