Answer:
- C) (x − 3)2 = 25
- C) Factor out 4 from 4x2 + 40x.
Step-by-step explanation:
1. Adding the square of half the x-coefficient to both sides of the equation will "complete the square." That square is 9, so the result on the right is 16+9 = 25. Only selection C matches.
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2. To complete the square, you want to be able to put the quadratic into the form a(x -h)^2 = -k. For the purpose, it is most convenient to first factor "a" from the given quadratic. Then you can determine "-h" to be half the x-coefficient inside the parentheses.
Here, that looks like ...
4(x² +10x) = 80 . . . . . . . . . . step 1: factor out 4
4(x² +10x +25) = 180 . . . . . add 25 inside parentheses and the same number (4·25) on the right side of the equation
4(x +5)² = 180 . . . . . . . . . . . written as a square
This translates to "a number" is greater than 45. All you have to do now is translate these words into an algebraic statement. Basically, you replace "a number" with the variable which it is defined for, and you use the "greater than" symbol to show that the variable is greater than the value of 45.
Answer:
6.81m
Step-by-step explanation:
Using the formula for finding the length of am arc
L = theta/360° × 2πr
theta is the angle subtended by the drum in rotation
r is the radius of the drum
Given theta = 315.7°
r = 1.1m
Substituting the given values into the formula we have:
L = 315.7/360 × 2π(1.1)
L = 315.7/360 × 2.2π
L = 315.7/360 × 2.2(3.14)
L = 315.7/360 × 6.91
L = 6.81metres
Line of about 6.81metres will be wounded around the drum
Answer:
81.71"
Step-by-step explanation:
Circumference = 2*pi*radius
pi = 22/7
radius = 13
Circumference = 2*22/7*13 = 44*13 / 7 = 572/7 = 81.71"
