| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.94 |
| Score | 0% | 59% |
If a = 9, b = 5, c = 4, and d = 5, what is the perimeter of this quadrilateral?
| 28 | |
| 15 | |
| 23 | |
| 16 |
Perimeter is equal to the sum of the four sides:
p = a + b + c + d
p = 9 + 5 + 4 + 5
p = 23
Solve -8a + a = 3a + 8y + 8 for a in terms of y.
| 3y + 1\(\frac{1}{2}\) | |
| -\(\frac{7}{11}\)y - \(\frac{8}{11}\) | |
| 4y + 1 | |
| 1\(\frac{1}{2}\)y + \(\frac{3}{4}\) |
To solve this equation, isolate the variable for which you are solving (a) on one side of the equation and put everything else on the other side.
-8a + y = 3a + 8y + 8
-8a = 3a + 8y + 8 - y
-8a - 3a = 8y + 8 - y
-11a = 7y + 8
a = \( \frac{7y + 8}{-11} \)
a = \( \frac{7y}{-11} \) + \( \frac{8}{-11} \)
a = -\(\frac{7}{11}\)y - \(\frac{8}{11}\)
If angle a = 62° and angle b = 64° what is the length of angle c?
| 100° | |
| 59° | |
| 54° | |
| 82° |
The sum of the interior angles of a triangle is 180°:
180° = a° + b° + c°
c° = 180° - a° - b°
c° = 180° - 62° - 64° = 54°
Find the value of b:
-9b + z = -4
4b - 6z = 7
| 1\(\frac{9}{20}\) | |
| 11\(\frac{1}{2}\) | |
| 2\(\frac{1}{7}\) | |
| \(\frac{17}{50}\) |
You need to find the value of b so solve the first equation in terms of z:
-9b + z = -4
z = -4 + 9b
then substitute the result (-4 - -9b) into the second equation:
4b - 6(-4 + 9b) = 7
4b + (-6 x -4) + (-6 x 9b) = 7
4b + 24 - 54b = 7
4b - 54b = 7 - 24
-50b = -17
b = \( \frac{-17}{-50} \)
b = \(\frac{17}{50}\)
Solve for b:
b2 + 5b - 6 = 0
| 5 or -4 | |
| 3 or -3 | |
| 1 or -6 | |
| 7 or -1 |
The first step to solve a quadratic equation that's set to zero is to factor the quadratic equation:
b2 + 5b - 6 = 0
(b - 1)(b + 6) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (b - 1) or (b + 6) must equal zero:
If (b - 1) = 0, b must equal 1
If (b + 6) = 0, b must equal -6
So the solution is that b = 1 or -6