| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.83 |
| Score | 0% | 57% |
The dimensions of this cylinder are height (h) = 5 and radius (r) = 7. What is the volume?
| 128π | |
| 576π | |
| 245π | |
| 98π |
The volume of a cylinder is πr2h:
v = πr2h
v = π(72 x 5)
v = 245π
Find the value of c:
-3c + y = 5
-7c - 6y = -7
| 3 | |
| -\(\frac{5}{16}\) | |
| -\(\frac{23}{25}\) | |
| 2\(\frac{19}{27}\) |
You need to find the value of c so solve the first equation in terms of y:
-3c + y = 5
y = 5 + 3c
then substitute the result (5 - -3c) into the second equation:
-7c - 6(5 + 3c) = -7
-7c + (-6 x 5) + (-6 x 3c) = -7
-7c - 30 - 18c = -7
-7c - 18c = -7 + 30
-25c = 23
c = \( \frac{23}{-25} \)
c = -\(\frac{23}{25}\)
Simplify (2a)(6ab) - (6a2)(2b).
| 64a2b | |
| b2 | |
| 24ab2 | |
| 0a2b |
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.
(2a)(6ab) - (6a2)(2b)
(2 x 6)(a x a x b) - (6 x 2)(a2 x b)
(12)(a1+1 x b) - (12)(a2b)
12a2b - 12a2b
0a2b
What is 7a + 3a?
| 10a | |
| 21a2 | |
| 21a | |
| a2 |
To combine like terms, add or subtract the coefficients (the numbers that come before the variables) of terms that have the same variable raised to the same exponent.
7a + 3a = 10a
Solve -6b + 2b = -3b + 5y - 7 for b in terms of y.
| -y + 2\(\frac{1}{3}\) | |
| -1\(\frac{1}{9}\)y - \(\frac{4}{9}\) | |
| -\(\frac{7}{10}\)y + \(\frac{4}{5}\) | |
| -\(\frac{3}{11}\)y + \(\frac{7}{11}\) |
To solve this equation, isolate the variable for which you are solving (b) on one side of the equation and put everything else on the other side.
-6b + 2y = -3b + 5y - 7
-6b = -3b + 5y - 7 - 2y
-6b + 3b = 5y - 7 - 2y
-3b = 3y - 7
b = \( \frac{3y - 7}{-3} \)
b = \( \frac{3y}{-3} \) + \( \frac{-7}{-3} \)
b = -y + 2\(\frac{1}{3}\)