Solve the system of equations.

Mathematics

2 answers:

77julia77 [94]2 years ago

8 0

The answer should be The B

Karolina [17]2 years ago

5 0

Answer:

Step-by-step explanation:

y = - 2x + 5 → (1)

y = x² + 3x + 9 → (2)

substitute y = x² + 3x + 9 into (1)

x² + 3x + 9 = - 2x + 5 ( subtract - 2x + 5 from both sides )

x² + 5x + 4 = 0 ← in standard form

(x + 1)(x + 4) = 0 ← in factored form

equate each factor to zero and solve for x

x + 1 = 0 ⇒ x = - 1

x + 4 = 0 ⇒ x = - 4

substitute these values into (1) for corresponding values of y

x = - 1 : y = - 2(- 1) + 5 = 2 + 5 = 7 ⇒ (- 1, 7 )

x = - 4 : y = - 2(- 4) + 5 = 8 + 5 = 13 ⇒ (- 4, 13 )

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natta225 [31]

Answer:

Step-by-step explanation:

Let assume that the volume = 88 cubic feet

Then:

$L = 3w --- (1)volume = l \times w \times h \\ \\ 88 = (3w) \times w \times h \\ \\ 3w^2 h= 88 \\ \\ h = \dfrac{88}{3w^2}--- (2) \\ \\$

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Now, to determine the minimum cost:

$\dfrac{dC}{dw}= 0 \\ \\ \implies 24 w - \dfrac{176}{3w^2}- \dfrac{176}{w^2}=0 \\ \\ 24 w ^3 = \dfrac{176}{w^2}(\dfrac{1}{3}+1) \\ \\ 24 w ^3 = \dfrac{176(4)}{3} \\ \\ w^3 = \dfrac{88}{3(3)}$