HELLLLPPPP PLZZZZZ I WILL MARK BRAINLEIST

HELLLLPPPP PLZZZZZ I WILL MARK BRAINLEIST

Answers

Answer 1

Answer:

Step-by-step explanation:

4.

distance=2436-(-1020)=2436+1020=3456 ft

5.

in two turns points=3-4=-1

in 6 turns=-1/2×6=-3 points

6.

-23+40=17

she had 17 dollars balance.

Answer 2

Answer:

5 -3

Step-by-step explanation:


Related Questions

Is the value of the 8 in 12.984 the same as the value of the 8 in 7.38? Justify your response.

Answers

Answer:

Yes because they are both in the hundredths place

Step-by-step explanation:

yes , only because both of them are in the hundreds place :)

what is 9000/16000 as a decimal

Answers

Answer:

It is 0.56 Hope this helps!

Step-by-step explanation:

Answer:

0.5625

Step-by-step explanation:

divide and you get 0.5625. Simplified to the nearest tenth is .6

to the nearest hundreth if .56

A jeweler uses 3.685 grams of gold to make a ring. Enter the word form for 3.685.

Answers

Answer:

three and six hundrend eighty five thousands  grams of gold

Step-by-step explanation:

Three point six hundred eighty five pointer

What is the relationship between the value of the 4 in 3,642 and the value of the 4 in 5,401?

Answers

Answer: The 4 in the number 5,401 is 10 times greater than the 4 in the number 3,642.

In the number 3,642 the number 4 is in the Tens Place.

In the number 5,401 the number 4 is in the Hundreds Place.

Tens < Hundreds

40 < 400

Q: How do we know it's 10 times greater?

A: Multiply!

You multiply 40×10 and get 400! To see if the answer is right divide 400÷40 and get 10. Or divide 400÷10 and get 40.

Basically, when you're multiplying something by 10 you just add a 0. When you divide by 10 you remove a 0.

That's how the number 4 in 5,401 is 10 times greater than the number 4 in 3,642.

The relationship is in 3,642 it is in the tenth place and in 5,401 it is in the hundreds place!

the ratio of males to females at a camp is 5 to 4. If there are 40 males at the camp, how many females are there?

Answers

Answer:

5 males : 4 females

40 males : X females

5/40 =4/X

(cross multiplication)

5x = 4*40

5x = 160

(divide both sides by 5)

X = 32

therefore, there are 32 females at the camp

5 Males for every 4 female. 40/5 = 8. 4 x 8 = 32. 32 Females

Your fitness tracker overestimates the number of steps you take by 5%. The trackers indicates that you took 7350 steps today. Write and solve an equation to find the actual number of steps you took today.

Answers

the answer is 140000 steps

Answer:

bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbdrtgaethrtththt

Step-by-step explanation:

Simplify. 2x+7y+3x−4y please help

Answers

Answer:

5x +3y

Step-by-step explanation:

[tex]2x+7y+3x-4y\\\\\mathrm{Group\:like\:terms}\\=2x+3x+7y-4y\\\\\mathrm{Add\:similar\:elements:}\:2x+3x=5x\\=5x+7y-4y\\\\\mathrm{Add\:similar\:elements:}\:7y-4y=3y\\= 5x+3y[/tex]

●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●

Hi my lil bunny!

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

             [tex]\boxed{5x + 3y}[/tex]

Let's simplify step-by-step.

[tex]2x+7y+3x-4y[/tex]

[tex]= 2x+7y+3x-4y[/tex]

Combine Like Terms:

[tex]2x+7y+3x-4y\\= ( 2x + 3x ) + ( 7y + -4y ) \\= 5x + 3y[/tex]

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●

Have a great day/night!

❀*May*❀

Squidward loves playing his clarinet and believes it attracts more jellyfish than any other instrument he has played. In order to test his hypothesis, Squidward played a song on his clarinet for a total of 5 minutes and counted the number of jellyfish he saw in his front yard. He played the song a total of 3 times on his clarinet, and then repeated the experiment using a flute and a guitar. He also recorded the number of jellyfish he observed when he was not playing an instrument. The results are shown in the chart. number of jellyfish attracted to each instrument trial / without music / clarinet / flute / guitar 1 / 5 / 15 / 5 / 12 2 / 3 / 10 / 8 / 18 3 / 2 / 12 / 9 / 17 1) what is the dependent value? 2) what is the independent variable? 3) what should be Squidward’s conclusion? 4) are the results reliable? why or why not?

