A farmer sells peaches and kiwis at a farmers market. The peaches sell for $3.50 per pound and the kiwis sell for $2.75 per pound. The farmer's truck can carry 1,800 pounds of fruit.
If the farmer sells all 1,800 pounds of fruit that he brings to the market, what is the maximum and what is the minimum amount of money he can earn? Provide support for your answer.

Answer:

The rule of translation is [tex]A(x',y') = A(x,y) + (5,-3)[/tex].

The translated vector is [tex]A(x',y') = (9, 4)[/tex].

Step-by-step explanation:

Let supposed that translation to the right is in the +x direction and translation downwards in the -y direction.

We procced to translate the operation into mathematic terms. A translation consists in a vectorial sum on a given vector. That is:

[tex]A(x',y') = A(x,y) + U(x,y)[/tex] (Eq. 1)

Where:

[tex]A(x,y)[/tex] - Original vector, dimensionless.

[tex]U(x,y)[/tex] - Translation vector, dimensionless.

[tex]A(x',y')[/tex] - Translated vector, dimensionless.

If we know that [tex]U(x, y) = (5, -3)[/tex], then the rule of translation is described by:

[tex]A(x',y') = A(x,y) + (5,-3)[/tex] (Eq. 2)

If [tex]A(x, y) = (4,7)[/tex], then the new location of A is:

[tex]A(x',y') = (4,7)+(5,-3)[/tex]

[tex]A(x',y') = (9, 4)[/tex]

The translated vector is [tex]A(x',y') = (9, 4)[/tex].

- 3 x₂ + 7 x₃ = 3

x₁ + 2 x₂ - x₃ = 0

5 x₁ - 2 x₂ = 3

(a) I suppose this is asking for the determinant of the coefficient matrix.

[tex]\begin{vmatrix}0&-3&7\\1&2&-1\\5&-2&0\end{vmatrix}[/tex]

Using a cofactor expansion along the first row, this reduces to

[tex]0\begin{vmatrix}2&-1\\-2&0\end{vmatrix}-(-3)\begin{vmatrix}1&-1\\5&0\end{vmatrix}+7\begin{vmatrix}1&2\\5&-2\end{vmatrix}= 3(0 - (-5))+7(-2-10)=\boxed{-69}[/tex]

(b) Using Cramer's rule, we have

[tex]x_1=\dfrac{\begin{vmatrix}\mathbf 3&-3&7\\\mathbf 0&2&-1\\\mathbf 3&-2&0\end{vmatrix}}{\begin{vmatrix}0&-3&7\\1&2&-1\\5&-2&0\end{vmatrix}}[/tex]

[tex]x_2=\dfrac{\begin{vmatrix}0&\mathbf 3&7\\1&\mathbf 0&-1\\5&\mathbf 3&0\end{vmatrix}}{\begin{vmatrix}0&-3&7\\1&2&-1\\5&-2&0\end{vmatrix}}[/tex]

[tex]x_3=\dfrac{\begin{vmatrix}0&-3&\mathbf 3\\1&2&\mathbf 0\\5&-2&\mathbf 3\end{vmatrix}}{\begin{vmatrix}0&-3&7\\1&2&-1\\5&-2&0\end{vmatrix}}[/tex]

That is, solving for n-th variable consists of dividing [the determinant of the coefficient matrix with its n-th column replaced with the right side of the system, the numbers in boldface,] by [the determinant of the coefficient matrix].

