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.
Answers
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 ≥ 0And 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 ≥ 0The 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
Related Questions
What is the range of f(x)?
Answers
Answer:
{ f(x)| -∞ < f(x) ≤ 4 }
Step-by-step explanation:
The range of a function is the interval of every y-value represented on the function. Since the highest this function goes on the y-axis is to y=4, we know that the upper limit of the range is 4, which is inclusive because the function actually reaches this value. The function also appears to go down indefinitely on the right side, so the lower limit is -∞, which is non-inclusive because we will never reach that value.
The range is -∞ < f(x) ≤ 4
can i have help on this q plz
Answers
Answer:
No, they will need an additional £34 to stay the planned 10 nights.
Step-by-step explanation:
Attached screenshot of a spreadsheet.
The cost for 10 nights for the 2 people is £100.
The tent site rental (over 10m^2) for 10 nights is £150.
Savings for the two over the 9 weeks is £216.
They will need an additional £34 to camp as planned.
I suggest fibbing about the extra 0.5m^2 needed for the tent site. That will reduce the bill by £30, so they are only £4 short. Time to make a couple of friends.
I need help please !
Answers
Answer:
y column: 1st = -7 , 2nd = -5 , 3rd = -3 , 4th = -1 , 5th = 1
Which statement is an example of heat transfer by convection? Question 4 options: Jane's feet burned as she walked across the hot beach sand. Hot air from the sand rose and was replaced by cool air blowing in from the ocean as a sea breeze. The black asphalt of the parking lot was much warmer than the green grass surrounding the lot. People were scattered across the beach, sitting on chairs and towels, warming themselves in the bright sunshine.
Answers
Answer:
Step-by-step explanation
Hot air from the sand rose and was replaced by cool air blowing from the ocean as a sea breeze.
in the inequality 4> -4 which number appears farther right on a number line and why?
Answers
Answer:
4
Step-by-step explanation:
It is a positive number meanwhile -4 in negative.
if you add 5 to me then divide 7, and add 12 then subtract 7 you get 10 what number am i
Answers
Answer:
hii the answer is 30 :D have a nice day
i dont even think i'm right but ok
didn't you just say you got the number 10? i'm guessing the number is 10
PLEASE HELP NEED TO GET THIS RIGHT WILL GIVE BRAINLIEST
Answers
Answer:
27 / 4x^6y^8.
Step-by-step explanation:
= 4 * 3^3 x^6 y^12 / 16 x^12 y^20
= 4*27 / 16 x^6y^8
= 4*27/ x^6y^8
= 27 / 4x^6y^8
Please help!! Picture is provided
Quad. ABCD is a trapezoid.
XY is the median
XY = 12; AB=16
Find DC
Answers
Answer:
DC = 8
Step-by-step explanation:
The median is half the sum of the parallel bases, that is
[tex]\frac{AB+DC}{2}[/tex] = XY , substitute values
[tex]\frac{16+DC}{2}[/tex] = 12 ( multiply both sides by 2 to clear the fraction )
16 + DC = 24 ( subtract 16 from both sides )
DC = 8
Answer:
DC = 8
Step-by-step explanation:
The median XY of the trapezoid ABCD is half or the sum of AB and DC.
XY = 1/2 ( AB + DC)
We need to find out DC so we can rewrite this equation isolating DC
XY = (1/2)(AB+DC), multiply both sides by 2
2XY = AB + DC, subtract from both sides AB
2XY - AB = DC, now substitute the given AB = 16 and XY = 12
2* 12 - 16 = DC , using the order of operations rules we multiply first
24 -16 = DC, subtract
8 = DC
Solve the equation by completing the
square. Enter the smallest solution first
and round to the nearest tenth.
s2 - 10s - 23 = 0
-
s = [?]
