Manuel builds and sells wooden crates. He made this table to show how much his crates cost in dollars.

Number of crates 2 4 6 8

Cost ($) $25 $45 $65 $85

Which equation represents this situation, where x is the number of crates and y is the cost? A)y−2=−10(x−25) B) y−85=10(x−8) C)y−65=−10(x−6) D)y−4=10(x−45)

Answers

Answer 1
The difference between the costs is $20 and the difference in the crates is 2 so the slope is 20/2=10, the coefficient for x.
The equation then is y-k=10(x-h) where (x,y) is a pair of values from the table: (2,25), (4,45), (6,65), (8,85). Eliminate answers A and C because the coefficient is -10. Answer D has the (h,k) values the wrong way round, but B is correct in all respects so B is the answer.
Answer 2

The equation representing the Manuel's situation is -

y = 10x + 5

What is the general equation of a Straight line?

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of a straight line in point slope form can be also written as-

[tex]y-y_{1}=m\left(x-x_{1}\right)[/tex]

We have the following problem -

Manuel builds and sells wooden crates. He made this table to show how much his crates cost in dollars -

Number of crates (n)    2       4       6       8

Cost ($)                       $25   $45   $65   $85

We can write the equation as -

y = mx + c

y = {(45 - 25)/(4 - 2)}x + c

y = 10x + c

c = 25 - 10 x 2

c = 5

Therefore, the equation representing the Manuel's situation is -

y = 10x + 5

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Related Questions

lana is using a can opener to open a can of soup every time she twists the knob of the can opener the can turns 36 degress

Answers

It takes 10 turns. There is 360 degrees in a circle, 360/36=10. 

Answer= 10 turns

Kayte wants to buy a new sled she has already save 35% of them out she needs what fraction describes this percent

Answers

In order to find what fraction describes this percentage, you first need to know that no matter what percentage you are working with, if you want to convert it into a fraction, put the 35 as the numerator and 100 as the denominator. If you still don't know what I mean, 35 at the top of the fraction and 100 at the bottom. Like this; 35/100. Then, you can simplify it by finding a common multiple between 35 and 100. For example, 5 can be divided into 35 and 100. 35 divided by 5 is 7 and 100 divided by 5 is 20. Your result is 7/20, which can further no more be simplified because there are no more common multiples between the two numbers.

How can absolute value help you to understand the size of a quantity? Give an example.

Answers

The absolute value can tell you the distance from zero on the number line. 
For example, [tex]|-8| = 8 [/tex] that mean the distance from zero (absolute value) is 8.

There is 3/4 of a pizza leftover from the night before. How many 1/8 portions are there

Answers

there are 6 portions left because 3/4x2= 6/8, 6/8 divided by 1/8 = 6
If you would want to know how many 1/8's you would have to find the LCD or LCM. Least common denominator of 3/4. It is 8. You multiply 2 by each side and you get 6. There are 6/8 of portions there.

What is the solution of the system? Also if you can, explain please?


Use the elimination method.
−4x−2y=−12
2x+4y=−12

Answers

In order to find the solution (point of intersection) of two lines, you must solve them simultaneously for the x-coordinates and y-coordinates.

Let   -4x - 2y = -12    be (eq1)
 &     2x + 4y = -12    be  (eq2)

Now you have to find a way to multiply one or two of the equations so that upon adding or subtracting them, the two equations will become a single equation with one solvable variable.

     by multiplying (eq 1) by 2
                            2(-4x - 2y = -12)
             Now let     -8x - 4y = -24      (eq1ᵃ)

                          
        So,   -8x - 4y + (2x + 4y) = -24 + (-12)      [eq1ᵃ + eq2]
            ⇒   -8x + 2x - 4y + 4y = - 36 
                                       - 6x  = - 36
                                 ⇒       x  = 6

     By substituting x = 6 into  eq2
                ⇒ 2(6) + 4y = - 12
                       12 + 4y = - 12
                              4y = - 24
                            ⇒ y = -6

Thus the solution set is (6 , -6)

Which number supports the given conjecture? 

If the sum of the digits of a number is divisible by 9, then the number is also divisible by 9.



 
A.
19


 
B.
54


 
C.
87


 
D.
109

Answers

Your answer would be B:54

What is the measure of angle EXH?

