Paula knows the total cost for 100 students will be $750, and the cost total cost for 150 students is $1050. What is the caterer’s fixed cost and the rate per student served?

Answers

Answer 1

Answer:

The caterer’s fixed cost and the rate per student served is $6 and $150

How to choose what quantity to multiply the first equation?

This method is actually called method of elimination to solve a system of linear equations.

We make one specific variable's coefficients of equal magnitude so that we can subtract or add the equations and eliminate that variable to make it easy to get the value of the other variable which will then help in getting the value of the first variable (if working in dual variable system).

If we have equations:

$a_1x + b_1y = c_1\na_2x + b_2y = c_2$

then, if we want to eliminate variable x, then we have to multiply equation 1 with

$-(a_2)/(a_1)$

which will make coefficient of x in first equation as

$a_1 * - (a_2)/(a_1) = -a_1$

Then adding both equation will eliminate the variable x.

Given;

Cost of 100 students= $750

Cost of 150 students= %1050

Let the fixed cost of caterer be x

and the cost per student be y

x+100y=750...(1)

x+150y=1050...(2)

solving the above equations;

50y=300

y=6

x=750-600=150

The fixed cost is $150, while the per-student cost is $6.

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Answer 2

Answer:

Step-by-step explanation:

the price charged for 100 students reflects the cost per student that applies to the order as a whole.

100 * 6 = $600, so the fixed cost is 750-600 = 150.

...

We can check this by substituting in the other equation.

Does 150*6 + 150 = 1050?

150*6=900

900+150 = 1050.

Yes, it does

...

We can express this relationship by the equation:

y = mx + b

where

y = total cost

m = $6 per student

x = number of students

b = fixed costs = 150

y = 6x + 150

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The base of a triangle is 3 inches more than 2 times the height.If the area is 7 square inches, find the base and the height.
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Is this one correct?

Find the product. write your answer in exponential form 9²•9-⁶

Answers

Answer:

9^8

Step-by-step explanation:

9²•9⁶ = 9^(2+6) = 9^8

Answer:

IF the 6 is negative : $9^(2)$ · $9^(-6)$ then the answer is 1/ $9^(4)$

If the 6 is positive then the answer is $9^(8)$

Step-by-step explanation:

Exponents are add when their bases are similar.

Choose the two rectangular prisms that have a volume of 36 cm”.= 1 cm3
A.
D.
B.
E.
C.

Answers

Answer:

B & D

Step-by-step explanation:

Volume is calculated as:

$Volume = Length * Width * Height$

For (a):

$Length = 3cm$

$Width = 4cm$

$Height = 5cm$

$Volume = 3cm * 4cm * 5cm$

$Volume = 60cm^3$

For (b):

$Length = 3cm$

$Width = 4cm$

$Height = 3cm$

$Volume = 3cm * 4cm * 3cm$

$Volume = 36cm^3$

For (c):

$Length = 4cm$

$Width = 2cm$

$Height = 2cm$

$Volume = 4cm * 2cm * 2cm$

$Volume = 16cm^3$

For (d):

$Length = 2cm$

$Width = 3cm$

$Height = 6cm$

$Volume = 2cm * 3cm * 6cm$

$Volume = 36cm^3$

There's no need to check for (e)

Option b and d answers the question

Using the volumeof a rectangularprismto examine the volumesof the prism,the two prisms with a volumeof 36cm³are Band D

Recall:

Volumeofarectanglularprism=Length×width×Height

PrismA:

Length=3cm;Height=5cm;Width=4cm

Volume = 3cm × 5cm × 4cm = 60cm³

Prism B :

Length = 3cm ; Height = 3cm ; Width = 4cm

Volume = 3cm × 3cm × 4cm = 36 cm³

Prism C :

Length = 4cm ; Height = 3cm ; Width = 2cm

Volume = 4cm × 3cm × 2cm = 24 cm³

Prism D :

Length = 2cm ; Height = 6cm ; Width = 3cm

Volume = 2cm × 6cm × 3cm = 36 cm³

Prism E :

Length = 3cm ; Height = 5cm ; Width = 4cm

Volume = 4cm × 2cm × 2cm = 16 cm³

Hence, the two rectangularprismswith a volumeof 36cm³are Band D.

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What is the length of AC?

Answers

The length of AC found using the Pythagorean Theorem is C) 120.

The length of AC can be found using the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is AC, and the other two sides are AB and BC.

AB = 60 units

BC = 80 units

Plugging these values into the Pythagorean Theorem, we get:

$AC^2$ = $AB^2$ + $BC^2$

$AC^2$ = $60^2$ + $80^2$

$AC^2$ = 3600 + 6400

$AC^2$ = 10000

AC = $\sqrt{$ (10000)

AC = 100 * $\sqrt{$ (10)

AC = 120 units

Therefore, the length of AC is C) 120.

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B I think and I hope it’s right!

1. SPOTLIGHTS Ship A has coordinates (–1, –2) and Ship B has coordinates (–4, 1). Both ships have their spotlights fixated on the same lifeboat. The light beam from Ship A travels along the line y = 2x. The light beam from Ship B travels along the line y = x + 5. What are the coordinates of the lifeboat?

Answers

Answer:

( 5 , 10 )

Step-by-step explanation:

Solution:-

- There are two ships, A and B, currently located by their respective coordinates in the cartesian coordinate system:

Position of ship A: ( - 1 , -2 )

Position of ship B: ( -4 , 1 )

- Both ships try to locate a lifeboat. The spotlights used by each ship are modelled as straight line functions of cartesian coordinate originating from their respective ships.

- Spot lights for each ship were able to locate the same lifeboat. The respective spotlights are modelled by the following functions:

Spotlight Ship A: y = 2x

Spotlight Ship B: y = x + 5

- To locate the position of the lifeboat with respect to the origin ( 0 , 0 ) we will use the spotlight model functions and equate them. This is because the spotlights must converge or meet at the position of lifeboat provided the lifeboat is found by both ships.

- Therefore,

Spotlight A = Spotlight B

y = 2x = x + 5

2x = x + 5

x = 5 , y = 10

Answer:The two spotlight meet at the coordinates ( 5 , 10 ). This is also the position of the lifeboat located by both the ships.

A brownie recipe calls for 1 1/2 cups of flour and 1/2 cup of sugar. If you use 1 cup of sugar, how many cups of flour will you use

Answers

Answer:

1 and 2/4

or 2

Step-by-step explanation:

I would say that it is 3 cups of flower. B/c you doubled your sugar so you would double the flower. 1 1/2 + 1 1/2 = 3 cups of flower. Good luck

a tree needs to be stake with four wires, each wire is attached to the trunk 6 feet above the ground, and then anchored to the ground 8 feet from the base of the tree. How many feet of the wire is needed for 5 trees???

Answers

Answer:

Step-by-step explanation:

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