You earn
$10 per hour working as a manager at a grocery store.
You are required to work at the grocery store at least
8 hours per week. You also teach music lessons for
$15 per hour. You need to earn at least $120 per week,
$
do not want to work more than 20 hours
but you
per week.
a. Write and graph a system of linear inequalities
that represents the situation.
b. Identify and interpret a solution of the system.
c. Use the graph to determine whether you can work
8 hours at the grocery store and teach 1 hour of
music lessons.

You Earn$10 Per Hour Working As A Manager At A Grocery Store.You Are Required To Work At The Grocery

Answers

Answer 1

We want to get a system of inequalities that models the given situation.

The solutions are:

a) The system is:

x ≥ 8x*$10 + y*$15 ≥ $120x + y ≤ 20.y ≥ 0

And the graph can be seen at the end.

b) A solution can be x = 12 and y = 2

c) x = 8 and y = 1 is not a solution.

First, we need to define two variables:

x = number of hours working as a manager.y = number of hours teaching lessons.

a) First, we know that you must at least 8 hours per week in the grocery store, then:

x ≥ 8

We know that you need to earn at least $120 per week, then we have the inequality:

x*$10 + y*$15 ≥ $120

And you don't want to work more than 20 hours per week, this gives:

x + y ≤ 20.

We also add the trivial restriction:

y ≥ 0

Then the system is:

x ≥ 8x*$10 + y*$15 ≥ $120x + y ≤ 20.y ≥ 0

The graph can be seen at the end.

b) The solution region is the interception of the four shaded regions (is the dark blue part).

A solution in that region can be:

x = 12

y = 2

c) The point x = 8, y = 1 is graphed, you can see that it is outside the solution region, thus, this is not a solution.

If you want to learn more about inequalities, you can read:

https://brainly.com/question/2065712

You Earn$10 Per Hour Working As A Manager At A Grocery Store.You Are Required To Work At The Grocery

Related Questions

The Western inventory was written by 4 different authors. Author A wrote 1/4 of the books, author b wrote 5/16 of the books, and author c write 3/8 of the books. What part of the inventory did author D write?

Answers

Answer:

Author D write 1/16 of the total number of books.

Step-by-step explanation:

Let the total number of books be b.  Then the amounts written by the four authors would be represented by:

(1/4)A

(5/16)A

(3/8)A

( ? )A

Add these together, realizing that the LCD here is 16:

(4/16)A

(5/16)A

(6/16)A

( ? )  A

------------

(15/16)A must then equal the remainder of the work:  (16/16)A

Thus, Author D wrote (1/16)A of the books.  (Note that 4/16 + 5/16 + 6/16 + 1/16 = 1)

Author D write 1/16 of the total number of books.

A plane traveling to new york has 100 seats on board. if there are p passengers on the plane, which expression represents the number of empty seats there are on the plane

Answers

Hi math freindAnswer:

Step-by-step explanation:

Find the equation of the line L.

Answers

Answer:

y = ([tex]-\frac{1}{2}[/tex])x + 4

Step-by-step explanation:

(x1,y1) = (0,4) ; (x2,y2) = (8,0)

The equation will look like y=mx+b

Slope m = [tex]\frac{rise}{run}[/tex] =  [tex]\frac{y2-y1}{x2-x1}[/tex] = [tex]\frac{0-4}{8-0}[/tex] = [tex]\frac{-4}{8}[/tex] = [tex]-\frac{1}{2}[/tex]

Next, substitute either x1y1 or x2y2 (it's gonna give the same answer anyways) and m to the equation y=mx+b to find b.

y=mx+b

0 = ([tex]-\frac{1}{2}[/tex])8 + b

0 = -4 +b

0+4 = -4 +4 +b

b=4

Then substitute b and m to the equation y=mx+b

y = mx + b

y = ([tex]-\frac{1}{2}[/tex])x + 4


Which ordered pair represents a solution to both equations?


