| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.65 |
| Score | 0% | 53% |
Which types of triangles will always have at least two sides of equal length?
equilateral and right |
|
equilateral, isosceles and right |
|
equilateral and isosceles |
|
isosceles and right |
An isosceles triangle has two sides of equal length. An equilateral triangle has three sides of equal length. In a right triangle, two sides meet at a right angle.
The endpoints of this line segment are at (-2, 3) and (2, -5). What is the slope-intercept equation for this line?
| y = -\(\frac{1}{2}\)x - 3 | |
| y = -3x + 0 | |
| y = x - 1 | |
| y = -2x - 1 |
The slope-intercept equation for a line is y = mx + b where m is the slope and b is the y-intercept of the line. From the graph, you can see that the y-intercept (the y-value from the point where the line crosses the y-axis) is -1. The slope of this line is the change in y divided by the change in x. The endpoints of this line segment are at (-2, 3) and (2, -5) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(-5.0) - (3.0)}{(2) - (-2)} \) = \( \frac{-8}{4} \)Plugging these values into the slope-intercept equation:
y = -2x - 1
What is 9a5 - 5a5?
| 4a5 | |
| 14 | |
| a510 | |
| 4 |
To combine like terms, add or subtract the coefficients (the numbers that come before the variables) of terms that have the same variable raised to the same exponent.
9a5 - 5a5 = 4a5
Solve for b:
b2 - b + 0 = 2b - 2
| 2 or -3 | |
| 4 or -5 | |
| 1 or 2 | |
| 8 or 6 |
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 - b + 0 = 2b - 2
b2 - b + 0 + 2 = 2b
b2 - b - 2b + 2 = 0
b2 - 3b + 2 = 0
Next, factor the quadratic equation:
b2 - 3b + 2 = 0
(b - 1)(b - 2) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (b - 1) or (b - 2) must equal zero:
If (b - 1) = 0, b must equal 1
If (b - 2) = 0, b must equal 2
So the solution is that b = 1 or 2
On this circle, line segment CD is the:
diameter |
|
chord |
|
radius |
|
circumference |
A circle is a figure in which each point around its perimeter is an equal distance from the center. The radius of a circle is the distance between the center and any point along its perimeter. A chord is a line segment that connects any two points along its perimeter. The diameter of a circle is the length of a chord that passes through the center of the circle and equals twice the circle's radius (2r).