What are the solutions to the following system of equations?

2x − y = 6
y = x2 − 9

Answers

Answer 1

Answer:

(3, 0) and (-1, -8)

Step-by-step explanation:

Equation 1

2x - y = 6Rearrange it so that it is equal to 'y'-y = 6 - 2xy = 2x - 6

Substituting the value of y in Equation 2

y = x² - 9⇒ 2x - 6 = x² - 9⇒ x² - 2x - 3 = 0⇒ x² + x - 3x - 3 = 0⇒ x(x + 1) - 3(x + 1) = 0⇒ (x - 3)(x + 1) = 0⇒ x = 3, -1

Taking x = 3

y = 2(3) - 6y = 0Solution 1 = (3, 0)

Taking x = -1

y = 2(-1) - 6y = -2 - 6y = -8Solution 2 = (-1, -8)

Solutions

(3, 0) and (-1, -8)

Related Questions

4. Mindy has two secret numbers. Her numbers are prime numbers and they are between the
numbers 18 and 25. List Mindy's two numbers.
19, 25
18, 25
24, 25
19, 23

Answers

Answer:

19   23  

Step-by-step explanation:

19 and  23  are the only primes in her range

Please help!! Will mark brainlyest.

Answers

-4,0 …. jdjgblwockr w i need 20 words jfjejckrkwnskf

using the completing square method, what are the zeros of the quadratic function f(x) = 2x2 -3?

Answers

[tex]~~~~~2x^2 -3 =0\\\\\implies 2x^2 = 3\\\\\implies x^2 =\dfrac 32\\\\\implies x = \pm\sqrt{\dfrac 32 }[/tex]

A standard deck of playing cards is shuffled and three people each choose a card. Find the probability that the first two cards chosen are diamonds and the third card is black if the cards are chosen without replacement.

Answers

Answer:

don't worry about this question

Imani earned $48 in interest after two years on an account that paid 8% simple interest annually. Use the formula I = Prt to find Imaríi's principal balance.
$30.00
$76.80
$300.00
$768.00

Answers

Answer:

I=$48

t=2 years

r=8%

Principal=(I×100)/(t×r)

($48×100)/(2×8)

$4800/16

$300

Cooper gave out a survey to some students in his school about their favorite color. Students could choose between red and blue. 129 of those surveyed said their favorite color was red. 57% of the students surveyed said their favorite color was blue. How many students were surveyed in total?

Answers

Using proportions, it is found that since 43% of the total amount is 129, 300 students were surveyed in total.

What is a proportion?

A proportion is a fraction of a total amount.

In this problem, since 57% of the students surveyed said their favorite color was blue, hence 100 - 57 = 43% said it was red, and this amount is of 129 students, hence:

0.43n = 129

n = 129/0.43.

n = 300.

300 students were surveyed in total.

More can be learned about proportions at https://brainly.com/question/27396612

What’s The Answer Of This? Please Answer ASAP

Answers

Answer:

c) 80⁰

isosceles triangle, two sides and angels are equal.

Step-by-step explanation:

180⁰= full triangle

80⁰+20⁰=100⁰

180-100=80⁰

VERY EASY ITS FOR MY COUSIN AND I CANT FIGURE IT OUT NEITHER CAN SHE
A construction team builds a brick wall in 2 weeks. At the end of the

first week, the wall is 3.6 meters high. During the second week, the

team makes the wall 2.25 meters higher. The final height of the wall is

1.3 times the originally planned height.

How tall was the wall originally going to be?

Answers

Answer:

4.5 meters high

Step-by-step explanation:

3.6 + 2.25 = 5.85. 5.85 divided by 1.3 is 4.5.

help me out and please provide steps

Answers

Answer:

  3(x+2)/(2(x+4))

Step-by-step explanation:

A compound fraction is simplified by rewriting it as a simple fraction, and reducing it to lowest terms by cancelling common factors from numerator and denominator. The division of one fraction by another is accomplished in the usual way: multiply the numerator by the inverse of the denominator.

