Rewrite y - 2x = -6x + 12 using function notation

Answers

Answer 1

Answer:       -2x + y = -6x + 12
    + 6x + 6x
       4x + y = 12
4x - 4x + y = -4x + 12
   y = -4x + 12
      f(x) = -4x + 12

Answer 2

Answer: get y alone so add 2x to each side making it y=-4x+12

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What is a number mulitplyed by 8 and added by 6?

Answers

xy = 8
x + y = 6

x + y = 6
x - x + y = -x + 6
y = -x + 6

xy = 8
x(-x + 6) = 8
x(-x) + x(6) = 8
  -x² + 6x = 8
-x² + 6x - 8 = 0
-1(x²) - 1(-6x) - 1(8) = 0
-1(x² - 6x + 8) = 0
  -1 -1
  x² - 6x + 8 = 0
x² - 4x - 2x + 8 = 0
x(x) - x(4) - 2(x) + 2(4) = 0
x(x - 4) - 2(x - 4) = 0
(x - 2)(x - 4) = 0
  x - 2 = 0 or x - 4 = 0
+ 2 + 2   + 4 + 4
x = 2   or    x = 4

x + y = 6
2 + y = 6
- 2 - 2
y = 4
(x, y) = (2, 4)

or
x + y = 6
4 + y = 6
  - 4 - 4
y = 2
  (x, y) = (4, 2)

The two numbers that add up to 6 and multiply to 8 are 4 and 2.

Kari and Samantha have determined that their water-balloon launcher works best when they launch the balloon at an angle within 3 degrees of 45 degrees. Which equation can be used to determine the minimum and maximum optimal angles of launch, and what is the minimum angle that is still optimal?

Answers

|x - 45| = 3; minimum angle: 42 degrees

Answer:

The equation which can be used to determine the minimum and maximum optimal angles of launch is:

|x – 45| = 3

and the minimum angle that is still optimal is:

42 degrees.

Step-by-step explanation:

Let x be the optimal angle by which the balloon is launched.

Also, it is given that the they launch the balloon at an angle within 3 degrees of 45 degrees.

i.e. the range at which the angle is launched lie between 3 degree less than 45 degree and 3 degree more than 45 degree.

Hence, the equation that will represent this relationship is:

|x-45|=3

Hence, on solving for the maximum value we have:

$x-3=45\n\ni.e.\n\nx=45+3\n\ni.e.\n\nx=48\ degree$

and the smallest optimal angle is given by:

$x-45=-3\n\ni.e.\n\nx=45-3\n\ni.e.\n\nx=42\ degree$

Explaining How to Sve an ea
What should you do to solve the equation?
45 = x + 38
O Subtract 38 from both sides.
O Add 38 to both sides.
O Subtract 45 from both sides.
O Add 45 to both sides.

Answers

You subtract 38 from both sides

Answer:

Subtract 38 from both sides.

Step-by-step explanation:

THAT DA ANSWER

Trapezoid PSTK is isosceles. SK = 20, SH = 12, If ST = 1 4 HK, find HK, APTSK, m∠P, and PS. Find HK, Area of pstk, HK and PS

Answers

Answer:

HK = 16

Step-by-step explanation:

12^2+x^2=20^2

x = HK

Use the Law of Cosines to determine the indicated side x. (Assume b = 18 and c = 22. Round your answer to one decimal place.)

Answers

Answer:

Step-by-step explanation:

x2 = 302 + 302 - 2·30·30cos140° = 3178.88; x = √3178.88 = 56.38

For the graphed exponential equation, calculate the average rate of change from x=-2 to x= 0

Answers

Answer:

3/2

Step-by-step explanation:

Rate of change is given by

f(x2) -f(x1)

-----------------

x2 -x1

We know x2 is 0 and x1 is -2

f(x2) is -1 and f(x1) is -4

-1 - ( -4)

----------

0 - -2

-1 +4

--------

0+2

3/2

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