Answers

Answer:

-3,-1

its obvious because all you're doing is plting points

I need help

(No link please)

Answers

Answer:

the formula for finding the perimeter of a rectangle is P=2L+2W

an example of how to find the perimeter is

Explanation:

For a rectangle, its perimeter is the sum of all for sides.

The rectangle has a perimeter of 54. Find the lengths of the unknown side. That is, find S.

54=20+20+S+S

Simplify

54=40+2S

Solve for S

14=2S

S=7

Step-by-step explanation:

Mary is 4 years older than her sister Dawn.

In total the sisters have a combined age of 32.
Form an equation to show this. How old is Mary?

Answers

Mary is 18 . I’m not sure about the equation part

A
Plz help!!!!!! !!!!!!!!!!!

Answers

Answer:

R is at the ordered pair (4, -2)

Step-by-step explanation:

2-7/9x=5/6 without fractions

Answers

Answer:

x=0.6 repeating (meaning 6 is repeating so this is a repeating decimal)

Please help. Will give brainiest.
Write the equation of the line, in point-slope form. Identify (x 1 , y 1 ) as the point (-2, 2). Use the box provided to submit all of your calculations and final answers.

Answers

y-2=(-x+2)

point slope

equation is

y-y1=m(x-x1)

robin counts by 7 to 70. how many off numbers does robin say ?

Answers

Answer:

10

Step-by-step explain


Find the coordinates of the vertices of the triangle after a rotation
270° counterclockwise about the origin.

Answers

Answer:

it is a

Step-by-step explanation:

The coordinates of the triangle ΔC'D'E' will be (2, 1), (5, -3), and (2, -1). Then the correct option is C.

What is a transformation of a shape?

A point, line, or mathematical figure can be converted in one of four ways, and each has an effect on the object's structure and/or position.

Rotation does not change the shape and size of the geometry. But changes the orientation of the geometry.

The triangle ΔCDE is shown below.

The triangle ΔC'D'E' after a rotation 270° counterclockwise about the origin.

The triangle ΔCDE and ΔC'D'E' are shown on the graph.

The coordinates of the triangle ΔC'D'E' will be (2, 1), (5, -3), and (2, -1). Then the correct option is C.

The transformation of the triangle is given below.

More about the transformation of the shape link is given below.

https://brainly.com/question/27224339

#SPJ2

Help me on this mathwork please

Answers

Answer:

m∠I = 56°

m∠1 = 30°

Step-by-step explanation:

I WILL GIVE BRAINLIEST TO WHOMEVER ANSWERS (TRUTHFULLY) !!NO LINKS!!

Answers

Step-by-step explanation:

SAS ================

What it says:

If two sides and the angle between them on one triangle are congruent to the corresponding two sides and the angle between them on the other, the triangles are congruent.

Required information:

Two sets of congruent sides with a congruent angle between them

ASA ================

What it says:

If one side and both connected angles on one triangle are congruent to one side and both connected angles on the other, the triangles are congruent.

Required information:

One set of congruent sides with two sets of congruent angles on the sides

AAS ==================

What it says:

If two angles and the non-included side on one triangle are congruent to two angles and the non-included side on the other, the triangles are congruent.

Required information:

Two sets of congruent angles and one set of congruent non-included sides

HL =================

What it says:

If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg on the other, the triangles are congruent.

Required information:

Congruent hypotenuse and congruent leg

The base of the following pyramid is a square. If the volume of
the pyramid is 360 feet^3, what is the missing length? Round the
answer to the nearest hundredth.

Answers

Answer:

h = 12.52 ft

Step-by-step explanation:

volume of pyramid is 1/3*b*l. b is the base and l is the height we know that this equals 360 because it is given in the text. we also know b=8^2 since the base is a square so b=64. divide 360 by 1/3*64*pi to get l, l=5.3715. next we will use the pythagorean theorem to find h. first find the diagonal of the base: 8sqrt(2), now using the pythagorean theorem, we have h^2=5.3715^2 + (8sqrt(2))^2= 28.8528+128=156.8528. square root to get12.5241

helpppppp plzzzzzz is fue today

Answers

It’s 3 since it is going up on the y axis

Answer:

a) 3

Step-by-step explanation:

that's the correct answer

Please answer this question. No links :)

Answers

Step-by-step explanation:

[tex]\frac{rise}{run}[/tex]

Initially, as X increases, Y stays constant.

