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Gennadij [26K]
3 years ago
10

What is the answer to this

Mathematics
1 answer:
astraxan [27]3 years ago
5 0
It is convenient to do part b first, then use that result to do part a.

b. For some pair of points (x1, y1) and (x2, y2), you want to find a point (a, b) such that (a, b) - (x1, y1) = (x2, y2) - (a, b). That is, the differences of coordinates from one end to the center are the same as the differences from the center to the other end.
Adding (a, b) to the above equation gives
  2(a, b) - (x1, y1) = (x2, y2)
Adding (x1, y1) then gives
  2(a, b) = (x1, y1) + (x2, y2)
Finally, dividing by 2 gives a formula for (a, b):

  (a, b) = ((x1, y1) + (x2, y2))/2
The midpoint is the average of the end points.

a. Using the result from part b, the midpoint is
  midpoint = ((2, 3) + (6, 7))/2 = (8, 10)/2
  midpoint = (4, 5)
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Use substitution to solve the linear system of equations.
docker41 [41]

Answer:

2y=X-6

×=9

(9, 3/2)

Step-by-step explanation:

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7 0
3 years ago
A line is graphed below.<br> Write an equation in the form y = mx + b that represents this line
galben [10]
<h3><u>Explanation</u></h3>
  • Slope-Intercept form

y = mx + b \\ m = slope \\ b = y - intercept

  • Calculate the slope with two given coordinate by using rise over run.

\begin{cases}(x_1,y_1) = ( - 4,0) \\ (x_2,y_2) = ( 0,2) \end{cases}

These two coordinate points are part of the graph and can be used to find the slope.

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

Substitute the coordinate points in the formula.

m  =  \frac{2 - 0}{0 - ( - 4)}  \\ m =  \frac{2}{ 4}  \\ m =  \frac{1}{2}

Therefore, the slope is 2.

Rewrite the equation in slope-intercept.

y =  \frac{1}{2} x + b

  • Calculate the y-intercept by substituting any given points in new rewritten equation.

(x,y) = ( 0,2)

I will be substituting these coordinate points in the equation.

y =  \frac{1}{2} x + b

Substitute x = 0 and y = 5 in the equation.

2 =  \frac{1}{2} (0) + b \\ 2 = 0 + b \\ 2 = b

Therefore the y-intercept is (0,2).

Rewrite the equation.

y =  \frac{1}{2} x + 2

<h3><u>Answer</u></h3>

<u>\large \boxed{y =  \frac{1}{2} x + 2}</u>

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3 0
3 years ago
Oceanside Bike Rental Shop charges 17 dollars plus 8 dollars an hour for renting a bike. Sara paid 81 dollars to rent a bike. Ho
user100 [1]

Answer:

She paid paid for 8 hours on the bike.

Step-by-step explanation:

81 - 17 = 64.

64/8 = 8

She used the bike for 8 hours by paying 8 dollars an hour with an additional 17 dollars.

Hope this helps!

5 0
3 years ago
Read 2 more answers
Write the equation of a circle with a center at (1,-9) and a radius of 12
Andre45 [30]

The equation of the circle is (x - 1)^2 +(y + 9)^2 = 144

<h3>How to determine the circle equation?</h3>

The given parameters are:

Center, (a,b) = (1, -9)

Radius, r = 12

The circle equation is calculated as:

(x - a)^2 + (y- b)^2 = r^2

This gives

(x - 1)^2 +(y + 9)^2 = 12^2

Evaluate the exponent

(x - 1)^2 +(y + 9)^2 = 144

Hence, the equation of the circle is (x - 1)^2 +(y + 9)^2 = 144

Read more about circle equations at:

brainly.com/question/10618691

#SPJ1

8 0
2 years ago
a box of cereal states that there are 90 calories in a 3/4-cup serving. How many calories are there in 4 cups of the cereal.
PolarNik [594]

Answer:

480 calories

Step-by-step explanation:

4 ÷ 3/4= 5 1/3 servings

90 x 5 1/3= 480

3 0
3 years ago
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