Brandon is shopping at Old Navy during a sale. All shorts are $16 each and all t-shirts are $10 each.He has $100 to spend and would like to purchase at least 2 pairs of shorts.
a) Write a system of linear inequalities to represent
this situation, then graph.
b)Using your graph, give two possible combinations
of shorts and Brandon can buy.
Answers
x = the number of shorts bought
y = the number of t-shirts bought
A pair of shorts costs $16 and a t-shirt costs $10. Brandom has $100 to spend.
Therefore
16x + 10y ≤ 100
This may be written as
y ≤ - 1.6x + 10 (1)
Brandon wants at least 2 pairs of shorts. Therefore
x ≥ 2 (2)
Graph the equations y = -1.6x + 10 and x = 2.
The shaded region satisfies both inequalities.
Answer:
Two possible solutions are
(a) 3 pairs of shorts and 4 t-shirts,
(b) 4 pairs of shorts and 2 t-shirts.
Two possible solutions are (a) [tex]3[/tex] pairs of shorts and [tex]5[/tex] t-shirts
(b) [tex]4[/tex] pairs of shorts and [tex]3[/tex] t-shirts.
[tex]x=the\; number\; of shorts\\y=the\; number\; of\ t-shirt\; bought[/tex]
So equation formed is
[tex]16x+10y\leq 100[/tex]
[tex]10y\leq 100-16x\\y\leq 10-1.6x[/tex]---Eq [tex]1[/tex]
Bradon wants at least [tex]2[/tex] pair of shorts.Therefore
[tex]x\geq 2[/tex]--Eq [tex]2[/tex]
Now put,
[tex]x=3 \\y=10-1.6(3)\\y=10-4.8\\y=5\\[/tex]
Hence [tex]3[/tex] shorts and [tex]5[/tex] t-shirts
Now put,
[tex]x=4 \\y=10-1.6(4)\\y=10-6.4\\y=3\\[/tex]
Now graph the equation,
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Related Questions
What is the converse of the linear pairs theorem
Answers
For example, the logical statement "A implies B" has a converse of "B implies A"
The linear pairs theorem states that "if two angles form a linear pair, then they are supplementary".
The converse of the linear pairs theorem is therefore, "if two angles are suplementary, then they form a linear pair".
You have $200 in your savings account. You take $35 from your account each week for four weeks. How much is left in your account at the end of the four weeks?
Answers
3x4=140
140-200=60
35 dollars * 4 weeks = 140 dollars
subract this from 200, and at the end of the week you will have 60 dollars.
What is the period of the function y=-4sin (2/3x-pi?3)?
Answers
x = 2pi × 3/2 = 3pi
period = 3pi
Does 3.2 - 4d=2.3d+3 no solution or identity
Answers
The solution of expression is,
⇒ d = 5/16
We have to given that,
An expression is,
⇒ 3.2 - 4d = 2.3d + 3
Now, We can simplify the expression for solution as,
⇒ 3.2 - 4d = 2.3d + 3
Add 4d both side,
⇒ 3.2 - 4d + 4d = 2.3d + 3 + 4d
⇒ 3.2 = 6.3d + 3
Subtract 3 both side,
⇒ 3.2 - 3 = 6.3d
⇒ 0.2 = 6.3d
⇒ 6.3d = 0.2
Divide 6.3 both side,
⇒ d = 0.2/6.4
⇒ d = 20/64
⇒ d = 5/16
Thus, The solution of the expression is, d = 5/16
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The sum of three consecutive even integers is fifty four. what is the second integer?
Answers
Which shows one way to determine the factors of x3 – 9x2 + 5x – 45 by grouping?
Answers
(X2+5)(X-9)
(9,0) (0,-45)
If it takes six men six days to dig six holes, how long will it take one man to dig half a hole?
Answers
It will take 3 days for 1 man to dig half of that complete hole.
What are direct and inverse proportion ?Direct proportion if increase in one quantity also results in increase in another quantity for example price and weight of something.
Inverse proportion is when increase in one quantity results in decrease in another quantity for example time is inversely proportional to (speed when distance is constant.
