Can anyone help with this question ?

If (9x − 4)(9x + 4) = ax² − b, what is the value of a? (5 points)

lions [1.4K]

Given, (9x - 4)(9x + 4) = ax² - b

From algebraic identities:

We know, (a + b)(a - b) = a² - b²

Now, 81x² + 36x - 36x - 16 = ax² - b

81x² - 16 = axis² - b

So ax² = 81x²

a = 81

-b = -16

b = 16

Solution

Therefore, the value of a is 81.

<h2>MyHeritage</h2>

8 0

2 years ago

Read 2 more answers

What value of x is in the solution set of 2x-3 > 11 - 5x?

Nata [24]

Answer:

x ≤ 3

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Wich graph shous the solution set for -1.tx+84>-13?

alexandr402 [8]

Here is the graph for this solution

3 0

2 years ago

Which of the binomials below is a factor of this trinomial?

Leokris [45]

Answer:

x+5 is the factor..

Step-by-step explanation:

xsquare + (8+5)x + 40

or, xsquare +8x+5x+40

or, x(x+8)+5(x+8)

(x+5)(x+8)

4 0

3 years ago

MATH HELP PLEASE!!! PLEASE HELP!!!

grandymaker [24]

The answer is: [C]:  " f(c) = $\frac{9}{5}$ c + 32 " .
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Explanation:
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Given the original function:

" c(y) = (5/9) (x <span>− 32) " ; in which "x = f" ; and "y = c(f) " ;
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</span>→ <span>Write the original function as: " y = </span>(5/9) (x − 32) " ;

Now, change the "y" to an "x" ; and the "x" to a "y"; and rewrite; as follows:
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x = (5/9) (y − 32) ;

Now, rewrite THIS equation; by solving for "y" ; in terms of "x" ;
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→ That is, solve this equation for "y" ; with "c" as an "isolated variable" on the
"left-hand side" of the equation:

We have:

→ x = " ( $\frac{5}{9}$ ) * (y − 32) " ;

Let us simplify the "right-hand side" of the equation:
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Note the "distributive property" of multiplication:
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a(b + c) = ab + ac ; <u><em>AND</em></u>:

a(b – c) = ab – ac .
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As such:
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" ( $\frac{5}{9}$ ) * (y − 32) " ;

= [ ( $\frac{5}{9}$ ) * y ]   − [ ( $\frac{5}{9}$ ) * (32) ] ;

= [ ( $\frac{5}{9}$ ) y ]  − [ ( $\frac{5}{9}$ ) * ( $\frac{32}{1})$ " ;

= [ ( $\frac{5}{9}$ ) y ]  − [ ( $\frac{(5*32)}{(9*1)}$ ] ;

= [ ( $\frac{5}{9}$ ) y ]  − [ ( $\frac{(160)}{(9)}$ ] ;

= [ ( $\frac{5y}{9}$ ) ]  − [ ( $\frac{(160)}{(9)}$ ] ;

= [ $\frac{(5y-160)}{9}$ ] ;
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And rewrite as:

→ " x = $\frac{(5y-160)}{9}$ " ;

We want to rewrite this; solving for "y"; with "y" isolated as a "single variable" on the "left-hand side" of the equation ;

We have:

→ " x = $\frac{(5y-160)}{9}$ " ;

↔ " $\frac{(5y-160)}{9}$ = x ;

Multiply both sides of the equation by "9" ;

9 * $\frac{(5y-160)}{9}$ = x * 9 ;

to get:

→ 5y − 160 = 9x ;

Now, add "160" to each side of the equation; as follows:
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→ 5y − 160 + 160 = 9x + 160 ;

to get:

→ 5y = 9x + 160 ;

Now, divided Each side of the equation by "5" ;
to isolate "y" on one side of the equation; & to solve for "y" ;

→ 5y / 5 = (9y + 160) / 5 ;

to get:

→ y = (9/5)x + (160/5) ;

→ y = (9/5)x + 32 ;

→ Now, remember we had substituted: "y" for "c(f)" ;

Now that we have the "equation for the inverse" ;
→ which is: " (9/5)x + 32" ;

Remember that for the original ("non-inverse" equation); "y" was used in place of "c(f)" . We have the "inverse equation"; so we can denote this "inverse function" ; that is, the "inverse" of "c(f)" as: "f(c)" .

Note that "x = c" ;
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So, the inverse function is: " f(c) = (9/5) c + 32 " .
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The answer is: " f(c) = $\frac{9}{5}$ c + 32 " ;
_____________________________________________________
→ which is:

→ Answer choice: [C]: " f(c) = $\frac{9}{5}$ c + 32 " .
_____________________________________________________

6 0

3 years ago