Then, between x = 3 and x = 5, the graph rises by 4 and runs by 2, or rises by 2 and runs by 1, so the slope is 2.

Between x = 5 and x = 9, the graph "rises" by -1 and runs by 1, so the slope is -1.

The greatest value of y is 4 at x = 5. (5, 4)

Answer:

Initially, as x increases, y remains constant.

Afterward, the slope of the graph of the function is equal to 2 for all x between x = 3 and x = 5.

The slope of the graph is equal to -1 between x = 5 and x = 9.

The greatest value of y = 4, and it occurs when x = 5.

Step-by-step explanation:

Slope = [tex]\frac{rise}{run}[/tex]

The rise is how much it increases by y (up or down), and the run is how much it increases by x (right or left).

From 3-5 the slope = [tex]\frac{4}{2}[/tex] =  2 → it goes up 2 units for every one unit right.

From 5-9 the slope = [tex]\frac{-4}{4}[/tex] = -1 → it goes down (-) 1 unit for every one unit right.

Graph the triangle with the given vertices. Find the length of the hypotenuse of the triangle. Assume a is a positive number.

X(0,0)

Y(a,2)

Z(a,0)

Answers

X(0,0)Y(a,2)

[tex]\\ \sf\longmapsto XY=\sqrt{x^2+y^2}[/tex]

[tex]\\ \sf\longmapsto XY=\sqrt{a^2+2^2}[/tex]

[tex]\\ \sf\longmapsto XY=\sqrt{a^2+4}[/tex]

[tex]\\ \sf\longmapsto XY=2+a[/tex]

The first three terms in a pattern are shown in the
image below. How many circles would be in the
5th term?

A. 10
B. 15
C. 18
D.20

Answers

Answer: 15

Step-by-step explanation: you basically add n per sequence.

0+1 = 1

1+2 = 3

3+3 = 6

6+4 = 10

10+5 = 15

Hope this helps

the answer is b which is 15

is this true or false |-2.9|> 2.6​

Answers

Hello! :)

I will start by explaining what the l l notation means.

It means "absolute value" or a number's distance from zero.

Absolute value is always positive. Remember this:

lal=a

l-al=a

Now, using this, let's solve our math problem.

l-2.9l>2.6

2.9>2.6

Is this statement true? Is 2.9 greater than 2.6? Yes, it is. Therefore, the statement is true.

Hope it helps.

Feel free to ask me if you have any questions.

~A smiley teen who adores helping others

[tex]MagicalNature[/tex]

Answer:

True

Step-by-step explanation:

The absolute value of -2.9 is 2.9.

So 2.9>2.6

Remember, the absolute value of a number is always nonnegative (positive or zero). If a number is negative, negating that number will make it positive.

An item priced at $500 is bought on hire purchase, where $200 deposit is required, along with 12 monthly instalments of $40. How much would be saved if bought with cash?

Answers

$180 dollars would be saved. The 12 monthly investments of $40 dollars would be enough to pay for the item alone. The second option totals $680 while the first is $500 as stated.

Write the equation of the line in fully simplified slope-intercept form. ​

Answers

Answer:

 y = 4/3x - 3

Step-by-step explanation:

1. Find two pints on the line: ((3,1) and (6, 5).

2. Find the slope: Slope = (change in y-values)/(change in the x-values).

   Slope = (5 - 1)/(6 - 3) = 4/3

3. Use the slope and one point and substitute into y = mx + b to solve for "b"

     y = mx + b                 slope = 4/3   and point (3, 1)

      1 = 4/3(3) + b              4/3 · 3/1 =  12/3 = 4

      1 = 4 + b

      1 - 4 = b

       -3 = b

4.  Write the equation of the line: m = 4/3 and b = -3  Substitute into y = mx + b

      y = 4/3x - 3

Solve the System of Equations
3x^2-5y^2= 22
2x^2+4y^2 = 22

Answers

Lets try one way to solve this system. First, we want to isolate one of the unkown, lets choose y, so we need to remove x from an equation. In order to remove x from an equation, thats what we are going to do :

Line 1:

(3x² - 5y²) * 2 = 22 * 2

6x² - 10y² = 44

We simply multiplied Line 1 by the number 2, this doesn't change anything on the nature of Line 1.

