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Troyanec [42]
3 years ago
5

The hypotenuse of a right triangle is 7 inches longer than the base and 14 inches longer than the height. the permeter of the tr

iangle is 84 inches. find its area
Mathematics
1 answer:
emmainna [20.7K]3 years ago
3 0
To determine the area of a triangle, we calculate one half of the product of the base and the height of the triangle so we need data on its base and its height. We are given the following:

Hypotenuse = 7 + base = 14 + height
Perimeter = 84 inches

The perimeter of the triangle is equal to the sum of the three sides of the triangle which are the height, base and hypotenuse. So,

Perimeter = height + base + hypotenuse = 84

We let x = height and y = base. We calculate area as follows:

84 = x + y + (7 + y)
77 = x + 2y
x = 77 -2y

Hypotenuse is related to the other sides by the Pythagorean theorem.

Hypotenuse^2 = (x^2 + y^2)
(14 + x)^2 = x^2 + y^2
(14 + (77-2y))^2 = (77-2y)^2 + y^2
(91-2y)^2 = (77-2y)^2 + y^2

Solving for y and x
y = 28
x = 21

Area = (28)(21) / 2 = 294 square inches 
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In how many places did the japanese troops land on december 8, 1941?
bezimeni [28]
The first battle in the Pacific between the empire of Japan against the US and its allies took place on December 8, 1941. The Japanese forces began their conquest on the pacific islands and it started its invasion of the Malaya. They were held by a resistance of British Indian fighter however it was not enough to hold off the overwhelming Japanese force.
7 0
3 years ago
Express your answer in scientific notation. 4.9\cdot 10^{5} - 5.8 \cdot 10^{4} =4.9⋅10 5 −5.8⋅10 4 =4, point, 9, dot, 10, start
tatyana61 [14]

Answer:

4.32*10^{5}

Step-by-step explanation:

Given the expression 4.9*10^{5}-5.8*10^{4}, to solve the expression, we need to write both scientific notation to the same power of 10.

5.8*10^{4} is \ expressed\  as \ 0.58*10^{5}

The expression above becomes 4.9*10^{5}-0.58*10^{5}. On taking the difference;

4.9*10^{5}-0.58*10^{5}\\= (4.9-0.58)*10^{5} \\= 4.32*10^{5}

The final expression gives the right answer

4 0
3 years ago
Try to work out this equation! Type your answer below!<br> 65 x 589 x 653 - 65 + 36
neonofarm [45]

Answer:

25000076

Step-by-step explanation:

Hope this helps! :)

8 0
3 years ago
Write the vector u as a sum of two orthogonal vectors, one of which is the vector projection of u onto v
blagie [28]
U = ( -8 , -8)
v = (-1 , 2 )
<span>the magnitude of vector projection of u onto v =
</span><span>dot product of u and v over the magnitude of v = (u . v )/ ll v ll
</span>
<span>ll v ll = √(-1² + 2²) = √5
</span>
u . v = ( -8 , -8) . ( -1 , 2) = -8*-1+2*-8 = -8 
∴ <span>(u . v )/ ll v ll = -8/√5</span>
∴ the vector projection of u onto v = [(u . v )/ ll v ll] * [<span>v/ ll v ll]
</span>
<span>                          = [-8/√5] * (-1,2)/√5 = ( 8/5 , -16/5 )
</span>
The other orthogonal component = u - ( 8/5 , -16/5 )
                                   = (-8 , -8 ) - <span> ( 8/5 , -16/5 ) = (-48/5 , -24/5 )
</span>
So, u <span>as a sum of two orthogonal vectors will be
</span>
u = ( 8/5 , -16/5 ) + <span>(-48/5 , -24/5 )</span>










3 0
3 years ago
Read 2 more answers
An insurance company sells a one-year term life insurance policy to an 80-year-old woman. The woman pays a premium of $1000. If
Gekata [30.6K]

Answer:

The profit of the company will be $224.85

Step-by-step explanation:

Let the equation of profit be termed as E(x)

we are given

amount of purchasing the policy (let a)= $1000

probability that women will live for at least 1  year (let b) = 0.9581

amount lost by insurance company if the women dies (let c) = 18,500-1000 = 17,500

the probability woman dies within one year (let d) = 1-0.9581=0.0419

the equation will be

E(x) of profit= a*b - c*d = 1000*0.9581 - 17500*0.0419

                    = 958.1 - 733.25

                    =  224.85

7 0
3 years ago
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