Mathematics, 26.03.2020 22:54 ashleypere99

A company that rents small moving trucks wants to purchase 25 trucks with a combined capacity of 28,000 cubic feet. Three different types of trucks are available: a 10-foot truck with a capacity of 350 cubic feet, a 14-foot truck with a capacity of 700 cubic feet, and a 24-foot truck with a capacity of 1,400 cubic feet. How many of each type of truck should the company purchase

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Answer from: anishivaturi123

We have 4 solutions:

No 10-foot truck, 10 14-foot trucks, and 15 24-foot trucks2 10-foot trucks, 7 14-foot trucks, and 16 24-foot trucks4 10-foot trucks, 4 14-foot trucks, and 17 24-foot trucks6 10-foot trucks, 1 14-foot trucks, and 18 24-foot trucks

Step-by-step explanation:

Let the number of 10-foot truck with a capacity of 350 cubic feet purchased=a

Let the number of 14-foot truck with a capacity of 700 cubic feet purchased=b

Let the number of 24-foot truck with a capacity of 1,400 cubic feet purchased=c

The company wants to purchase 25 trucks, therefore.

a+b+c=25

Furthermore, the combined capacity of the trucks is 28,000 cubic feet.

350a+700b+1400c=28000

Since the number of equations is less than the number of variables, you can not use a matrix equation to solve this problem. The solution is most easily found using an augmented matrix.

The augmented matrix is presented below:

$\left[\begin{array}{ccc|c}1&1&1&25\\350&700&1400&28000\end{array}\right]$

Using the calculator, the reduced row echelon form is:

$\left[\begin{array}{ccc|c}1&0&-2&-30\\0&1&3&55\end{array}\right]$

where

a- 2c=-30 means a =2c-30

b+3c=55 means b= 55-3c

We alter the value of c as long as neither a nor b becomes negative. Suitable values for c are 15, 16, 17, and 18:

$\left|\begin{array}{|c||c||c|}a=2c-30&b=55-3c&c\\0&10&15\\2&7&16\\4&4&17\\6&1&18\end{array}\right|$

We can easily verify that, for each solution, the number of trucks adds up to 25 and the fleet capacity is 28,000 cubic feet.

We therefore have 4 solutions:

Answer from: Quest

First step is to get rid of the square root. remember that a square root is the same as raising to the (1/2) power. see below: $\sqrt{\frac{ {72x}^{16} }{ {50x}^{{{36} }}}} = \frac{ { \sqrt{72}x}^{ {16}^{ (\frac{1}{2}) } } }{ { \sqrt{50} x}^ {{36}^{ (\frac{1}{2}) } }}$ multiply exponents per exponent rules to get: $\frac{ { \sqrt{72}x}^{8} }{ { \sqrt{50}x}^{18} }$ remember you subtract exponents from the denominator and add exponents in the numerator so: $\sqrt{ \frac{72}{ 50}} \times ( {x}^{(8 - 18) } ) = \sqrt{ \frac{36}{25} } \times ( {x}^{ - 10} )$ simplify further: $\frac{6}{5} {x}^{ - 10} = \frac{6}{5 {x}^{10} }$ so a is the correct choice. if you don't understand this google exponent rules and it will you understand. look at the image results.
Plz hurrywhat is the simplified form of ? assume x ≠ 0.

Plz hurrywhat is the simplified form of  ? assume  x  ≠ 0.

Answer from: Quest

a) 0

step-by-step explanation:

i^413 x i^0 = 0 as any number multiplied by a zero is

happy to

pls mark as brainliest.

How do you solve this? show work, if possible. you!

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A company that rents small moving trucks wants to purchase 25 trucks with a combined capacity of 28,...