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yanalaym [24]
3 years ago
6

Find the missing side to the triangle in the attached image.

Mathematics
2 answers:
PolarNik [594]3 years ago
6 0

Answer:

<h2>15</h2>

Solution,

Hypotenuse(h)= 25

Base(b)= 20

perpendicular (p)= X

Now,

Using Pythagorean theorem:

{p}^{2}  =  {h}^{2}  -  {b}^{2}  \\  {x}^{2}  =  {25}^{2}  -  {20}^{2}  \\  {x}^{2}  = 625 - 400 \\  {x}^{2}  = 225 \\ x =  \sqrt{225}  \\ x =  \sqrt{ {15}^{2} } \\ x = 15

Hope this helps...

Good luck on your assignment..

Romashka [77]3 years ago
4 0

Answer:

x = 15

Step-by-step explanation:

Using Pythagoras' identity in the right triangle.

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

x² + 20² = 25² , that is

x² + 400 = 625 ( subtract 400 from both sides )

x² = 225 ( take the square root of both sides )

x = \sqrt{225} = 15

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Step-by-step explanation:

Part A:

So the height is going to be x when you fold the sides up. So that's one part of the volume but for the width it was going to be 4 but since two corners were cut out with the length x the new width is going to be (4-2x). The same thing applies for the length which should be 8 inches but since two corners were removed with the length x it's now (8-2x)

v = x(4-2x)(8-2x)

Part B:

The volume can be graphed although there must be a domain restriction since the height, width, or length cannot be negative. So let's look at each part of the equation

so for the x in front it must be greater than 0 to make sense

for the (4-2x), the x must be less than 2 or else the width is  negative.

for the (8-2x) the x must be less than 4 or else the length is negative

so the domain is going to be restricted to 0 < x < 2 so all the dimensions are greater than 0

By using a graphing calculator you can see the maximum of the given equation with the domain restrictions is 0.845 which gives a volume of 12.317  

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2 years ago
The radius of a circle is 8 feet. What is the area of sector bounded by a 90° arc?
Lera25 [3.4K]

Since 90 degree is 1/4 of a circle, the area will be 1/4 th area of the full circle.

The radius is given by, r = 8 ft, therefore, the area of the full circle is,

\begin{gathered} A=\pi\times r^2 \\ A=3.14\times8^2=200.96ft^2 \end{gathered}

Therefore, the area of the sector is,

A^{\prime}=\frac{1}{4}\times200.96ft^2=50.24ft^2\begin{gathered} A^{\prime}=\frac{\theta}{360}\times\pi\times r^2 \\ \text{ =}\frac{\text{90}}{360}\times\pi\times8^2 \\ \text{ =}\frac{1}{4}\pi\times64=16\pi \end{gathered}

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Using technology, determine the semi-annual payment on a 6 year loan of $19,264 at 7.2% compounded semi-annually. Round you answ
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D is the corrrect answer 
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What is 8% of 150 when you multiply it
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8% = 0.08
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3 years ago
10. The sum of the digits of a three-digit number is 11. If the digits are reversed, the new number is 46
Zarrin [17]

Answer:

hope this helps

Step-by-step explanation:

The sum of the digits of a three-digit number is 11.

If the digits are reversed, the new number is 46 more than five times the old number.

If the hundreds digit plus twice the tens digit is equal to the units digit, then what is the number?

:

Write an equation for each statement:

:

"The sum of the digits of a three-digit number is 11."

x + y + z = 11

:

The three digit number = 100x + 10y + z

The reversed number = 100z + 10y + x

:

" If the digits are reversed, the new number is 46 more than five times the old number."

100z + 10y + x = 5(100x + 10y + z) + 46

100z + 10y + x = 500x + 50y + 5z + 46

combine on the right

0 = 500x - x + 50y - 10y + 5z - 100z + 46

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:

"the hundreds digit plus twice the tens digit is equal to the units digit,"

x + 2y = z

x + 2y - z = 0

:

Three equations, 3 unknowns

:

x + y + z = 11

x +2y - z = 0

-----------------Addition eliminates z

2x + 3y = 11

From the 2nd equation statement, we know that the 1st original digit has to be 1

2(1) + 3y = 11

3y = 11 - 2

3y = 9

y = 3 is the 2nd digit

then

1 + 3 + z = 11

z = 11 - 4

z = 7

:

137 is the original number

:

:

Check solution in the 2nd statement

If the digits are reversed, the new number is 46 more than five times the old number."

731 = 5(137) + 46

731 = 685 + 46

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3 years ago
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