Tyler went to the supermarket to buy food for a food pantry. He has $36, and can carry up to 20 pounds of food in his backpack. Pasta costs $1 for a 1-pound package. Pasta sauce costs $3 for a 1.5 pound jar. Let x = the number of packages of pasta and y = the number of jars of pasta sauce. Identify each point as either a solution to the system or not a solution to the system of inequalities. (1, 12) (2, 10) (4, 5) (6, 10) (12, 8) (18, 6) .

Answers

Answer 1

Answer:

Solutions: (2,10), (4,5)

Not solutions: (1,12), (6,10), (12,8), (18,6)

Step-by-step explanation:

Let x be the number of packages of pasta and y be the number of jars of pasta sauce. If pasta costs $1 for a 1-pound package, then x packages of pasta cost $x and weigh x pounds. If pasta sauce costs $3 for a 1.5 pound jar, then y jars cost $3y and weigh 1.5y pounds.

1. Tyler has $36, then

[tex]x+3y\le 36.[/tex]

2. Tyler can carry up to 20 pounds of food in his backpack, then

[tex]x+1.5y\le 20.[/tex]

You get the following system of inequalities:

[tex]\left\{\begin{array}{l}x+3y\le 36\\ x+1.5y\le 20\end{array}\right.[/tex]

Now substitute the coordinates of each point:

(1,12):

[tex]\left\{\begin{array}{l}1+3\cdot 12=37> 36\\ 1+1.5\cdot 12=19\le 20\end{array}\right.[/tex]

False, because first inequality doesn't hold.

(2,10):

[tex]\left\{\begin{array}{l}2+3\cdot 10=32\le 36\\ 2+1.5\cdot 10=17\le 20\end{array}\right.[/tex]

True, both inequalities hold.

(4,5):

[tex]\left\{\begin{array}{l}4+3\cdot 5=19\le 36\\ 4+1.5\cdot 5=11.5\le 20\end{array}\right.[/tex]

True, both inequalities hold.

(6,10):

[tex]\left\{\begin{array}{l}6+3\cdot 10=36\le 36\\ 6+1.5\cdot 10=21> 20\end{array}\right.[/tex]

False, because secondt inequality doesn't hold.

(12,8):

[tex]\left\{\begin{array}{l}12+3\cdot 8=36\le 36\\ 12+1.5\cdot 8=24> 20\end{array}\right.[/tex]

False, because second inequality doesn't hold.

(18,6):

[tex]\left\{\begin{array}{l}18+3\cdot 6=36\le 36\\ 18+1.5\cdot 6=27> 20\end{array}\right.[/tex]

False, because second inequality doesn't hold.


Related Questions

HELP ME! DUE IN 5 MINUTES!
A group has an equal number of adults and children. When n oranges are given to the group, each adult gets two oranges while each child gets one orange and there are still 5 oranges left. Write an algebraic expression for the number of oranges given to the adults.

Answers

Answer:

Adults are given =

2n oranges

2n+n=once given

so

Step-by-step explanation:

Final answer:

The algebraic expression for the number of oranges given to adults in a group with an equal number of adults and children, with a specified distribution of oranges and a remainder, is 2A, where A represents the number of adults (or children, since they are equal).

Explanation:

The question requires us to find an algebraic expression for the number of oranges given to the adults in a group where there are an equal number of adults and children, and a specific distribution of oranges to adults and children with a remainder.

Let's denote the number of adults by A, and thus, the number of children will also be A since the group has an equal number of adults and children. If n oranges are distributed, and each adult receives 2 oranges, then the total number of oranges given to adults is 2A. Each child receives one orange, so the number of oranges given to children is A. Including the 5 oranges that are left, the equation representing the total number of oranges is: 2A (for adults) + A (for children) + 5 (leftover) = n (total oranges).

From this equation, if you want to isolate the expression that represents the number of oranges given to adults, it is simply 2A.

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A tessellation is an arrangement of repeating shapes that have what
characteristic?

Answers

Answer:

Option B is correct, (no spaces or overlaps exist between it's pieces).- APEX

Step-by-step explanation:

I hope this helps.

Answer: No spaces or overlaps exist between its pieces.

Which point is located at (4,-5)?

1. A

2. B

3. C

4. D​

Answers

Answer:

it is C

Step-by-step explanation:


10. Which of the following is a linear equation?
a. 4x² +9y2 = 25
b. 2+ 6 = 15
C. 2x-3y=7
d. 4x+6 = 30​

Answers

Answer:

C.

