A hill rises 30 ft for every horizontal 100 ft. Which of the following express its slope (or gra

Name: Problem 1, Chapter 2: Intermediate Algebra
Uploaded: 2022-02-16T09:13:08-08:00
Duration: 1 min 5 s
Channel: Aditya Yadav
Description: A hill rises 30 ft for every horizontal 100 ft. Which of the following express its slope (or grade)? (There are several correct choices.) A. 0.3 B. (3)/(10) C. 3 (1)/(3) D. (30)/(100) E. (10)/(3) F. 30 %

step 1 The definition of the slope is the ratio of the rise to the run. We can assume slope, it's repre

Question

A hill rises $30 \mathrm{ft}$ for every horizontal $100 \mathrm{ft}$. Which of the following express its slope (or grade)? (There are several correct choices.) A. 0.3 B. $\frac{3}{10}$ C. $3 \frac{1}{3}$ D. $\frac{30}{100}$ E. $\frac{10}{3}$ F. $30 \%$

   A hill rises $30 \mathrm{ft}$ for every horizontal $100 \mathrm{ft}$. Which of the following express its slope (or grade)? (There are several correct choices.)
A. 0.3
B. $\frac{3}{10}$
C. $3 \frac{1}{3}$
D. $\frac{30}{100}$
E. $\frac{10}{3}$
F. $30 \%$

Intermediate Algebra

John Hornsby; Terry… 13th Edition

Chapter 2, Problem 1

Instant Answer

Solved by Expert Aditya Yadav

02/16/2022

Step 1

Step 1: Compute the slope = rise/run = 30/100 = 3/10, so choices B and D match. Show more…

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A hill rises $30 \mathrm{ft}$ for every horizontal $100 \mathrm{ft}$. Which of the following express its slope (or grade)? (There are several correct choices.) A. 0.3 B. $\frac{3}{10}$ C. $3 \frac{1}{3}$ D. $\frac{30}{100}$ E. $\frac{10}{3}$ F. $30 \%$

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Key Concepts

Slope

Slope is a measure of how steep a line is, defined as the ratio of the vertical change (rise) to the horizontal change (run). It quantifies how much a quantity changes in response to a change in another quantity.

Ratio

A ratio expresses the relationship between two quantities by comparing their relative sizes. In the context of slope, the ratio compares the amount of vertical change to the amount of horizontal change.

Fraction, Decimal, and Percentage Representations

A single numerical relationship can be expressed in various forms including fractions, decimals, and percentages. Converting between these forms helps in understanding and communicating the steepness or grade in different formats.

Grade

Grade refers to the steepness of a slope, often expressed as a percentage. It is obtained by multiplying the slope (rise divided by run) by 100, indicating the rise per hundred units of horizontal distance.

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