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3 years ago

14

Kimi measured a city and made a scale drawing. The scale of the drawing was 6 inches = 2 yards. What scale factor does the drawi

ng use? Simplify your answer and write it as a ratio, using a colon.

1 answer:

Vika [28.1K]3 years ago

7 0

Answer:

1:12.

Step-by-step explanation:

The scale is 6 in : 2 yds.

There are 36 inches in a yard so this

= 6 : 72

= 1 : 12.

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It should be A.) 100

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3 years ago

Read 2 more answers

Please Please Please help with this math problem

katovenus [111]

The revenue as a function of x is equal to -x²/20 + 920x.
The profit as a function of x is equal to -x²/20 + 840x - 6000.
The value of x which maximizes profit is 8,400 and the maximum profit is $3,522,000.
The price to be charged to maximize profit is $500.

<h3>How to express the revenue as a function of x?</h3>

Based on the information provided, the cost function, C(x) is given by 80x + 6000 while the demand function, P(x) is given by -1/20(x) + 920.

Mathematically, the revenue can be calculated by using the following expression:

R(x) = x × P(x)

Revenue, R(x) = x(-1/20(x) + 920)

Revenue, R(x) = x(-x/20 + 920)

Revenue, R(x) = -x²/20 + 920x.

Expressing the profit as a function of x, we have:

Profit = Revenue - Cost

P(x) = R(x) - C(x)

P(x) = -x²/20 + 920x - (80x + 6000)

P(x) = -x²/20 + 840x - 6000.

For the value of x which maximizes profit, we would differentiate the profit function with respect to x:

P(x) = -x²/20 + 840x - 6000

P'(x) = -x/10 + 840

x/10 = 840

x = 840 × 10

x = 8,400.

For the maximum profit, we have:

P(x) = -x²/20 + 840x - 6000

P(8400) = -(8400)²/20 + 840(8400) - 6000

P(8400) = -3,528,000 + 7,056,000 - 6000

P(8400) = $3,522,000.

Lastly, we would calculate the price to be charged in order to maximize profit is given by:

P(x) = -1/20(x) + 920

P(x) = -1/20(8400) + 920

P(x) = -420 + 920

P(x) = $500.

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2 years ago

The population of at a town has grown 2% each year. In 1998, the population of the town was about 10,000 people. What was the po

Nuetrik [128]

Answer:

10200

Step-by-step explanation:

This is an example of a compound interest. The equation for this problem is 10000*(1+2/100)^n. The n is the year as 1999 is 1 year away from 1998, you just replace n with 1 and you have a simple equation.

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3 years ago

Given a quadratic function in vertex form:

Alja [10]

Answer:

See below

Step-by-step explanation:

<u>Part A</u>

A vertical stretch takes place when $a\cdot f(x)$ given that $|a| > 1$

<u>Part B</u>

A vertical compression takes place when $a\cdot f(x)$ given that $0 < |a| < 1$

<u>Part C</u>

A vertical stretch is different than a horizontal compression:

In a vertical stretch, the input stays the same, but the output is multiplied by the scale factor
In a horizontal compression, the output stays the same, but the input is multiplied by the scale factor

<u>Part D</u>

A reflection across the x-axis means that the output, our y-variable, is the opposite sign. This means that all values of $a$ must be negative such that $a\cdot f(x)$ as mentioned in parts A and B. Also, in part C, since our scale factor is negative, the output is the only one being multiplied by the scale factor.

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2 years ago

Determine which lines in the diagram are parallel. A) a || b B) b || c C) a || c D) b || d

spayn [35]

Line a and line c are parallel lines that are given as a || c. Then the correct option is C.

<h3>How are parallel straight lines related?</h3>

Parallel lines have the same slope since the slope is like a measure of steepness and since parallel lines are of the same steepness, thus, are of the same slope.

Since the given parallel line has equation y = 2x + 2, thus its slope is 2 and thus, the slope of the needed line is 2 too.

Then we have

The distance between line a and line c is constant. Then line a and line c are parallel lines.

Line a || line c. Then the correct option is C.

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2 years ago