8x > = -64
x > = -64/8
x > = -8
10x < 60
x < 60/10
x < 6
-8 < = x < 6
Answer:
The original side length of the square was 9 ft
Step-by-step explanation:
Consider that the square was initially of side length "x" (our unknown). Then the sides were all increased by 5 ft, and now the perimeter (addition of all four sides) of the square render 56 ft.
Let's write an equation that represents the addition of the four sides of this new rectangle, and set it equal to 56 ft. Then solve for the unknown "x":
Therefore, the original side of the square was 9 ft.
If there is no equation that means that x could equal anything.
Let x = amount of 45% antifreezeLet y = amount of 70% antifreeze EQUATION 1: x + y = 150 (total of 150 gallons mixed) EQUATION 2: .45x + .75y = .55(x + y) Simplify and solve the system of equations Multiply second equation by 100 on both sides to remove the decimals 45x + 75y = 55(x + y) Combine like terms 45x + 75y = 55x + 55y 45x - 55x + 75y - 55y = 0 -10x + 20y = 0 Now we have the following system of equations: x + y = 150 -10x + 20y = 0 Multiply the first equation by -10 to get opposite coefficients for x; add the equations to eliminate x 10x + 10y = 1500 -10x + 20y = 0 ------------------------------ 30y = 1500 Solve for y 30y = 1500 y = 50 Since the total mixed gallons is 150, x = 150 - 50 = 100 So we need 100 gallons of the 45% antifreeze and 50 gallons of the 70% antifreeze
The statements that are true about circle Q are:
- The ratio of the measure of central angle PQR to the measure of the entire circle is 1/8.
- The area of the shaded sector depends on the length of the radius.
- The area of the shaded sector depends on the area of the circle.
<h3>How to explain the circle?</h3>
The measure of the central angle is 45°. The measure of the entire circle is 360°. This makes the ratio of the central angle to the entire circle 45/360 = 9/72 = 1/8
To find the area of the shaded sector, this will be:
A = πr² = π(6²) = 36π
1/8(36π) = 36π/8 = 18π/4 = 9π/2 = 4.5π square units. This is not 4 square units.
The ratio of the area of the shaded sector to the area of the circle would not be the same as the ratio of the length of the arc to the area of the circle.
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