Answer:
Step-by-step explanation:
We can eliminate options C and D quite quickly because factoring either one would have one equation be y = x and the other either y = 72x - 96 or y = 72x + 108. Neither of these added to x will give either option A or B
so that leaves E.
72x² – 204x + 144 = 0
we can find the zeros
x = (204 ± √(204² - 4(72)(144))) / (2(72))
x = (204 ± 12) / 144
x = 1.5
x = 4/3
so the equation has factors
(x - 1.5)(x - 4/3)
and therefore also a factor in their product
x² - (
)x + 2
which is 1/72 of the original quadratic
so all factors of E are
72(x - 1.5)(x - 4/3)
now we need to distribute factors of 72 among the other two factors so that when we add them together the x¹ terms are either 16 or 17 and the x⁰ terms sum to -12. let "a" and "b" be the factors of 72.
ab = 72
a = 72/b
-1.5a - 4b/3 = -12
1.5a + 4b/3 = 12
1.5(72/b) + 4b/3 = 12
108/b + 4b/3 = 12
324/b + 4b = 36
324 + 4b² = 36b
81 + b² = 9b
b² - 9b + 81 = 0
b = (9 ±√(9² - 4(1)(81))) / 2(1))
b = (9 ± √-243) / 2
as both of these roots are imaginary numbers
there is no valid solution to this problem as posed
IF we allow a slight edit to answer B, we can factor 72 into 9•8
y = 8(x - 1.5) y = 9(x - 4/3)
y = 8x - 12 y = 9x - 12
so the sum of the two would be 17x - 24
Let, the width = w
We know, A = 2(lw + wh +hl )
250 = 2(10w + 5w + 50)
250 = 2(15w + 50)
250 = 30w + 100
30w = 250 - 100
w = 150/30
w = 5
In short, Your Answer would be Option C) 5 cm
Hope this helps!
Answer:
2 cats were cared for
Step-by-step explanation:
c= cats
d=dogs
c+d =7
1.5c+3.5d=20.50
c+d =7
solve for d
d = 7-c
substitute into 1.5c+3.5d=20.50
1.5 c + 3.5 (7-c) = 20.50
distribute
1.5c +24.5 -3.5 c = 20.5
combine like terms
24.5 -2c =20.5
subtract 24.5 from each side
-2c = -4
divide by -2
c =2
Answer:
10 million (10,000,000) tens can go into 100,000,000
Answer:
C
Step-by-step explanation:
My Apologies if Wrong!