Answers

Answer:

1. The amount of jellyfish attracted ,

2. The type of instrument played ,

3. The guitar attracts the most jellyfish,

4. the results are reliable. there are no big outliers .

URGENT!! I have been trying to ask this question for a while but I keep getting fake answers: Find an equation in standard form for a parabolic function that goes through the points (1,-12) (3,16) and has a stretch factor of 2

Answers

Answer:

Step-by-step explanation:

y=a(x-h)^2+k

-12=a(1-h)^2+k

16=a(3-h)^2+k

subtract

a(3-h)^2-a(1-h)^2=28

a[(3-h)^2-(1-h)^2]=28

a=2

2[(3-h)^2-(1-h)^2]=28

(3-h)^2-(1-h)^2=14

9+h^2-6h-(1+h^2-2h)=14

9+h^2-6h-1-h^2+2h=14

-4h+8=14

-4h=6

h=-3/2

16=2(3+3/2)^2+k

16=2×81/4+k

k=16-81/2=-49/2

so y=2(x+3/2)²-49/2

Answer: y=a(x-h)^2+k

-12=a(1-h)^2+k

16=a(3-h)^2+k

subtract

a(3-h)^2-a(1-h)^2=28

a[(3-h)^2-(1-h)^2]=28

a=2

2[(3-h)^2-(1-h)^2]=28

(3-h)^2-(1-h)^2=14

9+h^2-6h-(1+h^2-2h)=14

9+h^2-6h-1-h^2+2h=14

-4h+8=14

-4h=6

h=-3/2

16=2(3+3/2)^2+k

16=2×81/4+k

k=16-81/2=-49/2

so y=2(x+3/2)²-49/2

Step-by-step explanation:

Plz help me Now! Thx

Answers

Answer:

A or/and B

Step-by-step explanation:

in A the hundreds value is 8 and [tex]\frac{8}{10} = 0.8[/tex]

in B he hundreds value is 7 and [tex]\frac{7}{10} =0.7[/tex]

hope this helps you!

Answer:

C. 1.404

Step-by-step explanation:

The 1000ths place is the 1 in 0.01

The 100ths place is the 1 in 0.001

A = 0.881

The number in the 1000ths place is 1

The number in the 100ths place is 8

1/8 is not 1/10

B = 0.722

The number in the 1000ths place is 2

The number in the 100ths place is 2

2/2 is not 1/10

C = 1.404

The number in the 1000ths place is 4

The number in the 100ths place is 0

BUT the numbe rin the 100ths place could also be written as 40, where the 4 from the 40 has moved up a place to 10th

in which case, 4/40 = 1/10

Show that AC and BD bisect each other if A(–3, –5), B(2, –3), C(3, 5), and D(–2, 3). Find AC and BD

Answers

Answer:

Step-by-step explanation:

midpoint of AC=((-3+3)/2,(-5+5)/2)=(0,0)

midpoint of BD=((2-2)/0,(-3+3)/2)=(0,0)

coordinates  of midpoint of AC and BD are same.

∴ AC and BD bisect each other.

[tex]AC=\sqrt{(3-(-3))^2+(5-(-5))^2 } =\sqrt{6^2+10^2} =\sqrt{136} =2\sqrt{39} \\BD=\sqrt{((-2-2)^2+(3-(-3))^2} =\sqrt{16+36} =\sqrt{52} =2\sqrt{13}[/tex]

Midpoint of AC and BD is ( 0, 0 ), so both bisects each other.

The value of AC = 2 √39 and BD = 2 √13

Here, points given as,

A(–3, –5), B(2, –3), C(3, 5), and D(–2, 3).

We have to find,  AC and BD.

What is distance between two points?

Distance between two points [tex]P(x_{1} ,y_{1} )[/tex] and [tex]Q(x_{2} ,y_{2} )[/tex] is given by:

[tex]d(P, Q) = \sqrt{(x_{2}- x_{1} )^2 +(y_{2}- y_{1} )^2 }[/tex]

Now,

Midpoint of AC = [tex](\frac{-3+3}{2} ), (\frac{-5+5}{2} ) = ( 0, 0 )[/tex]

Midpoint of BD = [tex](\frac{-2+2}{2} ), (\frac{-3+3}{2} ) = ( 0, 0 )[/tex]

Hence, Both AC and BD bisects each other.

