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

Answers

Answer 1

Answer:

Answer:

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

Step-by-step explanation:

1. Solve the equations for x

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

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

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.

Answer 2

Answer:

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

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At a market, 2.4 pounds of peas cost $1.68. How many does one pound of peas cost

How to solve for x on a quadratic function

Answers

To find the x-intercepts of any equation, substitute 0 in for y and solve for x. So, we have 0 = 3x2+ x + 1. Now, use the quadratic equation to solve for x, wich a = 3, b = 1, and c = 1: So, now we can find the value of the x-intercepts and not have to estimate!

5. Trisha plans to invest $1,800.00 in a savings account. Savings account 1 earns 4% simple interest and savings account 2 earns 4% interest compounded quarterly. If she plans to deposit the $1,800.00 and leave it in the account for 2 years, in which savings account would she earn more interest? *savings account 1
savings account 2
The interest earned in both savings accounts will be the same.

Answers

The interest earned in both savings account will be the same.

Given:
Principal = 1,800
interest rate = 4%
term = 2 years

Savings Account 1 : simple interest
S.I = Principal x rate x term
= 1,800 x 0.04 x 2years
S.I = 144

Savings Account 2 : compound interest. Compounded quarterly for 2 years. The exponent is the number of times the interest is compounded.
4% is the annual rate. Since it is compound quarterly, 4% divide by 4 quarter is 1% per quarter.

C.I = Pricipal x (1+r/4)^t
C.I = 1,800 x 1.01⁸
= 1,800 x 1.08
C.I = 1,944

1,944 - 1800 = 144 interest earned.

Answer:

savings account 2

Step-by-step explanation:

5550 divided by 10 to the third power

Answers

Answer: 5.55

Step-by-step explanation:

5550/10^3

10 * 10 * 10 = 1,000

5550/1000 = 5.55

Answer:

5.55

Step-by-step explanation:

10*10=100

100*10=1000

5550/1000=

5.55

What is round to the nearst thounsand 3,489

Answers

Answer is 3000.

Explanation;

The given number is 3489.

Before rounding off the given number we should know the place values of the digits. Here,

ones - 9

tens - 8

hundreds - 4

thousands - 3

In this problem, we have to round off the given number to nearest thousand.

Before that, we should look at the digit at the hundreds place.

If that digit is equal or more than 5, we should add 1 to the digit in thousands place unless keep the digit same as it.

Here, 4 is the digit which is before thousands place. 4 is less than 5. Hence, we can keep the digit in thousands place as unchanged.

Hence, rounded off number to nearest thousand is 3000.

3,489 rounded to the nearest thousand would be 3,000. The reason for this is that, as we observe the number, the hundreds digit is lower than 5. Thus, it is closer to 3,000.

Use words to explain the relationship between the digit 9 in 79,401 and the digit 9 in 85,916

Answers

The 9 in 79,401 is in the thousands place, while the digit 9 in 85,916 is in the hundreds place. Hope this helped!

Please don't forget to choose which answer is the Brainliest!

The 9 in 79,401 is in the thousandths place.
The 9 in 85,916 is in the hundredths place.

HOPE THIS HELPED
:)

jill is thinking of two numbers. they have a sum of 27 and a difference of 7. what are the two numbers?

Answers

10 and 17. yay! 10 + 17 = 27 AND 17 - 10 = 7!!! hazzah hope i helped!!

they are 17 and 10, I have a special formula:
Two numbers , always have larger and smaller number
So, to find the larger number you will do
(Total+Difference)÷2 = (27+7)÷2= 17
To find the smaller number you will do
(Total-Difference)÷2= (27-7)÷2=10
Hoped it helped

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