Answer:
x = (1 + sqrt(253))/14 or x = (1 - sqrt(253))/14
Step-by-step explanation:
Solve for x:
7 x^2 = x + 9
Subtract x + 9 from both sides:
7 x^2 - x - 9 = 0
x = (1 ± sqrt((-1)^2 - 4×7 (-9)))/(2×7) = (1 ± sqrt(1 + 252))/14 = (1 ± sqrt(253))/14:
Answer: x = (1 + sqrt(253))/14 or x = (1 - sqrt(253))/14
Multiply the amount of the discount by pairs of shoes:
21.75 x 7 = 152.25
Add that to the total she spent:
152.25 + 654.50 = 806.75
Divide the total by pairs of shoes:
806.75/7 = $115.25
The answer is C. $115.25
Answer:
390 ft²
Step-by-step explanation:
The longer base of a trapezoid is 8 ft. The longer base of a similar trapezoid is 13 ft. The area of the smaller trapezoid is 240 ft² What is the area of the larger trapezoid?
We solve the above question using proportion
(Longer base/Area of trapezoid) smaller trapezoid = (Longer base/Area of trapezoid) bigger trapezoid
Let the the Area of the bigger trapezoid = x
Hence,
= 8ft/240ft = 13ft/x ft
Cross Multiply
8ft × x = 240ft × 13ft
x = 240ft² × 12 ft/8 ft
x = 390 ft²
Answer:
12, 13, 14
Step-by-step explanation:
Denote the integers as:
x
x+1
x+2
The sum of their squares, so that would be;
(x^(2)) + (( x + 1 )^(2)) + (( x + 2 )^(2)) = 509
write out the squares
x^2 + x^2 + 2x + 1 + x^2 + 4x + 4 = 509
combine like terms
3x^2 + 6x + 5 = 509
inverse operations
3x^2 + 6x + 5 = 509
-5 -5
3x^2 + 6x = 504
factor
3x^2 + 6x = 504
3 ( x^2 + 2x ) =504
Inverse operations
3 ( x^2 + 2x ) = 504
/3 /3
x^2 + 2x = 168
Factor again
x ( x + 2 ) = 168
At this point, it should be obvious that x is 12 (because 12 * 14 = 168)
So now substitute back into the consecutive numbers
x = 12
x + 1 = 13
x + 2 = 14
3 = AIA ( Alternate Interior Angles)
4 = Definition of AIA
