| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.34 |
| Score | 0% | 67% |
Solve for a:
a2 - 5a - 11 = 2a - 3
| 1 or -5 | |
| -1 or 8 | |
| -4 or -8 | |
| 4 or 1 |
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:
a2 - 5a - 11 = 2a - 3
a2 - 5a - 11 + 3 = 2a
a2 - 5a - 2a - 8 = 0
a2 - 7a - 8 = 0
Next, factor the quadratic equation:
a2 - 7a - 8 = 0
(a + 1)(a - 8) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (a + 1) or (a - 8) must equal zero:
If (a + 1) = 0, a must equal -1
If (a - 8) = 0, a must equal 8
So the solution is that a = -1 or 8
If angle a = 31° and angle b = 62° what is the length of angle c?
| 69° | |
| 87° | |
| 89° | |
| 99° |
The sum of the interior angles of a triangle is 180°:
180° = a° + b° + c°
c° = 180° - a° - b°
c° = 180° - 31° - 62° = 87°
If a = 3, b = 7, c = 6, and d = 4, what is the perimeter of this quadrilateral?
| 25 | |
| 24 | |
| 19 | |
| 20 |
Perimeter is equal to the sum of the four sides:
p = a + b + c + d
p = 3 + 7 + 6 + 4
p = 20
For this diagram, the Pythagorean theorem states that b2 = ?
c - a |
|
c2 - a2 |
|
c2 + a2 |
|
a2 - c2 |
The Pythagorean theorem defines the relationship between the side lengths of a right triangle. The length of the hypotenuse squared (c2) is equal to the sum of the two perpendicular sides squared (a2 + b2): c2 = a2 + b2 or, solved for c, \(c = \sqrt{a + b}\)
What is 5a + 3a?
| 8a | |
| 8a2 | |
| 8 | |
| 15a |
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.
5a + 3a = 8a