| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.95 |
| Score | 0% | 59% |
Solve for a:
a2 - 4a + 1 = -5a + 3
| -4 or -4 | |
| 1 or -2 | |
| 5 or -4 | |
| 4 or -3 |
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 - 4a + 1 = -5a + 3
a2 - 4a + 1 - 3 = -5a
a2 - 4a + 5a - 2 = 0
a2 + a - 2 = 0
Next, factor the quadratic equation:
a2 + a - 2 = 0
(a - 1)(a + 2) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (a - 1) or (a + 2) must equal zero:
If (a - 1) = 0, a must equal 1
If (a + 2) = 0, a must equal -2
So the solution is that a = 1 or -2
Order the following types of angle from least number of degrees to most number of degrees.
acute, obtuse, right |
|
acute, right, obtuse |
|
right, obtuse, acute |
|
right, acute, obtuse |
An acute angle measures less than 90°, a right angle measures 90°, and an obtuse angle measures more than 90°.
If the base of this triangle is 9 and the height is 4, what is the area?
| 36 | |
| 60 | |
| 18 | |
| 33 |
The area of a triangle is equal to ½ base x height:
a = ½bh
a = ½ x 9 x 4 = \( \frac{36}{2} \) = 18
Which of the following statements about a parallelogram is not true?
a parallelogram is a quadrilateral |
|
the area of a parallelogram is base x height |
|
opposite sides and adjacent angles are equal |
|
the perimeter of a parallelogram is the sum of the lengths of all sides |
A parallelogram is a quadrilateral with two sets of parallel sides. Opposite sides (a = c, b = d) and angles (red = red, blue = blue) are equal. The area of a parallelogram is base x height and the perimeter is the sum of the lengths of all sides (a + b + c + d).
Simplify (8a)(5ab) - (7a2)(2b).
| 117ab2 | |
| 26a2b | |
| -26ab2 | |
| 54ab2 |
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.
(8a)(5ab) - (7a2)(2b)
(8 x 5)(a x a x b) - (7 x 2)(a2 x b)
(40)(a1+1 x b) - (14)(a2b)
40a2b - 14a2b
26a2b