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SSSSS [86.1K]
2 years ago
12

HURRY PLEASE!! What is the solution to the system of equations?

Mathematics
1 answer:
NikAS [45]2 years ago
5 0

Answer:

(9/2, -1/2)

Step-by-step explanation:

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One month, ruby worked 6 more hours than Issac, and Svetlana worked 4 times as many hours as Ruby. Together they worked 126 hour
garik1379 [7]
Ruby's hours will represent x+6
Svetlana's hours will represent 4(x+6)
Issac will represent x.

The equation would read:
x+(x+6)+(4(x+6))=126
x+x+6+4x+24=126
6x+30=126
Subtract 30 from both sides.
6x=96
Divide 6 on both sides to get x by itself.
x=16

So:
Issac worked 16 hours
Ruby worked 22 hours
Svetlana worked 88 hours.

To check your answer, plug in the values:
16+22+88=126
126=126

Hope this helps.
8 0
3 years ago
Jenny went to the store with $10 and returned home
stira [4]

Answer:

The milk is priced at $1.74/gallon

Step-by-step explanation:

If Jenny started out with $10 and ended up with $1.30 in change, she must have spent $10 - $1.30, or $8.70.

                                                        $8.70

Then the unit price for the milk is ---------- = $1.74 per gallon

                                                         5 gal

8 0
2 years ago
Write the equation of a line in slope intercept form with the given slope and y-intercept
k0ka [10]

Answer:

Input work is the work done on a machine as the input force acts through the input distance. This is in contrast to output work which is a force that is applied by the body or system to something else. Output work is the work done by a machine as the output force acts through the output distance.Jan 15, 2020 hsysvd xhs dhdb shsbdhd dhs dys dhd shdbdyd hzgsvdyd xgdbd

5 0
3 years ago
Trigonometry questions. PLEASE HELP WILL GIVE LOTS OF POINTS
nalin [4]

Step-by-step explanation:

It is all done I am not sure if it is correct

7 0
3 years ago
Southern Oil Company produces two grades of gasoline: regular and premium. The profit contributions are $0.30 per gallon for reg
Contact [7]

Answer:

a) MAX--> PC (R,P) = 0,3R+ 0,5P

b) <u>Optimal solution</u>: 40.000 units of R and 10.000 of PC = $17.000

c) <u>Slack variables</u>: S3=1000, is the unattended demand of P, the others are 0, that means the restrictions are at the limit.

d) <u>Binding Constaints</u>:

1. 0.3 R+0.6 P ≤ 18.000

2. R+P ≤ 50.000

3. P ≤ 20.000

4. R ≥ 0

5. P ≥ 0

Step-by-step explanation:

I will solve it using the graphic method:

First, we have to define the variables:

R : Regular Gasoline

P: Premium Gasoline

We also call:

PC: Profit contributions

A: Grade A crude oil

• R--> PC: $0,3 --> 0,3 A

• P--> PC: $0,5 --> 0,6 A

So the ecuation to maximize is:

MAX--> PC (R,P) = 0,3R+ 0,5P

The restrictions would be:

1. 18.000 A availabe (R=0,3 A ; P 0,6 A)

2. 50.000 capacity

3. Demand of P: No more than 20.000

4. Both P and R 0 or more.

Translated to formulas:

Answer d)

1. 0.3 R+0.6 P ≤ 18.000

2. R+P ≤ 50.000

3. P ≤ 20.000

4. R ≥ 0

5. P ≥ 0

To know the optimal solution it is better to graph all the restrictions, once you have the graphic, the theory says that the solution is on one of the vertices.

So we define the vertices: (you can see on the graphic, or calculate them with the intersection of the ecuations)

V:(R;P)

• V1: (0;0)

• V2: (0; 20.000)

• V3: (20.000;20.000)

• V4: (40.000; 10.000)

• V5:(50.000;0)

We check each one in the profit ecuation:

MAX--> PC (R,P) = 0,3R+ 0,5P

• V1: 0

• V2: 10.000

• V3: 16.000

• V4: 17.000

• V5: 15.000

As we can see, the optimal solution is  

V4: 40.000 units of regular and 10.000 of premium.

To have the slack variables you have to check in each restriction how much you have to add (or substract) to get to de exact (=) result.  

3 0
3 years ago
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