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creativ13 [48]
3 years ago
15

Find the dimensions of a rectangle with perimeter 68 m whose area is as large as possible. (If both values are the same number,

enter it into both blanks.)
Mathematics
1 answer:
Lina20 [59]3 years ago
8 0

Answer:

<h2>Length is 17m and Breadth is also 17m</h2>

Step-by-step explanation:

The perimeter of a rectangle is expressed as 2(L+B) where;

L is the length and B is the breadth of the triangle.

P = 2(L+B)

68 = 2(L+B)

L+B = 68/2

L+B = 34

L = 34 - B ... 1

Area of the rectangle A = LB... 2

Substituting equation 1 into 2 will give;

A = (34-B)B

A = 34B-B²

To maximize the area of the triangle, dA/dB must be equal to zero i.e

dA/dB = 0

dA/dB = 34 - 2B = 0

34-2B = 0

2B = 34

Dividing both sides of the equation by 2 we will have;

B = 34/2

B = 17

Substituting B = 17 into equation 1 to get the length L

L = 34-17

L = 17m

This shows that the rectangle with maximum area is a square since L = B = 17m

The dimension of the rectangle is Length = 17m and Breadth = 17m

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3 years ago
A store manager wants to determine how much to pay her employees. The number of hours the employees work is x, and the hourly wa
Ivanshal [37]

Answer:

<em>The employees will work for 1 hour, will earn $5 per hour and will be paid $5</em>

Step-by-step explanation:

<u>System of Equations</u>

The number of hours the employees work is x.

And the hourly wage that they are paid is y. The store manager is willing to pay the employees a wage given by the equation

10y-30x=20

The business owner states that the employees should be paid a wage given by the equation

6y+30x=60

Adding both equations we have:

16y = 80

Dividing by 16:

y = 80/16 = 5

Substituting into the first equation:

10*5-30x=20

Operating and simplifying:

50-30x=20

50 - 20 = 30x

30x = 30

x = 30/30 = 1

Thus, the employees will work for 1 hour, will earn $5 per hour and will be paid $5

6 0
2 years ago
2. In a given country, records show that of the registered voters, 45% are Democrats, 35% are Republicans, and 20% are independe
Kitty [74]

Answer:

P(R) = 0.14

P(I) = 0.16

P(D) = 0.315

Step-by-step explanation:

Let Democrat = D

Republican = R

Independent = I

If 45% are Democrats, 35% are Republicans, and 20% are independents, then

Total registered voters = 100

 In an election, 70% of the Democrats, 40% of the Republicans, and 80% of the independents voted in favor of a parks and recreation bond proposal. That is,

D = 0.7 × 45 = 31.5

R = 0.4 × 35 = 14

I = 0.8 × 20 = 16

 If a registered voter chosen at random is found to have voted in favor of the bond, what is the probability that the voter is

a Republican:

P(R) = 14 /100 = 0.14

an Independent

P(I) = 16/100 = 0.16

a Democrat

P(D) = 31.5/100 = 0.315

6 0
2 years ago
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The empty jug weighs 0.75 lb

With the 3c, the total weighs 2.25 lb. That means:

3c + empty jug = 3c + 0.75 = 2.25

3c = 2.25 - 0.75
3c = 1.5
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Then the equation is:

y = 0.5x + 0.75


4 0
2 years ago
Luis has $20.He buys 4 cans of tennis balls and gets $8 back as change .How much did one can of tennis balls cost?
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Answer:

20-8 = 12 , he waste $12 if he got 4 cans 12 divide by 4 equal 3 so the one can cost $3

Step-by-step explanation:

3 0
3 years ago
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