Write a system of equations for the coefficients of a polynomial of degree 2 that passes through (1, - 2), (- 2, 7) and (- 5, - 2) Solve the system.

Answers

Answer 1

The system of equations is:

-2 = a + b + c

7 = 4a - 2b +c

-2 = 25a + 5b + c

The polynomial is:

y = (1/3)*x^2 - 6x - 1/3

How to write and solve the system of equations?

The general polynomial of degree 2 can be written as:

y = a*x^2 + b*x +c

If we use the fact that it passes through the 3 given points, then we can write the 3 equations:

-2 = a*1^2+ b*1 + c

7 = a*(-2)^2 + b*-2 + c

-2 = a*5^2 + b*5 + c

We can simplify these to get the system of equations:

-2 = a + b + c

7 = 4a - 2b +c

-2 = 25a + 5b + c

First, isolate c on the first equation to get:

c = -2 - a- b

Replace it on the other two:

7 = 4a - 2b + (-2 - a - b)

-2 = 25a + 5b + (-2 - a - b)

9 = 3a - 3b

0 = 24a + 4b

Using the second equation we can rewrite:

-24a = 4b

-24a/4 = b

-6a = b

Ande replace that in the other equation:

9 = 3a - 3*(-6a)

9 = 3a + 18a

9/21 = a

1/3 = a

And the value of b is:

-6*(1/3) = b

-2 = b

And the value of c is:

c = -2 - (-2) - 1/3

c = -1/3

The polynomial is:

y = (1/3)*x^2 - 6x - 1/3

Learn more about polynomials at:

https://brainly.com/question/4142886

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Related Questions

What is the line of reflection for the trapezoids?

On a coordinate plane, trapezoid A B C D has points (5, 4), (6, 4), (8, 3) and (5, 3). Trapezoid A prime B prime C prime D prime has points (1, 4), (0, 4), (negative 2, 3), (1, 3).

Answers

Answer:I believe it’s A(x=3)

Step-by-step explanation:

There was an activity planned outdoors, but it started to rain. They took a vote and 45 people of the 60 people wanted to stay inside. The other 15 people voted to go outside in the rain. What percent of the class wants to go outside? Round to the nearest percent if needed.

Answers

Answer:

15/60×100=25%

Step-by-step explanation:

the number of students wanted to go outside/the whole number of students×100

15/60×100=25%

Cheryl signs up for a savings account that guarantees an increase in her savings at a fixed rate of $15 per month. She plans to withdraw the money when it is more than twice the original amount of $200. Find the least number of complete months that Cheryl has to keep the money in the account for.

Answers

Answer: 14 months.

Step-by-step explanation:

Given: Original amount = $ 200

Fixed rate of growth = $15 per month

Let x be the number of months that Cheryl has to keep the money in the account for.

Then, [tex]200+15x=2(200)[/tex]

[tex]\Rightarrow\ 200+15x>400\\\\\Rightarrow\ 15x >400-200\\\\\Rightarrow\ 15x>200\\\\\Rightarrow x>\dfrac{200}{15}\\\\\Rightarrow x>13.333333\\\\\Rightarrow\ x=14[/tex]

Hence, it will take 14 months .


[tex] {n}^{6} \times \frac{4}{25} {n}^{2} \times \frac{5}{4} {n}^{3} \times n[/tex]

Answers

Step-by-step explanation:

reduce the numbers by solving and add the powers

(Grade 7 math) What is the area of the triangle when b=3.5 and h=3? B is the base and h is the height

Answers

Answer:

The area of the triangle

    A = 5.25 square units

Step-by-step explanation:

Explanation:-

Given that the base of the triangle(b) = 3.5

The height of the triangle(h)  = 3

The area of the triangle

                                 [tex]A = \frac{1}{2} base X height[/tex]

                                [tex]A = \frac{1}{2} (3.5) (3)[/tex]

                               A = 5.25 square units

its a screen shot do do do doooo

Answers

Depends on what pi is.

It could be

50.24 yards (pi is rounded)

OR

16π yards

A car travels at an average speed of 68 miles per hour. How many miles does it travel in 5 hours and 45 minutes?

Answers

Answer:

391.

Step-by-step explanation:

There is 60 minutes every hour, so you divide by 60. 68 / 60 = 1.1333333333.

