| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.21 |
| Score | 0% | 64% |
Find the value of b:
6b + z = -5
-b - 2z = 4
| -2\(\frac{11}{14}\) | |
| 2\(\frac{2}{23}\) | |
| 1\(\frac{3}{7}\) | |
| -\(\frac{6}{11}\) |
You need to find the value of b so solve the first equation in terms of z:
6b + z = -5
z = -5 - 6b
then substitute the result (-5 - 6b) into the second equation:
-b - 2(-5 - 6b) = 4
-b + (-2 x -5) + (-2 x -6b) = 4
-b + 10 + 12b = 4
-b + 12b = 4 - 10
11b = -6
b = \( \frac{-6}{11} \)
b = -\(\frac{6}{11}\)
The formula for the area of a circle is which of the following?
a = π d2 |
|
a = π r2 |
|
a = π d |
|
a = π r |
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.
The endpoints of this line segment are at (-2, 5) and (2, 1). What is the slope of this line?
| -3 | |
| -1 | |
| 1 | |
| -2 |
The slope of this line is the change in y divided by the change in x. The endpoints of this line segment are at (-2, 5) and (2, 1) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(1.0) - (5.0)}{(2) - (-2)} \) = \( \frac{-4}{4} \)If the area of this square is 4, what is the length of one of the diagonals?
| 7\( \sqrt{2} \) | |
| 8\( \sqrt{2} \) | |
| 6\( \sqrt{2} \) | |
| 2\( \sqrt{2} \) |
To find the diagonal we need to know the length of one of the square's sides. We know the area and the area of a square is the length of one side squared:
a = s2
so the length of one side of the square is:
s = \( \sqrt{a} \) = \( \sqrt{4} \) = 2
The Pythagorean theorem defines the square of the hypotenuse (diagonal) of a triangle with a right angle as the sum of the squares of the other two sides:
c2 = a2 + b2
c2 = 22 + 22
c2 = 8
c = \( \sqrt{8} \) = \( \sqrt{4 x 2} \) = \( \sqrt{4} \) \( \sqrt{2} \)
c = 2\( \sqrt{2} \)
Simplify 9a x 7b.
| 63\( \frac{a}{b} \) | |
| 63\( \frac{b}{a} \) | |
| 63a2b2 | |
| 63ab |
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.
9a x 7b = (9 x 7) (a x b) = 63ab