1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
jasenka [17]
3 years ago
14

Find the points where the line y = x - 1 intersects the circle x2 + y2 = 13

Mathematics
2 answers:
nata0808 [166]3 years ago
3 0

Answer:

(-2,-3) and (3,2)

Step-by-step explanation:

sub in x-1 into y

x^2 + (x-1)^2 = 13

x^2 + (x-1)(x-1)=13

x^2 + x^2 -2x +1 = 13

2x^2 -2x-12=0

solve for x by factoring (quadratic formula, product sum etc..)

x= -2 and 3

plug in those values into y=x-1 and solve for y

djverab [1.8K]3 years ago
3 0

Answer:

\large \boxed{(-2,-3) \text{ and } (3, 2)}

Step-by-step explanation:

1. Solve the equations for x

\begin{array}{lrcll}(1) & y & = & x - 1 & \\(2) & x^{2} + y^{2} &= &13& \\& x^{2} + (x - 1)^{2} &= & 13& \text{Substituted (1) into (2)}\\& x^{2} + x^{2} -2x +1 & = & 13 & \text{Squared (x - 1)} \\&2x^{2} -2x +1 & = & 13 & \text{Combined like terms} \\\end{array}\\

\begin{array}{lrcll}&2x^{2} -2x - 12 & = & 0 & \text{Subtracted 13 from each side}\\&x^{2} - x - 6 & = & 0 & \text{Divided each side by 2}\\& (x - 3)(x + 2) & = & 0 & \text{Factored the left-hand side} \\& x - 3 = 0 & \text{or} & x + 2 = 0 & \text{Applied zero product rule} \\& \mathbf{x = 3} & \text{or} & \mathbf{x = -2} & \text{Solved each equation separately} \\\end{array}

2. Calculate the corresponding values of y

Insert the values into equation (1)

(a) x = 3

y = 3 - 1 = 2

One point of intersection is (3, 2).

(b) x = -2

y = -2 - 1 = -3

The second point of intersection is (-2, -3).

\text{The line intersects the circle at $\large \boxed{\mathbf{(-2,-3)} \text{ and } \mathbf{(3, 2)}}$}

The diagram shows the intersection of the two graphs.

You might be interested in
Which of the following is a solution to this inequality?
Evgesh-ka [11]

Answer:

(1, 4)

Step-by-step explanation:

5 0
3 years ago
Genesis 19 number to each of her five questo they can have a chance to win door prices at her party she writes the numbers on st
zysi [14]

Answer:

What is the y-intercept of the quadratic function

f(x) = (x - 6)(x - 2)?What is the y-intercept of the quadratic function

f(x) = (x - 6)(x - 2)?What is the y-intercept of the quadratic function

f(x) = (x - 6)(x - 2)?What is the y-intercept of the quadratic function

f(x) = (x - 6)(x - 2)?

(0,12)

(0,12)

(0,12)

(0,12)

What is the y-intercept of the quadratic function

f(x) = (x - 6)(x - 2)?

(0,12)

6 0
3 years ago
Stefanie is painting her bedroom. She can paint 12 2/3 square feet in 2/5 of an hour. How many square feet can she paint in one
aalyn [17]

Answer:

31\frac{2}{3}

Step-by-step explanation:

since its only 2/5 of 1 hour, two 2/5 equal 4/5 so we divide the 12 2/3 by 2 to find the 1/5 which is 6 1/3

12\frac{2}{3}÷2=6\frac{1}{3}

12\frac{2}{3} +12\frac{2}{3}=25\frac{1}{3}

12\frac{1}{3} +6\frac{1}{3}=31\frac{2}{3}

4 0
3 years ago
Read 2 more answers
.In the coordinate x,y the point x is calledorigin<br>abscissa<br>line<br>y-axis<br>​
Dmitry [639]

<u>Answer:</u>

  • The x coordinate is known as <u>abscissa</u><u> </u><u>(</u><u>B)</u>

<u>Step-by-step</u><u> Explanation</u><u>:</u>

In a Cartesian plane, we learn many such terms which represent a point, or a line, or cooridnates of some points etc.

Such terms are:

  • Origin (Intersection of x axis and y-axis.)
  • x - axis (Horizontal line)
  • y - axis (Vertical line)
  • abscisaa (x -coordinate)
  • ordinate (y - coordinate)
5 0
2 years ago
What is the 56th term of the sequence below?<br> -29, -25, -21, -17, . . .
dimulka [17.4K]
The 56th term in the sequence is 195
6 0
3 years ago
Read 2 more answers
Other questions:
  • You are going to the grocery to buy the candies for you and your sisters/brothers. You want to buy
    5·1 answer
  • A Brainliest for the correct answer
    12·1 answer
  • Solve the system<br> x-0.25y=11750<br> -0.20x + y=10000
    6·1 answer
  • The longest side of the triangle section is 4 feet shorter than twice the shortest side. The third side is 3 feet longer than th
    10·2 answers
  • Using the quadratic formula to solve x2 + 20 = 2x, what are the values of x?
    5·1 answer
  • What is 3/7 - 1/4? .....
    5·1 answer
  • Which function is equivalent to g(x) = 9 x2 - 24 x + 16?
    13·1 answer
  • Please help me asap please and thank you :)
    14·1 answer
  • A store purchased a DVD for $15.00 and sold it to a customer for 50% more than the purchase price. The customer was then charged
    8·1 answer
  • Please help me!!!!!!!
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!