Which clipboard (A, B, or C) represents a 270 degree counter- clockwise rotation?
2 answers:
You might be interested in
Answer:
Step-by-step explanation:
Let the total number of votes to choose a color = x
Number of votes for blue =
Remaining votes = x -
=
=
Votes for green =
=
=
Finally remaining votes =
=
=
=
Since these votes are for red therefore,
= 48
x = 48×6
= 288
a) Votes for blue are
Therefore, exact number for blue votes =
= 5×36
= 180
b). Votes for green =
=
= 60
c). Since 25 students were absent on that day of the vote, number of students at Riverside Elementary School = 288 + 25
= 313
d). Since seven tenths of the votes for blue were made by the girls.
Therefore, number of girls voted for blue =
= 7×18
= 126
Since total votes made = 288
Therefore, half of the votes made =
= 144
Now it's clear that number of votes made by girls is less than half of all the votes.
e). 126 girls voted for blue.
NOTES:
Use the equation y = mx + b where m is the unit rate and b is the one-time flat fee
1. Answer:
<u>Step-by-step explanation:</u>
coffee maker costs $70 - this is a one-time flat fee
it costs $0.20 per cup of coffee - this is the unit rate
y = 0.20x + 70
y = 0.20(0) + 70 → y = 0.00 + 70 → y = 70.00
y = 0.20(1) + 70 → y = 0.20 + 70 → y = 70.20
y = 0.20(2) + 70 → y = 0.40 + 70 → y = 70.40
y = 0.20(3) + 70 → y = 0.60 + 70 → y = 70.40
*******************************************************************************
2. Answer:
<u>Step-by-step explanation:</u>
shoes costs $3.00 - this is a one-time flat fee
it costs $1.50 per game of bowling - this is the unit rate
y = 1.50x + 3.00
y = 1.50(1) + 3.00 → y = 1.50 + 3.00 → y = 4.50
y = 1.50(2) + 3.00 → y = 3.00 + 3.00 → y = 6.00
y = 1.50(3) + 3.00 → y = 4.50 + 3.00 → y = 7.50
y = 1.50(4) + 3.00 → y = 6.00 + 3.00 → y = 9.00
*******************************************************************************
3. Answer: Negative
<u>Step-by-step explanation:</u>
As the x-values increase, the y-values decrease. Opposite directions results in a negative slope.
*******************************************************************************
4. Answer: Gym A → y = 20x + 50 Gym B → y = 25x + 30
<u>Step-by-step explanation:</u>
Use the slope formula: . Then choose ONE of the points and input the point (x₁, y₁) and slope (m) into the Point-Slope formula: y - y₁ = m(x - x₁) and solve for y.
Gym A: (x₁, y₁) = (1, 70) and (x₂, y₂) = (2, 90)
y - 70 = 20(x - 1)
y - 70 = 20x - 20
y = 20x + 50
Gym B: (x₁, y₁) = (1, 55) and (x₂, y₂) = (2, 80)
y - 55 = 25(x - 1)
y - 55 = 25x - 25
y = 25x + 30
(A) We let y = the cost and are told x = the number of people. Since you pay $20 per person, the cost is 20x. That is, y=20x
(B) Again, let the cost =y and the number of people is given as x. You pay $10 per person or 10x plus an additional $50 for the room. That is, y=10x+50
(c) Link to graphs: https://www.desmos.com/calculator but if that doesn't work see the attachment for a screen shot. You just have to put the equations (type them) at left and the graph comes automatically.
(D) The admission price is the same when the two equations are equal. You can find this by setting them equal to each other as such: 20x = 10x+50 and solving for x. However, since you just graphed them the point of intersection (where the lines share/have the same point) gives the information. Remembers that (x,y) = (people, cost). The graphs intersect at (5, 100) so for 5 people the cost is the same and the cost is $100.
(E) For the regular rate we let x = 6 and solve for y (the cost). We get y = 20x which is y = (20)(6)=120. It costs $120 using the regular rate to take 6 people. Now let's use the equation for the group rate again with x = 6. Here we get y = 10x +50 or y = 10(6)+50 = $110. The group rate costs $110.
(F) The cost is the same at 5 people but if there are more than five the group rate is better as we saw in part E. So the regular rate is better for less than 5 people.
(G) Here y = $150. Let us use the group rate formula and solve for x (the number of people). 10x+50 = 150 so 10x = 100 and x = 10. Since 10 is more than 5 this is the better deal. However if you don't believe it or want to double check we can solve for x using y = 150 and the regular rate equation. We get: 20x = 150 so x = 7.5 Since we can't bring half a person we would only be able to bring 7 and that is less than 10 so this is not the best choice. Use the group rate and bring 10 people!
(B) Again, let the cost =y and the number of people is given as x. You pay $10 per person or 10x plus an additional $50 for the room. That is, y=10x+50
(c) Link to graphs: https://www.desmos.com/calculator but if that doesn't work see the attachment for a screen shot. You just have to put the equations (type them) at left and the graph comes automatically.
(D) The admission price is the same when the two equations are equal. You can find this by setting them equal to each other as such: 20x = 10x+50 and solving for x. However, since you just graphed them the point of intersection (where the lines share/have the same point) gives the information. Remembers that (x,y) = (people, cost). The graphs intersect at (5, 100) so for 5 people the cost is the same and the cost is $100.
(E) For the regular rate we let x = 6 and solve for y (the cost). We get y = 20x which is y = (20)(6)=120. It costs $120 using the regular rate to take 6 people. Now let's use the equation for the group rate again with x = 6. Here we get y = 10x +50 or y = 10(6)+50 = $110. The group rate costs $110.
(F) The cost is the same at 5 people but if there are more than five the group rate is better as we saw in part E. So the regular rate is better for less than 5 people.
(G) Here y = $150. Let us use the group rate formula and solve for x (the number of people). 10x+50 = 150 so 10x = 100 and x = 10. Since 10 is more than 5 this is the better deal. However if you don't believe it or want to double check we can solve for x using y = 150 and the regular rate equation. We get: 20x = 150 so x = 7.5 Since we can't bring half a person we would only be able to bring 7 and that is less than 10 so this is not the best choice. Use the group rate and bring 10 people!