Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. Today's cafeteria specials at a high school in Ashland are a deluxe turkey sandwich and a chef salad. During early lunch, the cafeteria sold 14 turkey sandwiches and 61 chef salads, for a total of $150. During the late lunch, 14 turkey sandwiches and 25 chef salads were sold, for a total of $78. How much does each item cost? A turkey sandwich costs $ , and a chef salad costs $ .

Answer:

[tex]108\ \text{m}^2[/tex]

Step-by-step explanation:

The sides are rectangle is shown in the diagram

The perimeter of the fence will be

[tex]3x+2y=36\\\Rightarrow x=\dfrac{36-2y}{3}[/tex]

Area of the smaller section of the garden

[tex]A=xy\\\Rightarrow A=\dfrac{36-2y}{3}y\\\Rightarrow A=\dfrac{36y-2y^2}{3}[/tex]

Differentiating with respect to y we get

[tex]\dfrac{dA}{dy}=\dfrac{1}{3}(36-4y)[/tex]

Equating with zero we get

[tex]\dfrac{1}{3}(36-4y)=0\\\Rightarrow 36-4y=0\\\Rightarrow y=\dfrac{36}{4}\\\Rightarrow y=9[/tex]

Double derivative of area

[tex]\dfrac{d^2A}{dy^2}=-4<0[/tex]

at y = 9 the area is maximum

[tex]x=\dfrac{36-2y}{3}=\dfrac{36-2\times 9}{3}\\\Rightarrow x=6[/tex]

The sides of the entire garden are [tex]2y=2\times 9=18\ \text{m}[/tex] and [tex]6\ \text{m}[/tex]

The maximum area of the natural fertilizer garden is [tex]18\times 6=108\ \text{m}^2[/tex]

Answer:

Fill in the blank with 14

Step-by-step explanation:

Given

The attached table

Required

Fill in the gap

Since, the table represents a linear function.

The first step is to calculate the slope of the table

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Where

[tex](x_1,y_1) = (1,2)[/tex]

[tex](x_2,y_2) = (2,6)[/tex]

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

[tex]m = \frac{6 - 2}{2 - 1}[/tex]

[tex]m = \frac{4}{1}[/tex]

[tex]m=4[/tex]

The equation of the table is calculated next as:

[tex]y - y_1 = m(x - x_1)[/tex]

This becomes

[tex]y - 2 = 4(x - 1)[/tex]

[tex]y - 2 = 4x - 4[/tex]

Solve for y

[tex]y = 4x - 4+2[/tex]

[tex]y = 4x -2[/tex]

To fill in the blank;

The value of x is 4

So, substitute 4 for x in [tex]y = 4x -2[/tex]

[tex]y = 4 * 4 - 2[/tex]

[tex]y = 16 - 2[/tex]

[tex]y = 14[/tex]

Answer:

whats the question? I don't see one to be abel to answer you

Answer:

Median: 3.5 Mode: 3, 7 Mean: 4.2

Step-by-step explanation:

hope this helps :)

Answer:

103 degrees

Step-by-step explanation:

180 - 77 = 103

Answer:

51.3°

Step-by-step explanation:

tan y = 10/8 = 1.25

y = 51.3°

Answer: 33%

Step-by-step explanation: 5/15 simplifies to 1/3 which is 33%

Answer:

33.333333333..... %

Step-by-step explanation:

(5/15)*100

Answer:

[tex]x = 2[/tex]

Step-by-step explanation:

[tex]x^{3} * 3^{3} = 6^{3}[/tex]

[tex]=> (3x)^{3} = 6^{3}[/tex]

[tex]=> 3x = \sqrt[3]{6^{3}} = 6[/tex]

[tex]=> x = \frac{6}{3} = 2[/tex]

Answer:

[tex] {x}^{3} \times {3}^{3} = {6}^{3} \\ take \: cube \: root \: on \: both \: side \ \\ \sqrt[3]{ {x}^{3} } \times \sqrt[3]{ {3}^{3} } = \sqrt[3]{ {6}^{3} } \\ x \times 3 = 6 \\ x = \frac{6}{3} \\ x = 2 \\ thnk \: you[/tex]

Step-by-step explanation:

8 will be the answer might be

Answer:

450.01

Step-by-step explanation:

Answer:

90 stamps from Canada, 108 stamps from the United States, and 135 stamps from the Rest of the World

Step-by-step explanation:

Since this is a problem of proportion we can use the Rule of three to solve this. We do this by multiplying the diagonal available values and dividing by the third value in order to get the missing variable, which in this case would be the number of stamps in the other country. Like so...

1.5  <=====>  135 stamps

1.2  <=====>  x  stamps (United States)

(1.2 * 135) / 1.5 = 108 stamps (United States)

1.5  <=====>  135 stamps

1  <=====>  x  stamps (Canada)

(1 * 135) / 1.5 = 90 stamps (Canada)

Finally, we can see that Katie had 90 stamps from Canada, 108 stamps from the United States, and 135 stamps from the Rest of the World. All creating a ratio or 1:1.2:1.5

Answer:

elaborate, this is vague

Step-by-step explanation:

Answer:

This is the answer. All the very best. Do it

Answer:

30

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

9514 1404 393

Answer:

  120

Step-by-step explanation:

The first one can be any of 6. The second can be any of the remaining 5, and the third can be any of the remaining 4. The total number of possible displays is ...