Now, we have to find out how many minutes there are in 5 hours and 45 minutes. Since there is 60 minutes every hour, 6 x 5 + 45 = 300 + 45 = 345. 1.1333333333 x 345 = 390.9999999885, rounded = 391.

In triangle ABC, point D is the centroid, and BD = 6. Find BE.

Answers

Given:

In triangle ABC, point D is the centroid, and BD = 6.

To find:

The measure of side BE.

Solution:

We know that the centroid divides each median in 2:1.

In the given figure BE is a median and point D is the centroid. It means point D divides the segment BE in 2:1.

Let BD and DE are 2x and x respectively.

We have, BD = 6 units.

[tex]2x=6[/tex]

[tex]x=\dfrac{6}{2}[/tex]

[tex]x=3[/tex]

Now,

[tex]BE=BD+DE[/tex]

[tex]BE=6+x[/tex]

[tex]BE=6+3[/tex]

[tex]BE=9[/tex]

Therefore, the measure of side BE is 9 units.

4 Mr. Von's 5th-grade class is going on a field trip. Each
student is given a name card to wear that is 1/4 foot wide 1/3 foot long


1/4foot x 1/3 foot = square foot

Answers

1/12 square feet is the correct answer1/4 x 1/3 = 1/12Please let me know if I am wrong.

Answer:

the answer is 1/12 square foot

Step-by-step explanation:

.

Need help with math question 8th grade math

Answers

Answer:

Step-by-step explanation:

I am also in 8th grade, anyways

x reprsents = 30 nickles

y represents = $1.02.

I am very sorry i do not know EQ1 and EQ2, but hopefully this is helpful!

Answer:

Step-by-step explanation:

x reprsents = 30 nickles

y represents = $1.02.

3 1183 long division​

Answers

= 394 R 1

= 394 1/3

1183 divided by 3 equals
394 with a remainder of 1

Rhea earned P9,876.88 a month while Jane earned P10,675.50. How much more did Jane earn month than Rhea?
1. What is asked in the problem?
2. What are the given facts?
3. What is the operation to be used?
4. What is the number sentence?
5. What is the correct answer​

Answers

Don’t worry someone will come along and help you. Good luck and I hope you get it right

possible number of learners in the
in a village, the bell rings every 30 minutes at the Junior School and every 40
minutes at the High School Both schools start lessons at 8:00 am
At what times between 8.00 am and 2.30p.m do the bells both rring

Answers

Find multiples of 30 and 40:

30: 30, 60, 90, 120, 150

40: 40, 80, 120, 160

The least common multiple is 120, so every 120 minutes they willl both ring.

1 hour = 60 minutes:

120/60 = 2 hours.

The bells ring together every 2 hours.

8 + 2  = 10 am

10 +  = 12pm

12 + 2 = 2 pm

The bells will ring together at am, 12 pm and 2 pm.

Answer:

Solution :-

At first common multiple of 30 an 40

[tex] \sf \to \: 30 = 30,60,90,120[/tex]

[tex] \sf \to \: 40 = 40,80,120[/tex]

Common Multiple = 120

Time taken = 120/60 = 2 hrs

Now,

8.00 + 2 = 10.00 am

10.00 + 2 = 12.00 noon

12.00 + 2 = 2.00 pm

[tex] \\ [/tex]

Calculate the area of a kite that has diagonals that measure 6 centimeters and 8 centimeters.

Answers

9514 1404 393

Answer:

  24 cm²

Step-by-step explanation:

When the diagonals of a quadrilateral cross at right angles, the area of it is half their product.

  A = (1/2)(d1)(d2)

  A = (1/2)(6 cm)(8 cm) = 24 cm²

The area of the kite is 24 square centimeters.

E
C
5
4
9
B
D
C
Solve for x

Answers

Que se debe hacer es una pregunta???

Is one-half of a square smaller than one-quarter of the same square? How do you know?

Answers

Answer:

No

Step-by-step explanation:

one-half is bigger than one-quarter of the same square

retail price= $120
markup percent= 40%
what is the original cost

Answers

I believe it would be 72

Help me please and thank you

Answers

True for one value: -1

True for no values: 0

True for all values: 5

Sam owns a chain of fast food restaurants that operated 200 stores in 1999. If the rate of increase is 8% annually, how many stores does the restaurant operate in 2007?

