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In-s [12.5K]
3 years ago
12

Write the equation in slope-intercept form with the point (2,7.5) with an x intercept of −1.

Mathematics
1 answer:
goblinko [34]3 years ago
7 0

Answer:  y=2.5x+2.5

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

y=mx+b

Where "m" is the slope and "b" is the y-intercept.

Since we know that the line passes through the point (2,7.5) and (-1,0), we can find the slope with this formula:

m=\frac{y_2-y_1}{x_2-x_1}

Substituting values, we get:

m=\frac{0-7.5}{-1-2}\\\\m=2.5

In order to find the y-intercept, we can substitute the slope and the point (-1,0) into y=mx+b and then solve fo "b":

0=(2.5)(-1)+b\\\\0=-2.5+b\\\\b=2.5

Then, the equation of this line in Slope-Intercept form is:

 y=2.5x+2.5

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The sum of two numbers is 56, and their difference is 10. What are the numbers?
Elanso [62]

Answer:

23 and 33

Step-by-step explanation:

23+33=56

33-23=10

6 0
3 years ago
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Need help on these !! 13 and 14! Please!!
katen-ka-za [31]

Question # 13

Answer:

The required equation for the given function is <em>y = 4sin(x/2+2π/3) -2 , as shown attached graph diagram.</em>

<em>Step-by-step explanation: </em>

As the general sine function is given by

y=asin(bx+c)+d.......[A]

  • amplitude = a
  • period = 2π ÷ b
  • Phase shift = -c ÷ b
  • Vertical shift = d

As in the question,  

  • amplitude = a = 4
  • period = 4π
  • phase shift = -4π/3
  • Vertical shift = d = -2

As  

period = 2π ÷ b  

b = 2π/period

b = 2π/4π ∵ period = 4π

b = 1/2  

Also

Phase shift = -c/b

-4π/3 = -c/b ∵ phase shift = -4π/3

4π/3 = c/b  

c = b × 4π/3  

c = 1/2 × 4π/3  

c = 4π/6  

c = 2π/3

So, putting Amplitude ⇒ a = 4, Vertical shift ⇒ d = -2, b = 1/2 ,  

and c = 2π/3 in Equation [A] would bring us the required equation for the given function.

y=asin(bx+c)+d

y = 4sin(x/2+2π/3)+(-2)

y = 4sin(x/2+2π/3) -2            

<em>Note: The graph is also shown in attached diagram.</em>

                                             Question # 14

<em>Answer:</em>

The required equation for the given function is y = cot(x+π/3)+2, as shown in attached graph diagram.

<em>Step-by-step explanation: </em>

As the general cotangent function is given by

y=acot(bx+c)+d.......[A]

  • amplitude = a
  • period = π ÷ b
  • Phase shift = -c ÷ b
  • Vertical shift = d

As in the question,  

  • period = π
  • phase shift = -π/3
  • Vertical shift = d = 2

As  

period = π ÷ b  

b = π/period

b = π/π ∵ period = 4π

b = 1  

Also

Phase shift = -c/b

-π/3 = -c/b ∵ phase shift = -π/3

π/3 = c/b  

c = b × π/3  

c = 1 × π/3  

c = π/3

So, putting vertical shift ⇒ d = 2, b = 1 and   c = π/3 in Equation [A] would bring us the required equation for the given function.

y=acot(bx+c)+d

y = cot(x+π/3)+2

<em>Note: The graph is also shown in attached diagram.</em>

Keywords: amplitude, period , phase shift , vertical shift

Learn more about trigonometric functions of equations from brainly.com/question/2643311

#learnwithBrainly

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3 years ago
AS one of her chores Staci must vacum 1/2 of the house. If she has already vacumed 1/3 of her share tonight whatp part of the li
Tatiana [17]

Answer:

1/6

Step-by-step explanation:

sim[le thought


3 0
3 years ago
I need help pls help me
kari74 [83]
The answer is 1/64 hope this helped!
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3 years ago
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What’s -2y+16=10 plz solve 2 step equation
konstantin123 [22]

Answer:

y=3

Step-by-step explanation:

To solve this 2 step equation, we need to get y alone. Lets write out the equation

-2y+16=10

Subtract 16 from both sides

-2y-16+16=10-16

Subtract

-2y=-6

divide both sides by -2

-2y/-2=-6/-2

divide

y=3

5 0
3 years ago
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