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pychu [463]
3 years ago
8

Is a triangle with sides of length 7 ft, 24 ft, and 25 ft a right triangle? Explain.

Mathematics
1 answer:
Lemur [1.5K]3 years ago
5 0
25^2 = 625
7^2 + 24^2 = 49+576 = 625

625 = 625

ANswer
Yes. It's right triangle

<span>the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse....It's right triangle angle</span>
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S KM ∥ JN? Why or why not?
bixtya [17]

Given: We have the given figure through which we can see

LK=16,

KJ=10,

LM=24,

MN=15

To Find: Whether KM || JN and the reasoning behind it.

Solution: Yes, KM || JN because \frac{16}{10}= \frac{24}{15}

Explanation:

For this solution, we use the concept of Similar Triangles.

Now, KM || JN if ΔLKM ~ ΔLJN (i.e., if ΔLKM is similar to ΔLJN).

Now, ∠MLK=∠NLJ

To prove similarity of the two triangles, we have to show that the sides are proportional. In other words, LK:KJ = LM:LN

LK:KJ=LM:LN\\\\ \frac{LK}{KJ} =\frac{LM}{LN}\\\\\frac{16}{26}= \frac{24}{39}\\\\

which is true as both sides simplify to \frac{8}{13}

Thus, we see that ΔLKM ~ ΔLJN (i.e., if ΔLKM is similar to ΔLJN).

Therefore, KM || JN.

To come to the reasoning, notice that

\frac{LK}{LJ} =\frac{LM}{LN}\\\\\frac{LK}{LK+KJ} =\frac{LM}{LM+MN}\\\\\frac{LK+KJ}{LK} =\frac{LM+MN}{LM}\\\\1+\frac{KJ}{LK}=1+ \frac{MN}{LM}\\\\\frac{LK}{KJ} =\frac{LM}{MN}

In other words, \frac{16}{10}= \frac{24}{15}


4 0
3 years ago
Read 2 more answers
Write two ratios that are equivalent to 3:11
maks197457 [2]
6:22, 9:33, are both equivalent to 3:11. 
7 0
3 years ago
Read 2 more answers
Choose the correct simplification of x to the 12th power times z to the 11th power all over x to the 2nd power times z to the 4t
Umnica [9.8K]

Answer:

<h3>The option A) x^{10}z^7 is correct answer.</h3><h3>The correct simplification for the given expression \frac{x^{12}\times z^{11}}{x^2\times z^4} is x^{10}z^7</h3>

Step-by-step explanation:

Given expression is x to the 12th power times z to the 11th power all over x to the 2nd power times z to the 4th power.

The given expression can be written as \frac{x^{12}\times z^{11}}{x^2\times z^4}

<h3>To choose the correct simplification of the given expression :</h3>

Now we have to simplify the given expression as below

\frac{x^{12}\times z^{11}}{x^2\times z^4}

=x^{12}\times z^{11}(x^{-2}\times z^{-4})   ( by using the identity \frac{1}{a^m}=a^{-m} )

=(x^{12}.x^{-2})\times (z^{11}.z^{-4})

=x^{12-2}\times z^{11-4} ( by using the identity a^m.a^n=a^{m+n} )

=x^{10}\times z^7

=x^{10}z^7

∴ \frac{x^{12}\times z^{11}}{x^2\times z^4}=x^{10}z^7

<h3>The correct simplification for the given expression \frac{x^{12}\times z^{11}}{x^2\times z^4} is x^{10}z^7</h3><h3>Hence option A) x^{10}z^7 is correct answer.</h3>

4 0
3 years ago
These are all my points, if you can do every single question you will get 55 points
Arturiano [62]

1) 6

2) 9

3) 7

4) 1

5) 8

6) 3

7) 0

8) 2

9) 4

10) 5

8 0
3 years ago
What is the slope of a line <br> parallel to the line 4x – 3y = 16?
galben [10]
"Parallel" means the same, which means the slope you find. The formula for slopes is y=mx+b, so we need to put this equation in the right order for that. ('m' is the slope.)
 Add 4x to each side, and get -3y=16+4x. Rearrange it to get it in the right order (y=mx+b).
This is -3y=4x+16. So the number in front of 'x' is 'm', which is the slope. You never actually see 'm', it is represented by a number. So four is the slope.
5 0
3 years ago
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