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3 years ago

Solve using completing the square x^2 – 8x + 16 = 25

1 answer:

5 0

First we need to factor the left side. Since it is a perfect square (as is the process with completing the square, we know we can take half of the middle number along with x to be in the two parenthesis.

(x - 4)(x - 4) = 25

Now we simplify to show it as a square.

(x - 4)^2 = 25

Next we take the square root of both sides

x - 4 = +/- 5

Note that we have plus or minus 5. This is because either square would give us positive 25. Now we add 4 to both sides

x = 4 +/- 5

4 + 5 = 9

4 - 5 = -1

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Multiply -4y(-6x2y + 8x3y2).

rodikova [14]

You can download this app called Symbolab but the answer is -144xy^2

3 0

3 years ago

A bacterial culture grows exponentially according to the function n(t)=n(e^n), where n(t) is the quantity after t hours and n is

mart [117]

Answer:

$n(t=2) = 2 e^{1.386294361(2)}=32 grams$

So then after 2 hours we will have 32 grams.

Step-by-step explanation:

For this case we have the followin exponential model:

$n(t) = n e^{rt}$

n(t) is the quantity after t hours, n is the original quantityand t represent the hours and r the rate constant.

For this case we know that n(0) = 2 grams and n(3) = 128 grams and we want to find n(2)=?

From the initial condition we know that n = 2, and we have the model like this:

$n(t) = 2 e^{rt}$

Now if we apply the other conditionn(3) = 128 we got:

$128 = 2 e^{3r}$

If we divide both sides by 2 we got:

$64= e^{3r}$

If we apply natural log for both sides we got:

$ln(64) = 3r$

$r = \frac{ln(64)}{3}=1.386294361$

And our model is this one:

$n(t) = 2 e^{1.386294361t}$

And if we replace t = 2 hours we got:

$n(t=2) = 2 e^{1.386294361(2)}=32 grams$

So then after 2 hours we will have 32 grams.

5 0

3 years ago

Determine whether the following is a statistical question.

natta225 [31]

Answer:

Not statistical

Step-by-step explanation:

This isn't a statistical question because if you try to find out how many teeth are in other people's mouths you still won't know how many are in Edna's mouth because everyone is different. Hope this helps! :)

5 0

3 years ago

1. If x³ +3x²-4=0 has x=-2 as a root (zero), find the other two roots.

castortr0y [4]

Answer:

1 and -2 (has a multiplicity of 2)

Step-by-step explanation:

so since x=-2 is a root then (x+2) is a factor of the polynomial. This means you can divide the polynomial by (x+2) by using synthetic or long division. So for this example I'll using synthetic division which is much more simple than long division

-2 | 1 3 0 -4

-2 -2 4

1 1 -2 0

(x+2)(x²+x-2)

Now you can factor the quadratic into

(x+2)(x-1)

x+2 = 0

x = - 2

x-1 =0

x = 1

6 0

2 years ago

pencils are in packages of 10. Erasers come in packages of 12. Phillip wants to purchase the smallest number of pencils and eras

Sonja [21]

The smallest number of pencils and erasers and 1 eraser per pencil so number of pencils and erasers are equal
*GCD( 12;10) = 60
So Philip buy 60÷12=5 packages of erasers
60÷10=6 packaes of pencils

8 0

3 years ago