Please help out !!!!!!!!

Factor 81z^4 - 16<br> Please answer asap

Oksanka [162]

81x%5E4-16 Start with the given expression.

%289x%5E2%29%5E2-16 Rewrite 81x%5E4 as %289x%5E2%29%5E2.

%289x%5E2%29%5E2-%284%29%5E2 Rewrite 16 as %284%29%5E2.

Notice how we have a difference of squares A%5E2-B%5E2 where in this case A=9x%5E2 and B=4.

So let's use the difference of squares formula A%5E2-B%5E2=%28A%2BB%29%28A-B%29 to factor the expression:

A%5E2-B%5E2=%28A%2BB%29%28A-B%29 Start with the difference of squares formula.

%289x%5E2%29%5E2-%284%29%5E2=%289x%5E2%2B4%29%289x%5E2-4%29 Plug in A=9x%5E2 and B=4.

So this shows us that 81x%5E4-16 factors to %289x%5E2%2B4%29%289x%5E2-4%29.

In other words 81x%5E4-16=%289x%5E2%2B4%29%289x%5E2-4%29.

Now let's factor 9x%5E2-4 further

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9x%5E2-4 Start with the given expression.

%283x%29%5E2-4 Rewrite 9x%5E2 as %283x%29%5E2.

%283x%29%5E2-%282%29%5E2 Rewrite 4 as %282%29%5E2.

Notice how we have a difference of squares A%5E2-B%5E2 where in this case A=3x and B=2.

So let's use the difference of squares formula A%5E2-B%5E2=%28A%2BB%29%28A-B%29 to factor the expression:

A%5E2-B%5E2=%28A%2BB%29%28A-B%29 Start with the difference of squares formula.

%283x%29%5E2-%282%29%5E2=%283x%2B2%29%283x-2%29 Plug in A=3x and B=2.

So this shows us that 9x%5E2-4 factors to %283x%2B2%29%283x-2%29.

In other words 9x%5E2-4=%283x%2B2%29%283x-2%29.

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Answer:

So 81x%5E4-16 completely factors to %289x%5E2%2B4%29%283x%2B2%29%283x-2%29

3 0

3 years ago

the length of a rectangle is four times its width. the rectangle has an area of 1024cm^2 work out the width of the rectangle

olga2289 [7]

The width is 16 so the length is 64 (TO clarify W=16)

Hope this helps :)

7 0

3 years ago

Read 2 more answers

Thomas drew a line of best fit for the scatter plot as shown. Enter an equation for the line of best fit in slope-intercept form

juin [17]

Answer:

Equation of line best fits the scatter plot is y = $-\frac{30}{7} x + 108$

Step-by-step explanation:

Let the equation of line be y = mx + c

where m = slope of line and c is the intercept on y -axis

from the graph intercept on y-axis is 108

and the slope of line is given by m = $\frac{y_2 - y_1}{x_2 - x_1}$ where ( $x_2,y_2$ ) and ( $x_1,y_1$ ) is the points on line

let, points be (4,96) and (18,36)

on calculating this m = $\frac{y_2 - y_1}{x_2 - x_1}$ = $-\frac{30}{7}$

Therefore equation of line best fits the scatter plot is y = $-\frac{30}{7} x + 108$

4 0

3 years ago

Please help. Marika is training for a race.

Anika [276]

Let's call n the number of days Marika's been training for the race, and $a_n$ the distance she runs on the nth day in meters. After the first day, when n = 1, she runs 100 meters, so

$a_1=100$

On the second day, she runs an additional 4 meters, on the third day, another 4, and so on. Here's what that looks like mathematically:

$a_2=100 + 4\\a_3=100 + 4 + 4\\a_4=100+4+4+4$

It would be easier to write this continued addition as multiplication, in which case those same equations would look like

$a_2 = 100 + 4(1)\\a_3 = 100 + 4(2)\\a_4=100+4(3)$

Notice that, in every case, the number 4 is being multiplied by is 1 less than n. We could even write for our first term that $a_1=100+4(0)$ . In general, we can say that

$a_n=100+4(n-1)$

Which is expressed by option B.

(Bonus: What piece of information from this question did we not need to use here?)

3 0

3 years ago

A strand of bacteria has a doubling time of 15 minutes. If the population starts with 10 organisms, how long would it take for t

slamgirl [31]

In 90 minutes the population to grow to 700 organisms.

Given that,

A strand of bacteria has a doubling time of 15 minutes.

If the population starts with 10 organisms.

We have to determine,

How long would it take for the population to grow to 700 organisms?

According to the question,

A strand of bacteria has a doubling time of 15 minutes.

If the population starts with 10 organisms.

In 15 minutes strand of bacteria has a doubling time the population starts with 10 organisms.

$\rm = 10 \times 2 = 20 \ bacteria$

In 15 minutes 20 bacteria for the population to grow.

In 30 minutes strand of bacteria has a doubling time the population starts with 20 organisms.

$\rm = 20 \times 2 = 40 \ bacteria$

In 30 minutes 40 bacteria for the population to grow.

In 45 minutes strand of bacteria has a doubling time the population starts with 40 organisms.

$\rm = 40 \times 2 = 80 \ bacteria$

In 45 minutes 80 bacteria for the population to grow.

In 60 minutes strand of bacteria has a doubling time the population starts with 80 organisms.

$\rm = 80 \times 2 = 160 \ bacteria$

In 60 minutes 160 bacteria for the population to grow.

In 75 minutes strand of bacteria has a doubling time the population starts with 160 organisms.

$\rm = 160 \times 2 = 320 \ bacteria$

In 75 minutes 320 bacteria for the population to grow.

In 90 minutes strand of bacteria has a doubling time the population starts with 320 organisms.

$\rm = 320 \times 2 = 640 \ bacteria$

In 90 minutes 640 bacteria for the population to grow.

In 120 minutes strand of bacteria has a doubling time the population starts with 640 organisms.

$\rm = 640 \times 2 = 1280 \ bacteria$

In 120 minutes 1280 bacteria for the population to grow.

Hence, In 90 minutes the population to grow to 700 organisms.

For more details refer to the link given below.

brainly.com/question/3188472

3 0

2 years ago

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