Luis can spend up to $240 buying men’s and women’s shirts for his club. Men’s shirts cost $8 each and women’s shirts cost $12 each. He needs to buy at least 3 men’s shirts and at least 8 women’s shirts. Also, the women’s shirts must be at least twice the number of men’s shirts.
The graph shows the feasible region, where x represents the number of men’s shirts and y represents the number of women’s shirts.
Which ordered pairs meet all the constraints and make sense in context of the situation?
Select each correct answer.
(4, 9)
(7, 13)
(2, 15)
(5,12)
(6, 15)
Answers
Let
x------> the number of men’s shirts
y-----> the number of women’s shirts
we know that
[tex]8x+12y \leq 240[/tex] ----> constraint A
[tex]x\geq 3[/tex] ----> constraint B
[tex]y\geq 8[/tex] ----> constraint C
[tex]y\geq 2x[/tex] ----> constraint D
using a graphing tool
see the attached figure N[tex]1[/tex]
The solution is the shaded area
Remember that
if an ordered pair meets all restrictions and makes sense in the context of the situation, then the ordered pair is a system solution
we're going to proceed to verify each pair ordered
case A) [tex](4,9)[/tex]
Substitute the value of x and y in each constraint
[tex]x=4\\y=9[/tex]
Verify constraint A
[tex]8*4+12*9 \leq 240[/tex]
[tex]140 \leq 240[/tex] -------> is true
Verify constraint B
[tex]4\geq 3[/tex] -------> is true
Verify constraint C
[tex]9\geq 8[/tex] ------> is true
Verify constraint D
[tex]9\geq 2*4[/tex]
[tex]9\geq 8[/tex] -----> is true
therefore
the ordered pair [tex](4,9)[/tex] is a system solution
case B) [tex](7,13)[/tex]
Substitute the value of x and y in each constraint
[tex]x=7\\y=13[/tex]
Verify constraint A
[tex]8*7+12*13 \leq 240[/tex]
[tex]212 \leq 240[/tex] -------> is true
Verify constraint B
[tex]7\geq 3[/tex] -------> is true
Verify constraint C
[tex]13\geq 8[/tex] ------> is true
Verify constraint D
[tex]13\geq 2*7[/tex]
[tex]13\geq 14[/tex] -----> is not true
therefore
the ordered pair [tex](7,13)[/tex] is not a system solution
case C) [tex](2,15)[/tex]
Substitute the value of x and y in each constraint
[tex]x=2\\y=15[/tex]
Verify constraint A
[tex]8*2+12*15 \leq 240[/tex]
[tex]196 \leq 240[/tex] -------> is true
Verify constraint B
[tex]2\geq 3[/tex] -------> is not true
Verify constraint C
[tex]15\geq 8[/tex] ------> is true
Verify constraint D
[tex]15\geq 2*2[/tex]
[tex]15\geq 4[/tex] -----> is true
therefore
the ordered pair [tex](2,15)[/tex] is not a system solution
case D) [tex](5,12)[/tex]
Substitute the value of x and y in each constraint
[tex]x=5\\y=12[/tex]
Verify constraint A
[tex]8*5+12*12 \leq 240[/tex]
[tex]184 \leq 240[/tex] -------> is true
Verify constraint B
[tex]5\geq 3[/tex] -------> is true
Verify constraint C
[tex]12\geq 8[/tex] ------> is true
Verify constraint D
[tex]12\geq 2*5[/tex]
[tex]12\geq 10[/tex] -----> is true
therefore
the ordered pair [tex](5,12)[/tex] is a system solution
case E) [tex](6,15)[/tex]
Substitute the value of x and y in each constraint
[tex]x=6\\y=15[/tex]
Verify constraint A
[tex]8*6+12*15 \leq 240[/tex]
[tex]228 \leq 240[/tex] -------> is true
Verify constraint B
[tex]6\geq 3[/tex] -------> is true
Verify constraint C
[tex]15\geq 8[/tex] ------> is true
Verify constraint D
[tex]15\geq 2*6[/tex]
[tex]15\geq 12[/tex] -----> is true
therefore
the ordered pair [tex](6,15)[/tex] is a system solution
therefore
the answer is
[tex](4,9)[/tex]
[tex](5,12)[/tex]
[tex](6,15)[/tex]
see the attached figure N[tex]2[/tex] to better understand the solution
Answer:
(4,9) (5,12) (6,15)
Step-by-step explanation:
Those were the correct options.
