| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.32 |
| Score | 0% | 66% |
If the base of this triangle is 5 and the height is 6, what is the area?
| 15 | |
| 60 | |
| 91 | |
| 42 |
The area of a triangle is equal to ½ base x height:
a = ½bh
a = ½ x 5 x 6 = \( \frac{30}{2} \) = 15
If side a = 6, side b = 3, what is the length of the hypotenuse of this right triangle?
| \( \sqrt{97} \) | |
| \( \sqrt{40} \) | |
| \( \sqrt{68} \) | |
| \( \sqrt{45} \) |
According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:
c2 = a2 + b2
c2 = 62 + 32
c2 = 36 + 9
c2 = 45
c = \( \sqrt{45} \)
If AD = 15 and BD = 7, AB = ?
| 11 | |
| 8 | |
| 15 | |
| 2 |
The entire length of this line is represented by AD which is AB + BD:
AD = AB + BD
Solving for AB:AB = AD - BDSolve for c:
c2 - 10c + 35 = c + 5
| 5 or -3 | |
| 9 or -7 | |
| 7 or -8 | |
| 5 or 6 |
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:
c2 - 10c + 35 = c + 5
c2 - 10c + 35 - 5 = c
c2 - 10c - c + 30 = 0
c2 - 11c + 30 = 0
Next, factor the quadratic equation:
c2 - 11c + 30 = 0
(c - 5)(c - 6) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (c - 5) or (c - 6) must equal zero:
If (c - 5) = 0, c must equal 5
If (c - 6) = 0, c must equal 6
So the solution is that c = 5 or 6
Simplify 3a x 8b.
| 11ab | |
| 24ab | |
| 24\( \frac{a}{b} \) | |
| 24\( \frac{b}{a} \) |
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.
3a x 8b = (3 x 8) (a x b) = 24ab