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Paraphin [41]
3 years ago
6

Find the equation of the form y=ax²+bx+c whose graph passes through the points (1,6), (3, 20), and (−2,15).

Mathematics
1 answer:
Korolek [52]3 years ago
6 0

Answer:

c = \dfrac{25}{4}

b = \dfrac{-13}{8}

a = \dfrac{11}{8}

Step-by-step explanation:

given ,

equation y=ax²+bx+c

passing through points (1,6), (3, 20), and (−2,15).

then these points will satisfy the equation

at (1,6)

y  = a x²+b x+c

6 = a(1)² + b (1) + c

a + b + c = 6------(1)

at (3 , 20)

y  = a x²+b x+c

20 = a(3)² + b (3) + c

9 a + 3 b + c = 20------(2)

at (−2,15)

y  = a x²+b x+c

15 = a(-2)² + b (-2) + c

4 a -2 b + c = 15------(3)

solving equation (1),(2) and (3)

a = 6 - b - c

9 (6 - b - c)+ 3 b + c = 20

6 b + 7 c = 34-------(4)

4 (6 - b - c) -2 b + c = 15

2 b + c = 3----------(5)

on solving equation (4) and (5)

c = \dfrac{25}{4}

b = \dfrac{-13}{8}

a = \dfrac{11}{8}

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3 years ago
Are there any outliers in the data? What does the outlier mean?
Brrunno [24]

Answer:

<em>44, definition below</em>

Step-by-step explanation:

  1. An outlier is a number that is much larger or smaller than the general populous of numbers. For example, if there was a dot plot with dots clustered at 2, 3, and 5, but there was one or two dots around 10, then 10 would be considered an outlier.
  2. I would consider 44 to be an outlier in the number set.

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Karolina [17]

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1000 is the best answer yet

8 0
3 years ago
If x + 2 is a factor of x^3 - 2ax^2 +16, then value of a is i) 3 ii) 1 iii) 4
grandymaker [24]

Answer:

a=1 is the answer

Step-by-step explanation:

let

p(x)=x³-2ax²+16

put x= -2

p(-2)=(-2)³-2a(-2)²+16

p(-2)=-8+16-8a

p(-2)=8-8a

as (x+2) is a factor of p(x) then p(x) is equal to zero

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i hope this will help you

3 0
3 years ago
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Olga is putting a border around her triangular flower bed. She has 20 feet of border material, which will fit perfectly around t
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Answer:

60 feet

Step-by-step explanation:

We know that a triangle has 3 sides, in this case we will call them a, b and c.

It tells us that everything is material, it measures 20, that is:

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They tell us that she wants to triple each side and to know how much material she would need in total. Then it would be:

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border material need = 3 * 20

border material need = 60

Which means that she needs a total of 60 feet of material.

3 0
2 years ago
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