Mathematics: If (4x−7)2=ax2+bx+c for all values of x, what is the value of c(b+a)?

If (4x−7)2=ax2+bx+c for all values of x, what is

Ответ:

applejulianamoreno

17.01.2022

Mathematics

-1960

Step-by-step explanation:

The expression on the left expands to ...

(4x -7)² = (4x)² +2(4x)(-7) +(-7)² = 16x² -56x +49

Matching coefficients, you have ...

a = 16b = -56c = 49

Then the expression c(b+a) evaluates to ...

49(-56+16) = 49(-40) = -1960

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Ответ:

cody1097

04.12.2021

Mathematics

Selling price of each corsage = $ 23

Selling price of each boutonniere = $26

Step-by-step explanation:

Let x =Selling price of each corsage.

y = Selling price of each boutonniere.

As per given, we have

$18x+21y= 960\ \ \ \ (i)\\\\ 25x+17y= 1017\ \ \ \ (ii)$

Divide (i) by 3, we get

$6x+7y=320\\\\\Rightarrow\ 6x=320-7y\\\\\Rightarrow\ x=\dfrac{320-7y}{6}\ \ \ \ (iii)$

Put this in (ii) , we get

$25(\dfrac{320-7y}{6})+17y=1017\\\\\Rightarrow\ \dfrac{25(320)-25(7y)}{6}+\dfrac{17\times6y}{6}=1017\\\\\Rightarrow\ \dfrac{8000-175y}{6}+\dfrac{102y}{6}=1017\\\\\Rightarrow\ \dfrac{8000-175y+102y}{6}=1017\\\\\Rightarrow\ 8000-73y=6\times1017\\\\\Rightarrow\ 8000-73y=6102\\\\\Rightarrow\ 73y=8000-6102\\\\\Rightarrow\ 73y= 1898\\\\\Rightarrow\ y=\dfrac{1898}{73}\\\\\Rightarrow\ y=26$

Put this in (iii),

$x=\dfrac{320-7(26)}{6}=23$

Hence, Selling price of each corsage = $ 23

Selling price of each boutonniere = $26

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If (4x−7)2=ax2+bx+c for all values of x, what is the value of c(b+a)?

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