All categories

3 years ago

(Constructed Response) Determine whether the binomial, 9x² - 49, is a difference of

Mathematics

1 answer:

vovikov84 [41]3 years ago

8 0

Answer: It is a difference of two squares, and it factors to (3x-7)(3x+7)

=============================================================

Explanation:

We can write the 9x^2 as (3x)^2 since

(3x)^2 = (3x)*(3x) = (3*3)*(x*x) = 9x^2

The 49 can be written as 7^2 because 7^2 = 7*7 = 49.

This means 9x^2 - 49 is the same as (3x)^2 - 7^2. We have a difference of two squares.

The difference of squares factoring rule is

a^2 - b^2 = (a-b)(a+b)

which we have a = 3x and b = 7 in this case

So,

a^2 - b^2 = (a-b)(a+b)

(3x)^2 - 7^2 = (3x-7)(3x+7)

9x^2 - 49 = (3x-7)(3x+7)

Side note: This is the same as (3x+7)(3x-7). We can multiply two numbers in any order.

You might be interested in

Let this be an easy 5 points for your brainly account all is ask for in return is a "thank you"

Alex Ar [27]

Answer:

deze nuts thanks u

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

Need answer ASAP!! Find the area of the shaded region.

qwelly [4]

Answer:

(5x² +7x -26) units²

Step-by-step explanation:

$\boxed{area \: of \: rectangle = length \times breadth}$

Area of shaded region

= Area of larger rectangle -area of smaller rectangle

Area of larger rectangle

= (3x -4)(2x +2)

= 3x(2x) +3x(2) -4(2x) -4(2) (Expand)

= 6x² +6x -8x -8

= 6x² -2x -8

Area of smaller rectangle

= (x -6)(x -3)

= x² -3x -6x +18 (Expand)

= x² -9x +18

Area of shaded region

= 6x² -2x -8 -(x² -9x +18)

= 6x² -2x -8 -x² +9x -18

= 5x² +7x -26

4 0

3 years ago

The amount of money it takes to fill up a gas tank varies directly with the number of gallons bought. It cost $21.87 to fill up

Kobotan [32]

I believe the answer is C. 2.43

5 0

3 years ago

226Ra has a half-life of 1599 years. How much is left after 1000 years if the initial amount was 10 g?

Ray Of Light [21]

$\bf \textit{Amount for Exponential Decay using Half-Life}\\\\
A=P\left( \frac{1}{2} \right)^{\frac{t}{h}}\qquad 
\begin{cases}
A=\textit{accumulated amount}\\
P=\textit{initial amount}\to &10\\
t=\textit{elapsed time}\to &1000\\
h=\textit{half-life}\to &1599
\end{cases}
\\\\\\
A=10\left( \frac{1}{2} \right)^{\frac{1000}{1599}}$

8 0

3 years ago

For the composite function, identify an inside function and an outside function and write the derivative with respect to x of th

alexira [117]

Answer:

The inner function is $h(x)=4x^2 + 8$ and the outer function is $g(x)=3x^5$ .

The derivative of the function is $\frac{d}{dx}\left(3\left(4x^2+8\right)^5\right)=120x\left(4x^2+8\right)^4$ .

Step-by-step explanation:

A composite function can be written as $g(h(x))$ , where $h$ and $g$ are basic functions.

For the function $f(x)=3(4x^2+8)^5$ .

The inner function is the part we evaluate first. Frequently, we can identify the correct expression because it will appear within a grouping symbol one or more times in our composed function.

Here, we have $4x^2+8$ inside parentheses. So $h(x)=4x^2 + 8$ is the inner function and the outer function is $g(x)=3x^5$ .

The chain rule says:

$\frac{d}{dx}[f(g(x))]=f'(g(x))g'(x)$

It tells us how to differentiate composite functions.

The function $f(x)=3(4x^2+8)^5$ is the composition, $g(h(x))$ , of

outside function: $g(x)=3x^5$

inside function: $h(x)=4x^2 + 8$

The derivative of this is computed as

$\frac{d}{dx}\left(3\left(4x^2+8\right)^5\right)=3\frac{d}{dx}\left(\left(4x^2+8\right)^5\right)\\\\\mathrm{Apply\:the\:chain\:rule}:\quad \frac{df\left(u\right)}{dx}=\frac{df}{du}\cdot \frac{du}{dx}\\f=u^5,\:\:u=\left(4x^2+8\right)\\\\3\frac{d}{du}\left(u^5\right)\frac{d}{dx}\left(4x^2+8\right)\\\\3\cdot \:5\left(4x^2+8\right)^4\cdot \:8x\\\\120x\left(4x^2+8\right)^4$

The derivative of the function is $\frac{d}{dx}\left(3\left(4x^2+8\right)^5\right)=120x\left(4x^2+8\right)^4$ .

3 0

3 years ago