Line 2:

(2x² + 4y²)*3 = 22*3

6x² + 12y² = 66

We simply multiplied Line 2 by the number 3, this doesn't change anything on the nature of Line 2.

Solving your system of equations is exactly the same thing as solving this new system of equation :

6x² - 10y² = 44

6x² + 12y² = 66

It is exactly the same. But it is easier now, because we can remove x from the equation simply by subtracting line 2 from line 1 :

L1 - L2 :

(6x² - 10y²) - (6x² + 12y²) = 44 - 66

6x² - 10y² - 6x² - 12y² = - 22

- 22y² = - 22

y² = 1

y = + 1 or y = - 1

We know have the value of y, we just have to replace it in the equation to solve the entire system :)

3x² - 5y² = 22

since y² will always be equal to one, wether y = 1 or y = - 1, we can write :

3x² - 5 = 22

3x² = 22 + 5

3x² = 27

x² = 27/3

x² = 9

x = + 3 or x = - 3

So the solutions are the following couples in the form (x,y) :

S = { (3 ; 1) , (-3;1) , (3 ; - 1) , (-3 ; -1))

Good Luck

A pyramid has a square base of length of 12m. Given the slant height of the pyramid is 15 m, draw its net and hence, find its total surface area.

Answers

Answer:

the surface area is 180 if u use multiplication

Step-by-step explanation:

the surface is 0.8 if you use devide

the surface is 3 if u use subtract

and the surface is 27 if you use addition

correct me if I'm wrong :)

6th Grade End-of-Module Review Part-xwhole Name Adam Robertson Date 1/12/21 1. Jazzlyn is applying for a job online. She has completed 12 questions. Throughout the application, a bar shows up to represent what percentage of questions she's completed. The progress bar currently shows 25%How many questions are there for the job application? Use a table, diagram, or equation to justify your answer.​

Answers

Answer:

48 questions.

Step-by-step explanation:

x is for the unknown variable, the number you are trying to figure out.

12= 25%x

if you convert to a fraction, 12 is 1/4 of x. if you then multiply your answer by 4, 12 is 25% of 48.

to figure this out you can also ask, 12 is 25% of what number?

Suppose that the functions f and g are defined for all real numbers x as follows.
f(x)=x+3
g(x) = 4x+4

Answers

Step-by-step explanation:

when you do an arithmetic operation to functions, you do it for the defining expressions.

so,

(f+g)(x) = (x + 3) + (4x + 4) = x + 3 + 4x + 4 = 5x + 7

(f*g)(x) = (x+3)*(4x+4) = 4x² + 12x + 4x + 12 = 4x² + 16x + 12

= 4(x² + 4x + 3)

(f-g)(4) = (4+3) - (4×4+4) = 7 - (16+4) = 7 - 20 = -13

True or False?
If you graph the points (2,4) and (-1.-1). Do they would represent a proportional
relationship.

Answers

Answer:

1

Step-by-step explanation:

helpppppp plss thanks​

Answers

Answer:

I can even see anything can you reupload your answer, please?

Step-by-step explanation:

Level: Easy

A football team loses 6 yards on their first play. It gains 8 yards on the next play. Which number line best represents the sum -6+8?

A)
B)
C)
D)

Answers

D is the answer please mark me brainliest

The box plots below show the average daily temperatures in January and December for a US city:
January
TH
December
What can you tell about the means for these two months (1 point)

Answers

Answer:

like i said no graph i cant help

Step-by-step explanation:

13. On a snow day, the temperature at 8 AM was 2°F. Later in the day the temperature rose 6º. What was the resulting temperature?​

Answers

The resulting temperature was 8°F.

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