Answer:
Step-by-step explanation:
A function maps an x-value to a single y-value. The graph of the parabola on the left does that.
The table on the right maps -1 to both 10 and 20, so does not meet the definition of a function.
Answer:
5.5
Step-by-step explanation:
y = 0.5x + 5
Use the slope-intercept form to find the slope and y-intercept.
Slope: 0.5
y-intercept: 5
Any line can be graphed using two points. Select two x values, and plug them into the equation to find the corresponding values.
To find the y intercept using the equation of the line, plug in 0 for the x variable and solve for y.
y = 0.5(0) + 5
y = 5
To graph the y intercept using the equation of the line, plug in 1 for the x variable and solve for y.
y = 0.5(1) + 5
y = 5.5
Which means when x is 0, y intercept at 5 and when x is 1 y intercept at 5.5. Graph the line using the slope and the y-intercept, or the points.
This tells us, in practical terms, that, for every one unit that the x-variable increases (that is, moves over to the right), the y-variable increases (that is, goes up) by 50% of a unit.
Answer:
The budget line will remain unchanged.
Step-by-step explanation:
A budget line helps in showing the possible combinations of two commodities.
We can find the slope of the budget line that is also called the price ratio between two things. If we get a straight line, we say the slope is constant.
Here in the question its given that the initial constraints are (3,15) with initial income of $60. Then the price increases and constraints become (6,30) with an increase in income up to $120.
Therefore, the budget line will not be affected and remain unchanged as each constraint is doubling and the slope will be constant.
P = 3x + 2y
There is an accompanying graph in this problem. In the graph, there are 4 points to consider. I'll just assign letters on each point.
Point O is found in x = 0 ; y = 0 or (0,0)
Point A is found in x = 8 ; y = 0 or (8,0)
Point B is found in x = 6 ; y = 5 or (6,5)
Point C is found in x = 0 ; y = 8 or (0,8)
We will substitute x and y in the equation by its values per point.
Point A = 3(8) + 2(0) = 24 + 0 = 24
Point B = 3(6) + 2(5) = 18 + 10 = 28
Point C = 3(0) + 2(8) = 0 + 16 = 16
The maximum value of the function P = 3x+2y is 28 and its minimum value is 16.
Answer:
28 in of red and 7 in. of yellow.
Step-by-step explanation:
Red ribbon: 7 * 4 = 28 in,
Yellow ribbon: 7 * 1 = 7 in.
