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DerKrebs [107]
3 years ago
11

Lucero wants to hang 3 paintings in her room. The widths of the paintings are 10 1/2 inches, 3 1/2 feet, 2 feet, and 2 3/4 inche

s. If she hangs them next to each other with 3 inches between them, what is the total width of the wall space she will need?
Mathematics
1 answer:
Marina86 [1]3 years ago
8 0

Answer:

  7 ft 1 1/4 in

Step-by-step explanation:

The total width of 3 paintings and 2 spaces is ...

  (10.5 in) + (3 in) + (3 ft 6 in) + (3 in) + (2 ft 2 3/4 in)

  = (10.5 +3 +6 +3 +2.75) in + (3 +2) ft

  = 25.25 in + 5 ft = 1.25 in + 24 in + 5 ft

  = 7 ft 1 1/4 in

The total width of wall space needed for the paintings is 7 feet 1 1/4 inches.

_____

If two more 3-inch spaces are added, one on each end, then the total width is 7 feet 7 1/4 inches. The problem isn't clear about that, saying only that there are spaces between the paintings.

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Answer:

(a) Brenda saved $23.50.

(b) The rate at which Brenda is saving money is<u> 0.5 dollars per day</u>.

(c) money saved on J(14) is <u>$27.</u>

Step-by-step explanation:

Given:

Initial amount in the jar is, J(0)=\$20

Amount in the jar after a week or 7 days is, J(7)=\$23.50

Brenda is saving money at a linear rate.

(a)

Now, money at the end of the week is the total money saved by Brenda.

Therefore, total money saved by Brenda is equal to the money saved at the end of the week. So,

Total money saved by Brenda = J(7)=\$23.50

(b)

The rate of change of a function is given as:

Rate=\frac{f(x_2)-f(x_1)}{x_2-x_1}

Here, x_1=0,x_2=7, f(x_1)=J(0),f(x_2)=J(7)

Therefore, the rate at which Brenda saves money is given as:

Rate=\frac{J(7)-J(0)}{7-0}\\Rate=\frac{23.50-20}{7}\\Rate=\frac{3.5}{7}=0.5\ dollars/day

Therefore, the rate at which Brenda is saving money is<u> </u>0.5 dollars per day.

(c)

A linear function is of the form f(x)=mx+b, where 'm' is the rate and 'b' is the initial value of the function.

Therefore, the linear function for the money saved by Brenda can be written as:

J(x)=(Rate)x+J(0)\\J(x)=0.5x+20

Now, J(14) is given by plugging in 14 for 'x' in the above expression. So,

J(14)=0.5\times 14+20\\J(14)=7+20=\$27

Therefore, money saved on J(14) is $27.

4 0
2 years ago
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