Related Questions
Julie is selling candy bars to raise money for new band uniforms. Candy bar x sells for $2 and candy bar y sells for $3. The number of y candy bars Julia sells must be greater than or equal to three times the number of x candy bars she sells. She has at most 36 candy bars to sell. What is the maximum revenue she can make? $36 $99 $108 $216
Answers
The number of candy Y must be >= 3 times candy X. Since this won't limit candy Y selling, then you can convert all 36 candy into candy Y and 0 candy X
36 candy (Y) >= 0 candy(X) ----> the requirement is met.
The revenue would be 36 candy Y * $3/candy Y= $108
Correct Answer.
$36
$99 <---
$108
$216
How many terms are in the expression shown below?
a2 - ab + 8b + b2 - 1
2
3
4
5
Answers
The expression have five terms.
Shannon wants to buy cupcakes for her friend's birthday party. The bakery she goes to sells cupcakes for $3.50 each. The bakery also sells gift cards for $2.00, and Shannon decides to buy one card. If Shannon buys 10 cupcakes, how much money does she spend at the bakery?
Answers
Solve the inequality.
-x/4 ≤ 2
Answers
-x<8
Switch the signs as you make 8 negative and x positive
x>-8
(Make sure to make the signs greater and less than or equal to
Michelle listed her three children as equal beneficiaries on her life insurance policy. If she has a $400,000 policy, how much will each receive in the event of her death?
Answers
The beneficiaries received by each of Michelle children is $133333.3.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given that, Michelle listed her three children as equal beneficiaries on her life insurance policy.
Here, insurance amount received by each is
400000/3
= $133333.3
Therefore, the beneficiaries received by each of Michelle children is $133333.3.
To learn more about the unitary method visit:
brainly.com/question/22056199.
#SPJ2
Final answer:
Each of Michelle's three children would receive $133,333.33 from her $400,000 life insurance policy if they are listed as equal beneficiaries.
Explanation:
Michelle has a $400,000 life insurance policy and has listed her three children as equal beneficiaries. To calculate how much each child will receive in the event of her death, we divide the total policy amount by the number of beneficiaries.
$400,000 ÷ 3 = $133,333.33
Therefore, each child would receive $133,333.33 from the life insurance policy. In this scenario, the division of the life insurance policy ensures an equal distribution among Michelle's three children, with each child entitled to $133,333.33. This approach maintains fairness in the allocation of the financial benefit, aiming to provide an equitable share to each beneficiary.
the formula P=2I + 2w means that the perimeter of a rectangle is equal to twice the sum of its length and its width
Answers
Answer:
Step-by-step explanation: simple Answer I got
I=p-2w over 2
One number is 4 more than 3 times another. Four times the larger decreased by 5 times the smaller is equal to the smaller subtracted from 32. Find the numbers
Answers
A storeowner places a “No Smoking” sign in front of their store. This would be classified as a type of what factor.
Answers
This is because it mainly aims at preventing possible diseases that can occur to those who are smoking as well as those who are inhaling the gases produced in the air from smokers.
This sign encourages active smokers to put off their cigarettes and throw them away and it protects the non-smokers from being subjected to the smoke produced from smokers. By this, it reduces the risk of cancer.
Answer:
external pressure
Explanation:
This is the full question:
A sign in front of a store says "No Smoking.” What kind of factor is this sign?
external pressure
internal pressure
media influence
peer pressure
write an expression to model the following phrase an hourly wage of 13.50 plus a 75 bonus
Answers
ok guys so i had trouble on this algrebra question for a while if you can help me out thxs so much: Jenny had 2 apples if she added two more how many would she have altogether. Im stuck plz help
Answers
She had 2 Apples
If she added 2 more
What does 2 + 2 equal? It equals to 4
Same thing here,
2 apples that she had + 2 apples that she added = 4 apples
Thus,
She will have 4 apples.
I hope I helped~
what is the property of 7(3+4y)=21+28y
Answers
One third of a number is three more than one fourth the same number. What is the number.
Answers
is the same as
(4/12)x=(36/12)+(3/12)x
subtract the 3/12x from each side
(1/12)x=36/12
multiply by 12 on each side
x=36
in the chorus there is 12 more girls than boys there 32 students in the chorus how many boys are there and how many girls are there
Answers
Hope this helps!! Message me with questions
How to do the how long will it take two people to paint a room problem?
