find an equation in standard form of a parabola passing through the points below
(1,-1),(5,31),(6,44).

Answers

Answer 1

Answer:

Basic parabola:  y = ax2 + bx + c

We have 3 points we can plug in for (x, y) to create 3 simultaneous equations

(-2, 24):  24 = 4a - 2b + c   {equation 1}

(3, -1):   -1 = 9a + 3b + c    {equation 2}

(-1, 15): 15 = a - b + c        {equation 3}

Solve this system to find the values of a, b, c

Let's first eliminate variable c:

4a - 2b + c = 24   {equation 1}

 a -  b + c = 15    {equation 3}

---------------------  subtract

3a - b = 9

9a + 3b + c = -1    {equation 2}

 a -  b + c = 15    {equation 3}

--------------------  subtract

8a + 4b = -16

We now have two equations with 2 unknowns we can use to find a, b

3a - b = 9         {equation 4}

8a + 4b = -16   {equation 5}

Multiply equation 4 through by 4 and add equations

12a - 4b = 36

8a + 4b = -6

-----------------   add

20a = 30

a = 30/20

a = 3/2

8a + 4b = -6

8(3/2) + 4b = -6

12 + 4b = -6

4b = -6- 12

4b = -18

b = -18/4

b = -9/2

Plug these 2 values into one of the original equations and solve for c

15 = a - b + c        {equation 3}

15 = 3/2 + 9/2 + c

15 = 12/2 + c

15 = 6 + c

c = 15-6

c = 9

y = (3/2)x2 - (9/2)x+ 9

Upvote

0

Downvote

Add comment

Still looking for help?

Step-by-step explanation:


Related Questions

ANSWER ASAP PLS

convert 70m/s to km/hr
1000=1km

Answers

Answer:

70 m/s = 252 km/hr

1 m/s = 3.6 km/hr

Jayden's car gets 23 miles to a gallon of gasoline. He filled up his car's gas tank with g gallons. Write an expression that shows how far Kurt can drive on a tank of gasoline.

Answers

Answer:

D= distance covered by amount (g) gallons

D=23g

Step-by-step explanation:

What is the perimeter of figure 12? (Show your work).

Answers

where is the picture of figure 12?

Round or fraction form round all the WAY!

Answers

Answer:

The answer to the question provided is

[tex] - \frac{3}{2} [/tex]

Solve the equation.
x2 + 13x + 30 = 0
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
O A. The solution(s) is/are x =
(Type an integer or a simplified fraction. Use a comma to separate answers as needed.)
O B. There is no solution.

Answers

Given that,

An equation : [tex]x^2 + 13x + 30 = 0[/tex]

To find,

The value of x.

Solution,

We have, [tex]x^2 + 13x + 30 = 0[/tex]

We can solve it as follows :

[tex]x^2 + 10x +3x+ 30 = 0\\\\x(x+10)+3(x+10)=0\\\\(x+3)(x+10)=0\\\\(x+3)=0\ \text{and}\ (x+10)=0\\\\x=-3\ \text{and}\ x=-10[/tex]

So, the solution of the given equations are -3 and -10.

250% of a number is the same as increasing the number by what percent?

Answers

Answer:

Since I am not given an increase number i will solve for numbers 1-5

1 - 25000%

2 - 12500%

3 - 8333.333333333332%     (I recommend you don't use this one)

4 - 6250%

5 - 5000 %

Each number, it will increase by 250% no matter what

Its the same as increasing by 250%

Hope this helps <3

I NEED HELP PLZ I WILL GIVE THANKS AND BRAINLIST

Answers

Answer: Yes, it is in the blue shaded area

Step-by-step explanation:

Yes it is the blue shaded area

15 = 5/ 3(x + 12) solve for x in simplest form

Answers

Answer:

x= -10 1/5 or -10.2

Step-by-step explanation:


Round the number 2.72603 to 2 decimal places.

Answers

Answer:

2.73

Step-by-step explanation:

You round 6 up to get 2.73

Please give brainliest and thank me if it helped

2.70
rounded seven back coz 2 is less than 5

Which is the constant of proportionality for the relationship shown in the graph?

