| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.23 |
| Score | 0% | 45% |
Find the value of b:
3b + x = -4
6b - x = 2
| -3\(\frac{1}{2}\) | |
| 2\(\frac{8}{11}\) | |
| -\(\frac{2}{9}\) | |
| 2\(\frac{1}{3}\) |
You need to find the value of b so solve the first equation in terms of x:
3b + x = -4
x = -4 - 3b
then substitute the result (-4 - 3b) into the second equation:
6b - 1(-4 - 3b) = 2
6b + (-1 x -4) + (-1 x -3b) = 2
6b + 4 + 3b = 2
6b + 3b = 2 - 4
9b = -2
b = \( \frac{-2}{9} \)
b = -\(\frac{2}{9}\)
Solve for y:
-8y - 1 < \( \frac{y}{-3} \)
| y < -\(\frac{4}{11}\) | |
| y < -\(\frac{3}{23}\) | |
| y < 1\(\frac{7}{23}\) | |
| y < -\(\frac{16}{31}\) |
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 < sign and the answer on the other.
-8y - 1 < \( \frac{y}{-3} \)
-3 x (-8y - 1) < y
(-3 x -8y) + (-3 x -1) < y
24y + 3 < y
24y + 3 - y < 0
24y - y < -3
23y < -3
y < \( \frac{-3}{23} \)
y < -\(\frac{3}{23}\)
Which of the following is not required to define the slope-intercept equation for a line?
\({\Delta y \over \Delta x}\) |
|
x-intercept |
|
slope |
|
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.
For this diagram, the Pythagorean theorem states that b2 = ?
c2 + a2 |
|
c - a |
|
a2 - c2 |
|
c2 - a2 |
The Pythagorean theorem defines the relationship between the side lengths of a right triangle. The length of the hypotenuse squared (c2) is equal to the sum of the two perpendicular sides squared (a2 + b2): c2 = a2 + b2 or, solved for c, \(c = \sqrt{a + b}\)
Solve for a:
a2 - 14a + 50 = a - 4
| 4 or -6 | |
| 3 or -5 | |
| 6 or 9 | |
| 4 or -1 |
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:
a2 - 14a + 50 = a - 4
a2 - 14a + 50 + 4 = a
a2 - 14a - a + 54 = 0
a2 - 15a + 54 = 0
Next, factor the quadratic equation:
a2 - 15a + 54 = 0
(a - 6)(a - 9) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (a - 6) or (a - 9) must equal zero:
If (a - 6) = 0, a must equal 6
If (a - 9) = 0, a must equal 9
So the solution is that a = 6 or 9