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Likurg_2 [28]
3 years ago
11

Jack cuts four squares with side length X inches from corners by a 5" x 7" cardboard rectangle. He folds the remaining cardboard

to make a tray that is x inches high. Write and simplify a function for the volume V of the tray in terms of X.
Mathematics
2 answers:
viktelen [127]3 years ago
6 0

Answer:

V = x^3-24x^2+35x

Step-by-step explanation:

Jack makes a cuboid. If the length is <em>l</em>, the width is <em>w</em> and the height is <em>h</em>, then its volume is

V = lwh

The height is determined by the side of the square cut out of each corner.

h = x

Along the length of the width, the length of two sides of the square are cut.

l = 7 - 2x

w = 5 - 2x

V = lwh = (7-2x)(5-2x)(x)

V = x(35-24x+4x^2) = x(x^2-24x+35) = x^3-24x^2+35x

scoundrel [369]3 years ago
4 0

Answer:

Step-by-step explanation:

Given:

Dimensions of rectangle cardboard:

Length, l = 7 inches

Width, b = 5 inches

if the square of sides x inches is cut from each corner of the rectangular cardboard and folded to make a tray, therefore:

Length of the tray = length of cardboard - 2 (side of the square )

= 7 - (2 × x)

= 7 - 2x inches

Width of the tray = width of cardboard - 2(side of square)

= 5 - (2 × x)

= 5 - 2x inches

                   

height of tray = cut sides of square

= x inches

                     

volume of tray = Length × width × height

= (7 - 2x) × (5 - 2x) × x

Volume of tray = 35x - 10x^2 - 14x^2 + 4x^3

Simplifying further,

= (35x - 24x^2 + 4x^3) cubic inches

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Is (-5,6) a solution for 4x + 3y = 9
ozzi

Answer:

No.

Step-by-step explanation:

Insert the x and y, (-5 is x and 6 is y) into the equation. It should look like 4(-5)+3(6)=9. 4(-5)=-20 and 3(6)=18. -20+18=2 not 9.

(hope this helps :P)

5 0
3 years ago
Read 2 more answers
Thirty students bought pennants for the football game. Plain pennants cost $4 each and fancy ones cost $8 each. If the total bil
sammy [17]

Answer:

number o students bought pennants = 18

 number of student bought fancy ones=12

Step-by-step explanation:

Let x be the number o students bought pennants

and y be the number of student bought fancy ones

total 30 students

x+y= 30

y=30-x

Plain pennants cost $4 each and fancy ones cost $8 each.

4x+8y=168

Substitute 30-x for y in second equation

4x+8(30-x)=168

4x+240-8x=168

240-4x=168

Subtract 240 from both sides

-4x=-72

divide both sides by -4

x=18

y=30-x

y=30-18= 12

number o students bought pennants = 18

 number of student bought fancy ones=12

6 0
4 years ago
Please helpp me very easy
Anni [7]

Answer:

Here ya gooooo: $313,300

4 0
4 years ago
Read 2 more answers
PLEASE HELP!! I’LL MAKE YOU BRAINIEST!
Leokris [45]

Answer:

1. Markup: $2.70, Retail: $20.70

2. Markup: $9.45, Retail: $31.95

3. Markup: $25.31, Retail: $59.00

4. Markup: $24.75, Retail: $99.74

5. Markup: $48.60, Retail: $97.20

6. Markup: $231.25, Retail: $416.25

Step-by-step explanation:

To get the markup price of an item, multiply it by the markup percentage as a decimal. To get the decimal of a percentage, divide the number by 100. For example, 15% would be 0.15. And then to find how much the item has been marked up by, multiply the current price by the decimal.

$18 * 0.15 = $2.70

So $2.70 is the markup. To find the retail price, you need to add the markup price to the current price given.

$18 + $2.70 = $20.70

So your retail price is $20.70. Repeat these steps for each question to get the answers above.

Hope this helps.

7 0
3 years ago
Find the quotient<br>9) 4,878​
guajiro [1.7K]

Answer: 542

Step-by-step explanation:

The quotient is known as the final answer gotten after the value of 4878 has been divided using 9. The answer as such will be 542 (i.e 4878/9)

9 goes in 48 five times, 5 is written and remainder of 3 is kept above 7 to make it 37; then 9 goes in 37 four times, 4 is written and the reminder of 1 is written above 8 to make it 18; and finally 9 goes in 18 two times without remainder, then we write 2. Combining the answers gives our Final answer 542.

8 0
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