Answers

Answer:

COP: 2X

Step-by-step explanation:

K= Y/X

K= 4/2

K= 8/4

K= 12/6

K=16/8

A computer’s random number generator produces random integers from 1 to 50. What is the probability that the first 3 integers generated are single-digit numbers?

Answers

Answer:

A. 0.0058

Step-by-step explanation:

John jogged 4.5 miles on Thursday, 7 2/5 miles on Friday, and 10.4 miles on Saturday. How many miles does John have to run in order to run 25 miles for the week


im giving 20 points

Answers

Answer:

2.7 miles

Step-by-step explanation:

25 - 10.4 - 4.5 - 7 2/5 will give you 2.7

Answer:

8 miles

Step-by-step explanation:

If we divide 70 by 50, we get the unit rate for the ratio 70 minutes for every 50 miles.

70÷50=1.4

So the runner is running 1.4 minutes per mile. We can multiply this unit rate by the number of miles:

1.4 minutes mile × 5 miles = 7 minutes

Thus it will take her 7 minutes to run 5 miles at this pace.

If it takes her 7 minutes to run 5 miles, it will take her 7÷5 = 1.4 minutes to run 6÷3=2 miles at the same pace.

If it takes her 1.4 minutes to run 5 miles, it will take her 1.4×5=7 minutes to run 4×2=8 miles at the same pace. Since 60 minutes is 1 hour, she is running at a speed of 8 miles per hour.

We found her pace in minutes per miles in part (a).

Please help!!:
What is the length of DE in the image provided? (Please explain so I can understand in the future)

A. DE=4
B. DE=5
C. DE=6
D. DE=7

Answers

Answer:  D.  DE = 7

==========================================================

Explanation:

We have these three facts:

The arc markings on angles C and D indicate those angles are congruent. We can say that angle ACB = angle EDB.Another pair of congruent angles are angle ABC and angle EBD. These are vertical angles. Lastly, we have a pair of congruent sides AB and BE because of the tickmarks.

Those three facts allow us to use the AAS (angle angle side) congruence theorem to prove that triangle ABC is congruent to triangle EBD.

Then by CPCTC (corresponding parts of congruent triangles are congruent), we know that AC = DE. Note how 'A' and 'C' are the first and last letters of ABC; similarly, 'E' and 'D' are the first and last letters of EBD. Segment ED is the same as segment DE.

So to find the length of DE, we need to find the length of AC. To do that, we need the value of x.

----------------

Recall earlier that AB = BE. Use this to find x

AB = BE

1.5x = 3x-6

1.5x-3x = -6

-1.5x = -6

x = -6/(-1.5)

x = 4

Now we can find the length of AC

AC = x+3

AC = 4+3

AC = 7

This must mean DE = 7 as well.

Answer:

DE=7

Step-by-step explanation:

I just took test

Also please make me Brainliest

Solve for p. p/8 + 12 = 36

Answers

9514 1404 393

Answer:

  p = 192

Step-by-step explanation:

p/8 +12 = 36 . . . . . given

p/8 = 24 . . . . . . . . .subtract 12

p = 8·24 . . . . . . . . .multiply by 8

p = 192

the two angles measuring (30 + 2 a)degree and (125 -a) degree supplementary to each other, then find the value of a.​

Answers

Answer:

The value of a is 25

Step-by-step explanation:

When two angles are supplementary, they add up to 180 degrees

Mathematically,

(30 + 2a) + (125-a) = 180

30 + 2a + 125 - a = 180

a + 155 = 180

a = 180-155

a = 25 degrees

(9x + 5) - (4x + 3)

Please show work

Answers

Answer:

Step-by-step explanation:

Simplifying

(9x + 5) + -1(4x + 3) = 0

Reorder the terms:

(5 + 9x) + -1(4x + 3) = 0

Remove parenthesis around (5 + 9x)

5 + 9x + -1(4x + 3) = 0

Reorder the terms:

5 + 9x + -1(3 + 4x) = 0

5 + 9x + (3 * -1 + 4x * -1) = 0

5 + 9x + (-3 + -4x) = 0

Reorder the terms:

5 + -3 + 9x + -4x = 0

Combine like terms: 5 + -3 = 2

2 + 9x + -4x = 0

Combine like terms: 9x + -4x = 5x

2 + 5x = 0

Solving

2 + 5x = 0

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2' to each side of the equation.