Answers

add the 3 angles together:

 30 + 30 + 30 = 90

 the answer is 90 degrees

THat would be the sum of the 3 marked angles

That is  90 degrees.

At the market, 8 batteries cost $10 .How much do 6 batteries cost

Answers

divide 10 by 8 to get price per battery

10/ 8 =1.25 per battery

 now multiply 1.25 x 6 for total

1.25 * 6 = $7.50 for 6 batteries


Given that eight batteries cost $10, six batteries will cost $7.5

How much do 6 batteries cost?

Given that;

8 batteries cost $101 battery = ?

If 8 batteries cost $10, 1 battery will be;

1 battery = $10 / 8

1 battery = $1.25

Now, given that;

1 battery cost $1.256 batteries = ?

If 1 battery cost $1.25, 6 batteries will be;

6 batteries = $1.25 × 6

6 batteries = $7.5

Given that eight batteries cost $10, six batteries will cost $7.5.

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Which of the following rational numbers is equal to 3 point 1 with bar over 1?

1) 22 over 9
2) 24 over 9
3) 26 over 9
4) 28 over 9

Answers

28 over 9 is equal to 3.1 with a bar over the one

Answer: Option 4 is correct.

Step-by-step explanation:

Since we have given that

[tex]\dfrac{3.\bar{1}}{1}[/tex]

so, Let x = 3.1111......... (1)

Now, multiply by 10, we get that

10x = 31.1111.............(2)

Now, subtract (2)-(1)

[tex]10x-x=31.1111...-3.1111............\\\\9x=28\\\\x=\dfrac{28}{9}[/tex]

Hence, Option 4 is correct.

John Took a 5 1/2 mile walk to his friends house. He left at 11 AM and arrived at his friends house at 1 PM

a. What was his average speed of walking

Answers

Hi there! 11AM and 1PM are two hours apart, so John walked for 2 hours. To find his average speed of walking, we can basically divide both numbers, because speed = distance/time. To divide fractions, keep the first fraction the same, change division into multiplication, and flip the second fraction over. 5 1/2 as a mixed number is 11/2. 11/2 * 1/2 is 11/4 or 2 3/4 in simplest form. John walked 2 3/4 miles per hour.

Determine the length of the hypotenuse

Answers

21^2 + 28^2 = Hypotenuse^2

441 + 784 = 1225

sqrt (1225) = 35

hypotenuse = 35

Which one is greatest 4 or 4.022

Answers

4.022 is greater than 4 by 0.022

hope this helps

Solve the equation for the variable (solve for the second c)
10c - f= -13 + cd

Answers

by making c the subject, I arrived to that answer in the above pic

How to multiply fractions

Answers

To multiply fractions you multiply the numerator and that becomes the answer to the numerator
And then you do the same for the denominator
Then simplify if you can
Example:
2/5 * 3/6 = 6/30 = 1/5

Hello There!

To multiply fractions, you first want to line up the numerator and the denominator together so they line up with each other.

Next, you want to multiply across. This includes multiplying the numerators together and then multiplying the denominators together.

Finally, you want to find the greatest common factor but only if the fraction can be simplified.

That Is How To Multiply Fractions

what is true about the solution of x^2 / 2x - 6 = 9 / 6x - 18

Answers

[tex] \text{The domain}\\2x-6\neq0\ \wedge\ 6x-18\neq0\to x\neq3\\\\\dfrac{x^2}{2x-6}=\dfrac{9}{6x-18}\\\\\dfrac{x^2}{2(x-3)}=\dfrac{9}{6(x-3)}\ \ \ |\cdot6\\\\\dfrac{3x^2}{x-3}=\dfrac{9}{x-3}\iff3x^2=9\ \ \ |:3\\\\x^2=3\to x=\pm\sqrt3 [/tex]

Answer:

A on edge/e2020

Step-by-step explanation:

Question 5 / 5 The homegrown Turkey farm is preparing their Thanksgiving shipment. In one container they can put 8 big turkey boxes or 10 small turkey boxes. They send 96 turkey boxes using more big boxes than small boxes. How many containers did they use?

