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goldenfox [79]
3 years ago
15

How to find the point that is equidistant from (5,-5) and (1,1)

Mathematics
1 answer:
Lina20 [59]3 years ago
3 0

Answer:

(3, -2)

Step-by-step explanation:

The <em>midpoint</em> of two points is half-way between the x-values and the y-values.

The formula is

M = ((x₁ + x₂)/2, (y₁ + y₂)/2)

For the points (5,-5) and (1,1),

Half way between the x values is

(x₁ + x₂)/2 = (5 + 1) /2 =  6/2 =  3

Half way between the y values is

(y₁ + y₂)/2= (-5 + 1)/2  = -4/2 = -2

M = (3, -2)

The graph below shows your two points at (5,-5) and (1,1) and the mid-point at (3, -2).

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What percent of 95 is 74
Softa [21]
74 is what percent of 95?


74 is P% of 95


Equation: Y = P% * X


Solving our equation for P

P% = Y/X

P% = 74/95

p = 0.7789

Convert decimal to percent:

<span>P% = 0.7789 * 100 = 77.89%
</span>

Hope I helped!

Let me know if you need anything else!

~ Zoe
7 0
3 years ago
Translate<br> Solve the equation.<br> 3m= 5(m + 3)-3<br> HELP
kvasek [131]

Answer:

m = -6

Step-by-step explanation:

3m= 5(m + 3)-3

Distribute

3m = 5m +15 -3

Combine like terms

3m = 5m +12

Subtract 5m

3m-5m = 5m+12-5m

-2m = 12

Divide by -2

-2m/-2 = 12/-2

m = -6

7 0
3 years ago
use the general slicing method to find the volume of The solid whose base is the triangle with vertices (0 comma 0 )​, (15 comma
lyudmila [28]

Answer:

volume V of the solid

\boxed{V=\displaystyle\frac{125\pi}{12}}

Step-by-step explanation:

The situation is depicted in the picture attached

(see picture)

First, we divide the segment [0, 5] on the X-axis into n equal parts of length 5/n each

[0, 5/n], [5/n, 2(5/n)], [2(5/n), 3(5/n)],..., [(n-1)(5/n), 5]

Now, we slice our solid into n slices.  

Each slice is a quarter of cylinder 5/n thick and has a radius of  

-k(5/n) + 5  for each k = 1,2,..., n (see picture)

So the volume of each slice is  

\displaystyle\frac{\pi(-k(5/n) + 5 )^2*(5/n)}{4}

for k=1,2,..., n

We then add up the volumes of all these slices

\displaystyle\frac{\pi(-(5/n) + 5 )^2*(5/n)}{4}+\displaystyle\frac{\pi(-2(5/n) + 5 )^2*(5/n)}{4}+...+\displaystyle\frac{\pi(-n(5/n) + 5 )^2*(5/n)}{4}

Notice that the last term of the sum vanishes. After making up the expression a little, we get

\displaystyle\frac{5\pi}{4n}\left[(-(5/n)+5)^2+(-2(5/n)+5)^2+...+(-(n-1)(5/n)+5)^2\right]=\\\\\displaystyle\frac{5\pi}{4n}\displaystyle\sum_{k=1}^{n-1}(-k(5/n)+5)^2

But

\displaystyle\frac{5\pi}{4n}\displaystyle\sum_{k=1}^{n-1}(-k(5/n)+5)^2=\displaystyle\frac{5\pi}{4n}\displaystyle\sum_{k=1}^{n-1}((5/n)^2k^2-(50/n)k+25)=\\\\\displaystyle\frac{5\pi}{4n}\left((5/n)^2\displaystyle\sum_{k=1}^{n-1}k^2-(50/n)\displaystyle\sum_{k=1}^{n-1}k+25(n-1)\right)

we also know that

\displaystyle\sum_{k=1}^{n-1}k^2=\displaystyle\frac{n(n-1)(2n-1)}{6}

and

\displaystyle\sum_{k=1}^{n-1}k=\displaystyle\frac{n(n-1)}{2}

so we have, after replacing and simplifying, the sum of the slices equals

\displaystyle\frac{5\pi}{4n}\left((5/n)^2\displaystyle\sum_{k=1}^{n-1}k^2-(50/n)\displaystyle\sum_{k=1}^{n-1}k+25(n-1)\right)=\\\\=\displaystyle\frac{5\pi}{4n}\left(\displaystyle\frac{25}{n^2}.\displaystyle\frac{n(n-1)(2n-1)}{6}-\displaystyle\frac{50}{n}.\displaystyle\frac{n(n-1)}{2}+25(n-1)\right)=\\\\=\displaystyle\frac{125\pi}{24}.\displaystyle\frac{n(n-1)(2n-1)}{n^3}

Now we take the limit when n tends to infinite (the slices get thinner and thinner)

\displaystyle\frac{125\pi}{24}\displaystyle\lim_{n \rightarrow \infty}\displaystyle\frac{n(n-1)(2n-1)}{n^3}=\displaystyle\frac{125\pi}{24}\displaystyle\lim_{n \rightarrow \infty}(2-3/n+1/n^2)=\\\\=\displaystyle\frac{125\pi}{24}.2=\displaystyle\frac{125\pi}{12}

and the volume V of our solid is

\boxed{V=\displaystyle\frac{125\pi}{12}}

3 0
3 years ago
Is (-2, 6) a solution to this system of linear equations? (HINT: Substitute x
Serggg [28]

Answer:

1st Equation: -8x + y = 22

At (-2,6)

(-8*-2)+ 6 =16+6= 22: That is correct

2nd Equation: -8x - y =10

At (-2,6)

(-8*-2)-6= 16-6= 10: That is correct

Both are correct.

Hope it helps you.

5 0
3 years ago
876,302 to the nearest 10,000
Nataliya [291]

Answer:

Simple answer: 880,302

Step-by-step explanation:

Rule is if the number before the number your rounding is above 4 then it should round up

if its lower than 4 the number your rounding stays as is and the number before it goes down to 0

5 0
2 years ago
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