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inn [45]
3 years ago
13

Sebastian is working to summer jobs, making $8 per hour walking dogs and $10 per hour clearing tables. In a given week, he can w

ork no more than 12 total hours and must earn a minimum of $100. If X represents the number of hours walking dogs and Y represents the number of hours clearing tables, right and solve a system of inequalities graphically and determine one possible solution.

Mathematics
1 answer:
True [87]3 years ago
8 0

Answer:

The graph in the attached figure

One possible solution is the ordered pair (3,8)

see the explanation

Step-by-step explanation:

Let

x ---> the number of hours walking dogs

y ----> the number of hours clearing tables

we know that

He can work no more than 12 total hours

so

x+y\leq 12 ----> inequality A

He must earn a minimum of $100

so

8x+10y\geq 100 ----> inequality B  

Solve the system of inequalities by graphing

using a graphing tool

The solution is the triangular shaded area

see the attached figure

Remember that

If a ordered pair is a solution of the system of inequalities, then the ordered pair must lie in the shaded area of the solution set (the ordered pair makes true both inequalities)

so

One possible solution is the ordered pair (3,8)

That means

In the given week, the number of hours walking dogs was 3 and the number of hours clearing tables was 8

<u><em>Verify algebraically</em></u>

Substitute the value of x and the value of y in the inequality A and in the Inequality B

<em>inequality A</em>

3+8\leq 12

11\leq 12 ----> is true

<em>Inequality B</em>

8(3)+10(8)\geq 100

104\geq 100 ---> is true

therefore

the ordered pair (3,8) is a possible solution of the system

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(y-y1)=m(x-x1) where m is the slope and (x1 and y1 ) are the points

(y-2) = 3(x-2)

y-2=3x-6  add 2 to each side

y-2+2=3x-6+2

y=3x-4

5 0
3 years ago
On a manufacturer's assembly line, 3% of its merchandise comes off defective. If the company has 354 defective items, how many t
evablogger [386]

Answer: this is the steps to working the problem and the answer is 54: 3% means 3 out of each 100. if you have 100 items, 3% is just 3. You need more than 100 times as many (you want 354), so x must be more than 100 * 100, right? 3% of 10.62 is less than 1, and the problem says there are 354 :-)

Step-by-step explanation:

6 0
2 years ago
What is the equation of the line that is used to show the reflection of a relation and its inverse?
Artyom0805 [142]

The graph and inverse of a function are reflections of each other along the line y = x.

A relation made up of ordered pairs (x, y) has as its inverse the set of all ordered pairs (y, x).

When a point is mirrored over the line y = x, the x- and y-coordinates swap places. Similarly, when a point is mirrored over the line y = -x, the x- and y-coordinates swap places and become negated.

Therefore,

The point (x, y)'s reflection over the line y = x is (y, x).

The point (x, y)'s reflection over the line y = - x is (-y, -x).

Thus, the graph and inverse of a function are reflections of each other along the line y = x.

Learn more about reflections for inverse of a function at

brainly.com/question/14544356

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5 0
1 year ago
Nacy walked 50 minutes each day for 4 days last week . gillian walked 35 minutes each day for 6 days last week.how does the tota
frez [133]
G > n. gill walked more than nancy

3 0
3 years ago
seorang tukang kayu akan memotong tripleks berukuran 3,5 meter x 3,5 meter. tentukan luas dan keliling tripleks tersebut​
g100num [7]

Answer:

Part 1) A=12.25\ m^2

Part 2) P=14\ m

Step-by-step explanation:

<u><em>The question in English is</em></u>

A carpenter will cut plywood measuring 3.5 meters x 3.5 meters. Determine the area and perimeter of the plywood.

Part 1) Determine the area

we know that

The area of a square is given by the formula

A=b^2

where

b is the length side

we have

b=3.5\ m

substitute

A=3.5^2=12.25\ m^2

Part 2) Determine the perimeter

we know that

The perimeter of a square is given by the formula

P=4b

where

b is the length side

we have

b=3.5\ m

substitute

P=4(3.5)=14\ m

8 0
3 years ago
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