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ozzi
3 years ago
8

Fit a quadratic function to these three points: (-2,8), (0, -4), and (4, 68) Respuesta

Mathematics
1 answer:
zloy xaker [14]3 years ago
3 0

Answer:

f(x) = 4x^2 + 2x - 4.

Step-by-step explanation:

Let the quadratic function be y = f(x) = ax^2 + bx + c.

For the point (-2, 8)  ( x = -2 when y = 8) we have:

a(-2)^2 + (-2)b + c = 8

4a - 2b + c = 8      For (0, -4) we have:

0 + 0 + c = -4   so c = -4.    For (4, 68) we have:

16a + 4b + c = 68  

So we have 2 systems of equations in a and b ( plugging in c = -4):

4a - 2b - 4 = 8

16a + 4b - 4 = 68

4a - 2b = 12

16a + 4b = 72    Multiplying 4a - 2b = 12 by 2 we get:

8a - 4b = 24  

Adding the last 2 equations:

24a = 96

a = 4

Now plugging a = 4 and c = -4 in the first equation:

4(4) - 2b - 4 = 8

-2b = 8 - 16 + 4 = -4

b = 2.

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Kindly solve this question 6 too !!
Shkiper50 [21]

Answer:

x=1

Step-by-step explanation:

~~~~~x = \dfrac{1}{2 - \dfrac 1{2-\dfrac{1}{2-x}}}\\\\\\\implies x = \dfrac{1}{2 - \dfrac 1{\dfrac{4-2x-1}{2-x}}}\\\\\\\implies x= \dfrac{1}{2 - \dfrac{2-x}{3-2x}}\\\\\\\implies x = \dfrac{1}{\dfrac{6-4x-2+x}{3-2x}}\\\\\\\implies x = \dfrac{3-2x}{4-3x}\\\\\\\implies 4x -3x^2 = 3-2x\\\\\\\implies 3x^2 -4x +3-2x = 0\\\\\\\implies 3x^2 -6x +3 = 0\\\\\\\implies 3(x^2 -2x +1) =0\\\\\\\implies x^2 -2x +1 = 0\\\\\\\implies (x-1)^2 = 0\\\\\\\implies x -1 = 0\\\\\\\implies x = 1

7 0
2 years ago
M&lt;2 = 4x - 26,<br> m&lt;3 = 3x + 4
mestny [16]

Answer:

m<2 = 4x - 26 = 4(30) - 26 = 94 degrees

m<3 = 3x + 4 = 3(30) + 4 = 94 degrees

Step-by-step explanation:

Congruent angles are equal, so m<2 = m<3

4x - 26 = 3x + 4

x = 30

m<2 = 4x - 26 = 4(30) - 26 = 94 degrees

m<3 = 3x + 4 = 3(30) + 4 = 94 degrees

8 0
3 years ago
74°. 2x° what is the value of x
horrorfan [7]

Answer:

2x-7

Step-by-step explanation:

5 0
3 years ago
a biker travel 5ft in .05seconds. At that same rate of speed , how far will the biker travel in 1minute?
Solnce55 [7]

Biker's rate is:

v = 5/0.5

v = 10 ft per sec

t = 1 min = 60 sec

d = the distance the biker travels in 1 minute

v = d/t

d = v*t

d = 10*60

d = 600 ft

The biker travels 600 feet in 1 minute

5 0
3 years ago
A dealer buys oranges for 100000, he sold 60% of them for buying price, he sold 50% of the remaining for profit of 60% then he s
suter [353]

Based on the amount of oranges bought, those sold at a profit and those sold at a loss, the overall profit is 14.2%

<h3>What is the overall profit?</h3>

Assume that the buying price was $1 each.

The amount earned from 60% of them is:

= 60% x 100,000 x 1

= $60,000

The profit from selling 50% of the remaining is:

= (50% x 40,000) x 1.60

= $32,000

The loss from selling the other 50%:

= (50% x 40,000) x 0.90

= $22,222.22

Total selling price:

= 60,000 + 32,000 + 22,222.22

= $114,222.22

Total profit:

= (114,222.22 - 100,000) / 100,000

= 14.2%

Find out more on sales profit at brainly.com/question/19104371

#SPJ1

7 0
1 year ago
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