MATHEMATICS COLLEGE

David is having a cookout. Hot dogs and buns are sold based on the following quantities per package.Item
Amount Per Package
Hot dog buns
12
Hot dogs
10
A
David thought that he would have to buy 12 packages of hot dog buns and 10 packages of hot dogs to have one bun for each hot dog.
What is the LEAST amount of each David would need to buy to have an equal number of hot dogs and buns?
David should buy 2 packages of buns and 2 packages of hot dogs,
David should buy 6 packages of buns and 5 packages of hot dogs.
с David should buy 5 packages of buns and 6 packages of hot dogs,
D David should buy 22 packages of buns and 22 packages of hot dogs
B

Answers

Answer 1

Answer:

Answer: Choice C) David should buy 5 packages of buns and 6 packages of hot dogs.

========================================================

Explanation:

Focus on the hot dog buns for now

1 package = 12 hot dog buns

2 packages = 24 hot dog buns (multiply both sides by 2)

3 packages = 36 hot dog buns (multiply original equation by 3)

We can see that the multiples of 12 are being listed. So we have

12, 24, 36, 48, 60, 72, 84, ...

as the possible number of hot dog buns we could get if we buy 1,2,3... packages.

The possible number of hot dogs we can get are

10, 20, 30, 40, 50, 60, 70, 80, ...

which are multiples of 10. Simply add 10 to each item to get the next one.

--------------------------------

Considering these two sets

12, 24, 36, 48, 60, 72, 84, ...

10, 20, 30, 40, 50, 60, 70, 80, ...

what is the lowest common multiple? That would be 60 since it is found in both lists and it is the smallest in common.

The LCM of 12 and 10 is 60.

If he wanted 60 hot dog buns, then 60/12 = 5 packages of buns is what he needs.

If he wanted 60 hot dogs, then he needs 60/10 = 6 packages of hot dogs.

Therefore, David should buy 5 packages of buns and 6 packages of hot dogs. The answer is choice C.

--------------------------------

Side note: a different way to find the LCM is to multiply 10 and 12 to get 10*12 = 120. Then we divide by the GCF 2 getting 120/2 = 60.

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4x (7+8) = (4x _) + (4x _)
Find the slope of (5,-5) and (-4,5)

Enter the sum of numbers as a product of their GCF. 45 + 30

Answers

45 + 30 = 15(3 + 2) = 15(5) = 75

Find the perimeter of WXYZ. Round to the nearest tenth if necessary.

Answers

Answer:

C. 15.6

Step-by-step explanation:

Perimeter of WXYZ = WX + XY + YZ + ZW

Use the distance formula, $d = √((x_2 - x_1)^2 + (y_2 - y_1)^2)$ to calculate the length of each segment.

✔️Distance between W(-1, 1) and X(1, 2):

Let,

$W(-1, 1) = (x_1, y_1)$

$X(1, 2) = (x_2, y_2)$

Plug in the values

$WX = √((1 - (-1))^2 + (2 - 1)^2)$

$WX = √((2)^2 + (1)^2)$

$WX = √(4 + 1)$

$WX = √(5)$

$WX = 2.24$

✔️Distance between X(1, 2) and Y(2, -4)

Let,

$X(1, 2) = (x_1, y_1)$

$Y(2, -4) = (x_2, y_2)$

Plug in the values

$XY = √((2 - 1)^2 + (-4 - 2)^2)$

$XY = √((1)^2 + (-6)^2)$

$XY = √(1 + 36)$

$XY = √(37)$

$XY = 6.08$

✔️Distance between Y(2, -4) and Z(-2, -1)

Let,

$Y(2, -4) = (x_1, y_1)$

$Z(-2, -1) = (x_2, y_2)$

Plug in the values

$YZ = √((-2 - 2)^2 + (-1 -(-4))^2)$

$YZ = √((-4)^2 + (3)^2)$

$YZ = √(16 + 9)$

$YZ = √(25)$

$YZ = 5$

✔️Distance between Z(-2, -1) and W(-1, 1)

Let,

$Z(-2, -1) = (x_1, y_1)$

$W(-1, 1) = (x_2, y_2)$

Plug in the values

$ZW = √((-1 -(-2))^2 + (1 - (-1))^2)$

$ZW = √((1)^2 + (2)^2)$

$ZW = √(1 + 4)$

$ZW = √(5)$

$ZW = 2.24$

✅Perimeter = 2.24 + 6.08 + 5 + 2.24 = 15.56

≈ 15.6

Answer:CCCCCCCCCCCCCCCCC

Step-by-step explanation:

Which formula shows a joint variation?

Answers

The answer is the first option: I, II and III.

The explanation is shown below:

1. By definition, there is a joint variation when a variable depends on two or more different variables. Therefore, you can express it as following:

$y=kxz$

Where $x,y$ and $z$ are the variables and $k$ is the constant of proportionality.

As you can see, $y$ is directly proportional to $x$ and $z$ .

2. Keeping the information above, you have:

I) $V=lwh$ ( $V$ varies jointly with $l$ , $w$ and $h$ .

II) $V=(1)/(3)r^(2)h\pi$ (If $(\pi)/(3)$ is the constant of proportionality, $V$ varies jointly with $r^(2)$ and $h$ ).

III) $V=Bh$ ( $V$ varies jointly with $B$ and $h$ .

Answer : I, II and III

To find volume formula that shows joint variation we analyze each option

Joint variation always depends on atleast two dependent variables

for example y = kxy

The variable y depends on x and y and k is constant of proportionality

V= lwh

It means volume depends on length , width and height. 1 is the constant of proportionality .

$v=(1)/(3) \pi r^2h$

V depends on radius r and height h. Here 1/3 pi is the constant of proportionality

V= BH

V depend on base b and height h . 1 is the constant of proportionality .

So answer is I, II , III

Classify the following triangle as acute, obtuse, or right.
30°
249
126

Answers

Answer:

30 - Acute

249 - Obtuse

126 - Obtuse

Step-by-step explanation:

Less than 90 - Acute

90 - Right

More than 90 - Obtuse

F(x)=3x-7 and g(x)=(1/3)x+7 are inverses of each other.

.True
.False

Answers

Answer:

False

Step-by-step explanation:

Sorry for the lat reply hopefully you still have that question ready. But basically in order for these equations to be considered inverses of one another it has to map its domain value and switch it to the range value and in this case it does not match the inverse when graphed.

Final answer:

The functions f(x) = 3x - 7 and g(x) = (1/3)x + 7 are inverses of each other.

Explanation:

Two functions are inverses of each other if the composition of the functions results in the identity function. To check if f(x) = 3x - 7 and g(x) = (1/3)x + 7 are inverses, we need to find their composition.

Let's substitute g(x) into f(x) and simplify: f(g(x)) = f((1/3)x + 7) = 3((1/3)x + 7) - 7 = x + 7 - 7 = x.

Since f(g(x)) = x, it means that f(x) and g(x) are inverses of each other, and therefore the statement is True.

Learn more about Inverses of Functions here:

brainly.com/question/38141084

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GUYS HELP ME PLS. Tina is standing at the bottom of a hill. Matt is standing on the hill so that when Tina's line of sight isperpendicular to her body, she is looking at Matt's shoes.
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