2 + -2 + 5x = 0 + -2

Combine like terms: 2 + -2 = 0

0 + 5x = 0 + -2

5x = 0 + -2

Combine like terms: 0 + -2 = -2

5x = -2

Divide each side by '5'.

x = -0.4

Simplifying

x = -0.4

easy boy

sorry but i have another question :| tysm all yall for helping meee ^w^

Answers

9514 1404 393

Answer:

4: {8, 12, 16, 24}7: {7, 42, 49}neither: {6, 11, 17}

Step-by-step explanation:

Looking at the numbers individually, we have ...

16 = 4×4

42 = 2×3×7

6 = 2×3

17 = 1×17 (prime)

12 = 3×4

49 = 7×7

24 = 2×3×4

7 = 1×7 (prime, a multiple of 7)

11 = 1×11 (prime)

8 = 2×4

__

Multiples of 4:

  16, 12, 24, 8

Multiples of 7:

  42, 49, 7

Multiples of neither:

  6, 17, 11

90 coins
Use the original price and the markup to find the retail price.

Original price: $50; Markup: 15%


The retail price is $ ?

Answers

Answer:

50 + 50(.15)

50(1+ .15)

50(1.15)

RP= $57.5

Step-by-step explanation:

[tex]f(x)= \frac{X^2-x-12} {5x^2+4x}[/tex]

Find all x-intercepts of the following function. Write your answer or answers as coordinate points. Be sure to select the appropriate number of x-intercepts.

Answers

Answer:

(- 3, 0 ), (4, 0 )

Step-by-step explanation:

To find the x- intercepts let f(x) = 0

[tex]\frac{x^2-x-12}{5x^2+ 4x}[/tex] = 0

The denominator cannot equal zero as this would make f(x) undefined.

Equate the numerator to zero and solve for x

x² - x - 12 = 0 ← in standard form

(x - 4)(x + 3) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 4 = 0 ⇒ x = 4

x + 3 = 0 ⇒ x = - 3

x- intercepts are (- 3, 0 ) and (4, 0 )

7th grade math help me please :)

Answers

Answer:

8x+10y cannot be simlified because they do not have a common variable

so until you find the value for x and y u cannot simplify

Answer:8 x+ 10 y can not be simplified .

Step-by-step explanation:

Explanation:This is because the term are not the same.8x has the term x while 10 y has the term y.

If there are 5 soccer players, 10 baseball players, and 15 basketball players, what is the ratio of baseball players to soccer players?

Answers

Answer:

2 to 1

Step-by-step explanation:

baseball=10

soccer =5

10:5 = 2:1(lowest term)

There are 24 carnations in each bunch and 12 roses in each bunch. Use your expression from question 1 or question 2 to determine the total number of carnations and the total number of roses Alison will distribute to each flower shop this week.

Answers

Answer: r/c  

Step-by-step explanation:

96/48

or

24/12

need help on this asap pleaase

Answers

I think it’s 2, -2 but I am not completely sure. Sorry if it’s wrong if it right pls mark branliest

Maria and laurie are making orange juice.Maria use 2 cups of concentrate and 5 cups of water. Laurie uses 3 cups of concentrate and 7 cups of water . Whose mix would be the strongest? Why?

Answers

Answer:

Step-by-step explanation:

To obtain the strongest mix :

Maria:

2 cups of concentrate ; 5 cups of water

Ratio = 2/5 = 0.4 concentrate per 1 cup of water

Laurie:

3 cups of concentrate ; 7 cups of water

Ratio = 3/7 = 0.4285714 concentrate per 1 cup of water

0.4285714 > 0.4

Hence, Laurie's mix is the strongest as it has higher concentrate per cup of water.

In March, you have $220 in your savings account. By the end of April, your savings have increased by 30%. How much money do you have in your savings account at the end of April?

