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3 years ago

Find the center and the radius of the circle with the equation: x^2 +2x + y^2-2y-14 =0

Mathematics

2 answers:

maw [93]3 years ago

6 0

X²+2x+y²-2y=14
adding 1+1 both sides

x²+2x+1+y²-2y+1=14+1+1

(x+1)² +(y-1)² = 4²

x=-1 y= 1 r = 4

hope it helps !!

FrozenT [24]3 years ago

5 0

We need to convert the equation of the circle to standard form only then we can find the radius and the center of the circle.

$x^{2} +2x+ y^{2}-2y-14=0 \\ \\ 
x^{2} +2x+ y^{2}-2y=14 \\ \\ 
x^{2} +2(x)(1)+ y^{2}-2(y)(1)=14 \\ \\ 
 x^{2} +2x+1 + (y^{2}-2y+1)=14+1+1 \\ \\ 
(x+1)^{2}+(y-1)^{2} =16 
$

From this equation we can write:

Center of the circle is (-1,1) and the radius of the circle is 4.

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Mrs. Carlyle bought a bag of nuts for her children. Phillip, Joy, Brent, and Preston took some from the bag.Phillip took 1/3. Jo

BARSIC [14]

Answer:

Originally there was 324 nuts in the bag.

Phillip took 108, Joy took 54, Brent took 81 and Preston took 10.

Step-by-step explanation:

Let's call the total amount of nuts N, and the number of nuts each child took by the initial of their name (Phillip will be P1 and Preston will be P2).

So we can write the following equations:

P1 = N/3

After removing N/3, the remaining nuts is (N - N/3):

J = (N - N/3)/4 = (2N/3)/4 = N/6

After removing N/6 from (N - N/3), the remaining nuts is (N - N/3 - N/6):

B = (N - N/3 - N/6)/2 = (N/2)/2 = N/4

P2 = 10

In the final there were 71 nuts remaining, so we have that:

N - N/3 - N/6 - N/4 - 10 = 71

N - N/3 - N/6 - N/4 = 81

N/4 = 81

N = 324 nuts

The amount of nuts took by each child is:

P1 = N/3 = 108 nuts

J = N/6 = 54 nuts

B = N/4 = 81 nuts

P2 = 10 nuts

8 0

4 years ago

Solve the problem.

Alex

Answer:

0.081

Step-by-step explanation:

Given parameters:

Vertical drop = 70ft

Horizontal distance = 866ft

Unknown:

Slope of the rapids =?

Solution:

Slope is the rise or vertical height divide by the horizonal distance.

Slope = $\frac{vertical drop}{horizontal distance}$

Insert the parameters and solve;

Slope = $\frac{70}{866}$ = 0.081

8 0

3 years ago

Sienna planned a rectangular pool, as shown in the scale drawing below.

svlad2 [7]

Answer:

The scale factor is

27.5 feet / 22 feet = 1.25.

Explanation:

Whenever you are calculating factors, you are comparing two measurements. In this problem we compared a longer length to a shorter length pool. The length was changed to (27.5 feet) and youre comparing to the length it was originally (22 feet).

Ok so you know the two measurements being compared, but how come it’s 27.5/22 and not 22/27.5? Because the value got bigger.

In this problem you had a pool with long side of 22 ft. But then you made it longer to 27.5 ft. So it scales up,

It went from 100% its length to 125% its length. So the length is 125% / 100% = 1.25 times longer than it used to be.

Here’s another example:

How do you calculate your grade percentage on a test? You take the amount of points you earned and divide by the total possible points. Your grade percentage is a comparison of your score (Compare value) compared to a perfect score (reference value) .

So lets say your test had 22 total points. You get all the answers correct so you get 22/22 points which is 22/22*100 = 100%. Let’s say you get an extra bonus question correct so you end up with even more points and you get 27.5 points out of 22. By getting the bonus points you scaled up your score! Now your score is 27.5/22 * 100 = 125%. So you went from 100% to a 125%. Or from a scale factor of 1 to 1.25.

Whenever the value is getting bigger than it was, you’re going to have a compared percentage over 100%. If the value gets smaller, then you would get a compared percentage less than 100%. Similarly a factor scale is going to be over 1 if the compared value is getting bigger, and less than 1 if it’s getting smaller.

So you don’t need to use percentages, factors are the same they just look a little different.

27.5/22 = 125% / 100% = 1.25

In summary just do this division:

(compare value)/(reference value). The result is how big the top value is compared to the bottom value.

5 0

3 years ago

Read 2 more answers

sarah can complete a project in 90 minutes and her sister betty can complete it in 120 minutes if they both work on the project

alukav5142 [94]

Answer:

It will take them approximately 51.43 minutes to complete the project together

Step-by-step explanation:

This is what is called a "shared job" problem.

The best way to work on them is to start by finding the "portion" of the job done by each of the people in the unit of time.

So, for example, Sarah completes the project in 90 minutes, so in the unit of time (that is 1 minute) she completed 1/90 of the total project

Betty completes the project in 120 minutes, so in the unit of time (1 minute) she completes 1/120 of the total project.

We don't know how long it would take for them to complete the project when working together, so we call that time "x" (our unknown).

Now, when they work together completing the entire job in x minutes, in the unit of time they would have done 1/x of the total project.

In the unite of time, the fraction of the job done together (1/x) should equal the fraction of the job done by Sarah (1/90) plus the fraction of the job done by Betty. This in mathematical form becomes:

$\frac{1}{x} =\frac{1}{90} +\frac{1}{120}\\\frac{1}{x} =\frac{4}{360} +\frac{3}{360}\\\frac{1}{x} =\frac{7}{360} \\x=\frac{360}{7} \\x=51.43\,\,min$

So it will take them approximately 51.43 minutes to complete the project together.

8 0

4 years ago

HELP PLSSSSSSSSSSSSSSSSSSSSSSSSS

Monica [59]

C , I took a guess so if it’s wrong sorry

7 0

3 years ago