A worker can assemble 3 shelf units each hour. the same worker can assemble 6 tv stands each hour. if x = hours assembling shelf units, y = hours assembling tv stands, and 24 = total number of furniture pieces made, write a function in standard form modeling the situation.

Hello!

Step-by-step explanation:

Slope: [tex]\frac{Y^2-Y^1}{X^2-X^1}=\frac{rise}{run}[/tex]

[tex]\frac{5-(-3)=5+3=8}{(-9)-(-3)=-9+3=-6}=\frac{8}{-6}=\frac{8/2}{-6/2}=\frac{4}{-3}[/tex]

Slope is -4/3

Answer is -4/3

Hope this helps!

-Charlie

Thank you!

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Answer: This is the CORRECT answer ----> y = 2x + 20

Step-by-step explanation: slope, y2 - y1/x2 - x1

replace it with these numbers 120 - 60/50 - 20=60/30

than,simplified it we get 2/1. so, now we  have the slope of our equation

y = 2x + b. but we still have b (or where the y intersects.) now are slope we have to change it to 1/2 because we are going backwards. So multiply 60 by .5, Thus will give us 30

Now we have y = 2x + 30, But that's not one of your answer,

So y = 2x + 20 cant be -20 because this is a positive y intersect and We know it is a slope of 2.

Therefore the answer is : y = 2x + 20

ALSO I know it's correct because I got it right on the test!! Hoped I helped :))

To solve this problem, all we have to do is to convert the pounds to ounce. We know that the conversion factor is:

1 pound = 16 ounce

Therefore:

cost per ounce = ($ 4.48 / pound) * (1 pound / 16 ounce) = $0.28 / ounce

Answer: There is cost $0.28 per ounce.

Step-by-step explanation:

Since we have given that

Cost per pound = $4.48

We need to find the cost per ounce.

As we know that

1 pound = 16 ounces

So, Cost per ounce would be

[tex]\dfrac{4.48}{16}\\\\=\$0.28[/tex]

Hence, there is cost $0.28 per ounce.

The number of unique license plates are [tex]26^{22}[/tex] for the letters and [tex]10^{44}[/tex]for the numbers, then multiply the two results.

Each letter on the license plate can be any one of the 26 letters in the English alphabet.

So, for 22 letters, the total possible combinations are calculated as:

[tex]26^{22}[/tex]

Each number on the license plate can be any one of 10 digits (0 through 9).

So, for 44 numbers, the total possible combinations are calculated as:

[tex]10^{44}[/tex]

So, the total number of different license plates can be found by multiplying these two results:

Total combinations = [tex]26^{22}[/tex] × [tex]10^{44}[/tex]

A = larger number

B = smaller number

A -B = 10

A + B = 4B

A=10+B

10+B+B = 4B

10 +2B = 4B

10=2B

B = 10/2 = 5

A = 10+5 =15

15-5 =10

15+5 = 20, 4*5 = 20

 the numbers are 5 & 15

To find the difference between two times in military format, convert each time to minutes. Subtract the later time from the earlier one, and then convert the result back to hours and minutes. The difference between 2330 and 0540 is 17 hours and 50 minutes.

To calculate the difference between two military times, we first need to understand that military time runs on a 24-hour clock rather than a 12-hour clock. In this instance, you are being asked to subtract 05:40 from 23:30.

First, it would be easier to convert these times into minutes. So, 23:30 becomes (23*60) +30 = 1410 minutes. Similarly, 05:40 becomes (5*60) +40 = 340 minutes.

Then we subtract the two: 1410 - 340 = 1070 minutes. Now, we convert it back to hours and minutes. There are 17 hours and 50 minutes in 1070 minutes. Therefore, the difference between 2330 and 0540 in military time is 1750 or 17 hours and 50 minutes.

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Final answer:

To subtract the military times 2330 from 0540, convert 1 hour to 60 minutes, add to the minutes of 2330, and then subtract both the hours and minutes separately. The result is 17 hours and 50 minutes.

Explanation:

Subtracting military times requires understanding the 24-hour clock system and being able to handle situations where you must "borrow" time from one hour to subtract minutes from another. To subtract 2330 (11:30 PM) from 0540 (5:40 AM), we need to do the following:

The result is 17 hours and 50 minutes.

The maximum and minimum heights for the zebra fence, considering the 3-inch allowance, are 5.25 feet (63 inches) and 4.75 feet (57 inches), respectively. This was computed by converting the standard height to inches, and applying an absolute value equation to figure out the range for the fence's height.

The recommended height of the fence is 5 ft, but this can vary by 3 inches due to uneven ground surfaces. The question asks for an equation to calculate the maximum and minimum heights.