Answers

Answer:

370 stores

Step-by-step explanation:

Given data

initial number of stores P= 200

r= 8%

t= 1999-2007=  8 years

Let us apply the compound interest expression to find the final amount of stores

A= P(1+r)^t

A= 200(1+0.08)^8

A= 200(1.08)^8

A= 200*1.85

A=370

Hence the number of stores in 2007 is 370 stores

Pls help me with this my sister’s going to take my phone in 10 minutes and I will give brainleast

Answers

Answer:

What are the closer two numbers together the then you find the slope

Step-by-step explanation:

Answer:

1x-6

Step-by-step explanation:

Slope Form: Mx+b

Slope Formula: y2-y1/x2-x1

(4,-2) (5,-1)

-1-(-2)= 1

5-4=1

1/1=1

Y-intercept: -6

Hope this helps!

Factorise x²+8x+12plz give answer ​

Answers

Answer:

(x+6)(x+2)

Step-by-step explanation:

we have

ax²+bx+c

To factor parabolas we need to find a number that adds to b (or 8) and mulitplies to a*c (or 12)

The numbers 6 and 2 fit this criteria which means we have

(x+6)(x+2)

Answer:

i.d.k the answer so sorry

Step-by-step explanation:

knkn

What is the average rate of change of g over the interval [-2,4]

Answers

Answer:

3

Average = sum of all the observations

Total number of observations

Average = 2+4

2

Average = - 6

2

3

Please I need help.
Find the measure of the angle DCB in the rhombus ABCD.

Answers

Answer:

53

Step-by-step explanation:

its the same to DAB because it is in the opposite side to the DAB

Answer:

Step-by-step explanation:

In Rhombus, diagonals are angle bisectors.

So, ∠DAC = ∠CAB

∠A = ∠DAC+∠CAB

    = 53 + 53

∠A = 106

In Rhombus, opposite angles are equal.

∠DCB = ∠A

∠DCB = 106°

EXERCISE 6.1
1. What will be the unit digit of the squares of the following numbers?
(i)81 -
(ii) 272 -
(iii) 799 -
(iv) 3853 -
(v) 1234 -
(vi) 26387-
(vii) 52698
(vii) 99880
(ix) 12796
(x) 55555-​

Answers

Unit digit of a square of a number is equal to the unit digit of square of unit digit of that number.
So,
(i)81
- Unit digit of square of 81
will be 1
.
(ii)272
- Unit digit of square of 272
will be 4
.
(iii)799
- Unit digit of square of 799
will be 1
.
(iv)3853
- Unit digit of square of 3853
will be 9
.
(v)1234
- Unit digit of square of 1234
will be 6
.
(vi)26387
- Unit digit of square of 26387
will be 9
.
(vii)52698
- Unit digit of square of 52698
will be 4
.
(viii)99880
- Unit digit of square of 99880
will be 0
.
(ix)12796
- Unit digit of square of 12796
will be 6
.
(x)55555
- Unit digit of square of 55555
will be 5

.

Calculate the slope of the line that contains the points (-3, -2) and (7, 2)

Answers

Answer:

the slope= 2/5        

the slope is 2/5

use the formula (y2-y1)/(x2-x1) to get the slope

Find the value of x and y.

Answers

Answer:

This is a triangle with 2 equal angles and equal to 60

=> this is an equilateral triangle

=> y = 60

    4x.3 = 54

=> y = 60

    x = 54/12 = 4.5

Step-by-step explanation:

Answer:

Step-by-step explanation:

if two angles are 60 degrees, the third one is also 60 degrees

that means all the sides are equal

if one side is 4x

4x+4x+4x=54

12x=54

x=4.5

just answer please hurry

Answers

Answer:

2.7 pages and 1.7 pounds of rice

Step-by-step explanation:

2.7 pages in one minute because 27/10=2.7

and 1.7 pounds of rice can be purchased for a dollar because 15/9 is about 1.7

Eight less than 7 times a number is -29.​

Answers

Answer:

7x-8=-20

Step-by-step explanation:

7 + 9 divided by 2
zzzzzzzzzzzzz
Pewdie-pie coco-melon dis-track cause yt banned. You can find it on StilBS chan.nel

Answers

Letssss gooooooooooooooo
Also (8)

Andre has 5 notebooks. Each notebook contains 60 sheets of paper. How many total sheets of paper does Andre have in his notebooks?

Answers

Answer:

5 x 60 = 300 pages

Step-by-step explanation:

Answer:

5x60=300

Step-by-step explanation:

If he has 5 note books with 60 pages each he has 300 pieces of paper

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