Answers

Question 5 / 5 The homegrown Turkey farm is preparing their Thanksgiving shipment. In one container they can put 8 big turkey boxes or 10 small turkey boxes. They send 96 turkey boxes using more big boxes than small boxes. How many containers did they use?
Final answer:

To find the number of containers used, set up a system of equations using the given information. Solve for the number of big and small boxes used, and then divide the total number of boxes by the number of boxes that can be put in one container to find the number of containers.

Explanation:

To find the number of containers used, we need to determine the number of big boxes and small boxes used. Let's assume the number of big boxes used is 'x', and the number of small boxes used is 'y'.

According to the given information, the total number of turkey boxes used is 96. So, we have the equation: x + y = 96.

We also know that in one container, they can put 8 big turkey boxes or 10 small turkey boxes. Using this information, we can create another equation: 8x + 10y = 96.

Solving these two equations will give us the values of 'x' and 'y', which represent the number of big and small boxes used, respectively. Then, we can find the number of containers by dividing the total number of boxes by the number of boxes that can be put in one container.


the graph F (x) and its transformation g (x)

which equation correctly models g (x)

Answers

Step-by-step explanation:

Answer is the third question

Which set of values could be the side lengths of a 30-60-90 triangle?

Answers

3×10 3×20 3×30 that would be The length ×width to figure that out

Answer:

can we see an example

Step-by-step explanation:

PLEASE HELP!
Write an algebraic expression for 9 groups of w

Answers

The algebraic expression is 9w.

Hope this helps!

It is 9w hope this helps


Which of the following is an institution that functions much like a business, but does not operate for the purpose of generating profits? a business franchise a nonprofit organization a consumer cooperative a labor union

Answers

Non-profit organization

Answer:

a nonprofit organization

Step-by-step explanation:

A non profit organization is an organization that works with humanitary goals, and has non profit characteristics, they can not have a profit from their activities, but are able to gather money and to pay wages to their employees, they can also receive donations and are exempted from paying some kind of taxes.

round to the nearest centemeter

Answers

Translate this statement into an equation.

16 cm = (1/4)d + 2.5 cm

64 cm = d + 10

54 cm = d  (answer)
Final answer:

Rounding to the nearest centimeter involves adjusting a precise measurement to the nearest whole centimeter mark on a measuring tool. Millimeters and centimeters are appropriate units for measuring small objects, and understanding the conversion between these units is important for accurate rounding.

Explanation:

When you are asked to round to the nearest centimeter, you are being tasked with adjusting a measurement to reduce its precision to the nearest whole number of centimeters. In the context of using a measuring device such as a meterstick, you typically have the ability to measure in centimeters (cm) as well as millimeters (mm), with 10 millimeters making up 1 centimeter. For example, if you have a measurement that falls between the 1.2 cm and 1.3 cm marks, you will evaluate which of those two centimeters marks is closest to your measurement. If your object's measurement to the nearest millimeter is beyond the 1.25 cm mark (or 12.5 mm), you will round up to 1.3 cm; if it's less, you'll round down to 1.2 cm.

It's important to choose an appropriate unit of measurement based on the size of the object being measured. For an item like a paper clip, a large unit such as kilometers or meters would not be practical. Instead, you'll choose between millimeters and centimeters, which are better suited to small objects. When converting measurements from a smaller unit like millimeters to a larger unit like centimeters, you would divide the number by 10, moving the decimal point one place to the left because there are 10 millimeters in 1 centimeter.

Fill in blank to show steps in solving the inequality.
-2x + 12 < -4
-2x + 12 - __________ < -4 - _________
-2x < ________________
-2x divided by __________> _______ divided by _______
x > ______________

Answers

-2x +12 < -4
-2x +12 -12 < -4 - 12
-2x < -16
-2x divided by -2 > -16 divided by -2
x > 8

Answer:

x > 8

Step-by-step explanation:

To isolate the variable, you must follow the order of the operations in reverse: that is, from the sum the opposite operation is the subtraction and from the multiplication the inverse is the division. As first you must undo the sum or subtraction before the multiplication, on both sides of the inequality you subtract 12, with the objective, as it was said, of isolating the variable x using the inverse operations.

