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ipn [44]
3 years ago
6

The shortest side of a fight triangle measures20 m. The lengths of the other two sides are censecutive odd integers. Find the le

ngth of the two aides
Mathematics
1 answer:
slamgirl [31]3 years ago
6 0
A² + b² = c²
20² + n² = (n+2)²
400+ n² = (n+2)(n+2)
400 + n²=n² + 2n + 2n +4
400 + n² = n² +4n +4
400 + n²-n² = n²-n² + 4n+4
400 = 4n + 4
400-4 = 4n +4-4
396 = 4n
396/4 = 4n/4
n= 99

20²+ 99² = (99+2)²
400 + 9801 =10201
10201=10201
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Simplify this equation <br> Thanks a lot!!!
den301095 [7]

Answer:

-1

Step-by-step explanation:

We need to simplify the given expression . The given expression is ,

\rm\implies ( 2 \sqrt6 +5)^{2n-1} ( 2\sqrt6 - 5)^{2n-1}

Here we can see that the power of the both exponent is same that is (2n+1) . Recall the property of exponents ,

\bf\implies a^m \times b^m = (ab)^m

Using this property , we have ,

\rm\implies ( 2 \sqrt6 +5)^{2n-1} ( 2\sqrt6 - 5)^{2n-1}

This can be written as ,

\rm\implies\{( 2 \sqrt6 +5) ( 2\sqrt6 - 5)\}^{2n-1}

Simplifying using ( a+b)(a-b) = a² - b² ,

\rm\implies\{( 2 \sqrt6)^2 -5^2 \}^{2n-1}\\\\\rm\implies ( 24 - 25)^{2n-1}

Subtracting the numbers inside the brackets ,

\rm\implies (-1)^{2n - 1 }

Now we know that every odd number is in the form of 2n -1 , where n is any integer. Therefore , the <u>power is odd</u> .

Since the base is (-1) , for even power it is 1 and for odd power it is -1 . Therefore the final answer is ,

\rm\implies\boxed{\quad \red{ -1 }\quad }

<u>Hence </u><u>the</u><u> </u><u>required</u><u> answer</u><u> is</u><u> </u><u>(</u><u>-</u><u>1</u><u>)</u><u> </u><u>.</u>

4 0
3 years ago
Answer the following questions CORRECTLY I will know if this is wrong. I WILL REPORT ANY INCORRECT ANSWERS!
Alexxx [7]

Hi There!

Answer: Bowler 2

Why: if you notice that line in the box plot shows the median and it specifically shows that the meadian is 20 or so greater than Bowler 1.

4 0
4 years ago
Read 2 more answers
The length of a rectangle is 5 inches more than 3 times the width. If the area of the rectangle is 68 square inches, what is the
Paladinen [302]

Answer:

Width=4, and Length=17

Step-by-step explanation:

first you will make a variable for the width which i will say is x

now make it an equation (3x+5) (x) = 68

then solve 3x^2+5x=68

then 3x^2+5x-68=0

then x=4

then you have to substitute so 3(4)+5= 17 and 4

6 0
3 years ago
What’s the answer to the top question and steps how to solve?
Leviafan [203]

Answer:

-3.69

Step-by-step explanation:

Exponential equations can be solved by taking Ln (natural logarithm) of both sides. The rule we need to know is:

Ln(a^b)=bLn(a)

Now lets work out this problem:

16^{2x+3}=13^{x-1}\\Ln(16^{2x+3})=Ln(13^{x-1})\\(2x+3)Ln(16)=(x-1)Ln(13)

Using calculator, we take the values of Ln 16 and Ln 13 as:

Ln 16 = 2.7726

Ln 13 = 2.5649

Now, we can solve for x:

(2x+3)Ln(16)=(x-1)Ln(13)\\(2x+3)2.7726=(x-1)2.5649\\5.5452x+8.3178=2.5649x-2.5649\\2.9803x=-10.8827\\x=-3.69

x is -3.69 (rounded to 2 decimal places)

3 0
4 years ago
Which function has a graph with a vertical
raketka [301]

Answer:

f(x)=\frac{1}{x-7}-3, see the graph attached for a visual reference.

Step-by-step explanation:

Vertical asymptotes are only present in rational functions where the parent function f(x)=\frac{1}{x} has a vertical asymptote at the line x=0 and a horizontal asymptote at the line y=0. Because the vertical asymptote has to be x=7, the denominator must be x-7 in order for the denominator to equal 0. For the horizontal asymptote to be y=-3, then 3 must be subtracted from the rational function. Therefore, the function that has these asymptotes is f(x)=\frac{1}{x-7}-3.

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3 years ago
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