Simultaneous equations
y=x+2
y=x^2

Answers

Answer 1

Answer:

(- 1, 1 ) and (2, 4 )

Step-by-step explanation:

Given the 2 equations

y = x + 2 → (1)

y = x² → (2)

Substitute y = x² into (1)

x² = x + 2 ( subtract x + 2 from both sides )

x² - x - 2 = 0 ← in standard form

(x - 2)(x + 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 2 = 0 ⇒ x = 2

x + 1 = 0 ⇒ x = - 1

Substitute these values into (1) for corresponding values of y

x = 2 → y = 2 + 2 = 4 ⇒ (2, 4 )

x = - 1 → y = - 1 + 2 = 1 ⇒ (- 1, 1 )


Related Questions

The absolute value of ______ is the same number

Fill in the blank

Answers

Answer: I dont know what the fill in the blank would be, but simply make any number not negative

Step-by-step explanation: Example |-3| = 3

there are always positive

What’s the value of c ? Just type in the answer!!!

Answers

Answer:

43

Step-by-step explanation:

−x + y = 2 2x + 4y = 32 What action was completed to create this new equivalent system of equations? −x + y = 2 x + 2y = 16

A. Divide the second equation, 2x + 4y = 32, by 2.
B. Divide the first equation, −x + y = 2, by 2.
C. Multiply the second equation, 2x + 4y = 32, by −1.
D.Multiply the first equation, −x + y = 2, by −1.

Answers

Answer:The answer is A

Step-by-step explanation:

A circular rug has a circumference of 314 inches. What is the approximate area? Round to the nearest whole inch. Use 3.14 for pie 

Answers

Answer:

The area is 7850 square inches

Step-by-step explanation:

Given the circumference, we want to calculate the area

mathematically, the circumference is;

C = 2 pi r

So r is C/2 pi

Area = pi * r^2

Substitute value for r from circumference;

Area = Pi * c^2/4pi^2

Area = C^2/4pi

Area = 314^2/4 * 3.14

Area = 7850 Inches square

Answer:

7,850

Step-by-step explanation:

Look at the picture I need help

Answers

Answer:its 7 because half of 14 cp=14 so pd =7

Step-by-step explanation:

What's the square root of 17 rounded to the nearest tenth

Answers

Answer:

4.0

Step-by-step explanation:

Answer:

4.1

Step-by-step explanation:

4.1231056 is [tex]\sqrt{17}[/tex]

When rounding to the nearest tenth, we get

4.1

Hope I helped,

PumpkinSpice1

What’s the answers? ,,

Answers

Positive , negative , positive, negative

Mark and his 3 friends are out at Applebee's. Their bill totaled $52.35. If they left the server a 20% tip, how much would each person pay splitting the bill evenly

Answers

27.92 each person would have to pay

Jerilyn made 40 treats for her birthday. She gave away 14 to her family before taking the rest to school. What percent did she give away to her family?

Answers

The answer is 35%

This is because Jerilyn gave away 14 of her sweets.
100/40 = 2.5
2.5 x 14 = 35%

Find the factors of function f, and use them to complete this statement.
f(x)= 2x^4 - x^3 -18x^2 + 9x

Answers

Answer:

-3, 0, 1/2, 3

The factors of function f is -3, 0, 1/2, 3

We have given that,

the factors of function f, and use them to complete this statement.

f(x)= 2x^4 - x^3 -18x^2 + 9x

What is the function?

A function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function. Functions were originally the idealization of how a varying quantity depends on another quantity.

We have to determine the factor of the given function

[tex]2x^4 - x^3 -18x^2 + 9x =0[/tex]

[tex]x(2x^3-x^2-18x+9)=0[/tex]

[tex]x=0 \ and \ 2x^3-x^2-18x+9=0[/tex]

[tex]2x^3-x^2-18x+9=0[/tex]

[tex]2x-1=0\quad \mathrm{or}\quad \:x+3=0\quad \mathrm{or}\quad \:x-3=0[/tex]

Therefore the factors  [tex]2x^3-x^2-18x+9=0[/tex] are

[tex]x=\frac{1}{2},\:x=-3,\:x=3[/tex]

-3, 0, 1/2, 3

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TRUE/FALSE: The slope of the line that is PEREPNDICULAR to this line is -3/2.

Answers

Answer:

True

Step-by Step Explanation:

#11
write the equation of a line in point slope-form

Answers

Answer:

y - 5 = 1/4 (x+1)

Step-by-step explanation:

y - 5 = 1/4 (x - (-1))

to simplify the problem you can change (x - (-1)) to (x+1) because subtracting a negative is the same as adding a positive

y - 5 = 1/4 (x+1)

and that is your final answer if you want to keep it in point slope formula

4 fl oz for $8.36 unit rate

Answers

Answer:

I'm pretty sure it's $2.09 for 1 fl oz.

Find the measure of the indicated arc.

Answers

I think that the answer is 61 because the measure of angle B has to be the same of that arc so I find the measure of B adding 70+49=119 and subtract 119 to 180 because triangles add up to 180 and I got 61.

Hope this helps :D

SOMEONE HELP I DONT KNOW WHAT THE HECK IM DOING (7th grade)

Answers

Answer:

Step-by-step explanation:

I'm 8th grade, G

For this problem, you can start by taking the 35 and dividing it by 5 to get 7. Then you need to take 300 and divide that by 5 to get the right proportions. Then you can take your new number from 300 and divide that by 7, and you should not be on the right path because I'm probably an idiot.

Sorry bout it

Answer:

hi

Step-by-step explanation:

PLEASEE HELP.!! ILL GIVE BRAINLIEST.!! *EXTRA POINTS* DONT SKIP:((

Answers

Answer:

undefined slope

Step-by-step explanation:

This is a vertical line parallel to the y- axis.