To start, we need to convert all measurements to the same units. 5 feet is equivalent to 60 inches.

Next, we can set up the absolute value equation to represent the possible variation in height. This may look like |x - 60| ≤ 3. Here, x is the actual height of the fence.

Then, solve the equation to get our two possible results: x ≤ 60 + 3 and x ≥ 60 - 3. Therefore, the maximum and minimum heights of the fence are 63 inches (or 5.25 feet) and 57 inches (or 4.75 feet) respectively.

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Answer:

2x²+3x-54

Step-by-step explanation:

To simplify the expression

(2x − 9)(x + 6)

We will multiply both linear equations together to get a quadratic equation of second degree.

(2x − 9)(x + 6)

= 2x²+12x-9x-54

= 2x²+3x-54

This gives the required quadratic expression after simplification.

Hey!

Hope this helps...

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Like equations with the same variable on both sides...

We want to get c by itself...

T - yc = b   [Subtract T from both sides]

-yc = b - T  [divide -y from both sides]

c = -(b - T)/y

So...

The answer is: c = -(b - T)/y

Using an equation, Marissa has 2 brothers with her 2 sisters, making 4 siblings.

An equation is a mathematical statement of the equality or equivalence of two or more mathematical expressions.

We can use an equation to solve the above problem.

The number of brothers that Marissa has = x

The number of sisters Marissa has = 2

The cost of each shirt = $7.50

The total amount spent = $30

The total number of shirts Marissa can buy with $30 = 4 ($30/$7.50)

Equation:

7.5x + 7.5(2) = 30

7.5x + 15 = 30

7.5x = 15

x = 2

Thus, Marissa has 2 brothers, based on the solved equation.

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The height h of a guardrail = 106 centimeters

absolute deviation =  7 centimeters

To find the acceptable heights of a guardrail , we add and subtract absolute deviation(7) from the mean height(106)

The acceptable range of height is 7 cm away from 106 to the left and then to the right.

106 + 7 = 113

106 - 7 = 99

acceptable heights are defined by

99 <=h<=113

The absolute value inequality is |x-106|<=7

The acceptable range of heights of a guardrail are 99 cm to 113 cm.

We want to write an absolute value equation for the acceptable range of the height of a guardrail.

The acceptable range of heights of a guardrail is 99cm to 113cm.

And the absolute value equation is:  |h - 106cm| ≤ 7cm

We know that the height should be 106cm with an absolute deviation of no more than 7 cm.

So the maximum height is:

106cm +7cm = 113cm

The minimum is:

106cm -7cm = 99cm

The absolute value equation that represents this is:

|h - 106cm| ≤ 7cm

Where h is the height of the guardrail.

The acceptable range of heights of a guardrail is 99cm to 113cm.

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The graph which represents Jack and Jill's number of pails over time is:

It is given that:

Jack and Jill had 5 pails of water. Each trip up the hill, Jack and Jill obtained 2 more buckets of water.

Let x be the number of hills they tripped.

and y denote the number of buckets of water they have.

Then the equation which represent the relationship between y and x is:

             [tex]y=5+2x[/tex]

On making  a table for x and y:

        x             y

        1              7

        2             9

        3             11

        4             13

        5             15

        6             17

Hence, the graph will pass through the points (1,7) (2,9) (3,11) (4,13) (5,15) (6,17) and many more.

The equation can be solved for h by isolating h on one side. This is achieved by dividing A by 12(a+b), resulting in h = A / 12(a+b).

To solve for h in the equation A=12h(a+b), we first need to isolate h. This can be done by dividing both sides of the equation by 12(a+b). Therefore, the equation becomes: h = A / 12(a+b).

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To find the height h in A = 12h(a + b), isolate h by dividing both sides by 12(a + b), yielding [tex]\( h = \frac{A}{12(a + b)} \)[/tex]. This formula relates height to area and base lengths in geometric contexts.

To solve for h in the equation A = 12h(a + b), we need to isolate h on one side of the equation. Begin by dividing both sides by 12(a + b):

[tex]\[ \frac{A}{12(a + b)} = h \][/tex]

This gives us the expression for h. The solution is [tex]\( h = \frac{A}{12(a + b)} \)[/tex]. This formula represents the height h in terms of the area A, and the values of a and b.

The denominator 12(a + b) reflects the combined base lengths scaled by 12, and the height h is determined by the ratio of the given area A. This formula allows you to compute the height when the area and base lengths are known, providing a versatile tool for various geometric applications, especially in contexts like rectangular shapes or parallelograms.