Answer:
a), b), e)
Step-by-step explanation:
<em>a) -30(3 + 2w) = -90 - 60w</em>
<em>b) (-9 − 6w) x 10 = -90 - 60w</em>
c) -3(30 - 20w) = -90 + 60w
d) (6 + 4w) × 15 = 90 + 60w
<em>e) −20(4.5 + 3w) = -90 - 60w</em>
Answer:
Part one: The function rule for the area of the rectangle is A(x) = 3x² - 2x
Part two: The area of the rectangle is 8 feet² when its width is 2 feet
Step-by-step explanation:
Assume that the width of the rectangle is x
∵ The width of the rectangle = x feet
∵ The length of the rectangle is 2 ft less than three times its width
→ That means multiply the width by 3, then subtract 2 from the product
∴ The length of the rectangle = 3(x) - 2
∴ The length of the rectangle = (3x - 2) feet
∵ The area of the rectangle = length × width
∴ A(x) = (3x - 2) × x
→ Multiply each term in the bracket by x
∵ A(x) = x(3x) - x(2)
∴ A(x) = 3x² - 2x
∴ The function rule for the area of the rectangle is A(x) = 3x² - 2x
∵ The rectangle has a width of 2 ft
∵ The width = x
∴ x = 2
→ Substitute x by 2 in A(x)
∵ A(2) = 3(2)² - 2(2)
∴ A(2) = 3(4) - 4
∴ A(2) = 12 - 4
∴ A(2) = 8
∴ The area of the rectangle is 8 feet² when its width is 2 feet
Answer:
Ox+y+z=180
Step-by-step explanation:
The new price after the sales is $68
Step-by-step explanation:
The cost of a pair of sneakers = $80
Discount / sales offer= 15% off
New price = $80- 15% of $80
15% of $80 = 15 x 80/100
= $12
New price = 80 - 12
= $68
The new price after the sales is $68
Answer:
The correct Option is B. Statement: ∠AFE ≅ ∠AFD Reason: Transitive Property of Equality
Step-by-step explanation:
A is true, but unnecessary. Because after proving statement A, it will imply BC ⊥ GH but that is not required.
C is also true, but this condition is also not useful in the proving the required statement which is to be proved.
D can be proved. But that is not required hence this will make the solution much bigger.
Now, let us take B. we need 2 facts to prove that lines are perpendicular when parallel lines with a transversal is given.
1. We need that the line we want to show perpendicular to the transversal and the transversal itself to form supplementary angles.
2. And the supplementary angles thus formed to be equal.
Condition 1 has been proved by the step 4.
So it must be condition 2 that you need in step 3.
∠AFD = ∠AFE
Reason : Two angles that are equal to the same angle must themselves be equal.( Transitive property of equality)