| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.75 |
| Score | 0% | 55% |
Solve for c:
c2 + 3c + 3 = -5c - 4
| -1 or -7 | |
| 9 or 7 | |
| 6 or 6 | |
| 3 or -8 |
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 + 3c + 3 = -5c - 4
c2 + 3c + 3 + 4 = -5c
c2 + 3c + 5c + 7 = 0
c2 + 8c + 7 = 0
Next, factor the quadratic equation:
c2 + 8c + 7 = 0
(c + 1)(c + 7) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (c + 1) or (c + 7) must equal zero:
If (c + 1) = 0, c must equal -1
If (c + 7) = 0, c must equal -7
So the solution is that c = -1 or -7
A cylinder with a radius (r) and a height (h) has a surface area of:
2(π r2) + 2π rh |
|
4π r2 |
|
π r2h |
|
π r2h2 |
A cylinder is a solid figure with straight parallel sides and a circular or oval cross section with a radius (r) and a height (h). The volume of a cylinder is π r2h and the surface area is 2(π r2) + 2π rh.
If the area of this square is 49, what is the length of one of the diagonals?
| \( \sqrt{2} \) | |
| 8\( \sqrt{2} \) | |
| 6\( \sqrt{2} \) | |
| 7\( \sqrt{2} \) |
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 = \( \sqrt{a} \) = \( \sqrt{49} \) = 7
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 = 72 + 72
c2 = 98
c = \( \sqrt{98} \) = \( \sqrt{49 x 2} \) = \( \sqrt{49} \) \( \sqrt{2} \)
c = 7\( \sqrt{2} \)
Which of the following statements about math operations is incorrect?
all of these statements are correct |
|
you can multiply monomials that have different variables and different exponents |
|
you can add monomials that have the same variable and the same exponent |
|
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.
Which of the following statements about parallel lines with a transversal is not correct?
same-side interior angles are complementary and equal each other |
|
all of the angles formed by a transversal are called interior angles |
|
angles in the same position on different parallel lines are called corresponding angles |
|
all acute angles equal each other |
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°).