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Nonamiya [84]
3 years ago
12

a right triangle has a hypotenuse with a length of 20. the lengths of the legs are whole numbers. what are the lengths of the le

gs​
Mathematics
1 answer:
Y_Kistochka [10]3 years ago
5 0

Answer:

12;16

Step-by-step explanation:

The Pythagorean theorem states that

a^2+b^2=c^2 where a and b are legs of a triangle, and c is the hypotenuse.

This means that we have to find 2 values that once squared, add up to 400. (20^2)

Based on this, we can use the values of 12 and 16 to satisfy this.

12^2+16^2=144*256=400

Therefore, the legs of the triangle are 12 and 16.

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In triangle ABC, AB = 5 inches and BC = 3 inches. Which of the choices represents all possible values for AC, inches?
shusha [124]

Answer:

-2 < AC < 8

Step-by-step explanation:

The last side has to be less than the sum of the other 2 sides, or less than 8. The only answer choice with this is the 3rd one.

8 0
2 years ago
Each of these extreme value problems has a solution with both a maximum value and a minimum value. Use Lagrange multipliers to f
tino4ka555 [31]

Answer:

The minimum value of the given function is f(0) = 0

Step-by-step explanation:

Explanation:-

Extreme value :-  f(a, b) is said to be an extreme value of given function 'f' , if it is a maximum or minimum value.

i) the necessary and sufficient condition for f(x)  to have a maximum or minimum at given point.

ii)  find first derivative f^{l} (x) and equating zero

iii) solve and find 'x' values

iv) Find second derivative f^{ll}(x) >0 then find the minimum value at x=a

v) Find second derivative f^{ll}(x) then find the maximum value at x=a

Problem:-

Given function is f(x) = log ( x^2 +1)

<u>step1:</u>- find first derivative f^{l} (x) and equating zero

  f^{l}(x) = \frac{1}{x^2+1} \frac{d}{dx}(x^2+1)

f^{l}(x) = \frac{1}{x^2+1} (2x)  ……………(1)

f^{l}(x) = \frac{1}{x^2+1} (2x)=0

the point is x=0

<u>step2:-</u>

Again differentiating with respective to 'x', we get

f^{ll}(x)=\frac{x^2+1(2)-2x(2x)}{(x^2+1)^2}

on simplification , we get

f^{ll}(x) = \frac{-2x^2+2}{(x^2+1)^2}

put x= 0 we get f^{ll}(0) = \frac{2}{(1)^2}   > 0

f^{ll}(x) >0 then find the minimum value at x=0

<u>Final answer</u>:-

The minimum value of the given function is f(0) = 0

5 0
3 years ago
If a person blinks their eyes once every 3 minutes on the average, then how many times
Paha777 [63]

Answer:

480

Step-by-step explanation:

If a person blinks every 3 minutes, there is 60 minutes in 1 hour. So, multiply 60 by 24 (hours a day), 60 x 24 = 1440 minutes.

1440/3 = 480

5 0
3 years ago
X+25+7x-65=180 solve for x
kozerog [31]
X = 27.5

8x = 220, so 220/8 = 27.5
6 0
2 years ago
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The table shows the volume V (in cubic feet) of a cube with a side length of x feet.
Dmitriy789 [7]
It has the same side of the length and feet
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