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Olin [163]
1 year ago
10

City planners are creating a 3-dimensional model of a city park to find the best placement for a new tennis court. The city park

is on a rectangular plot of land that is 1,500 ft long and 600 ft wide. The scale model of the park measures 7.5 ft x 3 ft. If the dimensions of the actual tennis court must be 120 ft long and 60 ft wide, what are the dimensions of the tennis court in the scale model?
Mathematics
1 answer:
inn [45]1 year ago
8 0
First, divide the original measurements with the scaled ones. You'll get the same answer meaning that is the scale used by the model.
1500 ft. ÷7.5 ft = 200
600 ft. ÷ 3 ft. = 200
 
To simply check, if you divide 1500 with 200, the answer is 7.5 and 600 divided by 200 is 3.
To find the  scaled dimension of the tennis court with actual dimension of 120 ft by 60 ft, divide both values with the scale used in the model which is 200.

120 ft. ÷ 200 = 0.6 ft
60 ft. ÷ 200 =  0.3 ft

The dimension of the tennis court in the scaled model is 0.6 ft long and 0.3 ft. wide.

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josh is 6 years older than 4 times Kim's age. The sum of their ages is less than 31. what is the oldest Kim could be? show all y
Mice21 [21]

Answer:

4 years old.

Step-by-step explanation:

Lets say that Josh's age is j and Kim's age is k. As Josh is 6 years older than 4 times Kim's age, we can write this as an equation:

j = 4k + 6

This is, John's age is equal to four times Kim's plus 6 years.

We then know that, when summed their ages is less than 31, so:

k + j < 31

Replace John's age by our first equation:

k + 4k + 6 < 31

5k + 6 < 31

Subtract 6 in both sides:

5k + 6 - 6 < 31 - 6

5k < 25

Dividing both sides by 5:

5k/5 < 25/5

k < 5

So, Kim's age MUST be less than 5.

If we talk about discrete values, this is 1, 2, 3, 4, 5, 6...., we will say than the oldest Kim could be is 4. If Kim is 5 years old, the sum of ages is 31 and we need it ti be LESS than 31. (we are not considering fractional numbers as 4.5 years old).

So, Kim can be, at maximum, 4 years old.

7 0
1 year ago
Alexa buys 27 stamps, each stamp is of 1 square unit of area. She exchanges them for 8 sugar cubes, whose total volume is numeri
Vikentia [17]
The answer is 8 sugar cubes
8 0
2 years ago
Evie and her father are comparing their ages. At the current time, Evie's father is 36 years older than her. Theee years from no
artcher [175]
Let F be the father's current age, and E be Evie's current age.
F = E + 36                 this is the current relation between the ages
F + 3 = 5(E + 3)        this the relationship in 3 year (hence the + 3)
Then solve by substituting one equation into another:
(E + 36) + 3 = 5(E + 3)
         E + 39 =  5E + 15
                24 = 4E
                  6 = E
Evie's current age is 6.
7 0
2 years ago
Elijah and Jonathan play on the same soccer team. They have played 3 of their 15,
Lynna [10]

Answer:

Only Elijah's model is correct

Step-by-step explanation:

The data given in the question tells us they have 12 games left on their soccer team. Each one of them tried to simulate the fact by creating some model which look like a balance between quantities.

Elijah placed 3 cubes of value 1 and a cube of value x on one side of a balance. On the other side, he placed 15 cubes of value 1. He was obviously modeling the fact that 15 cubes (games due to play in our case) should be equal to 3 cubes (games already played) plus the x numbers left to play

This model if perfect, since the only way to equilibrate the balance is setting x to 12, the games left to play

Jonathan used a table with 3 x's in a row and a 15 in the second row, trying to model the same situation. To our interpretation, this table doesn't show the number of games left to play. If we equate 3x = 15, we get x=5 which has nothing to do with the situation explained in the question, so this model is not correct.

5 0
2 years ago
categorize the graph as linear increasing, linear decreasing, exponential growth, or exponential decay.
soldier1979 [14.2K]
It is exponential growth
5 0
2 years ago
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