4.2475 rounded to the nearest ten or hundred

Distance between the points (4, 7) and (4, –5) is 12 units and distance between the points (–3, 5) and (2, –6) is 12.01 units.

What is Distance?

The length along a line or line segment between two points on the line or line segment.

Distance=√(x₂-x₁)²+(y₂-y₁)²

The distance between the points (4, 7) and (4, –5)

x₁=4, y₁=7, x₂=4, y₂=-5

Distance=√(x₂-x₁)²+(y₂-y₁)²

Distance=√(4-4)²+(-5-7)²

=√(-12)²

=√144

=12

Hence  distance between the points (4, 7) and (4, –5) is 12 units.

the distance between the points (–3, 5) and (2, –6)

x₁=-3, y₁=5, x₂=2, y₂=-6

Distance=√(x₂-x₁)²+(y₂-y₁)²

=√(2-(-3))²+(-6-5)²

=√(5)²+(-11)²

=√25+121

=√146

=12.08

So distance between the points (–3, 5) and (2, –6) is 12.01 units.

Hence  distance between the points (4, 7) and (4, –5) is 12 units and distance between the points (–3, 5) and (2, –6) is 12.01 units.

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Final answer:

To solve this problem, set up an equation using the given weights and solve for 'x' to find the weights of each friend's bag.

Explanation:

To solve this problem, we need to set up an equation based on the given information.

First, let's express the weights of Randall's, Seth's, and Joanna's bags in terms of 'x':

• Randall's bag: 3x - 7 pounds
• Seth's bag: 2x - 10 pounds
• Joanna's bag: 2x + 2 pounds

According to the problem, Randall's and Joanna's bags together weigh 3 times as much as Seth's bag. Mathematically, this can be written as:

(3x - 7) + (2x + 2) = 3(2x - 10)

Solving this equation will give us the value of 'x', which we can then use to find the weights of each friend's bag.

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Answer:

Randall=68 pounds, Seth's=40, Joanna's=52

Step-by-step explanation:

Randall's = 3x-7

Seth's = 2x-10

Joanna's = 2x+2

Randall's + Joanna's = 3 (Seth's)

Find X:

1. Form into an equation (add parentheses)
2. (3x-7) + (2x+2) = 3 (2x-10)
3. REmove parentheses on left side
4. 3x-7+2x+2 = 3 (2x-10)
5. Distribute right side
6. = 6x-30
7. 3x-7+2x+2 = 6x-30
8. Combine like terms
9. 5x-5=6x-30
10. subtract 5x from BOTH sides (always subtract, add, multiply, and divide both sides at the same time)
11. -5=x-30
12. Add 30 to BOTH sides
13. 25=x

Find how many pounds of trash each friend picked up:

Randall's:

1. 3x-7
2. plug in x  
3. 3(25)-7
4. Distribute
5. 75-7
6. = 68

Seth's:

1. 2x-10
2. 2(25)-10
3. 50-10
4. = 40

Joanna's:

1. 2x+2
2. 2(25)+2
3. 50+2
4. =52

Double check your answers:

Randall's+Joanna's= Seth's(3)

68+52=40(3)

120=120

You're good to go!