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 5, - 3) and (x₂, y₂ ) = (- 5, - 6) ← 2 points on the line

m = [tex]\frac{-6+3}{-5+5}[/tex] = [tex]\frac{3}{0}[/tex]

Since division by zero is undefined then the slope is undefined.

Note that all vertical lines have an undefined slope

Giving 15 points plz plz help me

Answers

30 dollars equals the slope and 100 dollars equal y intercept

On the set of axes below, triangle ABC is graphed. Triangles A'B'C'
and A"B"C", the images of triangle ABC, are graphed after a
sequence of rigid motions.

Answers

Answer:

Step-by-step explanation:

a reflection followed by a rotation

The sequence of rigid motions of the triangle is a reflection followed by a rotation, option (D) is the correct answer.

What is graph?

A graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner. Graphs are used to map out functions of two variables on a Cartesian coordinate system, which is composed of a horizontal x-axis and a vertical y-axis.

For the given situation,

The graph shows the triangle ABC plotted in the fourth quadrant.

The triangle A'B'C' are graphed in the third quadrant as its reflection.

The triangle A''B''C'' are graphed in the second quadrant by reflecting the triangle A'B'C' and then rotating it.

Hence we can conclude that the sequence of rigid motions of the triangle is a reflection followed by a rotation, option (D) is the correct answer.

Learn more about graphs here

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Aretha Foster, single, is marketing director for
The Canterbury Community, a senior living center. She is paid
a weekly salary of $735.00. If her weekly federal income tax
withholding is $66.84, find the number of withholding allowances
she claims if the tax is computed using the percentage method.

Answers

Answer:

11.14       brailiest please

Step-by-step explanation:


I NEED HELP PLEASE I WILL MARK

Answers

Answer:

-22

Step-by-step explanation:

-22 is the quotient

Answer: -22

Hope this helps.

A spinner with 9 equal sections is numbered 1 through 9. The probability of spinning a 3 is
What is the probability of not spinning a 3?
Enter your answer as a fraction, in simplest form, in the box.

Answers

Answer:

8/9

Step-by-step explanation:

the probability of spinning 3 is 1/9 so just subtract with 1 or 9/9

After 3 hours of of driving, Paul had gone 183 miles. What was his average rate of speed? Explain your answer.

Answers

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[tex]s(av) = \frac{∆x}{∆t} \\ [/tex]

[tex]s(av) = average \: \: speed[/tex]

[tex]∆x = covered \: \: distance[/tex]

[tex]∆t = time \: \: of \: \: the \: \: covered \: \: distance \\ [/tex]

_________________________________

[tex]s(av) = \frac{183}{3} \\ [/tex]

[tex]s(av) = 61 \: \: \frac{mile}{hour} [/tex]

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Three more than the product of a number and 5 is equal to 6.

Answers

3/5 or .60 is the correct answer!


5x + 3 = 6

5x = 3

x = 3/5 or .60
5x + 3 = 6
5x = 3
x = 3/5

Six girls of differing heights are arranged in 2 rows of 3 each. Each girl is taller than the girl in front of her and also taller than the girl to her right. How many arrangements of the six girls are possible?

Answers

Answer:

5 possible ways

Step-by-step explanation:

Questions like this are a bit technical. Therefore, there are no perfect formula, all you have to do is picture the scene and count. Having said that. Let us use name the positions the girls are standing according to the question:

D E F

A B C

I have arranged this according to how the question has specified, meaning F is the tallest and A is the shortest if I take F to be at the back right and A to be at the front left.

In reality, A and F can never change their positions if we maintain the arrangement specified.

What we have left is to look for how to rearrange, D, E, B and C that will still make it fit the arrangement. Take note that E cannot be in front of B because she is taller than B.

Since positions for shortest and tallest are fixed, you are left with 4 people and you need two of them for the front position. This can be gotten using 4C2 = 6, but the two tall persons can't be in the front else it will disrupt the arrangement, so we have to eliminate that case which will occur once, therefore we have 5 possible ways we can make the arrangements as required.

i'll mark you as brainliest​

Answers

Answer:

y=x+30

Step-by-step explanation:

use y2-y1/x2-x1 to find the slope

the y-int is 30 since looking at the answer choices

Answer:

y=x+30

Step-by-step explanation:

Solve for AB


a: 3.6
b: 15
c: 4
d: 10

Answers

A because 9 divided by 15 equals 0.6. Then I multiply 0.6 times 6 which equals 3.6. I didn’t 9 divided by 15 because they are congruent.

The sum of four times a number and negative three is twelve. What is the number?

2 1/4
3 3/4
-2 1/4
6

Answers

The second one because, 3 3/4 x 4 equals 15 which is the sum of 3 3/4 x 4, minus 3 equals 12.

Answer:

Dgfyb

Step-by-step explanation:

What is the slope of the line that passes through the points (2, 6) and (-1, -9).

Answers

5 is the slope ummmmm so yea

Plz quick can some one help me with these two questions also plz show working out

Answers

22a. ¼ of salary = £3600
total salary = £3600 x 4 = £14400
total amount of salary spent
= (£14400x20%) + (2/5 x £14400) + £3600
= £2880 + £5760 + £3600
= £12240

total amount saved
= £14400 - £12240
= £2160

23a. amount anwar saves = 12%
= 0.12 of his salary
amount bethany saves = 1 - 7/8
= 1/8 = 0.125 of her salary

hence, bethany saves more money each week.

3. Multiply and simplify: (4x + 3)(x - 1)
Answer =

Answers

4x^2-x-3 is the correct answer:)

Answer: = 4x² - x - 3

(4x+3)(x -1 ) = 4x² + 3x - 4x - 3 = 4x² - x - 3

Step-by-step explanation:

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