The gas tank in Feliz's car is full. Each time he drives to or from work, he uses 1 of a full
tank of gas. Which equation represents the number of times Feliz can drive to or from work
with the gas in his tank?

number of times feliz can drive to or from work with the gas in his tank is 10 times

Step-by-step explanation:

Let's start by reviewing the slope-intercept formula:

y = mx + b

At the start of the journey, we have a tank that's 5/6 full and have yet to go anywhere. That means that our b is 5/6.

Thus:

y = mx + 5/6

Now, every time he drives to or from work, be loses 1/12 of a full tank.

Thus;

y = -(1/12)x + 5/6

negative because the initial volume of gas is decreasing whenever he goes out.

Now, to get the number of times feliz can drive to or from work with the gas in his tank, y = 0.

Thus,

0 = -(1/12)x + 5/6

Add (1/12)x to both sides to give;

(1/12)x = 5/6

x = 5/6 ÷ 1/12

x = 10

2.2°  

step-by-step explanation:

let θ = the angle of elevation.

tanθ =77/2020

tanθ = 0.038 12

      θ = tan⁻¹0.038 12

      θ = 2.2°

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.