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Solve 7c - 4c = -4c + 5y + 9 for c in terms of y.
| \(\frac{9}{11}\)y + \(\frac{9}{11}\) | |
| -\(\frac{3}{11}\)y + \(\frac{9}{11}\) | |
| 1\(\frac{1}{7}\)y + \(\frac{4}{7}\) | |
| y - \(\frac{2}{5}\) |
To solve this equation, isolate the variable for which you are solving (c) on one side of the equation and put everything else on the other side.
7c - 4y = -4c + 5y + 9
7c = -4c + 5y + 9 + 4y
7c + 4c = 5y + 9 + 4y
11c = 9y + 9
c = \( \frac{9y + 9}{11} \)
c = \( \frac{9y}{11} \) + \( \frac{9}{11} \)
c = \(\frac{9}{11}\)y + \(\frac{9}{11}\)
Find the value of b:
9b + z = 1
b - 4z = 9
| \(\frac{13}{37}\) | |
| -\(\frac{27}{52}\) | |
| \(\frac{21}{23}\) | |
| -3\(\frac{4}{7}\) |
You need to find the value of b so solve the first equation in terms of z:
9b + z = 1
z = 1 - 9b
then substitute the result (1 - 9b) into the second equation:
b - 4(1 - 9b) = 9
b + (-4 x 1) + (-4 x -9b) = 9
b - 4 + 36b = 9
b + 36b = 9 + 4
37b = 13
b = \( \frac{13}{37} \)
b = \(\frac{13}{37}\)
The formula for the area of a circle is which of the following?
c = π r |
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c = π d |
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c = π r2 |
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c = π d2 |
The circumference of a circle is the distance around its perimeter and equals π (approx. 3.14159) x diameter: c = π d. The area of a circle is π x (radius)2 : a = π r2.
A(n) __________ is two expressions separated by an equal sign.
problem |
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formula |
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expression |
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equation |
An equation is two expressions separated by an equal sign. The key to solving equations is to repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the equal sign and the answer on the other.
Simplify 8a x 8b.
| 16ab | |
| 64ab | |
| 64\( \frac{b}{a} \) | |
| 64\( \frac{a}{b} \) |
To multiply monomials, multiply the coefficients (the numbers that come before the variables) of each term, add the exponents of like variables, and multiply the different variables together.
8a x 8b = (8 x 8) (a x b) = 64ab