Compute each determinant:

[tex]\begin{vmatrix}\mathbf 3&-3&7\\\mathbf 0&2&-1\\\mathbf 3&-2&0\end{vmatrix}=3\begin{vmatrix}2&-1\\-2&0\end{vmatrix}+3\begin{vmatrix}-3&7\\2&-1\end{vmatrix}=3(0-2)+3(3-14)=-39[/tex]

(expanding along the first column)

[tex]\begin{vmatrix}0&\mathbf 3&7\\1&\mathbf 0&-1\\5&\mathbf 3&0\end{vmatrix}=-1\begin{vmatrix}3&7\\3&0\end{vmatrix}+5\begin{vmatrix}3&7\\0&-1\end{vmatrix}=-1(0-21)+5(-3-0)=6[/tex]

(again, along the first column)

[tex]\begin{vmatrix}0&-3&\mathbf 3\\1&2&\mathbf 0\\5&-2&\mathbf 3\end{vmatrix}=-1\begin{vmatrix}-3&3\\-2&3\end{vmatrix}+5\begin{vmatrix}-3&3\\2&0\end{vmatrix}=-1(-9-(-6))+5(0-6)=-27[/tex]

(first column)

So, we get the solution

[tex]x_1=\dfrac{-39}{-69}=\boxed{\dfrac{13}{23}},x_2=\dfrac6{-69}=\boxed{-\dfrac2{23}},x_3=\dfrac{-27}{-69}=\boxed{\dfrac9{23}}[/tex]

(c) Using elimination:

- 3 x₂ + 7 x₃ = 3

x₁ + 2 x₂ - x₃ = 0

5 x₁ - 2 x₂ = 3

Swap the first two equations:

x₁ + 2 x₂ - x₃ = 0

- 3 x₂ + 7 x₃ = 3

5 x₁ - 2 x₂ = 3

Add -5(equation 1) to equation 3:

x₁ + 2 x₂ - x₃ = 0

- 3 x₂ + 7 x₃ = 3

- 12 x₂ + 5 x₃ = 3

Add -4(equation 2) to equation 3:

x₁ + 2 x₂ - x₃ = 0

- 3 x₂ + 7 x₃ = 3

- 23 x₃ = -9

Multiply through equation 3 by -1/23:

x₁ + 2 x₂ - x₃ = 0

- 3 x₂ + 7 x₃ = 3

x₃ = 9/23

Add -7(equation 3) to equation 2:

x₁ + 2 x₂ - x₃ = 0

- 3 x₂ = 6/23

x₃ = 9/23

Multiply through equation 2 by -1/3:

x₁ + 2 x₂ - x₃ = 0

x₂ = -2/23

x₃ = 9/23

Add -2(equation 2) and equation 3 to equation 1:

x₁ = 13/23

x₂ = -2/23

x₃ = 9/23

(50×20) - (1×20)

Step-by-step explanation:

there is 50 twenties (20) so its 50 × 20 and 1 twenty is 20

Answer:

It will take 6.4 minutes for Cedrick to type 1 full page of the report.

Step-by-step explanation:

1. First, we want to find out how long it takes Cedrick to type 1/8 of a page. If it takes him 4 minutes to write 5/8 of a page, we can do 5/8 divided by 5, which equals 1/8. We also have to divide 4 by 5 which equals 4/5. So, it takes Cedrick 4/5 of a minute to write 1/8 of a page.

2. We now want to find out how long it takes him to write one page, so we should multiply 1/8 and 4/5 by 8. 1/8 times 8 equals one, and 4/5 times 8 equals 32/5. That means that it takes 32/5 (in decimal form it is 6.4) minutes to write one page of the report.

Cedrick will type one whole page of the report in 6.4 minutes.

Mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.

Given that Cedrick is writing a report. It takes him 4 min to type 5/8 pages of the report.

In the beginning, we need to ascertain how long it takes Cedrick to type 1/8 of a page. We can do 5/8 divided by 5 to get 1/8 if it takes him 4 minutes to write 5/8 of a page.

Additionally, we must divide 4 by 5, which is 4/5. Cedrick, therefore, needs 4/5 of a minute to complete 1/8 of a page.

We need to multiply 1/8 and 4/5 by 8 to get how long it takes him to write one page. 8 divided by 1/8 = 1, while 8 multiplied by 4/5 equals 32/5.

This suggests that writing one page of the report requires 32/5 (6.4 in decimal form) minutes.

