| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.26 |
| Score | 0% | 65% |
If the base of this triangle is 2 and the height is 9, what is the area?
| 91 | |
| 25 | |
| 39 | |
| 9 |
The area of a triangle is equal to ½ base x height:
a = ½bh
a = ½ x 2 x 9 = \( \frac{18}{2} \) = 9
If BD = 11 and AD = 18, AB = ?
| 5 | |
| 7 | |
| 1 | |
| 12 |
The entire length of this line is represented by AD which is AB + BD:
AD = AB + BD
Solving for AB:AB = AD - BDSolve for z:
z2 - 2z - 24 = 2z - 3
| -3 or 7 | |
| -6 or -7 | |
| 6 or -8 | |
| 7 or -2 |
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:
z2 - 2z - 24 = 2z - 3
z2 - 2z - 24 + 3 = 2z
z2 - 2z - 2z - 21 = 0
z2 - 4z - 21 = 0
Next, factor the quadratic equation:
z2 - 4z - 21 = 0
(z + 3)(z - 7) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (z + 3) or (z - 7) must equal zero:
If (z + 3) = 0, z must equal -3
If (z - 7) = 0, z must equal 7
So the solution is that z = -3 or 7
A(n) __________ is two expressions separated by an equal sign.
expression |
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formula |
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problem |
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equation |
An equation is two expressions separated by an equal sign. The key to solving equations is to repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the equal sign and the answer on the other.
If side a = 1, side b = 3, what is the length of the hypotenuse of this right triangle?
| \( \sqrt{145} \) | |
| \( \sqrt{20} \) | |
| \( \sqrt{8} \) | |
| \( \sqrt{10} \) |
According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:
c2 = a2 + b2
c2 = 12 + 32
c2 = 1 + 9
c2 = 10
c = \( \sqrt{10} \)