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mash [69]
2 years ago
5

Explain the steps to find x- and y- intercepts of an equation of the form Ax + By = C

Mathematics
1 answer:
slavikrds [6]2 years ago
4 0

Step-by-step explanation:

For an equation of form Ax + By = C, we are given A, B, and C.

The x intercept is when the line/equation is on the x axis, or when y=0.

Therefore, if we plug y=0 into the equation Ax+By=C, and anything multiplied by 0 is equal to 0, we can say that

Ax + 0 = C

Ax = C

divide both sides by A

x  = C/A

Therefore, the x intercept is equal to C/A

Similarly, for the y intercept, or when the line is on the y axis (or when x=0), we have

A*0 + By = C

By = C

divide both sides by B

y= C/B at the y intercept

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A sine function has the following key features: Period = 4 Amplitude = 3 Midline: y=−1 y-intercept: (0,-1) The function is not a
mezya [45]

Answer:

  • See the graphs attached and the explanation below

Explanation:

The most simple sine function, considered the parent function, is:

     y=sin(x)

That function has:

  • Midline, also known as rest or equilibrium position: y = 0
  • Minimum: - 1
  • Maximum: 1
  • Amplitude: the distance between a minimum or a maximum and the midline = 1
  • period: the interval of repetition of the function = 2π

The more general sine function is:

             y=Asin(Bx+C)+D

That function has:

  • Midline: y = D (it is a vertical shift from the parent function)
  • Minimum: - A + D
  • Maximum: A + D
  • Amplitude: A
  • period: 2π/B
  • phase shift: C (it is a horizontal shift of the from the parent function)

Now, you have to draw the sine function with the given key features:

  • Period = 4 ⇒ 2π/B = 4 ⇒ B = π/2
  • Amplitude, A = 3
  • midline y = - 1 ⇒ D = - 1
  • y-intercept = (0, -1)

Substitute the know values and use the y-intercept to find C:

       

            y=3sin(2x/\pi+C)-1

Substitute (0, -1)

             

              -1=3sin(0+C)-1\\ \\ 3sin(C)=0\\ \\ sin(C)=0\\ \\ C=0

Hence, the function to graph is:

              y=3sin(\pi x/2)-1

To draw that function use this:

  • Maxima: 3(1) - 1 = 3 - 1 = 2, at x = 1 ± 4n (n = 0, 1, 2, 3, ...)
  • Minima: 3(-1) - 1 = - 3 - 1 = -4
  • y-intercept: (0, - 1)
  • x-intercepts: the solutions to 0 = 3sin(πx/2) = - 1
  • first point of the midline: (0, -1) it is the same y-intercept

With that you can understand the graphs attached.

4 0
3 years ago
What is the axis of symmetry
Verdich [7]

Answer:

its is x=0

Step-by-step explanation:

5 0
3 years ago
A motorist took 1.2 hour to travel 96 km how far will he travel in 1 hour
miskamm [114]

Answer:

80km

Step-by-step explanation:

To solve this problem, we need to cross multiply. Lets input the values (1.2, 1.0, 96) as shown below:

\frac{1.2}{96} = \frac{1.0}{x}

Next we cross multiply. We multiply 1.2 and x, and we multiply 96 and 1.0.

1.2(x) = 1.2x

96 x 1.0 = 96

Now, lets put the values above back into the equation:

1.2x = 96

Lets solve this equation. First we divide 96 by 1.2.

1. x = \frac{96}{1.2}

2. x = 80

This means that our answer is 80km.

4 0
3 years ago
Relationship B has a greater rate than Relationship A. This graph represents Relationship A.
tester [92]

Answer:

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For Table A: Rate = (3 - 1.2)/(5 - 2) = 1.8/3 = 0.6

For table B: Rate = (3.5 - 1.4)/(5 - 2) = 2.1/3 = 0.7

For table C: Rate = (4 - 1.6)/(5 - 2) = 2.4/3 = 0.8

For table D: Rate = (2 - 1.5)/(4 - 3) = 0.5/1 = 0.5

Therefore, the correct answer is option C.

4 0
3 years ago
Urgent…. I need help
Firdavs [7]

A.

Step-by-step explanation:

To find out the answer, there is a method that can be used to find out if a line is a function. It is called the vertical line method. And it also has to be per x, One y value has to be there. Analyzing the graphs, the answer should be option A.

8 0
2 years ago
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