__

  [tex]\dfrac{\left(\dfrac{6x^2-24}{x^2+7x+12}\right)}{\left(\dfrac{4x^2-4x-8}{x^2+4x+3}\right)}=\left(\dfrac{6x^2-24}{x^2+7x+12}\right)\times\left(\dfrac{x^2+4x+3}{4x^2-4x-8}\right)\\\\=\dfrac{6(x-2)(x+2)}{(x+3)(x+4)}\times\dfrac{(x+1)(x+3)}{4(x-2)(x+1)}=\dfrac{3(x-2)(x+1)(x+2)(x+3)}{2(x-2)(x+1)(x+3)(x+4)}\\\\=\boxed{\dfrac{3(x+2)}{2(x+4)}}[/tex]

daniel is going to melt some wax and pour it into a mold shaped like the cone shown below

which is the closest volume to the cone

A.75in^3
B.226in^3
C.151in^3
D.301in^3

Answers

Answer:

A. 75 in³

Step-by-step explanation:

[tex]volume = \frac{1}{3} \times \pi \: {r}^{2} \: h = \frac{1}{3} \times \pi \times { 3}^{2} \times 8 = 75.4[/tex]

What is trigonometry and where is it used?​

Answers

Answer:

Trigonometric functions are used in obtaining unknown angles and distances from known or measured angles in geometric figures. Trigonometry developed from a need to compute angles and distances in such fields as astronomy, mapmaking, surveying, and artillery range finding.

Which term is defined as two intersecting lines that form four right angles in a plane?.

Answers

Answer:

Perpendicular.

Step-by-step explanation:

Two lines that come together and form 4 angles are known as perpendicular lines.

If the area of this rectangle is 55 square units, what is the perimeter. Help asap

Answers

Answer:

32 unit is your correct answer

Answer:

Step-by-step explanation:

the answer is 32

Select all the statements that are true. Explain your reasoning
4−2(3+7)=4−2⋅3−2⋅7
4−2(3+7)=4+−2⋅3+−2⋅7
4−2(3+7)=4−2⋅3+2⋅7
4−2(3+7)=4−(2⋅3+2⋅7)

Answers

Answer:

First and second are both true.

Third and fourth are not true.

Step-by-step explanation:

4−2(3+7)=4−2⋅3−2⋅7

4−2(3+7)= 4 - 2(3+7)  [  -2*3 - 2*7 :  the -2 can be removed from -2*3-2*7 to make -2(3 + 7); communative]  This results in 4-2(3+7), the same on the left side

4−2(3+7)=4+−2⋅3+−2⋅7

The (4+-2*3+-2*7) can be written as (4-2*3-2*7) to simplify the "-+" to simply "-".  That can be written as 4 - 2(3+7), the same as on the left side.

4−2(3+7)=4−2⋅3+2⋅7

The right side, 4-2*3+2*7, can be written as 4-2(3-7), which is NOT the same as on the left.

4−2(3+7)=4−(2⋅3+2⋅7)

The right side can be written as 4-2(3-7), which is not the same as on the left side.

What is the additive inverse of the polynomial –9xy2 6x2y – 5x3? –9xy2 – 6x2y 5x3 –9xy2 – 6x2y – 5x3 9xy2 6x2y 5x3 9xy2 – 6x2y 5x3

Answers

The additive inverse of the given polynomial is

-f(x,y)=-9xy^2+6x^2y-5x^3

You have the polynomial f(x,y)=-9xy^2+6x^2y-5x^3.

What is the additive inverse of a polynomial?

Additive inverse means changing the sign of the number and adding it to the original number to get an answer equal to 0.

The additive inverse of a polynomial f(x,y) is a polynomial that makes zero when it is added to polynomial f(x,y).

So additive inverse of polynomial f(x,y) will be -f(x,y).

