| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.75 |
| Score | 0% | 55% |
Solve for b:
b2 - 14b + 21 = -4b - 3
| 4 or 6 | |
| 6 or 5 | |
| 9 or 8 | |
| -4 or -5 |
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:
b2 - 14b + 21 = -4b - 3
b2 - 14b + 21 + 3 = -4b
b2 - 14b + 4b + 24 = 0
b2 - 10b + 24 = 0
Next, factor the quadratic equation:
b2 - 10b + 24 = 0
(b - 4)(b - 6) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (b - 4) or (b - 6) must equal zero:
If (b - 4) = 0, b must equal 4
If (b - 6) = 0, b must equal 6
So the solution is that b = 4 or 6
If the area of this square is 64, what is the length of one of the diagonals?
| 9\( \sqrt{2} \) | |
| 8\( \sqrt{2} \) | |
| \( \sqrt{2} \) | |
| 6\( \sqrt{2} \) |
To find the diagonal we need to know the length of one of the square's sides. We know the area and the area of a square is the length of one side squared:
a = s2
so the length of one side of the square is:
s = \( \sqrt{a} \) = \( \sqrt{64} \) = 8
The Pythagorean theorem defines the square of the hypotenuse (diagonal) of a triangle with a right angle as the sum of the squares of the other two sides:
c2 = a2 + b2
c2 = 82 + 82
c2 = 128
c = \( \sqrt{128} \) = \( \sqrt{64 x 2} \) = \( \sqrt{64} \) \( \sqrt{2} \)
c = 8\( \sqrt{2} \)
Which of the following is not true about both rectangles and squares?
all interior angles are right angles |
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the perimeter is the sum of the lengths of all four sides |
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the lengths of all sides are equal |
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the area is length x width |
A rectangle is a parallelogram containing four right angles. Opposite sides (a = c, b = d) are equal and the perimeter is the sum of the lengths of all sides (a + b + c + d) or, comonly, 2 x length x width. The area of a rectangle is length x width. A square is a rectangle with four equal length sides. The perimeter of a square is 4 x length of one side (4s) and the area is the length of one side squared (s2).
Solve for b:
8b - 2 = 3 - 3b
| \(\frac{5}{11}\) | |
| -3 | |
| \(\frac{1}{2}\) | |
| 4 |
To solve this equation, 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.
8b - 2 = 3 - 3b
8b = 3 - 3b + 2
8b + 3b = 3 + 2
11b = 5
b = \( \frac{5}{11} \)
b = \(\frac{5}{11}\)
Which of the following statements about parallel lines with a transversal is not correct?
all acute angles equal each other |
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same-side interior angles are complementary and equal each other |
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all of the angles formed by a transversal are called interior angles |
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angles in the same position on different parallel lines are called corresponding angles |
Parallel lines are lines that share the same slope (steepness) and therefore never intersect. A transversal occurs when a set of parallel lines are crossed by another line. All of the angles formed by a transversal are called interior angles and angles in the same position on different parallel lines equal each other (a° = w°, b° = x°, c° = z°, d° = y°) and are called corresponding angles. Alternate interior angles are equal (a° = z°, b° = y°, c° = w°, d° = x°) and all acute angles (a° = c° = w° = z°) and all obtuse angles (b° = d° = x° = y°) equal each other. Same-side interior angles are supplementary and add up to 180° (e.g. a° + d° = 180°, d° + c° = 180°).