  6 × 5 × 4 = 120

3 posters of 6 can be displayed 120 ways.

Answer:

2x + y = 17

-6x = 3y - 51

Step-by-step explanation:

You get an infinite number of solutions when two equations are really just the same. This means you can convert one into the other simply by multiplying one to get the other.

In the above answer, if you multiply the above by -3 you get:

-6x -3y = -51

which is of course -6x = 3y - 51

So that is an example of a pair that has infinite solutions.

To find all of them, you'd carefully have to compare each 2 and see if there is a multiplier to convert one into the other. You can do that!

Answer: the 2 on the right

Step-by-step explanation:

Answer:

They have to go 30 m below sea level to reach wreckage.

Step-by-step explanation:

jane and her friends are diving to explore a wreckage from a ship that is 40 meters below sea level the platform they dive from is 10 meters above sea level.

Below sea level means = -40 m

Above sea level means = +10 m

It means,

-40 m + 10 m

= -30 m

Hence, they have to go 30 m below sea level to reach wreckage.

Answer:

decimal: 0.32 percent: 32%

Step-by-step explanation:

Answer:

Step-by-step expla

To find the volume of a cone, use the equation: V = 1/3Bh.

In this equation, V is the volume, B is the base, and h is the height.

We are given that the base is 12 inches, and the height is 18 inches. With those necessary values, we can substitute those values, and calculate it.

V = 1/3(12)(18)

V = 4(18)

V = 72.0

Therefore, the volume of this glass is 72.0 cubic inches.

Answer:

NONONO the answer is C

Step-by-step explanation:

Multiply -3 by -1 gives 3. 3 plus 15 IS equal to 18!

Answer:

The answer is C

Step-by-step explanation:

3x+15=18

if x = -1

-3 (-1) + 15 = 18

negative times negative makes positive so

3+15=18

Answer:

(6, 8)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define Systems

1/2y = 4

x - 1/2y = 2

Step 2: Solve for y

Step 3: Solve for x

Answer: (6,8)

Step-by-step explanation:

1/2y = 4          

x - 1/2y = 2    

First  solve for y in the first equation.

1/2y = 4      Divide both sides by 1/2

y  =  8  

NOw substitute the value of y into the second equation and solve for x.

x

x - 1/2(8) = 2

x - 4 = 2

  +4     +4

x = 6    

THis makes the solution  (6,8)

Answer:

94. E

95. A

96. F

97. B

98. H

99. D

Hope this helps :)

Answer:

Given,

P = ₹5,000

R = 5%

T = 6 months

= 1/2 years

S.I = P×R×T/100

= 5,000 × 5 / 2×100

= 250 / 2

= ₹125

Step-by-step explanation:

The simple interest of principal of $ 6000 at an interest rate of 5% for a period of 6 months is $ 150

What is Simple Interest?

Simple interest is a method of calculating interest that ignores the impact of compounding. While interest frequently compounds throughout the course of a loan's set periods, simple interest does not. Simple interest is calculated by multiplying the principal amount by the interest rate, times the number of periods.

Simple Interest = ( Principal Amount x Rate x Time Period ) / 100

Given data ,

Let the total amount be Principal P = $ 6000

Let the interest rate be R = 5 %

Let the number of periods be T = 6 months

So , the value of T = 1/2

Now , the simple interest is given by the formula

Simple Interest = ( Principal Amount x Rate x Time Period ) / 100

Substituting the values in the equation , we get

Simple Interest = ( 6000 x 5 x ( 1 / 2 ) ) / 100

Simple Interest = ( 60 x 5 ) / 2

Simple Interest = $ 150

Therefore , the value of simple interest is $ 150

Hence , The simple interest of principal of $ 6000 at an interest rate of 5% for a period of 6 months is $ 150

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Answer:

B.

Step-by-step explanation:

To find the value of w in terms of x and y, we need to substitute the given values of x and y into the equation for w. First, we are given the equation [tex]x = 3(y + 2) - 1[/tex].

Let's simplify this equation before substituting it into the equation for w. Expanding the equation, we have: [tex]x = 3y + 6 - 1 x = 3y + 5[/tex] Now we can substitute the value of x into the equation for w. w [tex]= (x - 3y + 1) / 3[/tex] Substituting the value of x from the earlier equation: w [tex]= (3y + 5 - 3y + 1) / 3 w = (6y + 6) / 3[/tex]

At this point, we can further simplify the equation by dividing both the numerator and denominator by 3: w[tex]= 2y + 2[/tex]Therefore, the value of w in terms of x and y is w[tex]= 2y + 2. I[/tex]n summary: Starting with x [tex]= 3(y + 2) - 1,[/tex]we substituted the value of x into the equation for w and simplified to obtain w [tex]= 2y + 2.[/tex]

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