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anyanavicka [17]
3 years ago
8

Which ratio correctly compares 2 feet to 48 inches, when the lengths are written using the same units?

Mathematics
1 answer:
guajiro [1.7K]3 years ago
3 0

Answer: OPTION D

Step-by-step explanation:

To solve this problem you must apply the proccedure shown below:

- Convert from 48 inches to foot. You know that 12 inches=1 foot. Then you have:

 (48inches)(\frac{1foot}{12inches})=4feet

- Therefore, keeping on mind that 48 inches is 4 feet, and you must find the ratio that  correctly compares 2 feet to 48 inches, you can write:

ratio=\frac{2feet}{4feet}

- Reduce the fraction, then:

ratio=\frac{1}{2}

- You can rewrite it as following:

ratio=1:2

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Answer:

See below ~

Step-by-step explanation:

<u>Question 1</u>

  • -7x - y = -1
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⇒ -7x - 8x - 16 = -1

⇒ -15x = 15

⇒ x = -1

⇒ y = 8(-1) + 16 = 8

⇒ Solution = <u>(-1, 8)</u>

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<u>Question 2</u>

  • 3x + 4y = 0
  • y = -3x - 18

⇒ 3x + 4(-3x - 18) = 0

⇒ 3x - 12x - 72 = 0

⇒ -9x = 72

⇒ x = -8

⇒ y = -3(-8) - 18 = 6

⇒ Solution = <u>(-8, 6)</u>

<u>Question 3</u> (not clear)

<u>Question 4</u>

  • -8x - 7y = 0
  • y = 6x

⇒ -8x - 7(6x) = 0

⇒ -8x - 42x = 0

⇒ -50x = 0

⇒ x = 0

⇒ y = 6(0) = 0

⇒ Solution = <u>(0, 0)</u>

<u>Question 8</u>

  • 2x - 6y = -14
  • y = -5x - 19

⇒ 2x - 6(-5x - 19) = -14

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2 years ago
Learning Task 3
ASHA 777 [7]

Answer:

1. The sides are: 38.5, 39.5, 40.5 and 41.5

2. Presently, Inzo is 15 years old and Miz is 10 years old

3. Distance = 3682km

4. Possible pairs are: (12, 14), (16, 18) and (20, 24)

5. L < 38m

Step-by-step explanation:

The question has lots of missing details. See the comment section for complete question

Solving (a):

Given

Shape: Quadrilateral

Sides: Consecutive

Perimeter = 160

Let one of the sides be x. The other sides will be x + 1, x + 2 and x + 3.

So, the perimeter is:

Perimeter = x + x + 1 + x + 2 + x + 3

This gives:

160 = x + x + 1 + x + 2 + x + 3

Collect Like Terms

160 -1-2-3= x+x+x+x

154= 4x

Divide both sides by 4

38.5 = x

x =38.5

<em>So, the sides are: 38.5, 39.5, 40.5 and 41.5</em>

<em></em>

Solving (b):

Given

Presently: Inzo = 10 + Miz

Five years ago: Miz - 5= \frac{1}{3} * (Inzo-5) --- (Missing from the question)

Required: Determine their present ages

Substitute 10 + Miz for Inzo in the second equation

Miz - 5 = \frac{1}{3} * (10 + Miz - 5)

Miz - 5 = \frac{1}{3} * (Miz + 5)

Multiply both sides by 3

3Miz - 15 = Miz + 5

Collect Like Terms

3Miz -Miz = 15  + 5

2Miz= 20

Divide both sides by 2

Miz = 10

Substitute 10 for Miz in Inzo = 10 + Miz

Inzo = 10 + 5

Inzo = 15

<em>So presently, Inzo is 15 years old and Miz is 10 years old</em>

Solving (3):

Given

Express Train:

Speed = 100kph

Time = t

Local Train:

Speed = 45kph

Time = t + 45

Required: Determine the distance between A and B

Distance is calculated as:

Distance = Speed * Time

For the express train:

Distance = 100 * t

For the local train

Distance = 45 * (45 + t)

Distance between both stations are equal; So,

100 * t = 45 * (45 + t)

100 t = 2025 + 45t

Collect Like Terms

100 t -45t= 2025

55t= 2025

Divide by 55

t = 36.82

Substitute 36.82 for t in Distance = 100 * t

Distance = 100 * 36.82

Distance = 3682km

Solving (4):

Let the even numbers be: n and n + 2.

Sum greater than 24: n + n + 2 > 24

Sum less than 60: n + n + 2 < 60

So, we have:

n + n + 2 > 24

2n + 2 > 24

Collect Like Terms

2n > 24-2

2n > 22

n > 11

n + n + 2 < 60

2n + 2< 60

Collect Like Terms

2n < 60-2

2n < 58

Divide by 2

n

So, we have:

n > 11 and n < 29

So, possible pairs are: (12, 14), (16, 18) and (20, 24)

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Given

Perimeter < 152m

Required: Find the possible lengths

Let the length be L.

Perimeter is calculated as:

Perimeter =4 * L

Perimeter =4  L

So, we have:

4L < 152m

Divide through by 4

L < 38m

Hence, length is less than 38m (e.g. 37m)

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