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
Answer:
(x+1) meters
Step-by-step explanation:
Area is length times width so x^2-x-2 = L * (x-2)
factor and divide x-2 to get x+1
0.80 because when you line up the decimals 0.80 is bigger
0.80
0.08
Answer: The answer is ![\textup{The other root is }\dfrac{8}{3}~\textup{and}q=40.Step-by-step explanation: The given quadratic equation is[tex]3x^2+7x-q=0\\\\\Rightarrow x^2-\dfrac{7}{3}x-\dfrac{q}{3}=0.](https://tex.z-dn.net/?f=%5Ctextup%7BThe%20other%20root%20is%20%7D%5Cdfrac%7B8%7D%7B3%7D~%5Ctextup%7Band%7Dq%3D40.%3C%2Fstrong%3E%3C%2Fp%3E%3Cp%3E%3C%2Fp%3E%3Cp%3E%3Cstrong%3EStep-by-step%20explanation%3A%20%20%3C%2Fstrong%3EThe%20given%20quadratic%20equation%20is%3C%2Fp%3E%3Cp%3E%5Btex%5D3x%5E2%2B7x-q%3D0%5C%5C%5C%5C%5CRightarrow%20x%5E2-%5Cdfrac%7B7%7D%7B3%7Dx-%5Cdfrac%7Bq%7D%7B3%7D%3D0.)
Also given that -5 is one of the roots, we are to find the other root and the value of 'q'.
Let the other root of the equation be 'p'. So, we have

and

Thus, the other root is
and the value of 'q' is 40.
Answer:
Step-by-step explanation:
Given
y = 3x + 2
Comparing with y = mx + c
slope (m) = 3
y-intercept (c) = 2