| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.39 |
| Score | 0% | 48% |
Solve for b:
b2 + 8b - 11 = 2b - 4
| 3 or -8 | |
| 1 or -7 | |
| 7 or 3 | |
| 1 or -9 |
The first step to solve a quadratic expression that's not set to zero is to solve the equation so that it is set to zero:
b2 + 8b - 11 = 2b - 4
b2 + 8b - 11 + 4 = 2b
b2 + 8b - 2b - 7 = 0
b2 + 6b - 7 = 0
Next, factor the quadratic equation:
b2 + 6b - 7 = 0
(b - 1)(b + 7) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (b - 1) or (b + 7) must equal zero:
If (b - 1) = 0, b must equal 1
If (b + 7) = 0, b must equal -7
So the solution is that b = 1 or -7
Solve b + 6b = 3b - 8z + 1 for b in terms of z.
| -1\(\frac{2}{11}\)z + \(\frac{6}{11}\) | |
| -3z + 3 | |
| 7z - \(\frac{1}{2}\) | |
| 2\(\frac{2}{7}\)z - \(\frac{6}{7}\) |
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.
b + 6z = 3b - 8z + 1
b = 3b - 8z + 1 - 6z
b - 3b = -8z + 1 - 6z
-2b = -14z + 1
b = \( \frac{-14z + 1}{-2} \)
b = \( \frac{-14z}{-2} \) + \( \frac{1}{-2} \)
b = 7z - \(\frac{1}{2}\)
Find the value of b:
3b + x = -4
5b - 8x = -2
| 3\(\frac{1}{3}\) | |
| 2\(\frac{1}{2}\) | |
| -1\(\frac{5}{29}\) | |
| -2\(\frac{1}{5}\) |
You need to find the value of b so solve the first equation in terms of x:
3b + x = -4
x = -4 - 3b
then substitute the result (-4 - 3b) into the second equation:
5b - 8(-4 - 3b) = -2
5b + (-8 x -4) + (-8 x -3b) = -2
5b + 32 + 24b = -2
5b + 24b = -2 - 32
29b = -34
b = \( \frac{-34}{29} \)
b = -1\(\frac{5}{29}\)
Which of the following is not true about both rectangles and squares?
the area is length x width |
|
the perimeter is the sum of the lengths of all four sides |
|
the lengths of all sides are equal |
|
all interior angles are right angles |
A rectangle is a parallelogram containing four right angles. Opposite sides (a = c, b = d) are equal and the perimeter is the sum of the lengths of all sides (a + b + c + d) or, comonly, 2 x length x width. The area of a rectangle is length x width. A square is a rectangle with four equal length sides. The perimeter of a square is 4 x length of one side (4s) and the area is the length of one side squared (s2).
Which types of triangles will always have at least two sides of equal length?
equilateral, isosceles and right |
|
isosceles and right |
|
equilateral and isosceles |
|
equilateral and right |
An isosceles triangle has two sides of equal length. An equilateral triangle has three sides of equal length. In a right triangle, two sides meet at a right angle.