=
Answers
Answer:
s ≈ - 1.9 , s ≈ 11.9
Step-by-step explanation:
s² - 10s - 23 = 0 ( add 23 to both sides )
s² - 10s = 23
To complete the square
add ( half the coefficient of the s- term )² to both sides
s² + 2(- 5)s + 25 = 23 + 25
(s - 5)² = 48 ( take square root of both sides )
s - 5 = ± [tex]\sqrt{48}[/tex] ( add 5 to both sides )
s = 5 ± [tex]\sqrt{48}[/tex]
Then
s = 5 - [tex]\sqrt{48}[/tex] ≈ - 1.9 ( to the nearest tenth ) ← smaller solution
s = 5 + [tex]\sqrt{48}[/tex] ≈ 11.9 ( to the nearest tenth ) ← larger solution
You have 4 cups of flour and you need to us 1 3/4 cups of flour for a cookie recipe.how much flour will you have left?
Answers
HELP ME PLEASE
whats 9+10?
Answers
Answer:
21
Step-by-step explanation:
Answer:
19
Step-by-step explanation:
what is the unknown number to ( 6 x 2) + (6 x 3) = 6 x __
Answers
Answer:
6
Step-by-step explanation:
6
URGENT!!!
Peggy sue decided to enter her famous “Five- Alarm chili” at her local chili cooking contest. Normally, she needs 5 tomatoes to make enough chili for her family of 7
A. How many tomatoes should she expect to use to make her famous recipe for 100 people?
b. When she gets to the contest, she realizes that she only packed 58 tomatoes. How many people can she expect to feed?
Answers
5/7 = 0.714… tomatoes per person
Multiply this by one hundred
0.714 * 100 = 71.43 tomatoes.
Check:
5/7 = ?/100
Solve for ?
? = 71.43 tomatoes, but you technically can’t bring 0.43 tomatoes, so round that to 72 tomatoes
B. We would need to solve for
5/7 = 58/?
? = 81.2 people, but you should round down here because there isn’t enough chili for that 82 person, and there are not 20% of a person walking around looking for some chili.
plz help on this question;WORK OUT,1+2+3(1+2+3)
Answers
Answer:
21
Step-by-step explanation:
1) Simplify 1 + 2 to 3.
1 + 2 + 3 × ( 3 + 3 )
2) Simplify 3 + 3 to 6.
1 + 2 + 3 × 6
3) Simplify 3 × 6 to 18.
1 + 2 + 18
4) Simplify 1 + 2 to 3.
3 + 18
5) Simplify.
21
Pls help me
On June 1, Mary had a balance of $50 in her bank account. During June she made the four transaction below.
Deposited $25.62
Withdrew $19.76
Wrote a check for $56.29
Paid a bank fee of $25
If there were no other transaction, what was the balance in Mary's account at the end of the month?
Answers
Answer:
The balance in Mary's account at the end of the month is $14.09
Step-by-step explanation:
Step 1: 50+25.62=75.62
Step 2: 75.62+19.76=95.38
Step 3: 95.38-56.29=39.09
Step 4: 39.09-25= $14.09
-3 and -5 what is less, greater than , and or equal
Answers
Answer:
-3 is less and -5 is greater
Step-by-step explanation:
Answer:
less than
Step-by-step explanation:
because -5 would be less than -3 because it is bigger
A family buys a studio apartment for 120,000. They pay down payment of 18,000.
A. Their down payment is what percent of the purchase price?
B. What percent of the purchase price would a 48,000 down payment be?
Answers
Answer:
EZ
Step-by-step explanation:
A. 15 Percent
B. 40 Percent
Answer:
A) 15% B) 40%
Step-by-step explanation:
How much would it cost to buy three medium sodas and two hotdogs
Answers
Answer:
depends how much they cost each
On a coordinate graph the following points of a rectangle are given. A(0,2) B (0,-2) C (3,-2) 4 Where do the coordinates of Dneed to be to form the rectangle? 0 (3,2) O (2, 3) 0 (1,3) 0 (3,1)
Answers
Answer:
(3, 2)
Step-by-step explanation:
Please mark me brainliest if this helped! :P
The theater manager needs to set up 54 chairs for a show each row can be holed up to eight chairs the manager puts as many chairs in each row as possible how many rolls will the manager set up
Answers
Answer:
7 not 7 full rows though
Step-by-step explanation:
Drag the numbers to order them from least to greatest.
