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The perimeter of a rectangle is 52 feet. Describe the possible lengths of a side if the area of the rectangle is not to exceed 120 square feet. I need to find the solution set for this.

Answers

Answer 1

Answer:

Answer:

2x+2y=52

x*y=120

Step-by-step explanation:

Answer 2

Answer:

Final answer:

The possible lengths of a side of the rectangle are 22, 21, 20, 19, 18, 17, 16 feet.

Explanation:

To find the possible lengths of a side of the rectangle, let's use the formula for the perimeter of a rectangle, which is 2(length + width). We can set up an equation using the given information:

2(length + width) = 52

Dividing both sides by 2, we get:

length + width = 26

Now, to find the possible lengths, we need to consider the area. The formula for the area of a rectangle is length x width. We are given that the area is not to exceed 120 square feet, so we can set up the inequality:

length x width <= 120

Using the relationship length + width = 26, we can substitute length = 26 - width into the inequality:

(26 - width) x width <= 120

Simplifying the inequality, we get:

-width^2 + 26width - 120 <= 0

Now, we can solve this quadratic inequality to find the range of possible widths. Once we have the widths, we can substitute them back into the equation length + width = 26 to find the corresponding lengths.

By solving the quadratic inequality, we find that the possible widths are 4 <= width <= 10. Substituting these widths back into the equation length + width = 26, we get the corresponding lengths:

If width = 4, then length = 22

If width = 5, then length = 21

If width = 6, then length = 20

If width = 7, then length = 19

If width = 8, then length = 18

If width = 9, then length = 17

If width = 10, then length = 16

The possible lengths of a side of the rectangle are {22, 21, 20, 19, 18, 17, 16} feet.

Learn more about rectangle side lengths here:

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oint Q is plotted on the coordinate grid. Point P is at (40, −20). Point R is vertically above point Q. It is at the same distance from point Q as point P is from point Q. Which of these shows the coordinates of point R and its distance from point Q? (5 points) On a coordinate grid from negative 50 to positive 50 in increments of 10, Point Q is plotted at the ordered pair negative 10, negative 20. Group of answer choices Point R is at (−10, −10), a distance of 30 units from point Q Point R is at (−10, −30), a distance of 50 units from point Q Point R is at (−10, 30), a distance of 50 units from point Q Point R is at (−10, 10), a distance of 30 units from point Q

A plant produces 500 units/hour of an item with dimensions of 4” x 6” x 2”. The manager wants to store two weeks of supply in containers that measure 3 ft x 4 ft x 2 ft. (Note: She can store the units in the containers such as that the 4” dimension aligns with either the 3 ft width or the 4 ft length of the box, whichever allows more units to be stored.) A minimum of 2 inches of space is required between adjacent units in each direction. If the containers must be stacked 4-high, and the warehouse ceiling is 9 feet above the floor, then determine the amount of floor space required just for storage.

Answers

Answer:

564 ft²

Step-by-step explanation:

To account for the extra space between units, we can add 2" to every unit dimension and every box dimension to figure the number of units per box.

Doing that, we find the storage box dimensions (for calculating contents) to be ...

3 ft 2 in × 4 ft 2 in × 2 ft 2 in = 38 in × 50 in × 26 in

and the unit dimensions to be ...

(4+2)" = 6" × (6+2)" = 8" × (2+2)" = 4"

A spreadsheet can help with the arithmetic to figure how many units will fit in the box in the different ways they can be arranged. (See attached)

When we say the "packing" is "462", we mean the 4" (first) dimension of the unit is aligned with the 3' (first) dimension of the storage box; the 6" (second) dimension of the unit is aligned with the 4' (second) dimension of the storage box; and the 2" (third) dimension of the unit is aligned with the 2' (third) dimension of the storage box. The "packing" numbers identify the unit dimensions, and their order identifies the corresponding dimension of the storage box.

We can see that three of the four allowed packings result in 216 units being stored in a storage box.

If storage boxes are stacked 4 deep in a 9' space, the 2' dimension must be the vertical dimension, and the floor area of each stack of 4 boxes is 3' × 4' = 12 ft². There are 216×4 = 864 units stored in each 12 ft² area.

If we assume that 2 weeks of production are 80 hours of production, then we need to store 80×500 = 40,000 units. At 864 units per 12 ft² of floor space, we need ceiling(40,000/864) = 47 spaces on the floor for storage boxes. That is ...

47 × 12 ft² = 564 ft²

of warehouse floor space required for storage.

_____

The second attachment shows the top view and side view of units packed in a storage box.

Translate the English phrase into an algebraic expression: the sum of 17y² and 19.

Answers

Answer:

17y^2+19

Step-by-step explanation:

sum means add

Answer:

19+ 17y²

Step-by-step explanation:

Find the sum 5.5+7.25-5.5+(-7.25) show your work

Answers

Answer:

5.5+7.25−5.5−7.25 = 0

Step-by-step explanation:

To be honest, you shouldn't have to show work for an equation like this. But this is the answer. Hope it helped.

Answer:

5.5+7.25-5.5+(-7.25)

step 1: add 5.5 and 7.25

12.75−5.5−7.25

step 2: subtract 5.5 from 12.75

7.25−7.25

The answer is 0.

Step-by-step explanation:

Brainliest?

A restaurant has a capacity of 120 patrons. If the restaurant is full, how many patrons are at the restaurant?

Answers

Answer:120?

Step-by-step explanation:

Suppose that a digitized TV picture is to be transmitted from a source that uses a matrix of 480 * 500 picture elements (pixels), where each pixel can take on one of 32 intensity values. Assume that 30 pictures are sent per second. (This digital source is roughly equivalent to broadcast TV standards that have been adopted.) Find the source rate R (bps).

Answers

Answer:

36,000,000 bps

Step-by-step explanation:

Matrix of 480 by 500 = 480 X 500 = 240,000 pixels

Intensity values per pixel = 32. This simply means the color variations in this TV.

The bit per pixel for an intensity value of 32 is 5 (That's 2 raised to the power of 5)

Pictures sent per second = 30

Source rate R (bps) = Total number of pixels in the matrix X bit per pixel X Number of pictures sent per second.

Source rate R (bps) = 240,000 X 5 X 30 = 36,000,000 bps

Final answer:

The source rate for the digitized TV picture is 230,400,000 bps.

Explanation:

The source rate can be calculated by multiplying the number of pixels per picture element by the number of intensity values per pixel and by the number of pictures sent per second.

So, the source rate R (bps) is given by:

R = (480 * 500) * 32 * 30

Calculating this, we find that the source rate is 230,400,000 bps.