Step-by-step explanation:

It is linear because it have two variables (x and y) and the highest powers that they are raised to are 1

For this case we have that by definition, a linear equation is of the form:

[tex]ax + b = 0[/tex]

That is, the largest exponent of the variable is 1.

Then, according to the options given, we have that the correct option is option D, that is:

[tex]4x + 6 = 30[/tex]

Answer:

Option D

A
D
Given: _1= _2
If AC = 3, BC =5, and AB= 7, find AD

Answers

Final answer:

Using proportional relationships in similar triangles ABC and AED, the length of AD is calculated to be approximately 11.67.

Explanation:

In order to calculate the length of AD, we should first understand that given ΔABC is similar to ΔAED, and given lengths AC = 3, BC = 5, and AB = 7, the scale factor of ABC to AED is based on any of the corresponding dimensions. Here, _1 corresponds to BC(_2) in terms of proportions. Therefore _1(BC)/_1(AC) = _2(BD)/_2(AD). As we know the values of BC and AC, the equation becomes 5/3 = AD/7. Solving this for AD, we get AD = (7 * 5) / 3 = 35/3 = approx 11.67.

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A store is having a sale on walnuts and chocolate chips. For 3 pounds of walnuts and 2 pounds of chocolate chips, the total cost is $13. For 8 pounds of walnuts and 4 pounds of chocolate chips, the total cost is $33. Find the cost for each pound of walnuts and each pound of chocolate chips .

Answers

Final answer:

By setting up and solving a system of linear equations, we find that walnuts cost $3.50 per pound and chocolate chips cost $1.25 per pound.

Explanation:

The question involves using a system of two linear equations to find the cost per pound of walnuts and chocolate chips. We can define w to be the cost of one pound of walnuts and c to be the cost of one pound of chocolate chips. From the information given, we can set up the following two equations:

3w + 2c = 13

8w + 4c = 33

To solve these equations, we can use either substitution or elimination. Let's use elimination:

Multiply the first equation by 2 to align the coefficients of c. This gives us: 6w + 4c = 26.

Now, subtract the newly obtained equation from the second one: (8w + 4c) - (6w + 4c) = 33 - 26, which simplifies to 2w = 7.

Divide both sides by 2 to find w: w = 7/2, so w = $3.50 per pound for walnuts.

Substitute the value of w back into the first equation: 3(3.50) + 2c = 13. Therefore, 10.50 + 2c = 13.

Subtract 10.50 from both sides to find c: 2c = 2.50.

Divide both sides by 2 to get: c = 2.50 / 2, so c = $1.25 per pound for chocolate chips.

Therefore, walnuts cost $3.50 per pound and chocolate chips cost $1.25 per pound.

name a parallelogram that is neither a square, rhombus nor rectangle

Answers

With all due thinking...

I think a Diamond shape will befit your answer. So; The real answer is "Rhomboid"

The reason is that...

A rhomboid has four parallel sides. The opposite sides are equal, but the corners do not form right angles. Think of a rectangle that is slanted(a.k.a diamond) Thats what a Rhomboid is...

A parallelogram that dosent have equal sides is not a rhombus; and which dosent have Right angles are not rectangles and hence cannot be aquares either.

So in all Way a Rhomboid will mark the answer for your question.

Hope it helps..

Regards,

Leukonov/Olegion.

Answer;

TRAPEZOID

Step-by-step explanation:

The expression x2 – 25 is equivalent to which of the following expressions

Answers

The equivalent expression would be,

⇒ (x - 5) (x + 5)

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ x² - 25

Now, We can simplify as;

⇒ x² - 25

⇒ x² - 5²

⇒ (x - 5) (x + 5)

Thus, The equivalent expression would be,

⇒ (x - 5) (x + 5)

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Final answer:

The expression x²- 25 is a difference of squares and can be factored into (x - 5)(x + 5), which is the product of two binomials.

Explanation:

The expression x²² – 25 can be factored into a product of two binomials because it represents a difference of squares. A difference of squares is a specific type of polynomial that takes the form a²– b², which can be factored into (a – b)(a + b). In the case of x² – 25, we can identify a as x and b as 5 since 52 equals 25.

Therefore, we can factor the expression x² – 25 into:

(x – 5)(x + 5)

This utilizes the factoring technique, which is a crucial algebraic skill for simplifying expressions and solving equations.

Khaled and Wilma were asked to find an explicit formula for the sequence 1, 3, 9, 27. Khaled said the formula is f(n)=1*3^n-1 and Wilma said the formula is f(n)=1*3^n. Which one of them is right?

Answers

ANSWER

[tex]f(n) = 1 \times ( {3}^{n - 1} )[/tex]

EXPLANATION

The given sequence is 1, 3, 9, 27...