And, Distance between A and C is,

AC = [tex]\sqrt{(3 - (-3))^2 +(5 - (-5))^2 } = \sqrt{36 + 100} = \sqrt{136} = 2\sqrt{39}[/tex]

Distance between B and D is,

BD = [tex]\sqrt{( -2 -2))^2 +(3 - (-3))^2 } = \sqrt{16 + 36} = \sqrt{52} = 2\sqrt{13[/tex]

Learn more about the midpoint visit:

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What is-3.28-(4.4)+(-p) p=9.7?

Answers

Answer:

-17.38

Step-by-step explanation:

-3.28-(4.4) = -7.6

-7.6+(-9.7) = -17.38

I can confirm that he is correct ^

What is the simplified form of 3√7 - 5√7? A. -2√7 B. 2√7 C. -√14 D. 15√7

Answers

A Just finished this as well

What is the first step for solving this problem: 12÷ 6(3)+8

Answers

Answer: The first step would be to divide 12 by 6.

Step-by-step explanation:

Answer:

Division.

Step-by-step explanation:

There are two rules that you follow. One is PEMDAS, and the other is the     left -> right rule.

Note that PEMDAS =

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

The order of operation is: P , (E & R) , (M & D) , (A & S), parenthesis meaning they can be interchangeable, due to the left -> right rule.

Solve:

First, divide:

12/6 = 2

Next, multiply:

2 x 3 = 6

Finally, add:

6 + 8 = 14

14 is the answer.

Which of the following is another way to express the difference between -5 and 8?
-5 - (-8)
-5 + 8
8 - 5
-5 + (-8)

Answers

-5 - (-8) ............
-5 - ( -8) /////:///

Pls help me!! ASAP I WILL GIVE BRAINLIEST Brandon's bread recipe calls for milk powder, sugar, and flour in a ratio of 2:3:15, respectively. How many pounds of each does Brandon need if the three ingredients together weigh 2 lb?

Answers

Answer:

0.2 pounds of milk

0.3 pounds of sugar

1.5 pounds of flour

Step-by-step explanation:

If we have the ratio [tex]2:3:15[/tex], then we know that all of these ingredients together will be [tex]15+3+2=20[/tex]. If we want the whole thing to weight 2 pounds, then the total weight of everything else will be [tex]20\div2=10[/tex] percent of the original.

So,

[tex]2\cdot0.1=0.2\\\\3\cdot0.1=0.3\\\\15\cdot0.1=1.5[/tex]

We can confirm this is correct because [tex]1.5+0.3+0.2=2[/tex].

Hope this helped!

Step-by-step explanation:

Simple formula [tex]\frac{item ratio}{total ratio}[/tex]×total amount

milk powder;  ×2= 0.2 lb

sugar; [tex]\frac{3}{20}[/tex]×2= 0.3 lb

flour; [tex]\frac{15}{20}[/tex]×2= 1.5 lb

To check you can add them up :)

Hope this helps :)

The answers are bold*

Julie printed out a picture of each of the four members of her favorite band to decorate her bedroom door. Each picture measures 8 inches by 10 inches. Once decorated, how many square inches of Julie's door will be covered by these pictures?

Answers

Answer:

360 square inches

Step-by-step explanation:

(8*10)*4

 80*4

 360

What is the product of -8 and 5? A. 40 B. -40 C. 13 D. -3

Answers

Answer:b-40

Step-by-step explanation:

The answer is B -40 because product means multiply so just multiply those two numbers

Consider the line 9x+5y=6 What is the slope of a line parallel to this line? What is the slope of a line perpendicular to this line?

Answers

Answer:The equation of the line is 9x-5y=9

5y=9x-9

 

y=9/5x-9/5

Comparing with y=mx+c we get slope m=9/5

Slope of a line parallel to this line=9/5

Slope of a line perpendicular to this line=-5/9

Step-by-step explanation:

The slope for the parallel line is -9/5
And the slope for the perpendicular line is 5/9

The coordinates of three of the vertices of parallelogram ABCD are A(2, 0), B(4, 3), C(3, 1). How many possibilities are there for the position of the fourth vertex? What are coordinates of the fourth vertex?

Answers

Answer:

If you are given 3 vertices of a parallelogram, as a Geometry student, you will be asked to find the exact coordinates of the 4th vertex.  Just so that you can put your mind at ease, there can be different answers depending on how you decide to "draw" or "shape" your parallelogram.  So if your answer is different than another student, it does not mean that you have done it incorrectly.