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Answer:

1) Thousands

2) 5

3) ten million

4) 3,000,000

Step-by-step explanation:

Answer:

1.  hundred thousands

2. 5

3. ten millions

4.  3,000,000

Step-by-step explanation:

Answer:

The answer would be 2.5 oz. of solution

Step-by-step explanation:

If you need 1:6,000 ratio and the pool you are cleaning is 15,000 then you divide 15,000 by 6,000 and you get what your ratio should be

Answer:

120

Step-by-step explanation:

Answer:

29 units..

Step-by-step explanation:

well i don't know how to insert an image of the answer...but I did it...its (c): 29 units

Answer:

Multiply/divide both sides by the same non-zero constant

Step-by-step explanation:

5x = 20

Divide each side by 5

5x/5 = 20/5

x = 4

Answer:

<

Step-by-step explanation:

6.53 < 6.534

Answer:

What is 28/8 as a decimal you ask? Converting the fraction 28/8 into a decimal is very easy.

To get 28/8 converted to decimal, you simply divide 28 by 8. Don't worry. You don't need to get the calculator out, because we did this for you.

28/8 as a decimal is:

3.5

Answer:

6x + 2 = 3

Step-by-step explanation:

x would represent the unknown number

The sum refers to addition

6 times a number would be 6x (you can use any variable, but for this example I'm using x)

When you put it all together, it is 6x + 2 = 3

The required equation is 6x + 2 = 3.

It is required to find the equation.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign. Equation, statement of equality between two expressions consisting of variables and/or numbers

Given:

The sum of 6 times a number and 2 equals 3.

According to given question we have,

Let the number be x.

6 times a number would be

6x

The sum of 6 times a number and 2 equals 3.

6x + 2 = 3.

Therefore, the required equation is 6x + 2 = 3.

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Answer:

D

Step-by-step explanation:

This is saying 77.8% percent out of 100, therefore we right it like D

I hope this helped, please mark Brainliest, thank you!

Answer:

-Total amount Rafael ended up paying for the motorcycle: $25,186.2

-Interest: $1,586.2

Step-by-step explanation:

You can find the total amount Rafael ended up paying by adding up the down payment plus the result of multiplying the monthly payment for the number of months he paid:

Total payment=3,300+(364,77*60)

Total payment=3,300+21,886.2

Total payment=25,186.2

Now, to calculate the amount of interest that Raphael paid on the loan, you should subtract the price of the motorcycle from the total amount Raphael paid:

Interest=$25,186.2-$23,600

Interest=$1,586.2

Answer:

Ooooook?

Step-by-step explanation:

Fine

Answer:

y=-(1)/(7)x+8

Step-by-step explanation:

Answer:

9.1

Step-by-step explanation:

I think this because it is 9 boxes away from the other points, plus it sloped a bit...

Answer:

9.1

Step-by-step explanation:

Distance=[tex]\sqrt{(x_2-x_1)^{2} +(y_2-y_1)^{2} }[/tex]

=[tex]\sqrt{(4-3)^{2} +(-5-4)^{2} }[/tex]

=[tex]\sqrt{(1)^{2}+(-9)^{2} }[/tex]

=[tex]\sqrt{1+81}[/tex]

=[tex]\sqrt{82}[/tex]

≈9.1

Answer:

we need numbers please

Answer:

$1.76

Step-by-step explanation:

:)

Answer:

sometimes true

Step-by-step explanation:

9514 1404 393

Answer:

  $375

Step-by-step explanation:

The interest formula for simple interest is ...

  I = Prt . . . . on amount P, at annual rate r for t years.

Here, t = 3/12 = 1/4, r = 0.10, P = $15,000, so the interest is ...

  I = $15,000·0.10·0.25 = $375

The simple interest is $375.

Answer:

D. 30x + 120 ≤ 250

Step-by-step explanation:

Since we know that he bought one pair of shoes for $120 you would subtract 250-120=130 though you cant divide 130 into 30 so you would use ≤ so your answer is 30x + 120 ≤ 250

x= how many shirts he buys.

