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ki77a [65]
3 years ago
10

Use the quadratic regression to find the equation for the parabola going through these 3 points (-5, 161) (-2, 29) (6, 205)

Mathematics
1 answer:
Rama09 [41]3 years ago
6 0

Answer:

The equation of the parabola is y = 6x^{2}-2b+1

Step-by-step explanation:

First we write a quadratic equation of parabola as y = ax^{2}+bx+c

Now it is given in the question that parabola passes through three points (-5,161),(-2,29),(6,205).

To find the equation we have to get the value of a,b & c.

Now we form three equations to find the value of a,b,c.

We put the value (-5,161) in the equation

161 = a×25+b×(-5)+c

161 = 25a-5b+c----------(1)

Now we put (-2,29) in the equation

29 = a×4+b×(-2)+c

29 = 4a-2b+c---------(2)

Again we put (6,205) in the equation

205 = a×36+6b+c------------(3)

Now we subtract equation (1) from (2)

161-29 = 25a-4a-5b-(-2b)+c-c

132 = 21a-5b+2b

132 = 21a-3b

132 = 3(7a-b)

44 = 7a-b---------(4)

Now we subtract equation (2) from (3)

205-29 = 36a-4a+6b-(-2b)+c-c

176 = 32a+6b+2b

176 = 32a+8b

176 = 8(4a+b)

22 = 4a+b------------(5)

Now we add equation (5) and (4)

44+22 = 7a+4a-b+b

66 = 11a

a = 6

Now we put the value a in equation (4)

44 = 7×6-b

44 = 42-b

44-42 = -b

2 = (-b)

b = (-2)

Now we put the value of a and b in equation number (2)

29 = 4×6-2(-2)+c

29 = 24+4+c

29 = 28+c

c = 29-28

c =1

Finally we put the value of a,b,c in the quadratic equation

y = 6x^{2}+(-2)x+1

y = 6x^{2}-2+1

This is the final answer.

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2 years ago
What squared equals 125
OLga [1]

Answer:

The answer is about 11.1803399

Step-by-step explanation:

To find what squared equals 125, you will have to take the square root of 125.

\sqrt{125} ≈ 11.1803399

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4 0
3 years ago
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Can someone help me with this question for my homework 2x+29+11=x+28
givi [52]

Sure! I'll try!

2x + 29 +11 = x + 28

First, you would put like terms ( the x ) on the same side.

2x + 29 + 11 = x + 28

-2x                 -2x

Giving you: 29 + 11 = -3x + 28

Then, you would add 29 and 11 together to get 40.

Next, you'd put the 28 on the other side.

40 = -3x + 28

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Giving you: 12 = -3x

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3 years ago
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Point T is on line segment SU. Given ST=2x+6, TU=4, and SU=4x, determine the numerical length of ST.
serg [7]

The numerical length of ST is 16

<h3>How to determine the numerical length of ST?</h3>

The given parameters are:

ST = 2x + 6

TU = 4

SU = 4x

The above parameters can be represented as:

SU = ST + TU

This gives

4x = 2x + 6 + 4

Evaluate the like terms

2x = 10

Divide by 2

x= 5

Substitute x= 5 in ST = 2x + 6

ST = 2 * 5 + 6

Evaluate

ST = 16

Hence, the numerical length of ST is 16

Read more about line segments at:

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You decide to put $2,000 in a savings account to save for a $3,000 downpayment on a new car. If the account has an interest rate
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Answer:

10.153 years

Step-by-step explanation:

The future value of such an investment is given by ...

FV = P·(1 +r/12)^(12t)

where P is the principal invested, FV is the future value of it, r is the annual interest rate, and t is the number of years.

Dividing by P and taking the log, we have ...

FV/P = (1 +r/12)^(12t)

log(FV/P) = 12t·log(1 +r/12)

Dividing by the coefficient of t gives ...

t = log(FV/P)/log(1 +r/12)/12 = log(3000/2000)/log(1 +.003333...)/12 ≈ 121.842/12

t ≈ 10.153 . . . years

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