Suppose I am given 3 points as such, and I am looking for the coordinates of D:

A (2, 3)

B (8, 1)

C (11, 5)

D (x, y)

The line segments that make up our parallelogram is AD is parallel to BC, and CD is parallel to AB.  Since the definition of a parallelogram is a quadrilateral with 2 pairs of parallel sides, we can use this fact to find the coordinate to the 4 vertex.  A pair of parallel side also means that these 2 lines have the same slope.  So if we do this on both pairs of parallel lines, we should have 2 equations with 2 variables, which should be simple to solve.

Slope of CD = Slope Slope of AB

(y - 5)/(x - 11) = (1 - 3)/(8 - 2)

(y - 5)/(x - 11) = -2/6

6(y - 5) = -2(x - 11)

6y - 30 = -2x + 22

equation #1:  6y + 2x = 52

Slope of AD = Slope of BC

(y - 3)/(x - 2) = (5 - 1)/(11 - 8)

(y - 3)/(x - 2) = 4/3

3(y - 3) = 4(x - 2)

3y -9 = 4x - 8

equation #2:  3y - 4x = 1

We now we have 2 equations with 2 variables, and we can use any method (substitution, linear combination, matrix) to solve for the x and y coordinates.  

equation #1:  6y + 2x = 52

equation #2:  3y - 4x = 1

Multiply equation by -2

Equation 2: -2(3y - 4x = 1)

Equation 2:  -6y + 8x = -2

Add equation 1 to equation 2

equation 1:  6y + 2x = 52

equation 2:  -6y + 8x = -2

eq 1 + eq 2:  10x = 50

x = 5

Use any of the original equation to solve for y:

6y + 2x = 52

6y + 2(5) = 52

6y = 42

y = 7

So the 4th vertex for my first answer will be (5, 7)

If we draw the parallelogram in a different way using the given vertices, we will be looking for a different 4th vertex.  So in our original question:

A (2, 3)

B (8, 1)

C (11, 5)

D (x, y)

Our line segments in this case will be draw as such:

AC is parallel to BD and CD is parallel to AB.

Slope of AC = slope of BD

(5 - 3)/(11 - 2) = (y - 1)/(x - 8)

2/9 = (y - 1)/(x - 8)

2(x - 8) = 9(y - 1)

2x - 16 = 9y - 9

equation 1:  2x - 9y = 7

Slope of CD = slope of AB

(5 - y)/(11 - x) = (3 - 1)/(2 - 8)

(5 - y)/(11 - x) = 2/-6

-6(5 - y) = 2(11 - x)

-30 + 6y = 22 - 2x

equation 2:  2x + 6y = 52

Solve the following linear system:

equation 1:  2x - 9y = 7

equation 2:  2x + 6y = 52

eq 1 - eq2:  -15y = -45

-15y = -45

y = 3

Substitute y = 3 into any one of the original equation:

equation 1:  2x - 9y = 7

2x - 9(3) = 7

2x - 27 = 7

2x = 34

x = 17

So by drawing the parallelogram in a different way, the 4th vertex of this parallelogram is (17, 3).

Step-by-step explanation:

See Answer

The fourth coordinate for the given parallelogram will be (5, 7).

What is a parallelogram?

A basic quadrilateral with two sets of parallel sides is known as a parallelogram.

A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size.

There are 4 types of parallelograms, including 3 special types. The four types are parallelograms, squares, rectangles, and rhombuses.

Given the parallelogram ABCD are A(2, 0), B(4, 3), C(3, 1).

Now,

The slope of AB = Slope of CD

(y - 5)/(x - 11) = (1 - 3)/(8 - 2)

6(y - 5) = -2(x - 11)

⇒  6y + 2x = 52 will be the first equation.

Now,

The slope of BC = Slope of AD

[(y - 3)/(x - 2)] = [(5 - 1)/(11 - 8)]

[(y - 3)/(x - 2)] = 4/3

3(y - 3) = 4(x - 2)

⇒ 3y - 4x = 1 will be the second equation.

Now, By substitution

x = 5 and y = 7

Hence "The fourth coordinate for the given parallelogram will be (5, 7)".

Learn more about parallelograms ​here,

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Find the number if 18 is taken away from 8 times of a number gives 30.

Answers

Answer:

Let the number be x.