The first term of this sequence is

[tex]a = 1[/tex]

The common ratio is

[tex]r = \frac{3}{1} = \frac{9}{3} = \frac{27}{9} = 3[/tex]

The explicit formula for this geometric sequence is

[tex]f(n) = a ( {r}^{n - 1} )[/tex]

We substitute the first term and the common ratio to obtain,

[tex]f(n) = 1 ( {3}^{n - 1} )[/tex]

Answer:

khaled is correct. f(n)=1x3^n-1

Step-by-step explanation:

help me plz and god bless :/

Answers

Upper quartile would be 4.5. The interquartile range could be 6.


What is the value of x?

Answers

Answer:

do you have any more information to solve this ?????????

Step-by-step explanation:

what is the actual equation it goes with??

An olympian swam the 200-meter freestyle at a speed of 1.8 meters per second. An olympic runner ran the 200-meter dash in 21.3 seconds. How much faster was the runner’s speed than the swimmer’s speed to the nearest tenth of a meter per second?

Answers

Answer:

7.6m/s

Step-by-step explanation:

Find the time the Olympian swam

Speed=distance/time ⇒⇒Time=distance/speed

Distance=200m , speed= 1.8m/s   t= 200/1.8 = 111.11 seconds

Find the speed of the Olympic runner

Distance=200m  time = 21.3 sec  

s=200/21.3 = 9.4 m/s

Difference in speed= 9.4-1.8= 7.6m/s

Answer:

7.6 m/s faster

Step-by-step explanation:

Speed of swimmer = 1.8 meters per second

The distance covered by runner = 200

Time of runner = 21.3 sec

We have to find the speed of the runner first so that we can compare with the speed of swimmer.

Speed = Distance/Time

=> 200/21.3

=> 9.4 m/s

So we have to find the difference between both speeds

Difference = 9.4 - 1.8

=> 7.6 m/s

So the runner was 7.6 m/s faster..

what is the value of the inequality?
n+7 <5​

Answers

Hello there! n < -2.

Solve for n. To do this, you want to get all other terms on the other side of the equation. The only other term is 7 in this case, so subtract 7 from both sides of the equation.

n +7-7< 5​-7

n < -2

This is your final answer! I hope this helps and have a great day!

Answer:

The solution is n<-2

Step-by-step explanation:

The given inequality is:

n+7 <5​

We solve this inequality by adding -7 to both sides of the inequality:

n+7 +-7<5​+-7

We simplify to get:

n+0<5​-7

this finally gives us:

n<-2

The solution is n<-2

What is (u+2ax)(2u+2ax)

Answers

Answer:

2u^2 +6aux+4ax

Step-by-step explanation:

2u^2 because u×2u

2aux cuz u× 2ax

4aux cuz 2ax×2u

4ax. cuz 2ax time 2ax

Final answer:

The multiplication of the binomials (u+2ax)(2u+2ax) can be solved using the FOIL method. The steps result in 2u^2 + 2uax + 4uax + 4a^2x^2. Combining like terms yields the final answer: 2u^2 + 6uax + 4a^2x^2.

Explanation:

The problem (u+2ax)(2u+2ax) is a mathematical multiplication of two binomial expressions. You may solve it by applying the distributive property, also known as the FOIL method (First, Outer, Inner, Last). Let's walk through the steps to solve it:

First: Multiply the first terms in each binomial. u * 2u = 2u^2. Outer: Multiply the outer terms, which are u and 2ax. u * 2ax = 2uax. Inner: Multiply the inner terms, which are 2ax and 2u. 2ax * 2u = 4uax. Last: Multiply the last terms of each binomial. 2ax * 2ax = 4a^2x^2.

Then, add these results together: 2u^2 + 2uax + 4uax + 4a^2x^2. Combine like terms to get the final answer: 2u^2 + 6uax + 4a^2x^2.

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find the distance between A(2,3,5) and B(6,7,-2)
(pictures of the answer above)

Answers

Answer:

I think it's B (Sorry if im wrong)

Solve the matrix equation for X.