Answer:

Step-by-step explanation:

Question:

Prove the following statement directly from the definitions.

The difference of any two rational numbers is a rational number.

Answer, see attachment for proof.

Answer:

C. The population is all seniors at Riverview High; the sample is the 100 seniors surveyed.

Step-by-step explanation:

The Population in statistical terms refers to the objects, people, organisms, etc that a researcher wishes to study. Usually, the population is so large that it might be difficult for the researcher to study all of them. To solve this problem, a sample is thus obtained from the population in such a way that participants have an equal chance of being chosen for the study. The result gotten from this sample can then be generalized to the entire population.

In the example provided, all the seniors at Riverview High are the population under study. The 100 seniors chosen from this population are the sample.

The population in this setting is all seniors at Riverview High and the sample is the 100 seniors surveyed.

A population is the party of interest in an experiment. It is from a population the sample is derived. A population consists of all the members of the group.

A sample is a smaller group of the population. A sample is sometimes necessary because it might not be feasible or cost effective to access the whole population.

To learn more about population, please check: https://brainly.com/question/12982972

Answer:

( c + a + s) = 5000

(10c + 20a + 15s) = 72000

c = 3s

Step-by-step explanation:

Number of tickets sold = 5000

Proceeds from ticket Sale = $72,000

Tickets for children 16 and younger = $10

Adults = $20

seniors 60 and older = $15

Let :

number of children, c ;

adults, a;

seniors, s,

There were 3 times more children than seniors at the concert ; c = 3s

Total number of attendees = 5000 ;

( c + a + s) = 5000

Total proceeds or revenue

(10c + 20a + 15s) = 72000

Answer:

61.25

Step-by-step explanation:

48 goes into 2940 that many times.

Hope this helped :)

Answer:

61.25

Step-by-step explanation:

2,940 / 48 = 61.25

Hope this helps.

Answer:

Step-by-step explanation:

If the number is 10 so

Product of 10 and 3 = 10 x 3 = 30

Subtracting by 7 = 30 - 7 = 23

So the number is 10

Answer:

The proportion can be used to show that the slope of JL is equal to the slope of MP is  [tex]\frac{0-4}{-4-(-7)}[/tex] =  [tex]\frac{-4-8}{-1-(-10)}[/tex]  ⇒ G

Step-by-step explanation:

The rule of the slope of a line is [tex]m=\frac{y2-y1}{x2-x1}[/tex] , where (x1, y1) and (x2, y2) are two points on the line

∵ The coordinates of the point J are (-7, 4)

∵ The coordinates of the point L are (-4, 0)

∴ x1 = -7 and y1 = 4

∴ x2 = -4 and y2 = 0

→ Substitute them in the rule above to find the slope of LJ

∴ [tex]m_{JL}=\frac{0-4}{-4-(-7)}[/tex]

∵ The coordinates of the point M are (-10, 8)

∵ The coordinates of the point P are (-1, -4)

∴ x1 = -10 and y1 = 8

∴ x2 = -1 and y2 = -4

→ Substitute them in the rule above to find the slope of MP

∴ [tex]m_{MP}=\frac{-4-8}{-1-(-10)}[/tex]

∵ The slope of JL = the slope of MP

∴  [tex]\frac{0-4}{-4-(-7)}[/tex] =  [tex]\frac{-4-8}{-1-(-10)}[/tex]

The proportion can be used to show that the slope of JL is equal to the slope of MP is  [tex]\frac{0-4}{-4-(-7)}[/tex] =  [tex]\frac{-4-8}{-1-(-10)}[/tex]

The answer is B

Hope this helps! i just learned this today lol

I don't understand what you are talking about, but I can list you the factor pairs of 16!

16=1,16; 2,8; 4,4

Thise are all the factor pairs

Answer:

1 x 16,

2 x 8

4 x 4

Factors of 16: 1, 2, 4, 8, 16