0.7
-4.5
0.3
-0.5
2.3
Answers
Answer:
-4.5, -0.5, 0.3, 0.7, 2.3
Step-by-step explanation:
The higher the negative number the lower it really is.
Answer:
-4.5, -.5, .3, .7,2.3
Step-by-step explanation:
y=1/4x + 4 input (x) = 4 find (y) output PLEASE HELP
Answers
Answer:
y = 5
Step-by-step explanation:
y = (1/4)x + 4
input (x) = 4
plug in 4 for x
y = (1/4)(4) + 4
y = 1 + 4
y = 5
Answer this middle school math equation for 30 points lol
Answers
Answer:
n
Step-by-step explanation:
Answer:
[tex]x=14[/tex]
Step-by-step explanation:
Multiply both sides by -5:
[tex]-\frac{1}{5} (x-4)=-2[/tex]:
[tex]-\frac{1}{5} (x-4)*-5=-2*-5[/tex]
[tex]1(x-4)=10[/tex]
[tex]x-4=10[/tex]
Add 4 to both sides:
[tex]x-4+4=10+4[/tex]
[tex]x=14[/tex]
Find the area of the yellow region.
Round to the nearest tenth.
Answers
Answer:
13.7 cm square
Step-by-step explanation:
Here we see that the square has an area of 8x8= 64 centimeters square. We want to subtract the area of the white part from 64 to find the area of the yellow region. If we were to put the white parts together it would create a circle, so we need to find the area of the circle and then subtract it from 64. The circle would have a radius of one half the length of the square, which would be 4 cm. Area equals pi times radius squared so the area would be 50.27 cm square. 64-50.27= 13.7 cm square
Apply the distributive property to create an equivalent expression.
(3−8y)⋅(−2.5)=
Answers
Answer:
-7.5+20y
Step-by-step explanation:
To apply the distributive property, you have to distribute the multiplication of -2.5 to both 3 and -8y.
First, multiply 3 and -2.5 to get -7.5
Then, multiply -8y and -2.5 to get 20y.
Finally, add these values together
A regular polygon has 45 sides.
Find the size of each of its exterior angles.
100 POINTS
Answers
Answer:
8
Step-by-step explanation:
360/45 = 8
We know
Sum of exterior angles of any polygon is 360°Let every angle be x
[tex]\\ \sf\longmapsto 45x=360[/tex]
[tex]\\ \sf\longmapsto x=360/45[/tex]
[tex]\\ \sf\longmapsto x=8°[/tex]
Help! Please! Help! Please!
Answers
Step-by-step explanation:
a midsegment is the line segment connecting the midpoints of two sides of a triangle. Since a triangle has three sides, each triangle has three midsegments (that create the midsegment triangle). A triangle midsegment is parallel to the third side of the triangle and is half of the length of the third side (due to similar triangles and their constant scaling factors, when one side of the similar triangle is half of the sys of the original triangle, then all its sides are half of their original counterparts).
the 3 sides of the main triangle are
2x + 5
3x - 1
5x
the perimeter of the main triangle is the sum of these :
2x + 5 + 3x - 1 + 5x = 10x + 4
since the sides of the midsegment triangle are all exactly half the length of the sides of the main triangle, also the perimeter of the midsegment triangle is half of the perimeter of the original triangle :
(10x + 4) / 2 = 5x + 2
reorder the steps of the proof to make sure that steps that are logically dependent on prior steps are in the proper order.
Given:
A
B
‾
≅
C
D
‾
AB
≅
CD
and
B
C
‾
≅
A
D
‾
.
BC
≅
AD
.
Prove:
A
C
‾
AC
bisects
B
D
‾
BD
.
Answers
Answer: a
Step-by-step explanation:
what is 1 1/5 x 2 3/4
Answers
33
10
33
10
Decimal Form:
3.3
3.3
Mixed Number Form:
3
3
10
I hope it help #carry on learning
Step by step:
11(23)/5(4) (multiply 11 and 23)
253/5(4) (multiply 5 and 4)
=253/20
Can someone plz help with this
Answers
Answer:
hexagonal prism