Answers

See the attached picture:

Answer:

[tex]\large\boxed{\left[\begin{array}{ccc}-2&11\\-1&10\end{array}\right]}[/tex]

Step-by-step explanation:

[tex]\left[\begin{array}{ccc}8&-7\\1&-5\end{array}\right] +X=\left[\begin{array}{ccc}6&4\\0&5\end{array}\right]\\\\\left[\begin{array}{ccc}8&-7\\1&-5\end{array}\right] -\left[\begin{array}{ccc}8&-7\\1&-5\end{array}\right]+X=\left[\begin{array}{ccc}6&4\\0&5\end{array}\right] -\left[\begin{array}{ccc}8&-7\\1&-5\end{array}\right]\\\\X=\left[\begin{array}{ccc}6-8&4-(-7)\\0-1&5-(-5)\end{array}\right]\\\\X=\left[\begin{array}{ccc}-2&11\\-1&10\end{array}\right][/tex]

The constant of proportionality for the amount of electricity in kilowatt hours and the cost per kilowatt hour is $0.11. Which graph models this situation?

Answers

Answer:

The answer I beleive is actually A because if you divide the x value by the y-value it gives you 0.11 and no other graph gives you that exact amount dividing either y or x values

Step-by-step explanation:

Sorry for being so late lol

The answer is, electticity cost.

What is graph in math definition?Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter. Each object in a graph is called a node.

What is graph explain with example?A graph is a common data structure that consists of a finite set of nodes (or vertices) and a set of edges connecting them. A pair (x,y) is referred to as an edge, which communicates that the x vertex connects to the y vertex. In the examples below, circles represent vertices, while lines represent edges.

Why do we use graphs?Graphs and charts are effective visual tools because they present information quickly and easily. It is not surprising then, that graphs are commonly used by print and electronic media. Sometimes, data can be better understood when presented by a graph than by a table because the graph can reveal a trend or comparison.

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Lisa bought a tank for her hermit crab. The tank can hold 1,331 cubic inches of water and includes a top. The base fo the aquarium is a square. The height of the aquarium is 11 inches. a. What is the length of each side of the base of the tank

Answers

Answer:

11 in

Step-by-step explanation:

All we care about here is volume, not area.  So the top is irrelevant.

The volume of a rectangular tank with a square bottom, b, and height, h, is

V = b²h = 1,331 in³                       1,331 in³

Then b² = area of the base  = ---------------- = 121 in²

                                                    11 in

The square of the length of any one side of the base is 121 in².

Taking the square root of this yields 11 in.

The length of each side of the base is 11 in.

How can you tell whether or not a question is a statistical question?

Answers

A statistical question is one for which you don't expect to get a single answer. Instead, you expect to get a variety of different answers, and you are interested in the distribution and tendency of those answers. For example, "How tall are you?" is not a statistical question. But "How tall are the students in your school?" is a statistical question.

3 pizzas are shared equally between 10 people. What fraction of a pizza does each person receive?

Show your work, please!

Answers

Answer:

3/10 fraction of a pizza is received by each person.

Step-by-step explanation:

3 pizzas are shared among 10 people. We need to find the fraction of pizza each person receive.

No of pizzas = 3

Total People sharing = 10

Each person receive pizza = No of pizzas/ Total People sharing

                                             = 3/10

3/10 fraction of a pizza is received by each person.                                            

Answer:

dang

Step-by-step explanation:

2 years ago

What is the solution to the equation 3/5(x+4/3) = 1.04

1. 3.0666
2. 0.4
3. -0.4888
4. -.0709333

Answers

Answer:

2. 0.4

Step-by-step explanation:

Solve for "x" by simplifying both sides of the equation, then isolating the variable.

The solution of the equation is x = 0.4.

What is an Equivalent Expression?The expression where equivalent result is produced by the both sides of the expression.It is used to solve many critical mathematical problems.

Given: Equation

[tex]\frac{3}{5}(x+\frac{4}{3})=1.04[/tex]

Now, we have to solve for x.

[tex]\frac{3}{5}(x+\frac{4}{3})=1.04[/tex]

Multiplying both sides by 5, we get:

⇒ 3(x + 4/3) = 1.04 × 5

⇒ 3x + 4 = 5.2

⇒ 3x = 5.2 - 4

⇒ 3x = 1.2

Dividing both sides by 3, we get:

⇒ x = 0.4

Therefore, the solution of the given equation is x = 0.4.

Hence, option (2) is correct.

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Brian makes a 5,000 down payment on a car if he needs to pay $300 a month for the next 48 months how much will he pay for the car

Answers

Answer:

car cost 19400

Step-by-step explanation:

y = 5000 + 300*m where m is the number of months.

m = 48

y = 5000 + 300*48

y = 5000 + 14400

y = 19400

The cost of the car is 19400

Answer:

14,400 because if you multiply 300 and 48 because thats what he has to pay for the car and how long he has making that same payment

Then you add 5000 for the total payment because thats the car paid in full

* Therefor, the answer is 14,400

* Hopefully this helps:) Mark me the brainliest:)!!!

