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Reil [10]
3 years ago
15

Rachel hikes at a steady rate from a ranger station to a campground that is 20 mi away. After 2 h, she is 13 mi from the campgro

und. After 4 h, she is 6 mi from the campground. A graph shows her distance from the campground Y, in miles, after x hours. What is the slope of the graph and what does it represent?
Mathematics
1 answer:
Angelina_Jolie [31]3 years ago
8 0

Answer:

-3.5

The distance Rachel covers per hour is 3.5 miles

Step-by-step explanation:

After 2 hours, she is 13 miles from the campground.

After 4 hours, she is 6 miles from the campground.

Let x be the number of hours, y be the number of miles from the campground, then we have two points (2,13) and (4,6).

The equation of the line passing through the points (x_1,y_1) and (x_2,y_2) is

y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)

Substitute:

x_1=2\\ \\y_1=13\\ \\x_2=4\\ \\y_2=6

Hence,

y-13=\dfrac{6-13}{4-2}(x-2)\\ \\y-13=-3.5(x-2)\\ \\y=-3.5x+7+13\\ \\y=-3.5x+20

The slope of the line is -3.5 and it represents that  the distance Rachel covers per hour is 3.5 miles.

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Answer:

  156 cm³

Step-by-step explanation:

The volume of any prism is the product of the base area and the height of the prism. Here, we can take the "base" to be the front face of the assembly, and its "height" to be the 3 cm distance between the front and back faces.

The front face area is the sum of the triangle area and the rectangle area.

  A = 1/2bh + LW

  A = (1/2)(10 cm)(4 cm) + (16 cm)(2 cm) = 52 cm²

Then the volume is ...

  V = Bh = (52 cm²)(3 cm) = 156 cm³ . . . . total volume of the two blocks

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Answer:

x ≥ -0.75

Step-by-step explanation:

3.75 - 3x ≤ 6

Subtract 3.75 on both sides.

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What is the answer to this problem step by step (3+2)^2×7)-13+5^2?
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Answer:

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General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
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Step-by-step explanation:

<u>Step 1: Define</u>

(3 + 2)² × 7 - 13 + 5²

<u>Step 2: Evaluate</u>

  1. (Parenthesis) Add:                     5² × 7 - 13 + 5²
  2. Exponents:                                 25 × 7 - 13 + 25
  3. Multiply:                                      175 - 13 + 25
  4. Subtract:                                     162 + 25
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Sanjay can travel 342 miles in 6 hours. At this rate, how many miles can he travel in 5 hours?
MatroZZZ [7]

Answer:

57 miles

Step-by-step explanation:

342 divided by 5 equals 57 miles

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