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Arte-miy333 [17]
2 years ago
7

The hypotenuse of a right triangle is 7 feet long. One leg is 4 feet longer than the other. Find the lengths of the legs, Round

to the nearest tenth of a foot
The length of the shorter leg is ft, and the length of the longer leg is ft.
(Do not round until the final answer. Then round to the nearest tenth as needed)
Help Me Solve This
View any
Mathematics
1 answer:
Andrews [41]2 years ago
5 0

Answer:

Shorter leg = 2.5 ft.

Longer leg = 6.5 ft.

Step-by-step explanation:

a^2 + b^2 = c^2

Because the hypotenuse = 7 ft, a^2 + b^2 = 49

To represent the two legs, we can use x and x+4.

x^2 + (x+4)^2 = 49

Simplifying this equation using FOIL gives us 2x^2 + 8x - 33 = 0.

Then, using the quadratic formula, we find that x = 2.5.

Thus, the shorter leg is 2.5 ft. and, when 4 is added, the longer leg is 6.5 ft.

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Suppose you are managing 15 employees, and you need to form three teams to work on different projects. Assume that all employees
Afina-wow [57]

Answer:

There are 17,418,240 different ways to choose the teams.

Step-by-step explanation:

Arrangements of n elements:

The number of possible arrangements of n elements is given by:

A_{n} = n!

In how many different ways can the teams be chosen so that the number of employees on each project are as follows: 9, 4, 2?

This is:

Arrangement of 9 elements, followed by an arrangement of 4 elements followed by an arrangement of 2 elements. So

T = A_{9}*A_{4}*A_{2} = 9!*4!*2! = 362880*24*2 = 17418240

There are 17,418,240 different ways to choose the teams.

7 0
3 years ago
Find the first four terms of the sequence using the recursive formula. ​
frozen [14]

Answer:

- 3, - 11, - 35, - 107

Step-by-step explanation:

Using the recursive formula with f(1) = - 3 , then

f(2) = - 2 + 3f(1) = - 2 + 3(- 3) = - 2 - 9 = - 11

f(3) = - 2 + 3f(2) = - 2 + 3(- 11) = - 2 - 33 = - 35

f(4) = - 2 + 3f(3) = - 2 + 3(- 35) = - 2 - 105 = - 107

Thus the first four terms are

- 3, - 11, - 35, - 107

3 0
3 years ago
Jim is investing in the stock market. Jim is hoping to earn $2,000 in interest in order to take a trip to Mexico. Stock A earns
Vanyuwa [196]

Given:

Total amount for investment = $32000

Rate of interest for Stock A = 4%

Rate of interest for Stock B = 7%

Jim is hoping to earn $2,000 in interest.

To find:

The amount of investments in Stock A and Stock B.

Step-by-step explanation:

Let amount of investments in Stock A = $x

Amount of investments in Stock B = $y

Total amount for investment = $32000

x+y=32000        ...(i)

Rate of interests in Stock A and Stock B are 4% and 7%. Total interests is $2000.

0.04x+0.07y=2000           ...(ii)

From (i) and (ii), we get

0.04x+0.07(32000-x)=2000

0.04x+2240-0.07x=2000

-0.03x=2000-2240

-0.03x=-240

Divide both sides by -0.03.

x=\dfrac{-240}{-0.03}

x=8000

Put x=8000 in (i).

8000+y=32000  

y=32000-8000  

y=24000  

Therefore, the amount of investments in Stock A and Stock B are $8000 and $24000 respectively.

8 0
2 years ago
Salim says he cannot simplify the expression a^m • a^n. Complete the statement about Salim's claim.
Shkiper50 [21]

Answer:

Salim can simplify that and the answer will be a^m^+^n

Step-by-step explanation:

This is because of the law of multiplying powers, which states that you can add the exponents if the base is the same. So, you just add m and n and put that as the exponent and you will have the answer.

3 0
3 years ago
Read 2 more answers
Which expression is equivalent to: (x +9)(x+3)
labwork [276]

Answer:

c

Step-by-step explanation:

x*x=x^2

x*9=9x

x*3=3x

9x+3x=12x

9x3=27

x^2+12x+27

6 0
3 years ago
Read 2 more answers
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