MATHEMATICS COLLEGE

A(2,9), B(4,k), and C(9, -12) are 3 collinear points.
Find the value of k.

Answers

Answer 1
Answer:

Answer is   3

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Explanation:

We're going to be using the slope formula a bunch of times.

Find the slope of the line through points A and C

m = (y2 - y1)/(x2 - x1)

m = (-12-9)/(9-2)

m = -21/7

m = -3

The slope of line AC is -3. The slopes of line AB and line BC must also be the same for points A,B,C to be collinear. The term collinear means all three points fall on the same straight line.

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Let's find the expression for the slope of line AB in terms of k

m = (y2 - y1)/(x2 - x1)

m = (k-9)/(4-2)

m = (k-9)/2

Set this equal to the desired slope -3 and solve for k

(k-9)/2 = -3

k-9 = 2*(-3) ..... multiply both sides by 2

k-9 = -6

k = -6+9 .... add 9 to both sides

k = 3

If k = 3, then B(4,k) updates to B(4,3)

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Let's find the slope of the line through A(2,9) and B(4,3)

m = (y2 - y1)/(x2 - x1)

m = (3-9)/(4-2)

m = -6/2

m = -3 we get the proper slope value

Finally let's check to see if line BC also has slope -3

m = (y2 - y1)/(x2 - x1)

m = (-12-3)/(9-4)

m = -15/5

m = -3 we get the same value as well

Since we have found lines AB, BC and AC all have slope -3, we have proven that A,B,C fall on the same straight line. Therefore, this shows A,B,C are collinear.

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Western Company allocates $10 overhead to products based on the number of machine hours used. The company uses a plantwide overhead rate with machine hours as the allocation base. Given the amounts below, how many machine hours does the company expect in department 2?

Answers

Answer:

Your question needs more data, however; See a complete question and see how it is answered for your guidance.

Step-by-step explanation:

Total estimated machine hours

= Total manufacturing overhead / Plantwide predetermined overhead rate

= ( 255000 + 155000 ) / 10.00

= 41000 MH

Machine hours expected in Department 2

= Total estimated machine hours - Machine hours of Department 1

= 41000 - 15500

= 25500 MH

Classify the following triangle as acute, obtuse, or right.
30°
249
126

Answers

Answer:

30 - Acute

249 - Obtuse

126 - Obtuse

Step-by-step explanation:

Less than 90 - Acute

90 - Right

More than 90 - Obtuse

PLZ HELP ASAP!! WILL MARK BRAINLIEST!If the quantity 4 times x times y cubed plus 8 times x squared times y to the fifth power all over 2 times x times y squared is completely simplified to 2xayb + 4xcyd, where a, b, c, and d represent integer exponents, what is the value of a? _______

Numerical Answers Expected!

Answers

a=0.


(4xy^3+8x^2y^5)/(2xy^2) (4xy^3+8x^2y^5)/(2xy^2)  Since 2xy^2 is a common factor we have

Go to do 2y+4xy^3

Then do 2y=2x^ay^b

Then Do x^0=x^a


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A Cepheid variable star is a star whose brightness alternately increases and decreases. For a certain star, the interval between times of maximum brightness is 4.2 days. The average brightness of this star is 3.0 and its brightness changes by ±0.25. In view of these data, the brightness of the star at time t, where t is measured in days, has been modeled by the function B(t) = 3.0 + 0.25 sin 2πt 4.2 . (a) Find the rate of change of the brightness after t days. dB dt =

Answers

Answer:

a)(dB)/(dt) = (5\pi)/(4.2) \cdot \cos \left(2\pi\cdot (t)/(4.2) \right), b)(dB)/(dt)\approx 5.595

Step-by-step explanation:

a) The rate of change of the brightness of the Cepheid can be determined by deriving the function in time:

(dB)/(dt) = \left((2\pi)/(4.2) \right)\cdot 0.25\cdot \cos (2\pi\cdot (t)/(4.2))

(dB)/(dt) = (5\pi)/(4.2) \cdot \cos \left(2\pi\cdot (t)/(4.2) \right)

b) The rate of increase after one day is:

(dB)/(dt) = (5\pi)/(4.2) \cdot \left(2\pi \cdot (1)/(4.2) \right)

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Which of the following is equivalent to 46? 6 + 6 + 6 + 6 4 • 4 • 4 • 4 • 4 • 4 4 + 4 + 4 + 4 + 4 + 4 6 • 6 • 6 • 6

Answers

Answer:

None

Step-by-step explanation:

(4)^6              (6)^4                   6+6+6+6        4+4+4+4+4+4

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Answer: none

Step-by-step explanation:

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Answers

Answer:

For negative sign , the graph reflects over x -axis and for 1/2 there will be a vertical compression

Step-by-step explanation:

Parent function is f(x)= x

We need to find the effect of the graph when f(x) is replaced with -1/2f(x)

When negative sign is multiplied outside f(x) like -f(x),  then there will be a reflection over x-axis

When negative sign is multiplied inside f(x) like f(-x) then there will be a reflection over y-axis

When a number is multiplied outside f(x) then there will be a vertical stretch or compression

Here 1/2 is multiplied outside f(x). (1)/(2) is less than 1 so there will be a vertical compression

For negative sign , the graph reflects over x -axis and for 1/2 there will be a vertical compression
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