Answers

Answer:

286

Step-by-step explanation:

I dit 220+30%=286

Answer:

$286

Step-by-step explanation:

220 • 0.3 = 66

220 + 66 = 286

7th grade help me please:)

Answers

Answer:

4^9

262144

Step-by-step explanation:

What is the exact value of tan(67.5°) ?

Answers

Answer:

[tex]\sqrt\frac{2+\sqrt{2}}{2-\sqrt{2}}[/tex]

Step-by-step explanation:

correct on edge2020

The required exact value of tan(67.5°) is -2 + √(2).

What are trig ratios?

If you know the lengths of two sides of a right triangle, you can use trigonometric ratios to calculate the measures of one (or both) of the acute angles.

Here,
The exact value of tan(67.5°) can be found using the half-angle identity for the tangent, which states that:

tan(x/2) = (1 - cos(x)) / sin(x)

We can use this identity with x = 135 degrees since 67.5 degrees is half of 135 degrees. So:

tan(67.5°) = tan(135°/2) = (1 - cos(135°)) / sin(135°)

We can then use the following exact values:

cos(135°) = -√(2)/2

sin(135°) = -√(2)/2

Substituting these values, we get:

tan(67.5°) = (1 + √(2)/2) / (-√(2)/2)

Rationalizing the denominator, we get:

tan(67.5°) = -2 + √(2)

Therefore, the exact value of tan(67.5°) is -2 + √(2).

Learn more about trig ratios here:

https://brainly.com/question/14977354

#SPJ6

Arlene has raised $56 for her class field trip. This is $14
more than three times the amount Adam has raised.
Which equation could you use to find how much money
Adam has raised?

Answers

Assuming Adams amount is x, three times his amount will be 3x. $14 more than the times Adam's amount will be 14 +3x.

Therefore if Arlene's money is $56 which is $14 more than three times Adam's amount, then the equation will be ;

14+3x=56

2.(03.07)
Solve 2x^2 - 8x = -7. (2 points)

Answers

Answer:

Step-by-step explanation:

Make a quadratic:

2[tex]x^{2}[/tex]-8x+7=0

Then use quadratic formula to solve.

It would be x=   2 ±   [tex]\frac{2}{\sqrt{2} }[/tex]

Divide 2x^4+3x^3-5x+6 by x^2+3x-2 .

