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3 years ago

Y=-x+7 , y=x-1 and show your work Help !

Mathematics

1 answer:

Gelneren [198K]3 years ago

7 0

This is a system of equations. The best way to solve it is by realizing that you have two equations equal to y. Since y = y, it follows that $-x+7=x-1$ . Solving for x, you get 4.

$7=2x-1 \\ 8=2x \\ 4=x$

Then, substitute 4 into one of the original equations to find y.

$y=(4)-1=3$ .

The solution is $(4,3)$ . I have attached a graphical representation of the solution as well.

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Square RSTU is inscribed in circle P. Given the coordinates for the vertices of the square, find the equation of circle P.

svlad2 [7]

Answer:

$(x-2)^2+y^2=20$

Step-by-step explanation:

We want to find the equation of a circle P, and we know that the square RSTU is inscribed in the circle, this means that if we replace the points:

R(0,4) S(6,2) T(4,-4) and U(-2,-2) the equation must be verified.

Then, we have to replace the points in each option to see which one is the correct answer.

Option A: $(x-2)^2+y^2=68$

R(0,4):

$(x-2)^2+y^2=68\\(0-2)^2+4^2=68\\(-2)^2+16=68\\4+16=68\\20\neq 68$

We can see that R doesn't belong to the equation of the circle.

We could replace the rest of the points in the equation, but since we already know that R does not belong to the circle, we already know that it is not the right option.

Option B: $(x+2)^2+y^2=20$

R(0,4):

$(x+2)^2+y^2=20\\(0+2)^2+4^2=20\\2^2+4^2=20\\4+16=20\\20=20$

The point R(0,4) verifies the equation.

S(6,2):

$(x+2)^2+y^2=20\\(6+2)^2+2^2=20\\8^2+4^2=20\\64+16=20\\80\neq 20$

The point S doesn't belong to the equation of the circle, then we already know that this isn't the correct option.

Option C: $(x-2)^2+y^2=20$

R(0,4):

$(x-2)^2+y^2=20\\(0-2)^2+4^2=20\\(-2)^2+16=20\\4+16=20\\20=20$

The point R verifies the equation.

S(6,2):

$(x-2)^2+y^2=20\\(6-2)^2+2^2=20\\4^2+4=20\\16+4=20\\20=20$

The point S verifies the equation.

T(4,-4):

$(x-2)^2+y^2=20\\(4-2)^2+(-4)^2=20\\2^2+16=20\\4+16=20\\20=20$

The point T verifies the equation.

U(-2,-2):

$(x-2)^2+y^2=20\\(-2-2)^2+(-2)^2=20\\(-4)^2+4=20\\16+4=20\\20=20$

The point U verifies the equation.

We can see that the four points RSTU verifies the equation. This means that the square RSTU is inscribed in circle P whose equation is: $(x-2)^2+y^2=20$

We can see that the graph of the equation verifies the answer.

3 0

4 years ago

Michael paid $56,580 for an SUV. THIS IS 3,700 LESS THAN TWICE WHAT HIS WIFE PAID. HOW MUCH DID HIS WIFE.PAY?

guapka [62]

Add 3,700 to 56,580 so 60280

3 0

3 years ago

Read 2 more answers

The area of a square is 81 Square units. Find the length of a side.

MAVERICK [17]

Answer:

9 units

Step-by-step explanation:

To find the length of a side of a square, you need to square root the area

√81 = 9

5 0

4 years ago

Lainey is sliding down a water slide that is 376 feet long at a rate of 47 feet per second. How long will it take Lainey to trav

chubhunter [2.5K]

Answer:

8 seconds

Step-by-step explanation:

The length of the water slide is 376 feet and Lainey is sliding down at a rate of 47 feet per second. That is her speed.

Speed is given as distance divided by time or the time rate of displacement.

Therefore, time is:

Time = distance / speed

Therefore, the time it will take Lainey to get from the top to the bottom is:

Time = 376 / 47 = 8 seconds

It will take her 8 seconds to get from the top to the bottom.

8 0

3 years ago

What are the approximate solutions of 2x2 − 7x = 3, rounded to the nearest hundredth?

olganol [36]

Answer:

-0.39 and 3.89

Step-by-step explanation:

By using the quadratic formula it will give you the answers of x= 7 + or - square root of 73 all over 4.

When you do the math of both of the equations it will give you the answers above

7 0

4 years ago