Barry is measuring the length of his pencils. The red pencil is 4.32 inches long, the blue pencil is 6.1 inches long, and the gr
1 answer:
Answer:
Step-by-step explanation:
<u>Given information</u>
Red pencil = 4.32 inches
Blue pencil = 6.1 inches
Green pencil = 2.27 inches
<u>Expression deducted from the question</u>
Total length = Red pencil + Blue pencil + Green pencil
<u>Substitute values into the expression</u>
Total length = (4.32) + (6.1) + (2.27)
<u>Simplify by addition</u>
Total length = 10.42 + 2.27
Total length = 12.69 inches
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Answer:
The answer is below
Step-by-step explanation:
A) i)
For Anna initially, she has $0 from making 0 envelopes. After making 400 envelopes she has $20. Let x represent the number of envelopes and y the earnings. Hence this can be represented by the points (0, 0) and (400, 20). Using the equation of a line:
The table is:
x: 200 400 600 800 1000
y: 10 20 30 40 50
ii)
For Jason initially, he has $0 from making 0 envelopes. For every 250 envelopes he has $10. Let x represent the number of envelopes and y the earnings. Hence this can be represented by the points (0, 0) and (250, 10). Using the equation of a line:
The table is:
x: 200 400 600 800 1000
y: 8 16 24 32 40
The graph is plotted using geogebra online graphing
b) From the table above we can see that Anna makes more stuffing than Jason.
c) Anna has a savings of $100. Hence this can be represented by the points (0, 100) and (250, 10). Using the equation of a line:
We can see from the graph that there is a y intercept at 100. That is the earnings starts from 100.
The equation of a line is given as y = mx + b, where m is the slope and b is the y intercept (initial value)
For the first graph, the slope is 1/20 and the initial value is 0 while for the second graph the slope is 1/15 and the initial value is 100
D) The line pass through (10, 10) and (100, 40), hence:
The red line is represented by y ≥ -3x + 3.
The blue line is represented by y < 3/2x - 6.
A) In this system of inequalities, there is one solid line and one dashed line.
The solid line is the inequality y ≥ -3x + 3 because it has the symbol greater than or equal to. The "equal to" part of the symbol is important because it means that any coordinate located on the solid line is a solution.
However, the inequality y < 3/2x - 6 is a dashed line because it does not have "equal to." This makes the inequality a dashed line which means that all coordinates on it will not be a solution to the inequality.
In the inequality y ≥ -3x + 3, the shading is above the line. This means that all coordinates within the line and shaded area above the line will be a solution to the inequality.
In the inequality y < 3/2x - 6, the shading is below the line. This means that all coordinates within the shared area of the line will be a solution to the inequality. However, since y is not less than or EQUAL TO, all coordinates within the dashed line is not a solution to the inequality.
The solution area, where a coordinate is a solution to
both inequalities, is where the shaded areas of both inequalities overlap.
B) The point (-6, 3) is a not solution to both of the inequalities because it is not within the shared areas of the two inequalities.
Substitute the coordinate (-6, 3) in the inequality y < 3/2x - 6.
y < 3/2x - 6
3 < 3/2(-6) - 6
3 < -9 - 6
3 < -15
This is not true because a negative number cannot be greater than a positive number. Therefore, this proves that the coordinate (-6, 3) is not a solution for the inequality y < 3/2x - 6.
Check if the coordinate fits for the other inequality.
y ≥ -3x + 3
3 ≥ -3(-6) + 3
3 ≥ 18 + 3
3 ≥ 21
This is also not true because 3 is not greater than or equal to 21. Therefore, this coordinate is not a solution to the inequality y ≥ -3x + 3.
The coordinate (-6, 3) is not a solution for the system of inequalities because it is not a solution for both inequalities.
The blue line is represented by y < 3/2x - 6.
A) In this system of inequalities, there is one solid line and one dashed line.
The solid line is the inequality y ≥ -3x + 3 because it has the symbol greater than or equal to. The "equal to" part of the symbol is important because it means that any coordinate located on the solid line is a solution.
However, the inequality y < 3/2x - 6 is a dashed line because it does not have "equal to." This makes the inequality a dashed line which means that all coordinates on it will not be a solution to the inequality.
In the inequality y ≥ -3x + 3, the shading is above the line. This means that all coordinates within the line and shaded area above the line will be a solution to the inequality.
In the inequality y < 3/2x - 6, the shading is below the line. This means that all coordinates within the shared area of the line will be a solution to the inequality. However, since y is not less than or EQUAL TO, all coordinates within the dashed line is not a solution to the inequality.
The solution area, where a coordinate is a solution to
both inequalities, is where the shaded areas of both inequalities overlap.
B) The point (-6, 3) is a not solution to both of the inequalities because it is not within the shared areas of the two inequalities.
Substitute the coordinate (-6, 3) in the inequality y < 3/2x - 6.
y < 3/2x - 6
3 < 3/2(-6) - 6
3 < -9 - 6
3 < -15
This is not true because a negative number cannot be greater than a positive number. Therefore, this proves that the coordinate (-6, 3) is not a solution for the inequality y < 3/2x - 6.
Check if the coordinate fits for the other inequality.
y ≥ -3x + 3
3 ≥ -3(-6) + 3
3 ≥ 18 + 3
3 ≥ 21
This is also not true because 3 is not greater than or equal to 21. Therefore, this coordinate is not a solution to the inequality y ≥ -3x + 3.
The coordinate (-6, 3) is not a solution for the system of inequalities because it is not a solution for both inequalities.
Answer:
(fg)(-2) = 96
Step-by-step explanation:
Hope this helps