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Anna [14]
3 years ago
10

It takes Lacey 3 hours to knit a stocking cap and 5 hours to knit a pair of mittens. She has at most 20 hours of spare time in a

week and knits at least one pair of mittens each week. Let x stand for the number of stocking caps and let y stand for the number of pairs of mittens. Write a system of linear inequalities that models the number of stocking caps and pairs of mittens that Lacey can knit in a week. Graph the solution.
A. 5x+3y≤1x≤1

B. 3x+5y≤20y≥1

C. 3x+5y≥20y≥1

D. 3x+5y≤20x≥1
Mathematics
1 answer:
Elodia [21]3 years ago
6 0

Answer:

B. 3x+5y≤20y≥1  


Step-by-step explanation:

3 hours for a cap

x = cap

5 hours mittens

y = mittens

this is the amount of time

3x+5y <=20

she must do a pair of mittens

y>=1

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What is the difference 1/9 - 5/6 a 13/18 b 1/18 c - 1/18 d -13/18
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1/9 - 5/6

Convert both of them into denominators of 18.

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valina [46]

Part (a)

<h3>Answer: x^3 + 12x^2 + 47x + 60</h3>

--------------------------

Work Shown:

Let's say we have

  • L = length = x+5
  • W = width = x+4
  • H = height = x+3

To find the volume of the block, we multiply the length width and height.

So,

volume = (length)*(width)*(height)

V = L*W*H

V = LW*(x+3) .... replace H with (x+3)

V = LW*x + LW*3 .... distribute

V = Lx*(W) + 3L*(W)

V = Lx(x+4) + 3L(x+4) .... replace W with x+4

V = Lx^2 + 4Lx + 3Lx + 12L .... distribute

V = Lx^2 + 7Lx + 12L

V = x^2*(L) + 7x*(L) + 12*(L)

V = x^2*(x+5) + 7x*(x+5) + 12*(x+5) .... replace L with x+5

V = x^3 + 5x^2 + 7x^2 + 35x + 12x + 60 .... distribute

V = x^3 + 12x^2 + 47x + 60

x^3 + 12x^2 + 47x + 60 is the polynomial in standard form that represents the volume of the block.

=======================================================

Part (b)

<h3>Answer: 336 cubic feet</h3>

--------------------------

Work Shown:

We can plug x = 3 into the polynomial we found

V = x^3 + 12x^2 + 47x + 60

V = (3)^3 + 12(3)^2 + 47(3) + 60

V = 27 + 12(9) + 47(3) + 60

V = 27 + 108 + 141 + 60

V = 336

Or we could find the volume like this

V = L*W*H

V = (x+5)*(x+4)*(x+3)

V = (3+5)*(3+4)*(3+3)

V = (8)*(7)*(6)

V = 336

Either way, we get the same volume of 336 cubic feet.

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