| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.64 |
| Score | 0% | 53% |
Factor y2 - 4y - 21
| (y + 7)(y - 3) | |
| (y - 7)(y + 3) | |
| (y + 7)(y + 3) | |
| (y - 7)(y - 3) |
To factor a quadratic expression, apply the FOIL method (First, Outside, Inside, Last) in reverse. First, find the two Last terms that will multiply to produce -21 as well and sum (Inside, Outside) to equal -4. For this problem, those two numbers are -7 and 3. Then, plug these into a set of binomials using the square root of the First variable (y2):
y2 - 4y - 21
y2 + (-7 + 3)y + (-7 x 3)
(y - 7)(y + 3)
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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angles in the same position on different parallel lines are called corresponding angles |
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all of the angles formed by a transversal are called interior 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°).
If the area of this square is 16, what is the length of one of the diagonals?
| 9\( \sqrt{2} \) | |
| 8\( \sqrt{2} \) | |
| 2\( \sqrt{2} \) | |
| 4\( \sqrt{2} \) |
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 = \( \sqrt{a} \) = \( \sqrt{16} \) = 4
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 = 42 + 42
c2 = 32
c = \( \sqrt{32} \) = \( \sqrt{16 x 2} \) = \( \sqrt{16} \) \( \sqrt{2} \)
c = 4\( \sqrt{2} \)
Solve 6b - 9b = 9b - 6y - 4 for b in terms of y.
| -\(\frac{3}{17}\)y - \(\frac{1}{17}\) | |
| -1\(\frac{4}{5}\)y + \(\frac{4}{5}\) | |
| -y + 1\(\frac{1}{3}\) | |
| \(\frac{3}{10}\)y - \(\frac{1}{5}\) |
To solve this equation, isolate the variable for which you are solving (b) on one side of the equation and put everything else on the other side.
6b - 9y = 9b - 6y - 4
6b = 9b - 6y - 4 + 9y
6b - 9b = -6y - 4 + 9y
-3b = 3y - 4
b = \( \frac{3y - 4}{-3} \)
b = \( \frac{3y}{-3} \) + \( \frac{-4}{-3} \)
b = -y + 1\(\frac{1}{3}\)
Which of the following statements about math operations is incorrect?
you can add monomials that have the same variable and the same exponent |
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all of these statements are correct |
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you can multiply monomials that have different variables and different exponents |
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you can subtract monomials that have the same variable and the same exponent |
You can only add or subtract monomials that have the same variable and the same exponent. For example, 2a + 4a = 6a and 4a2 - a2 = 3a2 but 2a + 4b and 7a - 3b cannot be combined. However, you can multiply and divide monomials with unlike terms. For example, 2a x 6b = 12ab.