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AnnyKZ [126]
2 years ago
6

You have been asked to build a scale model of a restaurant out of bottle caps. The restaurant is 20 feet tall. Your scale is 2.4

cm: 1 foot. A bottle cap is 1.2 cm tall. About how many bottle caps tall will your model be?
Mathematics
1 answer:
Amanda [17]2 years ago
8 0

Answer:

40\ bottle\ caps

Step-by-step explanation:

we know that

The scale is \frac{2.4}{1}\ \frac{cm}{ft}

That means

2.4 cm in the model represent 1 foot in the real

In this problem

The restaurant is 20 feet tall

Find the height of the model

Multiply the actual height of the restaurant by the scale 2.4

20\ ft=20(2.4)=48\ cm

A bottle cap is 1.2 cm tall

To find out the number of bottle caps divide the height of the model by 1.2

\frac{48}{1.2}= 40\ bottle\ caps

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It is 42. It is easy like the bottom one
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2 years ago
The sum of three integers is 12
Liula [17]

The three integers are 5,17 and -10

Step-by-step explanation:

Let x, y and z be three integers then

x+y+z=12 \ \ \Eqn\ 1

'The sum of the first and second integers exceeds the third by 32'

x+y=z+32\ \ \ \ Eqn\ 2

The third integer is 15  less than the first.

z=x-15\ \ \ \ Eqn\ 3

From Eqn 2:

x+y=z + 32\\x+y-z=32

Subtracting Eqn 1 from eqn 2

x+y-z-(x+y+z)=32-12\\x+y-z-x-y-z=20\\-2z=20

Dividing both sides by -2

\frac{-2z}{-2}=\frac{20}{-2}\\z=-10

Putting z=-10 in Eqn 3

z=x-15\\-10=x-15\\x=15-10\\x=5

Putting x=5 and z=-10 in Eqn 1

x+y+z=12\\5+y-10=12\\y-5=12\\y=12+5\\y=17\\

Hence,

The three integers are 5,17 and -10

Keywords: Linear Equations, Variables

Learn more about linear equations at:

  • brainly.com/question/13219835
  • brainly.com/question/1836777

#LearnwithBrainly

3 0
2 years ago
Read 2 more answers
Simplify the expression:<br> – 10x + – 4 – 8 + 7x
Ivan

Answer:

-3x-12

Step-by-step explanation:

-10x-4-8+7x

-3x-4-8

-3x-12

5 0
3 years ago
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John drove to Daytona Beach, Florida, in hours. When he returned, there was less traffic, and the trip took only hours. If John
olga55 [171]

Question: John drove to a distant city in 5 hours.

When he returned, there was less traffic and the trip took only 3 hours.

If John averaged 26 mph faster on the return trip, how fast did he drive each way

Answer:

For the first trip he drove at a speed of 39 mph

For the second trip he drove at a speed of 65 mph

Step-by-step explanation:

Let the distance for both journey be Z because they are equal.

Let the speed for the first journey be X

Let the speed of the second journey be Y

Formula for speed = distance ÷ time

For the first journey the speed X = Z ÷ 5

For the second journey the speed Y = Z ÷ 3

Since John averaged 26 mph faster in the second trip than the first trip due to traffic, it means that the difference in speed between the first & second trip is 26 mph

Difference in speed = (Z÷3) - (Z÷5) = 26

subtracting both results to  (5Z-3Z) ÷ 15 = 26

Upon cross multiplication

2Z = 390

Z = 390÷2 = 195 miles

Therefore speed for first journey = 195 ÷ 5 = 39 mph

Speed for second journey = 195 ÷ 3 = 65 mph

To verify, 65 - 39 = 26 mph

8 0
3 years ago
HELP!!!! I have never seen this. I will award big brain.​
Jlenok [28]

Step-by-step explanation:

Angles APD, DPC and CPB are supplementary. (Angles on a straight line)

Therefore Angle APD + Angle DPC + Angle CPB = 180°.

Since Angle DPC = 90° (Right angle),

Angle APD + Angle CPB = 180° - 90° = 90°.

=> (7x + 1) + (9x - 7) = 90

=> 16x - 6 = 90

=> x = 6

Hence arc measure of minor arc AD

= (7x + 1)° = [7(6) + 1]° = 43°.

6 0
2 years ago
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