Answers
Let's example: Mark takes 3 hours, Jane takes 5 hours, to paint the same room.
Let x= the amount of the room each person paints in a given amount of time.
So, Mark's contribution is represented by x/3
Jane's contribution is represented by x/5
Together, they paint one entire room, so our equation will equal...1.
[Our working equation] x/3 + x/5 = 1
[Find common denominator] 5x/15 + 3x/15 = 1
[add fractions] 8x/15=1
[solve for x] 8x=15
x=15/8 or 1 7/8 hours. They can paint the room together in 1 7/8 hours.
If p: It is not cold. What is ~ p?
it is cold
it is mildly cold
it depends
none of the above
Answers
So, the answer is "it is cold".
Answer:
"it is cold"
Step-by-step explanation:
Find the coordinates of the missing endpoint if B is the midpoint of AC. C(-5,4), B(-2,5) I need the steps and answer pls and ty
Answers
[tex]\bf \left( \cfrac{-5+x}{2}~,~\cfrac{4+y}{2} \right)=\stackrel{B}{(-2,5)}\implies \begin{cases} \cfrac{-5+x}{2}=-2\\\\ -5+x=-4\\ \boxed{x=1}\\ ----------\\ \cfrac{4+y}{2}=5\\\\ 4+y=10\\ \boxed{y=6} \end{cases}[/tex]
The coordinates of the missing endpoints (1,6) and can be determined by using the midpoint formula.
Given :
B is the midpoint of AC. Points -- C(-5,4), B(-2,5)The following steps can be used in order to determine the coordinates of the missing endpoint:
Step 1 - According to the given data, points C(-5,4) and B(-2,5).
Step 2 - The mid-point formula is given below:
[tex]\rm x = \dfrac{x_1+x_2}{2}[/tex]
[tex]\rm y = \dfrac{y_1+y_2}{2}[/tex]
Step 3 - Let the endpoint be (x,y).
Step 4 - Now, substitute the values of the points in the above formula.
[tex]\rm -2= \dfrac{-5+x}{2}[/tex]
[tex]\rm 5 = \dfrac{4+y}{2}[/tex]
Step 5 - Simplify the above expression.
x = 1
y = 6
For more information, refer to the link given below:
https://brainly.com/question/10651868
Use the formula m = to calculate the slope of the line.
The slope of the line is .
Answers
[tex]\displaystyle{m= \frac{d-b}{c-a} [/tex]
that is, the slope is the ratio of the difference of the y-coordinates, to the difference of the x-coordinates:
In our problem we have points A(-6, -8) and B(2, 8),
applying the formula for the slope, we have:
[tex]\displaystyle{m= \frac{d-b}{c-a} = \frac{8-(-8)}{2-(-6)}= \frac{16}{8}=2 [/tex]
Answer: 2
The slope of the line passing through the points is 2
How to find the slope of a lineThe formula for calculating the slope of a line is expressed as:
m =y2-y1/x2-x1
Given the coordinate points expressed as(2, 8) and (-6, -8). Substitute the given values to have:
m =y2-y1/x2-x1
m =-8 -8/-6-2
M = -16/-8
M = 2
Hence the slope of the line passing through the points is 2
Learn more on slope here: https://brainly.com/question/3493733
The tangent of a 45 degree angle is _____.
1
0
1/2
-1
Answers
your answer is 1
reason to this being 1.. is 45 degrees is pi / 4
tan is composed of sin(x) over cos(x) which angels are sqrt 2 over 2
when you divide them by each other is the same as multiplying by their
reciprocals making the answer 1.
hope this helps and give brainliest, id appreciate it
Reduce to simplest form.
3 6/2 × 2 4/5
2 5/6 × 2 7/9
2 2/5 × 4 3/4
1/2 × 3
19/20 × 14
3/8 ×21
3/8 ×12
Answers
convert 2 4/5 to 14/5
multiply the numerators of the improper fractions so 12*14, which is 168.
multiple the denominators so 2*5, which is 10.
the new fraction is 168/10, so you divide 168 divided by 10, which is 16.8, or 16 4/5.
In ABC, C is a right angle, what is the measure of x?
A. 22.4°
B. 67.6°
C. 20.9°
D. 69.1°
Answers
B is the right answer
Answer:
Option B. 67.6°
Step-by-step explanation:
In the given triangle ABC angle C is the right angle, side AB = 21 and side AC = 8.
We have to find the measurement of angle A.
