All categories

3 years ago

What are the x-coordinates of the solutions to this system of equations? x2 + y2 = 100 y = x + 2

Mathematics

1 answer:

kiruha [24]3 years ago

6 0

Answer:

x = - 8, x = 6

Step-by-step explanation:

Given the 2 equations

x² + y² = 100 → (1)

y = x + 2 → (2)

Substitute y = x + 2 into (1)

x² + (x + 2)² = 100

x² + x² + 4x + 4 = 100

2x² + 4x + 4 = 100 ( subtract 100 from both sides )

2x² + 4x - 96 = 0 ( divide through by 2 )

x² + 2x - 48 = 0 ← in standard form

(x + 8)(x - 6) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 8 = 0 ⇒ x = - 8

x - 6 = 0 ⇒ x = 6

You might be interested in

Two numbers have an absolute value of 37. Which of the two number is farther from 1 on the number line

Brrunno [24]

If I understand what you're saying. It would be the absolute value of -37, which is 37. Also, the absolute value of 37 is 37.

3 0

3 years ago

Read 2 more answers

What number is 44% of 25

AysviL [449]

44 percent of 25 is 11 to get percentage u would take 44 and divide it by a hundred and u would get .44 and then u would multiply that by 25 and u get 11

8 0

3 years ago

Read 2 more answers

Please help me right away. There are 2 problems.

koban [17]

For #6;

We know that there are 46% male students and 30% of them are seniors. This means that we have to assume that 30% of the male students are seniors and that 30% of the female students are seniors. Taking 30% of 46% gives us 13.8%.

For #7;

We are looking for the possibility that we choose a junior student (22%) or a sophomore student (28%). This adds up to 50% (22%+28% = 50%). That is out answer.

7 0

3 years ago

Weight of a rock: In a geology course, students are learning to use a balance scale to accurately weigh rocks. One student plans

statuscvo [17]

Answer:

The student who weighted the rock 5 times has a 95% confidence interval of (25.2, 29.1) which is guaranteed to be more wider (less precise) than the other student who weighted the rock 20 times.

Step-by-step explanation:

What is Confidence Interval?

The confidence interval represents an interval that we can guarantee that the target variable will be within this interval for a given confidence level.

The confidence interval is given by

$CI = \bar{x} + t_{\alpha/2}(\frac{\sigma}{\sqrt{n} } ) \\$

Where $\bar{x}$ is the mean weight $\sigma$ is the standard deviation $t_{\alpha/2}$ is the critical value from t-table and n is the sample size.

The term $t_{\alpha/2}(\frac{\sigma}{\sqrt{n} } )$ is known as margin of error.

As the sample size is decreased the corresponding margin of error increases which results in wider confidence interval which means smaller precision.

The student who weighted the rock 5 times has a 95% confidence interval of (25.2, 29.1) which is guaranteed to be more wider (less precise) than the other student who weighted the rock 20 times.

We can say with 95% confidence that the true mean weight of the rock is within the interval of (25.2, 29.1).

7 0

3 years ago

Can someone please explain why x= -2! ASAP!!

bearhunter [10]

Because you add both negative x’s which is -2 and add the -6 in the right side so then it’s -2x=4
Divide and you get x=-2

6 0

3 years ago

Read 2 more answers