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Ronch [10]
3 years ago
14

Find K such that the points (-2, 5), (2, 8) and (6, K) are collinear.

Mathematics
1 answer:
damaskus [11]3 years ago
8 0

Answer:

k = 11

Step-by-step explanation:

let the points be A(-2,5), B(2,8), C(6,K).

for the points to be collinear slope of line AB maust be equal to line BC.

slope of line AB = \frac{8-5}{2+2}=\frac{3}{4}

slope of line BC = \frac{k-8}{6-2}=\frac{k-8}{4}

therefore \frac{k-8}{4}= \frac{3}{4}

therefore k = 8 + 3

k = 11

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Help on question 30!!
Basile [38]
The given identity tells you ...
.. (sum of numbers) * (sum of squares - product) = (sum of cubes)

Substituting the given information, you have
.. (sum of numbers) * (29 -10) = 133
Then you can divide by (29 -10) to get
.. sum of numbers = 133/19 = 7

The sum of the two numbers is 7.
3 0
3 years ago
Given the functions f(x) = 2x -1 and g(x) =
Novosadov [1.4K]

Answer:

Please check the explanation.

Step-by-step explanation:

Given

  • f(x) = 2x - 1
  • g(x) =  2 - x

a)

f(x) + g(x) = (2x - 1) + (2 - x)

                = 2x -1 + 2 - x

                = x + 1

b)

f(x) - g(x) = (2x - 1) - (2 - x)

              = 2x - 1 - 2 + x

               = 3x - 3

c)

g(-5) - f(-5)

Putting x = -5 in g(x) = 2 - x

g(x) = 2 - x

g(-5) = 2 - (-5) = 2+5 = 7

Putting x = -5 in f(x) = 2x - 1

f(x) = 2x - 1

f(-5) = 2(-5) - 1

       = -10 - 1

        = -11

Thus,

g(-5) - f(-5) = 7 - (-11) = 7+11 = 18

d)

f(x).g(x) = (2x - 1) (2 - x) = -2x² + 5x - 2

e)

f(g(x)) = f(2-x)

          = 2(2-x)-1

          = 4-2x-1

          = 3-2x

6 0
3 years ago
A bivariate data set has x = 21, sx = 13, y = 55, sy = 27, and r = .88. What is the equation for the regression line of y on x?
earnstyle [38]

Answer:

c) y=16.57+1.83x

Step-by-step explanation:

Equation for regression line of y on x is given as

\hat{y}=mx+b --- (1)

where

\hat{y} = predicted value

m = slope of line

b = intercept

m and b are found as

m=r\frac{S_{y}}{S_{x}}---(2)\\\\b=\bar{y}-m\bar{x}---(3)

r = correlation coefficient = 0.88

Sx = standard deviation for independent variable x = 13

Sy = standard deviation for dependent variable y = 27

\bar{x} = mean value of independent variable x = 21

\bar{x} = mean value of dependent variable y = 55

Substituting these values in (2) and (3)

m=r\frac{S_{y}}{S_{x}}\\\\m=(0.88)\frac{27}{13}\\\\m=1.83

b=\bar{y}-m\bar{x}\\\\b=55-(1.827)(21)\\\\b=16.57

Putting these values of m and b in (1)

y=1.83x+16.57

5 0
3 years ago
This is for middle school 9th grade please help me :)
Stolb23 [73]

Answer:

i think it's undefined

Step-by-step explanation:

7 0
3 years ago
Heres the revenue and expenses for the month. Calculate whether mia had a profite or loss
8_murik_8 [283]

Answer:

profit  $450

Step-by-step explanation:

subtract 9000 (expenses) from the revenue (9450) to get $450 of profit

8 0
3 years ago
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