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Colt1911 [192]
3 years ago
12

Find the midpoint of the segment from point a (6,3) to point B (8,1)

Mathematics
2 answers:
velikii [3]3 years ago
5 0

Answer: M=(7,2)

Step-by-step explanation:

You need to use the following formula:

 M=(\frac{x_A+x_B}{2},\frac{y_A+y_B}{2})

Given the points A(6,3) and B(8,1), you can identify that:

x_A=6\\x_B=8\\y_A=3\\y_B=1

Now, you can substitute these values into the formula M=(\frac{x_A+x_B}{2},\frac{y_A+y_B}{2}).

Therefore, you get this result:

M=(\frac{6+8}{2},\frac{3+1}{2})

M=(7,2)

LUCKY_DIMON [66]3 years ago
4 0

ANSWER

The midpoint is (7,2)

EXPLANATION

The midpoint is calculated using the formula:

M(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})

The x-coordinate of the midpoint is given by

x =  \frac{6 + 8}{2}

x =  \frac{14}{2}  = 7

The y-coordinate of the midpoint is given by:

y =  \frac{3 + 1}{2}

y =  \frac{4}{2}  = 2

The midpoint is (7,2)

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A soccer ball is kicked from 3 feet above the ground. the height,h, in feet of the ball after t seconds is given by the function
dexar [7]
Here's our equation.

h=-16t+64t+3

We want to find out when it returns to ground level (h = 0)

To find this out, we can plug in 0 and solve for t.

0 = -16t+64t+3 \\ 16t-64t-3=0 \\ use\ the\ quadratic\ formula\ \frac{-b\±\sqrt{b^2-4ac}}{2a}  \\ \frac{-(-64)\±\sqrt{(-64)^2-4(16)(-3)}}{2*16}  = \frac{64\±\sqrt{4096+192}}{32}

= \frac{64\±\sqrt{4288}}{32} = \frac{64\±8\sqrt{67}}{32} = \frac{8\±\sqrt{67}}{4} = \boxed{\frac{8+\sqrt{67}}{4}\ or\ 2-\frac{\sqrt{67}}{4}}

So the ball will return to the ground at the positive value of \boxed{\frac{8+\sqrt{67}}{4}} seconds.

What about the vertex? Simple! Since all parabolas are symmetrical, we can just take the average between our two answers from above to find t at the vertex and then plug it in to find h!

\frac{1}2(\frac{8+\sqrt{67}}{4}+2-\frac{\sqrt{67}}{4}) = \frac{1}2(2+\frac{\sqrt{67}}{4}+2-\frac{\sqrt{67}}{4}) = \frac{1}2(4) = 2

h=-16t^2+64t+3 \\ h=-16(2)^2+64(2)+3 \\ \boxed{h=67}


8 0
3 years ago
Mary bought these art supplies: 4 paint brushes @ $1.29 each, 6 dowel rods @ $1.49 each, a jar of paste @ $1.25, and 2 canvases
Sophie [7]

Answer:

Option (1) is correct

The amount she receives back from $40 is  $12.65

Step-by-step explanation:

Given: Mary bought the art supplies.

4 paint brushes @ $1.29 each, 6 dowel rods @ $1.49 each, a jar of paste @ $1.25, and 2 canvases @ $6.00 each.

We have to find the change she get from $40.

We first find the total cost of the art supplies.

Since, she brought 4 paint brushes @ $1.29 each,

Thus, cost of 4 paint brush is  1.29 × 4 = $5.16

Also, 6 dowel rods @ $1.49 each,

Thus, cost of 6 dowel rods is  1.49 × 6 = $8.94

Thus, cost of 1 jar of paste  is $1.25

and 2 canvases @ $6.00 each

Thus, cost of 2 canvases  is $12.00

Thus, total cost of art supplies = 5.16 + 8.94 + 1.25 + 12 =$27.35

Thus, amount she receives back from $40 is $40 - $12.35 = $12.65

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3 years ago
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12 for charity walk 3 miles how much did his cousin pay per mile
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His cousin paid 4 per mile. You have to find the unit rate and you find that by dividing 12 by 3 which gives you 4. 
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Yuki888 [10]

Answer:

2037.89

Step-by-step explanation:

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This means that the area of the pizza is π*17.5^2

This means that the area =962.11275016187

We then need to find the area of a rectangle which is shown throuhg lenght*width

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We then need to find out the area of the box excluding the pizza so we subtract the area of a pizza

so we have

3000-962.11275016187=2,037.88724983813

Round and get 2037.89

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