Thus, the additive inverse will be

-f(x,y)=-9xy^2+6x^2y-5x^3

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Answer:

D

Step-by-step explanation:

Need help 10 points

Answers

Answer:

The answer is B :)

Step-by-step explanation:

The closed dot means less than or equal to. That is why b is correct :)

Have an amazing day!!

Please rate and mark brainliest!!

Answer:

no a, is the answer not b. salamat po

solve 7^x-2 =30.
Type the correct answer in the box. Round your answer to three decimal places.

X=

Answers

Answer:

x = 3.748

Step-by-step explanation:

this problem requires logs

[tex]log_{7} 30 = x-2[/tex]

x = 2 + log_7 (30) or 3.7479

A spinner with 8 equally sized slices has 8 yellow slices. The dial spun and stops on a slice at random. What is the probability that the dial stops on a yellow slice? Write your answer as a fraction in the simplest form.

Answers

If it’s all yellow, and there’s only 8 slices, then it’s an 8/8 chance, or 100%.

what is 0.24x2.412 step by step

Answers

Answer:

0.57888

Step-by-step explanation:

0.24

2.412

----------

0.57888

Hope I helped

The radius and center of circle C are shown. Use 3.14 for pi . Round to the nearest tenth.

Answers

Answer:

See below

Step-by-step explanation:

Circumference = pi * d =  18 pi inches

Area = pi r^2     = pi * 9^2 = 81 pi  in^2

If secθ = -6.743, find the two values of θ
between 0° and 360°. Round your answers to one
decimal place.

Answers

Answer:

Θ ≈ 98.5° , 261.5°

Step-by-step explanation:

using the identity

cosΘ = [tex]\frac{1}{sec0}[/tex] , then

cosΘ = [tex]\frac{1}{-6.743}[/tex] ≈ - 0.1483

since cosΘ < 0 then Θ is in 2nd and 3rd quadrants

Θ = [tex]cos^{-1}[/tex] (- 0.1483) ≈ 98.5° ← in 2nd quadrant

related acute angle = 180° - 98.5° = 81.5° , then

Θ = 180° + 81.5° = 261.5° ← in 3rd quadrant

The range of which function is (2, infinity)? y = 2x y = 2(5x) y = 5x 2 y = 5x 2

Answers

The function which has range (2, infinity) from the provided function is y = 5ˣ +2. Option 4 is correct.

What is range of function?

Range of a function is the set of all the possible output values which are valid for that function.

The function whose range is (2, ∞) has to be find out.

The first function given in the problem is,

[tex]y=2^x[/tex]

This function has the periodic function with period of logarithmic function and the range of this function is all the real number. This is not the correct option.

The second function given in the problem is,

[tex]y=2(5)^x[/tex]

This function has the periodic function with period of logarithmic function and the range of this function is all the real number. This is not the correct option.

The fourth function given in the problem is,

[tex]y=(5)^x+2[/tex]

This function is translated 5 units up to the function 5ˣ which has the range (0,∞).

Thus, the range of this function is (2, ∞).

Hence, the function which has range (2, infinity) from the provided function is y = 5ˣ +2. Option 4 is correct.

Learn more about range of the function here;

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Answer:

D ) y = 5^x + 2

Step-by-step explanation:

Here ya go ladies and gentlemen

Isabelle runs a restaurant that offers a children's menu. This past week, 20 children ate at her restaurant, and 8 of them ordered grilled cheese. What is the probability that a randomly selected child eating in Isabelle's restaurant this past week ordered grilled cheese?
Write your answer as a fraction or whole number

Answers

Fraction=8/20 kids ate a grilled cheese at her restaurant in the last week. This simplifies to 2/5. Therefore the probability that a randomly selected child at her restaurant is eating a grilled cheese is 2/5.

