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11111nata11111 [884]
3 years ago
15

Find the exact length of the midsegment of the trapezoid with the vertices S(−2, 4), T(−2,−4), U(3,−2), V(13, 10).

Mathematics
1 answer:
Vlada [557]3 years ago
3 0

Check the picture below.

first off we'll need to know the midpoints of ST and UV, well, from ST as you can see in the picture, is just a vertical line, so its midpoint is simply (-2,0), let's find it for UV

\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ U(\stackrel{x_1}{3}~,~\stackrel{y_1}{-2})\qquad V(\stackrel{x_2}{13}~,~\stackrel{y_2}{10}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{13+3}{2}~~,~~\cfrac{10-2}{2} \right)\implies \left( \cfrac{16}{2}~~,~~\cfrac{8}{2} \right)\implies (8~~,~~4) \\\\[-0.35em] ~\dotfill

\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-2}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{4})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d = \sqrt{[8-(-2)]^2+[4-0]^2}\implies d=\sqrt{(8+2)^2+(4-0)^2} \\\\\\ d=\sqrt{10^2+4^2}\implies d=\sqrt{116}\implies d\approx 10.77

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If 7 - 2x = -27, what is the value of 3x + 5?
taurus [48]

Answer: 56

Step-by-step explanation:

7-2x=-27

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x=17

so 3x+5=3(17)+5=56

3 0
2 years ago
A corner store sells two kinds of baked goods: cakes and pies. A cake costs $4 and a pie costs $6. In one day, the store sold 9
Troyanec [42]

Answer:

the number of cakes sell is 5

Step-by-step explanation:

The computation of the number of cakes sold is shown below;

Let us assume

The cake be C

And, the pie cost be P

Given that

There is two types of baked goods sold

The cost of the cake is $4

And, the cost of the pie cost is $64

Now the store sold 9 baked goods for a total of $44

So, the equation would be

C + P = 9

P = 9 - C ...... (1)

4C + 6P = 44............(2)

Now put the value of P in equation 2

4C + 6(9 - C) = 44

4C + 54  - 6C = 44

-2C = -10

C = 5

And, P = 4

hence, the number of cakes sell is 5

8 0
3 years ago
4/5 dived by 3/4<br><br> Please help
Leto [7]

Answer:

1 1\15

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
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jarptica [38.1K]

Answer:

3 gallons

Step-by-step explanation:

Let

x ----> the amount of pure acid (100% solution) in gallons

Remember that

100\%=100/100=1

20\%=20/100=0.20

60\%=60/100=0.60

we know that

(1)(x)+(0.20)(3)=(0.60)(x+3)

solve for x

x+0.60=0.60x+1.80

x-0.60x=1.80-0.60\\0.40x=1.20\\x=3\ gal

therefore

3 gallons of pure acid should be mixed with 3 gallons of a 20% acid solution in  order to get a 60% acid solution

7 0
3 years ago
Given the two sets, which statement is true?
monitta
I think it is 3 A but it is hard to know what the question is asking... but my logic is that 3 A is right because A = 1+2 = 3
6 0
3 years ago
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