| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.76 |
| Score | 0% | 55% |
Which of the following is not required to define the slope-intercept equation for a line?
\({\Delta y \over \Delta x}\) |
|
slope |
|
x-intercept |
|
y-intercept |
A line on the coordinate grid can be defined by a slope-intercept equation: y = mx + b. For a given value of x, the value of y can be determined given the slope (m) and y-intercept (b) of the line. The slope of a line is change in y over change in x, \({\Delta y \over \Delta x}\), and the y-intercept is the y-coordinate where the line crosses the vertical y-axis.
If AD = 25 and BD = 23, AB = ?
| 13 | |
| 2 | |
| 14 | |
| 7 |
The entire length of this line is represented by AD which is AB + BD:
AD = AB + BD
Solving for AB:AB = AD - BDFind the value of a:
-8a + y = -2
-7a - 4y = -5
| \(\frac{31}{58}\) | |
| -1\(\frac{13}{16}\) | |
| -\(\frac{9}{17}\) | |
| \(\frac{1}{3}\) |
You need to find the value of a so solve the first equation in terms of y:
-8a + y = -2
y = -2 + 8a
then substitute the result (-2 - -8a) into the second equation:
-7a - 4(-2 + 8a) = -5
-7a + (-4 x -2) + (-4 x 8a) = -5
-7a + 8 - 32a = -5
-7a - 32a = -5 - 8
-39a = -13
a = \( \frac{-13}{-39} \)
a = \(\frac{1}{3}\)
Solve b - 5b = -7b - z - 4 for b in terms of z.
| \(\frac{1}{2}\)z - \(\frac{1}{2}\) | |
| z + \(\frac{1}{11}\) | |
| 2\(\frac{1}{2}\)z + 1\(\frac{1}{2}\) | |
| -z + 2\(\frac{1}{4}\) |
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.
b - 5z = -7b - z - 4
b = -7b - z - 4 + 5z
b + 7b = -z - 4 + 5z
8b = 4z - 4
b = \( \frac{4z - 4}{8} \)
b = \( \frac{4z}{8} \) + \( \frac{-4}{8} \)
b = \(\frac{1}{2}\)z - \(\frac{1}{2}\)
If side x = 5cm, side y = 9cm, and side z = 13cm what is the perimeter of this triangle?
| 30cm | |
| 27cm | |
| 21cm | |
| 36cm |
The perimeter of a triangle is the sum of the lengths of its sides:
p = x + y + z
p = 5cm + 9cm + 13cm = 27cm