All categories

3 years ago

What are the solutions of the equation x^4 + 95x^2 - 500= 0? Use factoring to solve

1 answer:

4 0

1) given x^4 + 95x^2 - 500

2) split in two factors with common factor term x^2: (x^2 + )(x^2 - )

3) find two numbers that add up 95 and their product is - 500:

=> 100*(-5) = - 500 and 100 - 5 = 95

=> (x^2 + 100)(x^2 - 5)

4) factor x^2 - 5 = (x + √5) (x - √5)

5) write the prime factors: (x^2 + 100) (x + √5) (x -√5)

6) find the solutions:

x^2 + 100 = 0 => not possible

x + √5 = 0 => x = - √5

x - √5 = 0 => x = √5

Answer: x = √5 and x = - √5

You might be interested in

Whats 354 sqaured ddd

sertanlavr [38]

354 × 354 = 125,316 :)

3 0

3 years ago

According to a Gallup poll of 1012 people, about one-third of (32%) of Americans keep a dog for protection. Find the:Margin of E

WINSTONCH [101]

The margin of error of the proportion given is of 2.9%.
Applying the margin of error, the confidence interval is (29.1%, 34.9%).

-----------------------

The margin of error of a confidence interval of a proportion $\pi$ in a sample of size n, with a confidence level of $1-\alpha$ , is:

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

In which z is the z-score that has a p-value of $1 - \frac{\alpha}{2}$ .

The confidence interval is:

$\pi \pm M$

In this problem:

Poll of 1012 people, thus $n = 1012$ .
32% keep a dog, thus $\pi = 0.32$

95% confidence level

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

The margin of error is:

$M = 1.96\sqrt{\frac{0.32(0.68)}{1012}} = 0.029$

As a percent, 2.9%, as 0.029 x 100% = 2.9%.

Now for the confidence interval, which is percentage plus/minus margin of error, thus:

$32 - 2.9 = 29.1$

$32 + 2.9 = 34.9$

The confidence interval is (29.1%, 34.9%).

A similar problem is given at brainly.com/question/16807970

4 0

3 years ago

Simplify -2+5(2+6r) I’ll mark brainlist

Dmitriy789 [7]

Answer:

10+30r

Step-by-step explanation:

-2+5(2+6r)

expand 5(2+6r)

5x2=10

(6r)x(5)=30r

so it is 10+30r

then add that to -2

8+30r

Hope that helps :)

6 0

3 years ago

Work out the difference between 1.95 and 13 ?

vagabundo [1.1K]

Okay, so to make 1.95 a 2 we need to add .05. Now we can just figure out the difference between 2 and 13 and add the .05 later.
13-2=11, so we know the difference between 1.95 and 13 is 11.05.

5 0

3 years ago

Need help please due tommorw

Kisachek [45]

Answer:

Solution (4,3)

Step-by-step explanation:

2x-7y= -13

(8x-7y=11)x-1

2x-7y= -13

-8x +7y= -11

$\frac{-bx}{-6} =\frac{-24}{-6}$

x= 4

__________

2x-7y= -13

2(4)-7y=-13

8-7y= -13

subtract 8 from both sides

$\frac{-7y}{-7} =\frac{-21}{-7}$

divide by -7

y= 3

hope it helps..

have a great day!!

6 0

3 years ago