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Rufina [12.5K]
3 years ago
10

The legs of a right triangle are 12 centimetres and 16 centimeters. What is the length of the hypotenuse?

Mathematics
2 answers:
hodyreva [135]3 years ago
8 0
Answer: c=20 Explanation in photo

antoniya [11.8K]3 years ago
5 0

Answer:

20 cm

Step-by-step explanation:

Using Pythagoras' identity in the right triangle.

The square on the hypotenuse h is equal to the sum of the squares on the other 2 sides, that is

h² = 12² + 16² = 144 + 256 = 400 ( take the square root of both sides )

h = \sqrt{400} = 20

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Eduardwww [97]

Answer:

Step-by-step explanation:

Using annuity, each sisters saving can be calculated.

Annuity formula:

Fv = PMT (( 1 + i)^n - 1) / i

where Fv is the future value (amount), PMT is the periodic payment ( $2000),

i is the rate per period ( 7%) and n is the number of payments.

Using the above formula to calculate each sister savings after their respective years of savings

Jane ( between 25 - 35, with n = 10 years)

Fv = 2000 (( 1 + 0.07)^10 - 1 ) / 0.07 = $ 27634.3

Joan ( between 35 - 65, with n = 30 years)

Fv = 2000((1 + 0.07)^30 - 1) / 0.07 = $ 188914

Joan actually have invested more since over 30 years she has invested $60000 while Jane on the other hand invested for 10 years which equals $20000 and Joan has more money after retirement. Going by the result it will make sense for Jane to emulate Joan or increase her number of years of saving in other to improve her retirement saving significantly close to Joan or even more.

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3 years ago
Use the method of lagrange multipliers to find
Yanka [14]

Answer:

a) The function is: f(x, y) = x + y.

The constraint is: x*y = 196.

Remember that we must write the constraint as:

g(x, y) = x*y - 196 = 0

Then we have:

L(x, y, λ) = f(x, y) +  λ*g(x, y)

L(x, y,  λ) = x + y +  λ*(x*y - 196)

Now, let's compute the partial derivations, those must be zero.

dL/dx =  λ*y + 1

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dL/dλ = (x*y - 196)

Those must be equal to zero, then we have a system of equations:

λ*y + 1 = 0

λ*x + 1 = 0

(x*y - 196) = 0

Let's solve this, in the first equation we can isolate  λ to get:

λ = -1/y

Now we can replace this in the second equation and get;

-x/y + 1 = 0

Now let's isolate x.

x = y

Now we can replace this in the last equation, and we will get:

(x*x - 196) = 0

x^2 = 196

x = √196 = 14

then the minimum will be:

x + y = x + x = 14 + 14 = 28.

b) Now we have:

f(x) = x*y

g(x) = x + y - 196

Let's do the same as before:

L(x, y, λ) = f(x, y) +  λ*g(x, y)

L(x, y, λ) = x*y +  λ*(x + y - 196)

Now let's do the derivations:

dL/dx = y + λ

dL/dy = x + λ

dL/dλ = x + y - 196

Now we have the system of equations:

y + λ = 0

x + λ = 0

x + y - 196 = 0

To solve it, we can isolate lambda in the first equation to get:

λ = -y

Now we can replace this in the second equation:

x - y = 0

Now we can isolate x:

x = y

now we can replace that in the last equation

y + y - 196 = 0

2*y - 196 = 0

2*y = 196

y = 196/2 = 98

The maximum will be:

x*y = y*y = 98*98 = 9,604

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Answer:

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Step-by-step explanation:

180+ (180* 18%)= Total Cost

180+ 32.40= Total Cost

212.40= Total Cost

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Based on the attendance at past picnics, Luis expects 95% of the students in his class to attend this years picnic. If 120 stude
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Answer:

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Answer:

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3n-6=33

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