There is only one solution to the equation. A quadratic equation has 2 solutions a positive and a negative, but since we are looking for length, the answer can only be postive. Area= side^2

400= x^2

sqrt(400)=x

20 inches = x

The length of one side is 20 inches

check: 20*20 = 400, which is the area of the square painting.

8 0

3 years ago

Determine the quadrants in which each angle lies

Vinvika [58]

0 to 90 degrees is located in quadrant one. 90 to 180 degrees is located in quadrant two. 180 to 270 degrees is located in quadrant three. 270 to 360 degrees is located in quadrant four. Is this what you were after?

8 0

3 years ago

A new car battery is sold with a two-year warranty whereby the owner gets the battery replaced free of cost if it breaks down du

Mariana [72]

Answer:

4.01% probability that the battery will break down during the warranty period

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

$\mu = 45, \sigma = 12$

a. What is the probability that the battery will break down during the warranty period

Warranty of 2 years = 24 months. So this is the pvalue of Z when X = 24.

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{24 - 45}{12}$

$Z = -1.75$

$Z = -1.75$ has a pvalue of 0.0401

4.01% probability that the battery will break down during the warranty period

7 0

3 years ago

What is the equation and the answer?

Nastasia [14]

Answer:

Step-by-step explanation:

So we begin by assigning variables to each side with:

DE = x

EF = y

DF = z

Now we start listing a system of equations from what is given:

x+y+z=81

x=2y

x-4=z

Once we solve that with substitution, we get the result of:

x=34

y=17

z=30.

Since z is the length of DF, the length of DF is 30.

I hope this helped! :D

7 0

3 years ago