According to the given question
6 men are working together then it takes them 6 days to dig 6 holes.
∴ Number of men days = 6 days × 6 men = 36 men days
So, in 36 men days 6 holes are dug. Now the men days and the number of holes being dug are in direct proportion with one another.
Hence number of men-days required to dig one hole
= 36/6 men days
= 6 men days
∴ No. of men days required to dig half a hole
= 6/2
= 3 men days
So, It takes 1 man 3 days to dig half a hole.
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Find the x-intercept of parabola with the vertex (-7,45) and y-intercept (0,-200). Write your answer in this form (x, y) , (x, y)
Answers
y = a(x + 7)^2 + 45 where a is some conatant
when x = 0 y = -200 so:-
-200 = a*7^2 + 45
a = -200 - 45 / 49 = -5
so the equation of the parabola is y = -5 (x + 7)^2 + 45
Solving for x intercepts:-
(x+7)^2 = -45/-5 = 9
x + 7 = +/- 3
x = -10 , -4
x intercepts at (-10,0) and (-4,0) Answer
Answer:
(-10,0),(-4,0) for Plato/Edmentum Users
Step-by-step explanation:
Have a great day
What is the measure of an exterior angle of a regular 7-sided polygon?
Enter your answer as a decimal in the box.
Round to the nearest tenth of a degree.
Answers
In a regular 7-sided polygon, the sum of the internal angles is
180*(7 - 2) = 900°
Each internal angle is 900/7 = 128.57°.
Because the sum of angles on one side of a straight line is 180°. therefore
each exterior angle is 180 - 128.57 = 51.43°
Answer: 51.4° (nearest tenth)
Answer: [tex]51.4^{\circ}[/tex]
Step-by-step explanation:
We know that the sum of all the exterior angles of a regular polygon with n sides is [tex]360^{\circ}[/tex].
The measure of an exterior angle of a regular n-sided polygon is given by :-
[tex]\dfrac{360^{\circ}}{n}[/tex]
Now, the measure of an exterior angle of a regular 7-sided polygon is given by :-
[tex]\dfrac{360^{\circ}}{7}=51.4285714286^{\circ}\approx51.4^{\circ}[/tex]
Hence, the measure of an exterior angle of a regular 7-sided polygon =[tex]51.4^{\circ}[/tex]
Find equation where line passes through (7,8) and perpendicular to line y=8
Answers
What is the factored form of 6n4 – 24n3 + 18n?
Answers
6n(n^3-4n^2+3)
6n(n-1)(n^2-3n-3)
Answer:
Step-by-step explanation:
Notice to facts:
The numbers 6, -4 and 18 have a common factor: 6.In all the terms (n⁴, n³, n) are a factor n.The expression has a common factor 6n. Then,
6n⁴-24n³+18n = 6n(n³-4n²+3).
In order to factor the term n³-4n²+3 we use Ruffini-Horner rule, which gives us that
n³-4n²+3 = (n-1)(n²-3n-3).
Then,
6n⁴-24n³+18n = 6n(n³-4n²+3) = 6n(n-1)(n²-3n-3).
If you don't know the formula for the general solution of second degree equation, you are done. Otherwise, it is only to use it in the quadratic factor.
Here is the other question, the last one for this weeks homework, help will be very much appreciated!
Answers
The Expression:
[tex]=(3x+5x^3-2x^2+13)+(11-2x^3+5x)[/tex]
Collect Like Terms.
[tex]=5x^3-2x^3-2x^2+3x+5x+13+11[/tex]
Combine Like Terms.
[tex]=3x^3-2x^2+8x+24[/tex]
Answer B) would be the correct answer.
Hope this helps.
-Benjamin
Answer:
B
Step-by-step explanation:
3x+5x= 8x
5x^3 - 2x^3= 3x^3
-2x^2= -2x^2
13+11=24
-2(5+6m)+16= -90 and then :(?
Answers
-10-12m+16=-90
Combine like terms
-12m+6=-90
Subtract 6 from both sides
-12m=-96
Divide both sides by -12
m=8
Final answer: m=8
Use the graph below to fill in the blank with the correct number
Answers
The answer is 1. If we go to where the x-coordinate is 1, we see that there is a point with a y-coordinate of 1.