8 times that number would be 8x, and taking away 18 from it 8x - 18. Knowing the result of doing this is 30, we can write the following equation:

8x - 18 = 30

And solve it. First we pass the -18 to the sight umming:

8x = 30 + 18

8x = 48

Then the 8 which is multiplying to the right dividig:

x = 48/8 = 6

Now we verify we have done it preporly:

8x - 18 = 30

8 * 6 - 18 = 30

48 - 18 = 30 TRUE

Answer:

x =6

Step-by-step explanation:

Translate into algebraic equation =

[tex]8(x)-18= 30\\= 8x-13=30[/tex]

Let's solve for x

[tex]\mathrm{Add\:}18\mathrm{\:to\:both\:sides}\\8x-18+18=30+18[/tex]

Simplify

[tex]8x=48[/tex]

Divide both sides by 8

[tex]\frac{8x}{8}=\frac{48}{8}[/tex]

Simplify

[tex]x =6[/tex]

Write the following statements in equation form: If the sum of a number and its two fifth is 70

Answers

Answer:

[tex]x + \frac{2}{5} \times x = 70 \\ x + \frac{2}{5} x = 70[/tex]

Answer:

Let it be x the number.

We have to sum to x two fifths of him and we know the result is 70, so:

[tex]x + \frac{2}{5}x = 70[/tex]

We could also solve it:

[tex]\frac{5x}{5}+\frac{2x}{5}=\frac{350}{5}[/tex]

[tex]5x + 2x = 350[/tex]

[tex]7x = 350[/tex]

[tex]x=\frac{350}{7}=50[/tex]

you have set a goal to drink more water every day. your water bottle holds 0.5 liters of water in the equation below, b is the number of times you drink all the water in your bottle and L is the number of liters of water you drink. The relationship between these two variables can be expressed by the following equation: L=0.5b Identify the dependent and independent variable.

Answers

Answer:

Step-by-step explanation:

B is the independent variable since the amount of times you drink the water is controlled by you.  

I is the dependent variable since it's depending on how much water you're drinking

b is the answer cause how many times he drinks. l is the dependent cause thats how much your drinking

If 38 = 11 + 3x, what is the value of x ?

Answers

Answer:

38-11=3x

27=3x

27/3=x

x=9

[tex]38=11+3x[/tex] collect like-terms

[tex]38-11=3x[/tex] subtract

[tex]27=3x[/tex] divide

[tex]x=\frac{27}{9}[/tex]

[tex]x=9[/tex]

plug [tex]x[/tex] in the equation to make sure of the answer

[tex]38=11+3x\\38=11+3(9)\\38=11+27\\38=38[/tex]

Your fitness tracker overestimates the number of steps you take by 5%. The trackers indicates that you took 7350 steps today. Write and solve an equation to find the actual number of steps you took today.

Answers

you would have taken 367.5 steps. you would divide 10% of the number by 2. to find 10% of the number you move the decimal point of one place

The equation (1 + 0.05)x = 7350 to find the actual number of steps you took today will be 7,000.

What is the percentage?

The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol ‘%’ is used to symbolize it.

Your fitness tracker overestimates the number of steps you take by 5%. The trackers indicate that you took 7350 steps today.

Let x be the actual number of steps. Then the equation will be given as,

(1 + 0.05)x = 7350

x = 7350 / 1.05

x = 7,000

The actual number of steps you took today will be

(1 + 0.05)x = 7350

x = 7350 / 1.05

x = 7,000

The equation (1 + 0.05)x = 7350 to find the actual number of steps you took today will be 7,000.

More about the percentage link is given below.

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plzzz help! will give branliest if you can do this one!!! i also need help with other math problems

Answers

I believe it’s the last answer. Rotation of 180 degrees clockwise with a dilation of 5.

Answer:

The answer is d

Step-by-step explanation:

The Bradenton Post polled 1,356 adults in the city to determine whether they wet their toothbrush before they put toothpaste on it. Of the respondents, 54% said they wet it first. Suppose 68% of all adults actually wet their toothbrush first. What are the mean and standard deviation of the sampling distribution?

Answers

Answer:

The mean is 0.68 and the standard deviation is 0.0127. I hope this helps

Step-by-step explanation:

Answer:

Standard = 922Answer: Mean

Step-by-step explanation: vote

=Step-by-step explanation:If they say 54% wet their toothbrush first, then that means that there are about 732 people ...  More

Louise measured the perimeter of her rectangular scrapbook to be 148 cm. If the scrapbook is 38 cm wide, how long is the scrapbook?

Answers

Answer:

36cm

Step-by-step explanation:

38 × 2 = 76

148 - 86 = 72

72/2 = 36

the volleyball team needs new uniforms. the students plan to sell plush toy Eagles ( the school mascot) for $5 each. The students find three companions on-line that sell stuff mascots. Company A cell's 12 eagles for $34.08. Company B cells 15 equals for $42.90. Company C charges $50.58 for 18 eagles. which company has the Best Buy?​

Answers

Answer:

Company C

Step-by-step explanation:

You divide the amount of money it all costs to the number of plushies they are selling it for.

