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ella [17]
3 years ago
5

An employment agency specializing in temporary construction help pays heavy equipment operators $ 134 per day and general labore

rs $ 92 per day. If thirty-eight people were hired and the payroll was $ 4756 , how many heavy equipment operators were​ employed? How many​ laborers?
Mathematics
1 answer:
Likurg_2 [28]3 years ago
5 0

x=heavy equipment

y= general labor

x+y=38

x=38-y

134x + 92y=4756

134(38-y)+92y =4756

5092-134y+92y=4756

-42y = -336

y = -336/-42 = 8

x=38-8=30

check 30*134 =4020

8*92 = 736

4020+736 = 4756


 8 general laborers

30 heavy equipment operators

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6 labour complete a work in 12 days. How many labours should added to complete the works in 8 days?​
mario62 [17]

Answer:

9 labours

Step-by-step explanation:

In order to solve this, we must know which kind of proportionality is this. There are two types of proportions, direct and indirect/inverse proportions. In direct proportion, if one quantity increases, the other quantity also increases.

In indirect proportion, if one quantity increases, the other decreases and vice versa.

As per this question, we know if the number of labour increases, the number of days to complete a work decreases, thus proving that this is an indirect/inverse proportion.

6 labours => 12 days

x labours =>  8 days

Since its an inverse proprotion, multiply 6 with 12, and x with 8.

8x = 6 × 12

x = \frac{6*12}{8}

∴ x = <u>9 labours</u>

7 0
2 years ago
Which of the following matrices is the solution matrix for the given system of equations? x + 5y = 11 x - y = 5
givi [52]
<h2>The required solution is x = 6 and y = 11 </h2>

Step-by-step explanation:

Given system of equations are

x+5y = 11 and x-y =5

A= \left[\begin{array}{cc}1&5\\1&-1\end{array}\right]                            X=\left[\begin{array}{c}x\\y\end{array}\right]

and          B= \left[\begin{array}{c}11\\5\end{array}\right]

∴AX=B

adj A = \left[\begin{array}{cc}{-1}&{-5}\\{-1}&1\end{array}\right]

A= \left|\begin{array}{cc}1&5\\1&-1\end{array}\right|=-6

∴A^{-1} =\frac{adj A}{|A|}

So,A^{-1} =\frac{ \left[\begin{array}{cc}{-1}&{-5}\\{-1}&1\end{array}\right]}{-6}

A^{-1} ={ \left[\begin{array}{c \c}  {{\frac{1}{6} }}&{\frac{5}{6}}\ \\  {{\frac{1}{6} }}&{\frac{-1}{6}} \end{array}\right]}

X =A^{-1}\times B

⇒\left[\begin{array}{c}x\\y\end{array}\right] ={ \left[\begin{array}{c \c}  {{\frac{1}{6} }}&{\frac{5}{6}}\ \\  {{\frac{1}{6} }}&{\frac{-1}{6}} \end{array}\right]} \times \left[\begin{array}{c}11\\5\end{array}\right]

⇒\left[\begin{array}{c}x\\y\end{array}\right] ={ \left[\begin{array}{c}  {6}\\  {11} \end{array}\right]}

∴ x= 6 and y = 11

The required solution is x = 6 and y = 11

7 0
3 years ago
from the edge of a cliff 180m high, the angles of depression of two boats at sea are 43° and 52° respectively what is the distan
MrRa [10]

tan 52 = 180/a; a = 180/tan 52

tan 43 = 180/b; b = 180/tan 43

you need to calculate, a-b = 180/tan 52 - 180/tan 43

substitute the value of tan thetas, and calculate it simply...


8 0
3 years ago
Mark is in training for a bicycle race. He needs to ride 50 kilometers a week as part of his training. He rode 18.23 kilometers
kirill115 [55]

the answer is B-about 18km


7 0
3 years ago
Jessica owns 1/8 of a company worth $56,000. What is the value of
rosijanka [135]
7000

1/8th in percentage form is 12.5%
12.5% of 56000 is 7000
8 0
3 years ago
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