Answers

2x^4 + 3x^3 - 5x + 6  ÷ x^2 + 3x - 2

= 2x^6 + 3x^5 − 2x^3 − 2x^2 + 6/ x^2

Other Questions
A circuit contains two 1.5 volt battery and a bulb with a resistance of 3 ohms. Calculate the current In the passage from The Heart Is a Lonely Hunter,which statement best describes the effect of thedifference between the reader's and Mick's points ofview? Read the information below. You just scratched a mineral sample with your fingernail. Your fingernail measures 2.5 on the Mohs scale and fluorite measures 4 on the Mohs scale. Explain why the mineral sample you have cannot be a piece of fluorite Please help me I need to write a 3 sentence Find the slope and the y-intercept of the line.y=-25Ex+6slope:.08$y-intercept: 0 What is point of view as it relates to culture? A. a belief or idea that a group of people share B. a type of narrator's perspective, such as first, second, or third person C. a way of noticing others' traitsD. a feeling of self-importance Morristown City Cafe recently introduced a new flavor of coffee. They served 24 grande cups and 51 jumbo cups of the new coffee today, which equaled a total of 1,506 ounces. The day before, 26 grande cups and 66 jumbo cups were served, which used a total of 1,868 ounces. How much coffee is required to make each size? Which of the following is the slope intercept form of the equation3x - 8y = 16A- y = 3/8x + 2B- y = 3/8x - 2C- y = -3/8x + 2D- y = -3/8x - 2 PLSS HELPP The question is in the picture! plz help im confused on how this works. If a triangle has side lengths of 7.5 and 4.8, what is the range of lengths for the third side The Ancient Chinese were famous for their inventions and technology. Many of their inventions had lasting impact on the entire world. Other inventions led to great feats of engineering like the Grand Canal and the Great Wall of China.Firing a rocket using gunpowder The Diamond Sutra is the world's oldest Printed BookHere are some of the notable inventions and discoveries made by the engineers and scientists of Ancient China:Silk - Silk was a soft and light material much desired by the wealthy throughout the world. It became such a valuable export that the trade route running from Europe to China became known as the Silk Road. The Chinese learned how to make silk from the cocoons of silkworms. They managed to keep the process for making silk a secret for hundreds of years.Paper - Paper was invented by the Chinese as well as many interesting uses for paper like paper money and playing cards. The first paper was invented in the 2nd century BC and the manufacture later perfected around 105 AD. (Modern paper, not papyrus paper).Printing - Wood block printing was invented in AD 868 and then moveable type around 200 years later. This was actually hundreds of years before the invention of the printing press by Gutenberg in Europe.The Compass - The Chinese invented the magnetic compass to help determine the correct direction. They used this in city planning at first, but it became very important to map makers and for the navigation of ships.Gunpowder - Gunpowder was invented in the 9th century by chemists trying to find the Elixir of Immortality. Not long after, engineers figured out how to use gunpowder for military uses such as bombs, guns, mines, and even rockets. They also invented fireworks and made great beautiful displays of fireworks for celebrations.Boat Rudder - The rudder was invented as a way to steer large ships. This enabled the Chinese to build huge ships as early as 200 AD, well before they were ever built in Europe.Other - Other inventions include the umbrella, porcelain, the wheelbarrow, iron casting, hot air balloons, seismographs to measure earthquakes, kites, matches, stirrups for riding horses, and acupuncture.Fun Facts Gunpowder, paper, printing, and the compass are sometimes called the Four Great Inventions of Ancient China. Kites were first used as a way for the army to signal warnings. Umbrellas were invented for protection from the sun as well as the rain. Chinese doctors knew about certain herbs to help sick people. They also knew that eating good foods was important to being healthy. Compasses were often used to make sure that homes were built facing the correct direction so they would be in harmony with nature. The Grand Canal in China is the longest manmade canal or river in the world. It is over 1,100 miles long and stretches from Beijing to Hangzhou. They invented the abacus in the 2nd century BC. This was a calculator that used sliding beads to help compute math problems quickly. A clear coating called lacquer was made to protect and enhance certain works of art and furniture. Paper money was first developed and used in China during the Tang dynasty (7th century) ________________________________________________________________Questions:4)What did ancient Chinese chemists discover when trying to find the Elixir of Immortality?A. Silk B. A cure for the Black Plague D. GunpowderC. How a compass worksD. Gunpowder5) What important ingredient was used by the Ancient Chinese to make silk?A. The cocoons of silkwormsB. The webs of silk spidersC. The leaves from the silk treeD. A special silk mineral found in mines throughout China6) What was the main use of the compass when it was first invented?A. As a child`s game for the young emperorB. To keep the army straight during battlesC. For city planningD. To help when lost in the woods As a leader, Louis XVI was best described by which of the following statements A)weak and indecisive B)strong and effective C) enlightened and democratic D) critical but well formed Yuto solved the equation below.Negative 2 (x + 5) = negative 2 (x minus 2) + 5What is the solution to Yutos equation? Evaluate 4(1/4)6x for x=1/3.Enter your answer as a fraction in simplest form in the box. Order the following fractions from least to greatest 2/8 2/3 2/9 The first West African civilization to be based on the salt and gold tradewas. A.BantuB. MaliC. GhanaD. Songhai A guitar player can change the frequency of a string by "bending" it-pushing it along a fret that is perpendicular to its length. This stretches the string, increasing its tension and its frequency. The B string on a guitar is 64 cm long and has a tension of 74 N. The guitarist pushes this string down against a fret located at the center of the string, which gives it a frequency of 494 Hz. He then bends the string, pushing with a force of 4.0 N so that it moves 8.0 mm along the fret.* What is the new frequency? the height of a shed is 6cm. a ladder leans agaisnt the shed with its base 4.5 m away, and its top just reaching the roof. what is the length of the ladder? This layer of soil has the highest proportion of organic material. Parallelogram PQRS is rotated 90 clockwise about the origin to create parallelogram P'QR'S'. Which rule describes this transformation? (Please leave a small explanation) help me with this please if u don't I won't be able to get my devices for the weekend