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
A family eats out at a restaurant and the total for their meals is $73.89. They also pay sales tax of 5.8% and leave a tip for t
MrMuchimi

Answer:

C.

Step-by-step explanation:

Edge 2020

4 0
3 years ago
Read 2 more answers
Solve for xxx. Your answer must be simplified. \dfrac x{-6}\geq-20 −6 x ​ ≥−20
Tems11 [23]

Answer:

x ≤ - 27

Step-by-step explanation:

\frac{x}{-9}\ge \:3\\\\\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}\\\\\frac{x\left(-1\right)}{-9}\le \:3\left(-1\right)\\\\Simplify\\\\\frac{x}{9}\le \:-3\\\\\mathrm{Multiply\:both\:sides\:by\:}9\\\\\frac{9x}{9}\le \:9\left(-3\right)\\\\\mathrm{Simplify}\\\\x\le \:-27

7 0
3 years ago
If you have 10 apples what where is the 9th one?
FromTheMoon [43]
To Your First Nine Friends, You Give Them 1 Apple Each. Your Tenth Friend, You Give Her The Basket With The Tenth Apple. She Has The Apple, And The Basket?
5 0
3 years ago
F(x) = -3(x - 1)2 + 3<br> How do you turn it into standard form
Zepler [3.9K]

Answer:

\displaystyle \boxed{f(x) = 6x - 3x^2}

Step-by-step explanation:

f(x) = −3(x² - 2x + 1) + 3

f(x) = −3x² + 6x - 3 + 3

f(x) = −3x² + 6x

** The above answer is written in reverse, which is the exact same result.

I am joyous to assist you anytime.

7 0
3 years ago
Can you answer ASAP please
SVETLANKA909090 [29]

Answer: C. The functions will have the same input when y=0.

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
Other questions:
  • I need the help if you can please help me
    5·2 answers
  • Henry is also eating pizza. He ate 7/8 of a whole pizza 7/8 of a whole pizza that had 12 pieces. How many pieces did he eat
    11·1 answer
  • Combine like terms to simplify the expression:<br> 1.17-0.07a+(-3.92a)
    10·1 answer
  • Help please <br> I forgot
    12·2 answers
  • How do the mathematical domain and reasonable domain compare
    13·1 answer
  • The graph of y&gt;1/2x-2 is shown. Which set contains only points that satisfy the inequality
    8·1 answer
  • What is 3(x-6)+4x+18
    12·2 answers
  • For g(x)= 1/5x^2+3x, find g'(1)<br> a. -1/4<br> b. 1/4<br> c. -7/4<br> d. -4/7<br> e. 7/4
    6·1 answer
  • $
    7·1 answer
  • Grayson charges $35 per hour plus a $35 administration fee for tax preparation. IAn chargers $45 per hour plus a 15$ administrat
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!