Hope this helps!
The grades received on a test by twenty students were 100, 55, 75, 80, 65, 65, 95, 90, 80, 45, 40, 50, 85, 85, 85, 80, 80, 70, 65, and 60. What is the average of these grades?
A.) 70.5
B.) 72.5
C.) 77
D.) 80.3
E.) 100
Answers
Please help me Factor -4d3 + 28d2 - 4d
Answers
Answer:
The factored form of the expression [tex]\( -4d^3 + 28d^2 - 4d \)[/tex] is [tex]\( -4d(d - 1)(d - 1)(6d - 1) \).[/tex]
Explanation:
To factor the expression [tex]\( -4d^3 + 28d^2 - 4d \)[/tex], we can first look for the greatest common factor (GCF) among the terms. In this case, the GCF is [tex]\( -4d \).[/tex]
So, we can factor out [tex]\( -4d \)[/tex] from each term:
[tex]\[ -4d(d^2 - 7d + 1) \][/tex]
Now, let's focus on factoring the quadratic expression inside the parentheses, [tex]\( d^2 - 7d + 1 \)[/tex]. To factor this quadratic expression, we need to find two numbers that multiply to give the constant term (1) and add to give the coefficient of the linear term (-7d). Since the constant term is 1, the only possible combination is 1 and 1.
So, we can rewrite the expression as:
[tex]\[ -4d(d^2 - 7d + 1) = -4d(d^2 - d - 6d + 1) \][/tex]
Now, we can group the terms and factor by grouping:
[tex]\[ -4d((d^2 - d) + (-6d + 1)) \][/tex]
[tex]\[ -4d(d(d - 1) - 1(6d - 1)) \][/tex]
Now, we can factor further:
[tex]\[ -4d(d - 1)(d - 1)(6d - 1) \][/tex]
During the month of February, Fabulous Feet Shoe Mart sold 30 pairs of red loafers. After an ad campaign to boost sales, they sold 39 pairs in March. Find the percent of increase in sales.
35%
30%
23%
18%
Answers
= (39 - 30) / 30......* 100
= 9/30 * 100
= 0.3 * 100
= 30% increase <===
Which mathematical property is demonstrated?
40 * (25 * 74) = (40 * 25) * 74
Question 3 options:
associative property of addition
commutative property of multiplication
commutative property of addition
associative property of multiplication
Answers
Knowing this, we can easily conclude that this is demonstrating the associative property of multiplication. The associative property of multiplication states that the product is the same regardless of their grouping. In this case, after simplifying the expression given, we can see that indeed the products are the same hence that fact that they have different grouping.
Answer:
Step-by-step explanation:
The associative property of multiplication states that the product is the same regardless of their grouping. In this case, after simplifying the expression given, we can see that indeed the products are the same hence that fact that they have different grouping
What is the distance between -3 and 6?
-9
-3
3
9
Answers
Hope this helps!
A taxi charges $2.50 for the first mile and $0.40 for each mile after that. The expression below shows how to find the total cost, in dollars, of a 20-mile taxi ride. 2.50 + 0.40 (20 - 1) What is the cost of the ride?
Answers
Answer:
Step-by-step explanation:
Alright , lets get started.
The first mile charge = [tex]$2.5[/tex]
Total miles taxi covered = [tex]20[/tex]
Subtracting first mile frm the total ride = [tex](20-1)[/tex]
Means the fare will apply on this mile.
So, cost of total ride = [tex]2.5 + 0.4 (20-1)[/tex]
cost of total ride = [tex]2.5+0.4*19[/tex]
cost of total ride = [tex]2.5+7.6[/tex]
cost of total ride = [tex]10.1[/tex]
The answer is $ 10.1 . : Answer
Hope it will help :)
Answer:
10.10 (B)
Step-by-step explanation:
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Find length of MN such that LN = 5.7 and LM = 1.3 MN= x + 2.1
Answers
Final answer:
To find the length of MN, we can set up an equation using the fact that LN + LM = MN and substitute the given values. Solving for x, the length of MN is found to be 4.9 units.