A: 34.08/12 = $2.84 each

B: 42.90/15 = $2.86 each

C: 50.58/18 = $2.81 each

So C has the least amount of money spent for a greater amount of plushies so C would be the Best Buy.

The correct answer would be c

PLEASE HELP!! what is the equation for the parabolic function that goes through the points (-3, 67) (-1, 1) and has a stretch factor of 9

Answers

Answer:

[tex]f(x)=9(x+\frac{1}{6})^2-\frac{21}{4}[/tex]

Step-by-step explanation:

So, we need to find the equation of a parabolic function that goes through the points (-3,67) and (-1,1) and has a stretch factor of 9.

In other words, we want to find a quadratic with a vertical stretch of 9 that goes through the points (-3,67) and (-1,1).

To do so, we first need to write some equations. Let's use the vertex form of the quadratic equation. The vertex form is:

[tex]f(x)=a(x-h)^2+k[/tex]

Where a is the leading coefficient and (h,k) is the vertex.

Since a is the leading coefficient, it's also our stretch factor. Thus, let a equal 9.

Also, we have two points. We can interpret them as functions. In other words, (-3,67) means that f(-3) equals 67 and (-1,1) means that f(-1) equals 1. Write the two equations:

[tex]f(x)=a(x-h)^2+k\\f(-3)=67=9((-3)-h)^2+k[/tex]

And:

[tex]f(x)=a(x-h)^2+k\\f(-1)=1=9((-1)-h)^2+k[/tex]

Now, we essentially have a system of equations. Thus, to find the original equation, we just need to solve for the vertex. To do so, first isolate the k term in the second equation:

[tex]1=9(-1-h)^2+k\\k=1-9(-1-h)^2[/tex]

Now, substitute this value to the first equation:

[tex]67=9(-3-h)^2+k\\67=9(-3-h)^2+(1-9(-1-h)^2)[/tex]

And now, we just have to simplify.

First, from each of the square, factor out a negative 1:

[tex]67=9((-1)(h+3))^2+(1-9(((-1)(h+1))^2)[/tex]

Power of a product property:

[tex]67=9((-1)^2(h+3)^2)+(1-9((-1)^2(h+1)^2))[/tex]

The square of -1 is positive 1. Thus, we can ignore them:

[tex]67=9(h+3)^2+(1-9(h+1)^2)[/tex]

Square them. Use the trinomial pattern:

[tex]67=9(h^2+6h+9)+(1-9(h^2+2h+1))[/tex]

Distribute:

[tex]67=(9h^2+54h+81)+(1-9h^2-18h-9)[/tex]

Combine like terms:

[tex]67=(9h^2-9h^2)+(54h-18h)+(81+1-9)[/tex]

The first set cancels. Simplify the second and third:

[tex]67=36h+73[/tex]

Subtract 73 from both sides. The right cancels:

[tex]67-73=36h+73-73\\36h=-6[/tex]

Divide both sides by 36:

[tex](36h)/36=(-6)/36\\h=-1/6[/tex]

Therefore, h is -1/6.

Now, plug this back into the equation we isolated to solve for k:

[tex]k=1-9(-1-h)^2[/tex]

First, remove the negative by simplifying:

[tex]k=1-9((-1)(h+1))^2\\k=1-9((-1)^2(h+1)^2)\\k=1-9(h+1)^2[/tex]

Plug in -1/6 for h:

[tex]k=1-9(-\frac{1}{6}+1)^2[/tex]

Add. Make 1 into 6/6:

[tex]k=1-9(-\frac{1}{6}+\frac{6}{6})^2\\ k=1-9(\frac{5}{6})^2[/tex]

Square:

[tex]k=1-9(\frac{25}{36})[/tex]

Multiply. Note that 36 is 9 times 4:

[tex]k=1-9(\frac{25}{9\cdot4})\\ k=1-\frac{25}{4}[/tex]

Convert 1 into 4/4 and subtract:

[tex]k=\frac{4}{4}-\frac{25}{4}\\ k=-\frac{21}{4}[/tex]

So, the vertex is (-1/6, -21/4).

Now, plug everything back into the very original equation with 9 as a:

[tex]f(x)=a(x-h)^2+k\\f(x)=9(x+\frac{1}{6})^2-\frac{21}{4}[/tex]

And this is our answer :)

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