Evaluate the following algebraic expression.4/5p, if p = 25
When
P = 25 ,4/5p =
enter your response here
Represent the relationship shown in the table using words, an equation, and a graph. Then determine whether the relationship is a linear function.Mountain Climbing
Number
of Hours
Climbing, x,0,1,2,3
Elevation (ft), y,1123,1216,1309,1402
Question content area bottom
Part 1
Represent the relationship using words. Choose the correct answer below.
A.
Starting from a height of
93 ft, you gain
1123 ft each additional hour of climbing.
B.
Starting from a height of
1123 ft, you lose
93 ft each additional hour of climbing.
C.
Starting from a height of
1123 ft, you gain
93 ft each additional hour of climbing.
D.
Starting from a height of
93 ft, you lose
1123 ft each additional hour of climbing.
C. Starting from a height of 1123 ft, you gain 93 ft each additional hour of climbing.
The equation representing the relationship is:
y = 93x + 1123
Yes, the relationship is a linear function because the equation y = 93x + 1123 represents a straight line when graphed.
Represent the relationship using an equation.
y
enter your response here (Simplify your answer. Type an expression using x as the variable.)
Is the relationship a linear function?
Yes
No
To evaluate the expression 4/5p, given that p = 25, you need to substitute the value of p into the expression.
So, substitute p = 25 into the expression 4/5p:
4/5p = 4/5 * 25
Now, perform the multiplication:
4/5 * 25 = 100/5
Simplify the fraction:
100/5 = 20
Therefore, 4/5p, when p = 25, equals 20.
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To represent the relationship between the number of hours climbing (x) and the elevation (y) using words:
Starting from a height of 1123 ft, you gain 93 ft each additional hour of climbing.
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To represent the relationship using an equation, you can use the slope-intercept form of a linear equation, which is y = mx + b. The slope (m) represents the rate at which the elevation changes, and the y-intercept (b) represents the initial elevation.
In this case, the initial elevation (y-intercept) is 1123 ft. The rate at which the elevation changes (slope) is 93 ft per hour. So, the equation would be:
y = 93x + 1123
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To represent the relationship using a graph, plot the points given in the table, where the x-values represent the number of hours climbing and the y-values represent the elevation. Then connect the points with a straight line. If the line is straight, the relationship is a linear function.
The graph of the points would look like this:
(0, 1123)
(1, 1216)
(2, 1309)
(3, 1402)
The graph shows a straight line, indicating that the relationship is a linear function.