The non-profit organization you volunteer for is throwing a fundraiser cookout. You are in charge of buying the hamburgers, which cost $3 per pound, and hot dogs, which cost $2 per pound. The meat budget you are given totals $600 dollars. The inequality 3x + 2y less than or equal to 600 represents the possible combinations of pounds of hamburgers (x) and hot dogs (y) you can buy.

Answers

Answer 1

Answer: Which of the following represents a solution to the inequality?
200 pounds of hamburgers and 140 pounds of hot dogs
150 pounds of hamburgers and 60 pounds of hot dogs
100 pounds of hamburgers and 240 pounds of hot dogs
240 pounds of hamburgers and 40 pounds of hot dogs

x = hamburger ; y = hot dog
3x + 2x < 600

3(200) + 2(140) = 600 + 280 = 880 No.
3(150) + 2(60) = 450 + 120 = 570 YES.
3(100) + 2(240) = 300 + 480 = 780 No.
3(240) + 2(40) = 720 + 80 = 800 No.

150 pounds of hamburgers and 60 pounds of hot dogs

Answer 2

Answer:

Answer:

$150$ pounds of hamburgers and $60$ pounds of hot dogs

Step-by-step explanation:

The options are

Which of the following represents a solution to the inequality?

$200$ pounds of hamburgers and $140$ pounds of hot dogs

$150$ pounds of hamburgers and $60$ pounds of hot dogs

$100$ pounds of hamburgers and $240$ pounds of hot dogs

$240$ pounds of hamburgers and $40$ pounds of hot dogs

Let

x------> the pounds of hamburgers

y------> the pounds of of hot dogs

we know that

The inequality that represent the situation is equal to

$3x+2y\leq 600$

Remember that

If a ordered pair is a solution of the inequality

then

the ordered pair must satisfy the inequality

Verify each case

case A) $200$ pounds of hamburgers and $140$ pounds of hot dogs

Substitute the value of x and the value of y in the inequality and then compare

$3(200)+2(140)\leq 600$

$880\leq 600$ ------> is not true

therefore

the case A) is not a solution

case B) $150$ pounds of hamburgers and $60$ pounds of hot dogs

Substitute the value of x and the value of y in the inequality and then compare

$3(150)+2(60)\leq 600$

$570\leq 600$ ------> is true

therefore

the case B) is a solution

case C) $100$ pounds of hamburgers and $240$ pounds of hot dogs

Substitute the value of x and the value of y in the inequality and then compare

$3(100)+2(240)\leq 600$

$780\leq 600$ ------> is not true

therefore

the case C) is not a solution

case D) $240$ pounds of hamburgers and $40$ pounds of hot dogs

Substitute the value of x and the value of y in the inequality and then compare

$3(240)+2(40)\leq 600$

$800\leq 600$ ------> is not true

therefore

the case D) is not a solution

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Explain this algebraic expression in your own words: 3x - y

Prove that there is a positive integer that equals the sum of the positive integers not exceeding it. Is your proof constructive or nonconstructive :)

Answers

Constructive. To prove that there is a positive integer that equals the sum of the positive integers not exceeding it. A plain and simple example is
1.1 + 2 = 3
2.10 + 50 + 100 =160
3.6x + 8x + 2x = 16 x

Notice that the sum of the numbers is always greater than the addends. This only proves that any positive sum of any two positive addends will not compare and thus the addends not exceeding a greater value than the sum.

Find the value of x so that lines l and m are parallel.

Answers

Final answer:

The value of x that will make the given lines parallel is 11. This is determined by setting up and solving the equation formed by setting the two given angles equal to each other.

Explanation:

In this question, you are provided with the two alternate interior angles formed by the two lines l and m that are supposedly parallel. We know that in the case of parallel lines, alternate interior angles are equal.

Therefore, for the lines l and m to be parallel, the equality 2x+22 = 4x must hold.

Let's solve this equation step by step:

Subtract 2x from both sides: 22 = 2x
Divide both sides by 2: x = 11

So, the value of x that makes lines l and m parallel is 11.

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$4x+2x+22=180\n\n6x=158\n\nx=(158)/(6)=(79)/(3)$

THIS IS FOR 10 POINTS!!!!!!!!!! PLEASE HELP ME12p=?

If p represents a proper fraction then your answer will be
A. Less than
B.Greater than
C. Equal to
AND
What fraction makes the above statement true
2/3 12/1 2/2 8/8 5/4 5/8 12 3/5 16/4

Answers

A proper fraction is a fraction that is less than 1, that is the nominator is smaller than the denominator.

an example of a proper fraction is 1/2.

so let's try it out:

12* $(1)/(2)$ =6

so if p represents a proper fraction, the result could be bigger than 1

but it could also be 1:

12* $(1)/(12)$ =1

or less than 1:

12* $(1)/(22)$ = $(1)/(12)$

So... I think you might have forgotten something?

The options (A. Less than
B.Greater than
C. Equal to)

need something else at the end: less than WHAT etc.

as for the second part, among the fractions:

2/3 12/1 2/2 8/8 5/4 5/8 12 3/5 16/4

Only those are proper fractions (so would make the statement true)

2/3

5/8

3/5

Which of the following is a solution of y - x < -3?

Answers

If you would like to find the solution for the inequation y - x < - 3, you can do this using the following steps:

y - x < - 3
y - x + x < - 3 + x
y < - 3 + x
y < x - 3

The correct result would be y < x - 3.

What is (7/12)/(5/9)? In simplest form..

Answers

$(7)/(12) / (5)/(9) =$

Change the division to multiplication through the reciprocal of the number being divided.

$(7)/(5) * (9)/(5) = (21)/(20)$

As mixed number:

$1 (1)/(20)$

7/12 times 5/9 equals 35/108. It is automatically in simplest form.

How long does it take to double a $1,000 investment that pays 6.5% annual interest, compounded monthly?Which equation can you use to solve this problem?
To the nearest year, it will take about ___
years to double the original investment.

Answers

To the nearest year, it will take about 10.7 years to double the original investment.

How to solbve for the period it would take

In this case, the principal P is $1,000, the interest rate r is 6.5% or 0.065 (in decimal form), the number of times compounded per year n is 12 (compounded monthly), and we want to find the time t when the investment doubles, so A is $2,000.

$2000 = 1000(1 + 0.065/12)^(12t)$

$2 = (1 + 0.065/12)^(12t)$

ln(2) = 12t * ln(1 + 0.065/12)

t = ln(2) / (12 * ln(1 + 0.065/12))

t ≈ 10.7

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Answer: edgen

B 2=(1+0.065/12)^12t

Step-by-step explanation:

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