Explanation:
To find the length of MN, we can use the fact that LN = 5.7 and LM = 1.3. We are also given that MN = x + 2.1. Since LN and LM are known, we can set up an equation using the fact that LN + LM = MN.
LN + LM = MN
5.7 + 1.3 = MN
Then, we can substitute the given value of MN = x + 2.1 into the equation and solve for x.
5.7 + 1.3 = x + 2.1
7 = x + 2.1
x = 7 - 2.1
x = 4.9
Therefore, the length of MN is 4.9 units.
There are 3 drama movies 8 comedy movies and 4 action movies what's the ratio of dramas to movies ?
Answers
How I got that was add all of the 3 types of movies together. 3+8+4= 15. And there are 3 drama movies. So I looked at "the ratio of DRAMA, to MOVIES.", and I wrote down what was first.
I'm not sure if I made sense, sorry. But
solve for n
4n + 2 = 6 (1/3n - 2/3)
Answers
The solution of expression for the value of n is, n = - 3.
Used the concept of expression that states,
Mathematical expression is defined as the collection of numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that,
The expression is,
[tex]4n + 2 = 6 (\dfrac{1}{3} n - \dfrac{2}{3} )[/tex]
Now simplify the expression by combining like terms and apply the distributive property as,
[tex]4n + 2 = 6 (\dfrac{1}{3} n - \dfrac{2}{3} )[/tex]
Apply distributive property,
[tex]4n + 2 = (\dfrac{6}{3} n - \dfrac{12}{3} )[/tex]
[tex]4n + 2 = 2n - 4[/tex]
Combine like terms,
[tex]4n - 2n = - 4 - 2\\[/tex]
[tex]2n = - 6\\[/tex]
[tex]n = - 3[/tex]
Therefore, the value of n is - 3.
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If someone could help me!
Answers
The domain is the set of allowed inputs (x). The points on this graph have x coordinates that span from x = 0 to x = 35. Because x is time in minutes, we can have fractions of a minute (eg: x = 7.5 ---> 7 and a half minutes). So we won't just have integers.
Suppose you buy two sweaters. each sweater costs the same amount. the amount of money you spend varies directly with the number of sweaters you buy. if you spent $37.50 for two sweaters, what is the constant of variation?
Answers
Thus, the constant of variation is 18.75
Answer with Step-by-step explanation:
We spent $37.50 for two sweaters.
Each sweater costs the same amount.
Cost of each sweater=$37.50/2
=$18.75
The amount of money you spend varies directly with the number of sweaters you buy.
We have to find the constant of variation.
Here, cost of each sweater is the constant of variation.
Hence, constant of variation is:
$18.75
Find the area of the shaded region. Show all work in order to receive credit.
Answers
area of square = 14^2 = 196 square cm
area of circle = 3.14 *7^2 = 153.86 square cm
196 - 153.86 = 42.14 square cm is shaded
Compare and contrast equation notation and function notation
Answers
An equation makes use of the equality (=) sign.
An example of an equation is x + 6 = 46.
A function is a mathematical machine whose purpose is to transform input variables into output according to the function rule.
A function can be described by an equation, a graph, a program, a table, etc.
An example of a function is y = 2x - 5.
1/3(9-6m)+1/4(12m-8)
Answers
Answer:
[tex]m+1[/tex]
Step-by-step explanation:
The question is
Simplify the expression
we have
[tex]\frac{1}{3}(9-6m)+\frac{1}{4}(12m-8)[/tex]
using the distributive property
[tex]\frac{1}{3}(9)-\frac{1}{3}(6m)+\frac{1}{4}(12m)-\frac{1}{4}(8)[/tex]
[tex]3-2m+3m-2[/tex]
Combine like terms
[tex]m+1[/tex]
What is a factored form of the following expression?
5x squared - 20x
A. 5(x squared - 4)
B. 5(x - 2) squared
C. 5x (x-4)
D. (5x-4)(x+5)
Answers
If you were to distribute the 5x to everything in parentheses, you would get 5x squared (5x × 5) and -20x (5x × -4)
What's the answer ????