Can you tell us what the missing number is in this sequence? 7,10,15,22, ?, 42

Answers

it’s counting up in odd numbers
so it would be counting up from 3,5,7…
in this case 22 + 9 is 31
answer = 31

Answer:

31

the difference between the numbers is the number, plus 2, so for example, the difference between 7 and 10 is 3, add two and you have 5, and ten plus 5 equals 15.  Using this formula, we have 5+2=7, which is 15+7=22.  For the missing number, we have 7 (the last number used) +2=9, so, 22+9=31.

Step-by-step explanation:

im kinda bad at explaining things, but i really hoped this helped :)

find the inverse of the function

Answers

If h⁻¹(x) is the inverse of h(x), then by definition of inverse function,

h(h⁻¹(x)) = x

Given that h(x) = 6∛(2x + 5) - 1, we have

h(h⁻¹(x)) = 6∛(2 h⁻¹(x) + 5) - 1 = x

Solve for h⁻¹(x) :

6∛(2 h⁻¹(x) + 5) - 1 = x

6∛(2 h⁻¹(x) + 5) = x + 1

∛(2 h⁻¹(x) + 5) = (x + 1)/6

[∛(2 h⁻¹(x) + 5)]³ = [(x + 1)/6]³

2 h⁻¹(x) + 5 = (x + 1)³/216

2 h⁻¹(x) = (x + 1)³/216 - 5

h⁻¹(x) = (x + 1)³/432 - 5/2

7 times what equals 12

Answers

Answer:

12/7

Step-by-step explanation:

Let the required number be 'n'.

Then, we need to find what the value of n is.

According to the question,

7 x n = 12

Multiply both sides by 1/7.

7 x n x 1/7 = 12 x 1/77/7 x n = 12/7n = 12/7

A right rectangular prism has a square base, with sides that are each 2 meters in length. The height of the prism is 34 meters. Find the volume of the prism in cubic meters

Answers

Answer:

136m

Step-by-step explanation:

The formula for the volume of a rectangular prism is V = L · W · H

We can take the given values and multiply them to find our answer.

L = 2

W = 2

H = 34

2x2x34 = 136

The volume of the rectangular prism will be 136 cubic meters.

What is a rectangular prism?

A rectangular prism is a solid three-dimensional shape with six faces and rectangular bases. A rectangular prism is also a cuboid. A cuboid and a rectangular prism have the same cross-section.

Given that a right rectangular prism has a square base, with sides that are each 2 meters in length. The height of the prism is 34 meters.

The formula for the volume of a rectangular prism is V = L · W · H

We can take the given values and multiply them to find our answer.

L = 2

W = 2

H = 34

The volume of the prism will be calculated as,

V = 2x2x34

V = 136 cubic meters

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Nicholas is 12 years old and he has collected 459 trading cards. Phillip is 14 years old and he has collected 721 trading cards. How many more cards does Phillip have than Nicholas?

Phillip has _____
more cards than Nicholas.

Answers

Answer: Phillip has 262 more cards than Nicholas

Step-by-step explanation:

Since we are looking for how many more cards Phillip has compared to Nicholas we can subtract Nicholas' amount from Phillip's amount to see how much more he has.

721-459=262

Taking a simple difference, we can see that Phillip has _262_

more cards than Nicholas.

How many more cards does Phillip have than Nicholas?

To find this, we need to take the difference between the number of cards that Philip has and the number of cards that Nicholas has, so we just need to solve a subtraction:

Phillip's cards - Nicholas' cards

Where:

Phillip's cards = 721

Nicholas' cards = 459

Then the difference is:

721 - 459 = 262

So we can see that Phillip has 262 more cards than Nicholas.

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What is the mean of the set of data?
25.2, 26.4, 28.7, 25.5

Answers

Check the picture below.

Veronica painted 6 doghouses. She used 5 quarts of paint. If she used the same amount of paint for each doghouse, how many quarts of paint did she use on each doghouse?

Answers:

A 1/5

B 5/6

C 1/6

D 6/5

Answers

Answer:

A. 1/5

Step-by-step explanation:

First, you do 6 and divide it by 5. 6 divided by 5 is 1/2. 1/5 times 6 equals 1/2.

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