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3 years ago

7. A 50 foot rope is cut into two pieces, one long piece and one short piece. The length of the long piece

Mathematics

1 answer:

Lapatulllka [165]3 years ago

4 0

Answer:

Short piece: 9 ft

Long piece: 41 ft

Step-by-step explanation:

The first step to solving this problem is to translate the given information into some equations. Since we know the total length of the rope is 50 feet, the solution when adding the equation for the short piece and the equation for the long piece must be 50. The information from the second sentence can be translated into a mathematical expression. The phrase "5 more than 4 times" has two key words. They are "times" and "more". "Times" implies multiplication while "more" implies addition. Therefore this sentence becomes the expressions 5+4x, where x is the length of the short piece.

The equations we have from the problem statement are:

L = 5+4x where L represents the length of the long piece and x represents the length of the short piece

x + L = 50

Substituting the equation for the long piece into the equation for total length:

x + (5+4x) = 50

5 + 5x = 50

5x = 45

x = 9 ft

Substituting x = 9 into the equation for the long piece:

L = 5 + 4(9)

L = 5 + 36

L = 41 ft

Checking the answers by substituting x = 9 and L = 41 into the equation for total length:

x + L = 50

9 + 41 = 50

50 = 50

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Solve the simultaneous equation 5x+3y=23 2x+4y=12

uranmaximum [27]

() = Fraction

Answer:

1. x= −(3 /5 y)+ (23 /5)

2. x=−2y+6

Step-by-step explanation:

Let's solve for x.

5x+3y=23

Step 1: Add -3y to both sides.

5x+3y+−3y=23+−3y

5x=−3y+23

Step 2: Divide both sides by 5.

5x /5 = −((3y+23) /5)

x= −(3 /5 y)+ (23 /5)

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Let's solve for x.

2x+4y=12

Step 1: Add -4y to both sides.

2x+4y+−4y=12+−4y

2x=−4y+12

Step 2: Divide both sides by 2.

(2x /2 )= −((4y+12) /2)

x=−2y+6

Hope it helped!

5 0

3 years ago

a fishing boat accidentally spills 15 barrels of diesel oil into the ocean. each barrel contains 42 gallons. if the oil film on

bezimeni [28]

The square meters of the area the oil slick will cover is 9.6 × 10⁶ m².

<h3>What is meant by volume?</h3>

Volume is defined as the amount of three-dimensional space enclosed by a closed surface.

The liter (L) is the metric system's base volume unit, with several extended volume units also available.
There are also many metric volume units based on the a cubic length dimension, including such cubic meters or cubic centimeters. Gallons and ounces are examples of imperial volume units.

Now, as per the given question;

First, we determine the entire volume of oil in gallons by multiplying the volume per barrel even by total number of barrels:

15×42 gal = 630 gal

This volume must be converted to square meters:

V = 630 gal × (0.00379 m³/ gal

V = 2.4 m³

The thickness (height) of a oil film in meters is required:

h = 250 nm × (m/10⁻⁹nm)

h = 2.5 × 10⁻⁷m

The surface area of a oil film is calculated by dividing the oil volume by height of the oil film.

A = V/h

A = 2.4 m³/2.5 × 10⁻⁷m

A = 9.6 × 10⁶ m²

Therefore, the area of the oil slick cover is found to be 9.6 × 10⁶ m².

To know more about the volume, here

brainly.com/question/463363

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5 0

1 year ago

How many oranges do you need for 1 cup

mel-nik [20]

You will need 2 oranges for 1 cup

8 0

3 years ago

The figures below are similar. Find the value of x. Have a good day

olya-2409 [2.1K]

Answer:

Step-by-step explanation:

The ratio is 1:2

The longer side ratio is 4:8 so that is how I got it

The shorter side would be 2:X. X=4

4 0

4 years ago

Read 2 more answers

In your quilt shop,you make and sell quilts. You like to have a total of 26 yards of royal blue fabric in stock at the beginning

Vera_Pavlovna [14]

Answer:

7 pieces

Step-by-step explanation:

Stock that must be available at the beginning of each month = 26 yards

Since,

1 yard = 36 inches

26 yards = 26 x 36 = 936 inches

This means 936 inches of fabric must be available at beginning of each month.

<u>Current Inventory:</u>

4 pieces that are each 22 1/2 (or 22.5) inches long. So total length of these fabrics = 4 x 22.5 = 90 inches

3 pieces that each 33 inches long. So total length of these fabrics = 3 x 33 = 99 inches

Therefore, the total length of current inventory = 90 + 99 = 189 inches.

<u>Length of fabric needed more:</u>

Length of fabric that must be bought more = 936 - 189 = 747 inches

It is given that the fabric must be bought in pieces are the 3 yards long. 3 yards is equal to 108 inches.

So, I have to buy pieces that are each 108 inches long and I need to complete 747 inches in total.

Therefore, the number of pieces that I need to buy = $\frac{747}{108}=6.9$

Since, the pieces cannot be bought in fraction, I need to buy 7 complete pieces to replenish my stock.

6 0

3 years ago