-2*x+12 -12 < -4 - 12

Resolving you get:

-2*x < -16

Now, to isolate the variable x, you reapply the inverse operation, in this case the opposite operation of the multiplication.  And ou should keep in mind that if the two members of an inequality are multiplied or divided by the same negative number, the resulting inequality changes direction. For this reason you get:

-2x divided by (-2) > (-16) divided by (-2)

Resolving these accounts, you finally get:

x > 8

Mr Paul drove to clay and back from drake he drove 312 miles took a break and then drove 244 miles to clay on his trip back to drake from clay he drove 305 miles before he took a break if he drove the same route back how many miles did he drive the second part of his return trip

Answers

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312+244=556, 556-305=251 miles
The second part of his trip he drove 251 miles

how do you graph y-6=(x+2)

Answers

To make your equation easier to graph, you can try simplifying it. Add 6 to both sides.

y-6 = (x+2)
  + 6     + 6
y = x + 8

Then, try plugging in values for x and using that output as your y value. Some coordinates on your graph would be (0, 8), (1, 9), (2, 10), (3, 11), etc.

Hope this helps!

explain how knowing 50 x 4 = 200 helps you find 500 X 400?

Answers

If you know the answer to 50 x 4 = 200 then you can just add the other zeros

Damian wrote the number four and twenty three thousandths as 4.23 describe and correct hi number

Answers

Final answer:

The correct representation of four and twenty three thousandths in decimal form is 4.023, not 4.23. The second decimal place represents hundredths and the third decimal place represents thousandths.

Explanation:

Damian's notation of four and twenty three thousandths as 4.23 is incorrect. This number should be represented as 4.023. The reason is in the understanding of decimal places. In decimal notation, the first place after the decimal point represents tenths, the second represents hundredths, and the third represents thousandths. Hence, twenty three thousandths is written as 0.023. Damian, therefore, mislocated the decimal point. So, to correct his number, it would be four (the whole number) + twenty three thousandths (0.023) = 4.023.

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If Dave drove one-third of the distance of his trip on the first day, and 60 miles on the second day, he figured out that he still had 1/2 of the trip to drive. What was the total length, in miles, of his trip?

Answers

process of elimination. one-third of 360 is 120. 120+60=180. Half of 360 is 180.

refer to the equation 3x-6y=18
A create a table of values for at east 4 points
(help plz)

Answers

3x-6y=18
  x - 2y = 6

if x = -4, then  -4 - 2y = 6...-2y = 10, so y = -5
if x = -2, then  -2 - 2y = 6...-2y = 8, so y = -4
if x = 0, then         -2y = 6.... y = -3
if x = 2, then     2 - 2y = 6...-2y = 4, so y = -2
if x = 4, then     4 - 2y = 6...-2y = 2, so y = -1

a stem-and-leaf plot shows the shape of data but not individual values true or false

Answers

The given statement "a stem-and-leaf plot shows the shape of data but not individual values" is true.

What is a stem-and-leaf plot?

A stem-and-leaf plot is a graphical representation of a dataset that shows the distribution of data. It is useful for quickly summarizing and visualizing data, especially for small to moderate-sized datasets.

In a stem-and-leaf plot, the "stem" represents the first digit or digits of the data values, and the "leaves" represent the remaining digits. Each leaf corresponds to a single data value. For example, if the stem is "5" and the leaf is "2", it would represent a data value of 52.

While a stem-and-leaf plot provides information on the shape of the data, such as the range of values and the distribution, it does not show the individual data values directly. Instead, it groups them into bins based on the stem and leaf representation. To get the actual values, one needs to refer to the original dataset.

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What percent of a circle is 2/5 of a circle? Explain

Answers

40 percent 2 divided by 5 equals .4
Final answer:

2/5 of a circle is equivalent to 40% of the circle. This is determined by multiplying 2/5 by 100%.

Explanation:

In the field of

Mathematics

, a circle is divided into an angle of 360 degrees or 100 percent. If we want to find out what percent of a circle is 2/5 of a circle, we need to perform a simple calculation.

Firstly, note that 1 whole circle (or 360 degrees) is equivalent to 100%.

When we say 2/5 of a circle, we are referring to 2/5 parts of the whole circle.

To find out what percent 2/5 of the circle is, we multiply 2/5 by 100%:

(2/5) * 100% = 40%

This means that 2/5 of a circle is 40% of the whole circle.

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