Answer:
see explanation
Step-by-step explanation:
Check the value of the discriminant
Δ = b² - 4ac
• If b² - 4ac > 0 then roots are real
• If b² - 4ac = 0 roots are real and equal
• If b² - 4ac < 0 then roots are not real
given (x - a)(x - b) = k² ( expand factors )
x² - bx - ax - k² = 0 ( in standard form )
x² + x(- a - b) - k² = 0
with a = 1, b = (- a - b), c = -k²
b² - 4ac = (- a - b)² + 4k²
For a, b, k ∈ R then (- a - b)² ≥ 0 and 4k² ≥ 0
Hence roots of the equation are always real for a, b, k ∈ R
Answer:
x is greater than or = to 8
Answer:
Half of the total cost was paid when her braces were put on. The total cost is $3,200. How much will Kelly's parents need to save each month to pay off the ..
Step-by-step explanation:
During 7 hours: 28 parts assembled
during 14 hours: 56 parts assembled
during 21 hours: 84 parts assembled
during 28 hours: 112 parts assembled
during 35 hours: 140 parts assembled
Answer:
The length of the four pieces of protective strip is 96 feet
Step-by-step explanation:
Let the w be the width of the rectangular house and L is length. Since L = w + 16, its perimeter P = 2(w + L)
= 2(w + w + 16)
= 2(2w + 16)
Since the perimeter of the house P = 136 feet,
136 = 2(2w + 16)
dividing through by 2, we have
136/2 = (2w + 16)
68 = (2w + 16)
collecting like terms, we have
68 - 16 = 2w
52 = 2w
dividing through by 2, we have
w = 52/2
w = 26 feet.
Now, since the side walk is 3 foot wide all around, the width of the house plus sidewalk = w + 3 and the length of the house plus sidewalk = L + 3 = w + 16 + 3 = w + 19.
So, the perimeter of the house plus sidewalk which is the perimeter of the four pieces of protective strip is P' = 2(w + 3 + w + 19)
= 2(w + 22)
= 2(26 + 22)
= 2(48)
= 96 feet
So, the length of the four pieces of protective strip is 96 feet.
