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emmainna [20.7K]
3 years ago
9

Find the midpoint of PQ P(4 1/3, 3 1/6), Q(-2 1/5, 3 2/3)

Mathematics
2 answers:
laiz [17]3 years ago
7 0

Answer:

(1.06, 3.41)

Step-by-step explanation:

Paha777 [63]3 years ago
6 0

Answer:

(1\frac{1}{15},3\frac{5}{12})

Step-by-step explanation:

To find the midpoint, you must average the x's then average the y's.

So the x's are 4 \frac{1}{3} and -2\frac{1}{5}.

The y's are 3\frac{1}{6} and 3\frac{2}{3}.

To find an average of a data with 2 elements you must add the two elements then take that sum and divide it by 2.

So this is what we will do with the x's then the y's.

So first x:

\frac{4\frac{1}{3}+-2\frac{1}{5}}{2}

Write as improper fractions:

\frac{\frac{13}{3}+\frac{-11}{5}}{2}

Division by 2 is the same as multiplying by 1/2:

\frac{13}{6}+\frac{-11}{10}

The least common multiple of 6 and 10 is 30.  We will multiply first fraction by 5/5 and 3/3 for the second so we can have the same denominator.

\frac{65}{30}+\frac{-33}{30}

Now that the bottoms are the same we can write as one fraction:

\frac{65+-33}{30}

Simplify:

\frac{32}{30}

If you want the answer as a mix fraction like your question began as we can do that by first figuring out how many 30's are in 32 and what is the remainder of that division.

There is one 30 and 32 and so 32-30=2 is the remainder.

1\frac{2}{30}

Reduce by dividing top and bottom by 2:

1\frac{1}{15}

Now for y:

\frac{3\frac{1}{6}+3\frac{2}{3}}{2}

Write the mix fractions as improper fractions:

\frac{\frac{19}{6}+\frac{11}{3}}{2}

Dividing by 2 is the same as multiplying by 1/2:

\frac{19}{12}+\frac{11}{6}

The least common multiple of 12 and 6 is 12 so I'm going to multiply the second fraction by 2/2 so the denominators will be the same:

\frac{19}{12}+\frac{22}{12}

Since the denominators are the same we can write as a single fraction:

\frac{41}{12}

How many 12's are in 41? 3 and so the remainder is 41-3(12)=41-36=5.

3\frac{5}{12}

So the midpoint is:

(1\frac{1}{15},3\frac{5}{12}).

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The measure of the exterior angle of the triangle is ___
mr_godi [17]

Answer: 114°

Step-by-step explanation:

<h2>Concept: </h2>

Here, we need to know the idea of the "Exterior Angle theorem".

<u>The exterior angle theorem</u> states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two opposite interior angles of the triangle.

If you are still confused, then refer to the attachment below for a graphical explanation.

<h2>Solve:</h2>

Given

24 + (2x + 18) = 3x + 6

Put like terms together

24 + 18 + 2x = 3x + 6

Combine like terms

42 + 2x = 3x + 6

Subtract 6 on both sides

42 + 2x - 6 = 3x + 6 - 6

36 + 2x = 3x

Subtract 2x on both sides

36 + 2x - 2x = 3x - 2x

x = 36

Exterior angle = 3x + 6 = 3(36) + 6 = 114°

Hope this helps!! :)

Please let me know if you have any questions

4 0
3 years ago
Read 2 more answers
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Answer:

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Step-by-step explanation:

4 0
3 years ago
What is the total number of digits required in numbering the pages in a book which has 1,724 pages?
Bond [772]

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Step-by-step explanation:

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5 0
2 years ago
Can someone solve this for me with their explanation please?
Lana71 [14]

First you want to subtract 36

so it looks like this \sqrt[4] {(4x+164)^3}=64

Then you want to cancel out the square root 4 by raising that to the 4th power (you must do this to both sides)

{(4x+164)^3}=64^4 which is equal to {(4x+164)^3}=16777216

Then you take the cube root to both sides [tex]\sqrt[3]{(4x+164)^3}=\sqrt[3]{16777216}[tex]

Then you end up with the equation 4x+164=256

Then subtract 164 to both sides

4x=92

then divide 92 by 4

Then you get x=23




7 0
3 years ago
Which of the following ratios are equivalent to 20%?
boyakko [2]

Answer:

C, D

Step-by-step explanation:

1/5 is .20 which is 20%

4/20 is equal to 1/5 which is 20%

Hope this helps

5 0
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