13. Suppose that the water level of a river is 45 feet after 3 days of no rain and 10 feet after 10 days of no rain. The river was 60 feet before the drought began.(4 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
a. What is the rate of change (slope) for this scenario? Response area
b. What is the y-intercept for this scenario? Response area
c. Write an equation for the scenario in slope-intercept form. Response area
d. Write an equation in standard form.
a. The rate of change (slope) for this scenario is -5 feet per day.
b. The y-intercept for this scenario is 60 feet.
c. The equation for the scenario in slope-intercept form is y = -5x + 75.
d. The equation in standard form is 5x + y = 75.
9. Solve 3x+2b=6c
for x.
Step 1: 3x+2b−2b=6c−2b
subtract 2b from both sides
Step 2: 3x=6c−2b
combine like terms/simplify
Step 3: 3x/3=6c/3−2b
divide by 3 on both sides to get x isolated
Step 4: x=2c−2b
simplify/final answer
Which statement is TRUE?
(1 point)
Responses
The process has an error. The correct answer is x=4bc/3
The process has an error. The correct answer is x is equal to the fraction with numerator 4 b c and denominator 3
The process has an error. The correct answer is x=−4b−c
The process has an error. The correct answer is x is equal to negative 4 b minus c
The process is correct.
The process is correct.
The process has an error. The correct answer is x=2c−2/3b
The process has an error. The correct answer is x = 2c - 2b.
a. To find the rate of change (slope), we can use the formula:
slope = (change in y)/(change in x)
In this scenario, the change in y is 10 - 45 = -35 feet, and the change in x is 10 - 3 = 7 days.
slope = (-35 feet)/(7 days) = -5 feet/day
b. The y-intercept represents the initial value or starting point, which in this case is when x = 0 (before the drought began). From the given information, we know that the water level was 60 feet before the drought began, so the y-intercept is 60.
c. To write the equation in slope-intercept form (y = mx + b), we have:
y = -5x + 60
d. To write the equation in standard form (Ax + By = C), we can rearrange the slope-intercept form equation:
5x + y = 60
To find the rate of change (slope) for this scenario, we need to calculate the change in the water level per day.
To do this, we can use the slope formula: slope = (change in y)/(change in x).
In this case, the change in y is the difference in the water level (45 - 10 = 35 feet), and the change in x is the difference in the number of days (3 - 10 = -7 days, since the water level decreased).
So the slope is: slope = (35 feet)/(-7 days) = -5 feet per day.
To find the y-intercept, we need to determine the water level when the number of days is 0.
From the given information, we know that the water level was 60 feet before the drought began. So the y-intercept is 60 feet.
Now, we can write the equation for the scenario in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
Substituting the values we found, the equation is: y = -5x + 60.
To write the equation in standard form, we need to rearrange the equation to have the variables on one side and the constant on the other side.
Adding 5x to both sides of the equation gives: 5x + y = 60.
Therefore, the equation in standard form is: 5x + y = 60.