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3 years ago

What are the solutions to x^2 + 8x + 7 = 0

1 answer:

7 0

So to solve this you need to reverse factor this problem

x^2 + 8x + 7 = 0

The common formula is this for factoring ax^2 + bx + c

Now you have to think what multplties to "c" and adds up to "b".

So in this case it's 7 x 1 = 7 and 7 + 1 = 8

So you set it up like this

(x + 7)(x + 1) = 0

So now you can check the factors by multiplying them together and see if it gets your original equation which is does.

So finally to get the answers you need to set each parenthesis to 0 and solve for x.

x + 7 = 0

x + 1 = 0

and we get x = -1 and - 7

You can also plug these two answers back into your original equation to see if it equals 0.

If you have any questions please feel free to comment

You might be interested in

Find the area of the blue shaded region. Round your answer to the nearest hundredth

jenyasd209 [6]

Answer:

173.01

Step-by-step explanation:

To area of a sector or portion of a circle is found using:

$A = \frac{N}{360} \pi r^2$

Substitute N = 50 and A = 27.93.

It becomes $27.93 = \frac{50}{360} \pi r^2\\27.93 = 0.139 \pi r^2\\200.94 = \pi r^2$

The area of the entire circle is 200.94. The area of the blue part of the circle can be found by subtracting the red section from the entire circle.

200.94 - 27.93 = 173.01

8 0

3 years ago

Suppose that the epidemiologist wants to re-estimate the population proportion and wishes for her 95% confidence interval to hav

Svetllana [295]

Answer:

She needs a sample of at least 385.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

The margin of error is:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

How large a sample should she take to achieve this?

She needs a sample of size at least n.

n is found when M = 0.04.

We do not know the true population proportion, so we use $\pi = 0.5$ , which is the case for which we are going to need the largest sample size.

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.05 = 1.96\sqrt{\frac{0.5*0.5}{n}}$

$0.05\sqrt{n} = 1.96*0.5$

Dividing both sides by 0.05

$\sqrt{n} = 19.6$

$(\sqrt{n})^{2} = 19.6^{2}$

$n = 384.2$

Rounding up

She needs a sample of at least 385.

3 0

3 years ago

Simplificar as expressões<br><br> 7√32 - 5√2 + √8<br><br> 2√150 - 4√54 + 6√24

SIZIF [17.4K]

We try to represent each number inside the square root as a product of a square and another number.

a) 7√32 - 5√2 + √8

√32 = √(16 *2) = √16 * √2 = 4* √2 = 4√2

√8 = √(4 *2) = √4 * √2 = 2* √2 = 2√2

7√32 - 5√2 + √8 = 7*(4√2) - 5√2 + 2√2 =

   = 28√2 - 5√2 + 2√2 Factorize out √2

   = (28 - 5 + 2)√2

= 25√2

b) 2√150 - 4√54 + 6√24

√150 = √(25 * 6) = √25 * √6 = 5*√6 = 5√6

√54 = √(9 * 6) = √9 * √6 = 3*√6 = 3√6

√24 = √(4 * 6) = √4 * √6 = 2*√6 = 2√6

2√150 - 4√54 + 6√24 = 2*(5√6) - 4*(3√6) + 6*(2√6)

= 2*5√6 - 4*3√6 + 6*2√6

      = 10√6 - 12√6 + 12√6 Factorize √6

   = (10 - 12 + 12)√6

   = 10√6

7 0

3 years ago

Read 2 more answers

Add. (5x - 2y + 7) + (3x + y - 8)

Schach [20]

Answer:

$=8x-y-1$