Solve the following inequality.
10x-8≤7
x≤ or ≥, _____
To solve the inequality 10x-8 ≤ 7, we need to isolate the variable x.
Add 8 to both sides of the inequality:
10x - 8 + 8 ≤ 7 + 8
10x ≤ 15
Divide both sides of the inequality by 10:
10x/10 ≤ 15/10
x ≤ 1.5
Therefore, x ≤ 1.5.
Find the slope between the points (6,-5) and (-7,7).
m=______
The slope between two points (x₁, y₁) and (x₂, y₂) is given by the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Using the points (6,-5) and (-7,7), we have:
x₁ = 6, y₁ = -5
x₂ = -7, y₂ = 7
Plugging in these values into the formula, we get:
m = (7 - (-5)) / (-7 - 6)
m = (7 + 5) / (-13)
m = 12 / -13
Therefore, the slope is m = -12/13.
Solve the following inequality.
-5/9y y ≤3
y ≤ or ≥, ______
To solve the inequality -5/9y ≤ 3, we need to isolate the variable y.
Divide both sides of the inequality by -5/9 (which is the same as multiplying both sides by -9/5, the reciprocal of -5/9):
(-5/9y) * (-9/5) ≥ 3 * (-9/5)
y ≥ -27/5
Therefore, the solution to the inequality is y ≥ -27/5.
Write an equation from slope-intercept from (y=mx+b) from the table below.
x y
0 3
9 0
18 -3
27 -6
y=_____x+________
To find the equation in slope-intercept form (y = mx + b), we need to determine the values of m (slope) and b (y-intercept).
Let's calculate the slope using the formula:
m = (change in y) / (change in x)
m = (0 - 3) / (9 - 0)
m = -3/9
m = -1/3
The slope is -1/3.
Next, we can substitute the slope and one point (x, y) from the table into the equation y = mx + b. I will choose the first point (0, 3).
3 = (-1/3)(0) + b
3 = 0 + b
b = 3
Therefore, the equation in slope-intercept form is:
y = -1/3x + 3.