Now from cosine rule we can write
[tex]CosA = \frac{Base}{hypotenuse}[/tex]
Here Base in the corresponding side of the angle A that is 8 and hypotenuse is 21.
Now we put the values
Cos x = 8/21 = 0.3809
[tex]x=cos^{-1}0.3809[/tex]
Or x = 67.61°
Therefore measurement of angle A or x = 67.6° is the answer.
One moving company charges $800 plus $16 per hour. another moving company charges $720 plus $21 per hour. at what number of hours will the charge be the same and what is the charge?
Answers
Hope this helps :)
After the drama club sold 100 tickets to a show, it had $300 in profit. After the next show, it had sold a total of 200 tickets and had a total of $700 profit. Which equation models the total profit, y, based on the number of tickets sold, x?
a. y – 300 = 4(x – 100)
b. y + 300 = 4(x + 100)
c. y + 300 = 2.5(x + 100)
d.y – 300 = 2.5(x – 100)
HELPPPPPPPPPPP
Answers
Answer:
Option a : [tex]y-300 = 4(x - 100)[/tex]
Step-by-step explanation:
Given :
The drama club sold 100 tickets to a show, it had $300 in profit.
The next show, it had sold a total of 200 tickets and had a total of $700 profit.
To Find : Equation models the total profit, y, based on the number of tickets sold, x
Solution :
For 100 tickets he had $300 in profit .
⇒ ([tex]x_{1} ,y_{1}[/tex])=(100,300)
For 200 tickets he had $700 in profit .
⇒ ([tex]x_{2} ,y_{2}[/tex])=(200,700)
We will use point slope form i.e.
[tex]y-y_{1} = m(x - x_{1})[/tex] --(A)
Now, to calculate m we will use slope formula :
[tex]m = \frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]
[tex]m = \frac{700 -300}{200-100}[/tex]
[tex]m =4[/tex]
Now, putting values in (A)
[tex]y-300 = 4(x - 100)[/tex]
Thus Option a is correct i.e. [tex]y-300 = 4(x - 100)[/tex]
Skylar needs to buy a pair of dress pants for $40, a shirt for $30, and a tie for $20. Skylar has three coupons. The first coupon gives him x percent off on a shirt. The second coupon gives him y percent off on the dress pants. The third coupon gives him z percent off on his total purchase. He cannot combine the coupon for the total purchase with the other two coupons. These expressions give both possibilities for the total cost of Skylar's purchase after the coupons are applied. The variables represent percentages as decimals. (1−x)30+(1−y)40+20 (1−z)(40+30+20) Skylar uses the dress pants coupon. Which part of the expression represents the percent that Skylar will pay for the dress pants?
Answers
so the part of the expression that represents the percent that skylar will pay for the dress pants is : (1-y)40
Answer: Hello there!
As we know, the dress pants cost a total of $40, and we also know that Skylar has a coupon of y percent in the dress pants and a coupon of z percent in the total purchase.
In this problem, the question is:
Skylar uses the dress pants coupon. Which part of the expression represents the percent that Skylar will pay for the dress pants?
Ok, if we have a discount of y percent, (where y is represented as decimals) means that you are paying the total price of something ( the 100%) minus the the decimal y multiplied by the price of the object.
this is: $40 - y*$40 = (1 - y)*$40
then if the dress pants cost $40, and Skylar only uses the dress pants coupon, he will pay (1 - y)*$40 for the dress pants.
28Students were surveyed and the results showed that of 18 of them loved to play video games what percentage of the students loved to play video game.
Answers
If the coefficient of static friction between the coffee cup and the roof of the car is 0.21, what is the maximum acceleration the car can have without causing the cup to slide? ignore the effects of air resistance.
Answers
I really need help with #4
Answers
If the product of two numbers is zero then at least one of the numbers must be zero
Answers
one serving of granola provides 4% of the protien you need daily. you must get the remaining 48 grans of protien fron other scources. how many grams of protein do you need daily?
Answers
40 POINTS
Which ordered pair is a solution to the system of inequalities?
Check image below.
Answers
solve for the 2nd equation with the answers:
A. 1+3 =4 ( not less than 4)
B. 0+4 = 4 ( not less than 4)
C. -3 + 5 = 2 ( less than 4) & y is >-2
D. -2 +-3 = -5 ( less than 4) but -3 is <-2
so answer is C
observation often starts the scientific process observation is useful because it helps scientist_____
a) form questions
b) develop opinions
c) summarize data
d) write laws