Which is the equation of the given line?

x = -7y
x = 7
y = -7x
y = -7

Answers

Answer:

x= -7y

Step-by-step explanation:

Your answer would be x= -7y. Hope this helps!!

This equation represents the given horizontal line is y = - 7. the correct option is d.

To find the equation of the line passing through the points (-10, -7) and (3, -7), we can use the point-slope form of a linear equation:

The point-slope form is given by: y - y₁ = m(x - x₁)

where (x₁, y₁) are the coordinates of one of the points on the line, and m is the slope of the line.

First, let's calculate the slope (m) using the two points:

m = (change in y) / (change in x)

m = (-7 - (-7)) / (3 - (-10))

m = 0 / 13

m = 0

Now, we have the slope (m = 0), and we can choose either of the given points to plug into the equation. Let's use the point (-10, -7):

y - (-7) = 0(x - (-10))

y + 7 = 0

Now, we can simplify the equation:

y = -7

So, the equation of the line passing through the points (-10, -7) and (3, -7) is y = -7. This equation represents a horizontal line at y = -7, as the slope is 0.

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Mrs. Piper is driving Anna, Jo, and Mai home from school. All of them want to ride in the front seat. How can she make a fair decision about who rides in the front seat?

Answers

Answer:

[tex]\frac{1}{3}[/tex]

Step-by-step explanation:

The question is on probability

We have three students, Anna, Jo and Mai

We have 1 seat at the front

P(S)=3

P(A)=1/3

P(J)=1/3

P(M)=1/3

a triangle has a base of 7m and a hypotenuse of 25m what is the area​

Answers

Answer:

84 m²

Step-by-step explanation:

If you mention "hypotenuse," I automatically assume that this is a right triangle.  We can find the length of the third side using the Pythagorean Theorem:  7² + x² = 25², or x² = 625 - 49 = 576.

Then the 3rd side (which is also the height of the triangle) is x = √576 = 24.

The base of this triangle is 7 m and the height is 24 m.

The area is thus:

A = (1/2)(base)(height) = (1/2)(7 m)(24 m) =   84 m²

Mathematics probability

Answers

Do you have a specific question or something like that which you need answering?

3/8(2x-8/3x)=21 solve the equation for x​

Answers

Answer:

[tex]\boxed{\bold{x=-84}}[/tex]

Explanation:

Multiply Both Sides By 8:

= [tex]\bold{8\cdot \frac{3}{8}\left(2x-\frac{8}{3}x\right)=21\cdot \:8}[/tex]

Simplify:

= [tex]\bold{-2x=168}[/tex]

Divide Both Sides By -2:

= [tex]\bold{\frac{-2x}{-2}=\frac{168}{-2}}[/tex]

Simplify:

= [tex]\bold{x=-84}[/tex]

//Mordancy //.

X= -84 this would be your answer also use photomath :)

2 Points
What is the point-slope form of a line with slope -5 that contains the point
(2,-1)?
O
O
O
O
A. y + 1 = -5(x - 2)
B. y-1 = 5(x + 2)
c. y- 1 = -5(x - 2)
D. y + 1 = 5(x + 2)
SUBMI

Answers

Answer:

A

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

here m = - 5 and (a, b) = (2, - 1), so

y - (- 1) = - 5(x - 2), that is

y + 1 = - 5(x - 2) → A

The point-slope form of a line with slope -5 that contains the point

(2,-1) is,

⇒ y + 1 = - 5 (x - 2)

Since, The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Here, Given that;

Slope = - 5

Point on line = (2, - 1)

Hence, The point-slope form of a line with slope -5 that contains the point

(2,-1) is,

⇒ y - y₁ = m (x - x₁)

⇒ y - (- 1) = - 5 (x - 2)

⇒ y + 1 = - 5x + 10

⇒ y =- 5x + 10 - 1

⇒ y = - 5x + 9

Thus, The point-slope form of a line with slope -5 that contains the point

(2,-1) is,

⇒ y + 1 = - 5 (x - 2)

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I could probably figure this out but I have way too much homework so It'd be nice to finish this pathway.

Answers

Yeah that's right always be a hardworking person

I am trying to find the next number in this number sequence and I dont know how! its like this, 2,9,37,149,597,2389, ... whats the next number?

Answers

[tex]\bf 2~~,~~\stackrel{2(4)+1}{9}~~,~~\stackrel{9(4)+1}{37}~~,~~\stackrel{37(4)+1}{149}~~,~~\stackrel{149(4)+1}{597}~~,~~\stackrel{597(4)+1}{2389}~~,~~\boxed{\stackrel{2389(4)+1}{9557}}[/tex]

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