My little sister needs help on her homework and I don't remember really how to do this. I can't tell her if the answers or if she is doing them is the correct way. So if you could please tell me the answer and how you got it that would be great!
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1.A ticket service is selling tickets to a concert. An order of 4 tickets has a price of $63 and an order of 6 tickets has a price of $91. Write an equation to find the price of any amount of tickets.
A.y = 9x
B.y = 32x
C.y = 14x + 7
2.A rental car company charges $75 for a 3-day rental and $155 for a 7-day rental. Write an equation to find the amount that the rental car company will charge for any number of days.
A.y = 20x + 15
B.y = 15x - 20
C.y = 25x
3.Write the point-slope form of an equation of the line that passes through (-2, 3) and has a slope of m = -3.
A.(y - 2) = -3(x + 3)
B.(y - 3) = -3(x + 2)
C.(y + 3) = -2(x + 2)
4.Write the slope-intercept form of an equation of the line that passes through
(3, 5) and has a slope of 6
A. y = 2x - 6
B.y = 6x - 13
C.(y - 5) = 6(x - 3)
5. State the domain of the function y=3/x
A. D: x ≠ 0
B.D: x <0
C.D: all real numbers
1.
Since adding 2 tickets increases the cost by $28, tickets must cost $14 each. The only logical choice is thus (C).
Check: 14*4+7 = 56+7=63 and 14*6+7=84+7=91
2.
This is exactly the same problem, just different numbers. Increasing the days by 4 raises the cost by $80,meaning $20/day. Choice (A)
3.
The slope between two points is m=∆y/∆x where ∆ means "change in"
So, the slope between (x,y) and any point on the line is the same value: -3.
In particular, the slop between (x,y) and (-2,3) is -3. Symbolically, that is
(y-3)/(x+2) = -3
or, (y-3) = -3(x+2)
Choice (C)
4.
This one starts the same way, getting you to:
(y-5)=6(x-3)
However, they asked for the slope-intercept form, y=mx+b. So, solve for y:
y-5=6x-18
y=6x-13
Choice (B)
5.
Division by 0 is not defined, so 3/x is not defined when x=0.
So, choice (A)
Sure! I can help you with that. Let's go through each question and find the correct answer.
1. To find the price of any amount of tickets, we can write an equation using the given information. We know that an order of 4 tickets is $63 and an order of 6 tickets is $91. We can set up a proportion to find the relationship between the number of tickets and the price.
Let's use the variable "x" to represent the number of tickets and "y" to represent the price. The equation will be in the form y = mx + b, where "m" represents the rate of change and "b" represents the y-intercept.
To find the rate of change, we can calculate the difference in price when the number of tickets increases by 2 (from 4 to 6).
(Price for 6 tickets) - (Price for 4 tickets) = $91 - $63 = $28
So, the rate of change is $28/2 = $14.
Now, we can write the equation: y = 14x + b.
To find the y-intercept, we can substitute the values of x and y from one of the given points. Let's use the point (4, 63) since we already have the price for 4 tickets.
63 = 14(4) + b
63 = 56 + b
b = 63 - 56
b = 7
Therefore, the equation to find the price of any amount of tickets is y = 14x + 7. So the answer is C.
You can double-check if this equation holds true for any other given points.
Now, let's move on to the next question.
2. Similar to the previous question, we can set up an equation using the given information. The rental car company charges $75 for a 3-day rental and $155 for a 7-day rental.
Let's use the variable "x" to represent the number of days and "y" to represent the cost. The equation will be in the form y = mx + b.
To find the rate of change, we can calculate the difference in cost when the number of days increases by 4 (from 3 to 7).
(Cost for 7-day rental) - (Cost for 3-day rental) = $155 - $75 = $80
So, the rate of change is $80/4 = $20.
Now, we can write the equation: y = 20x + b.
To find the y-intercept, we can substitute the values of x and y from one of the given points. Let's use the point (3, 75) since we already have the cost for a 3-day rental.
75 = 20(3) + b
75 = 60 + b
b = 75 - 60
b = 15
Therefore, the equation to find the amount that the rental car company will charge for any number of days is y = 20x + 15. So the answer is A.
Let's move on to the next question.
3. The point-slope form of an equation of a line is given by the equation (y - y1) = m(x - x1), where (x1, y1) is a known point on the line and "m" is the slope.
In this question, we are given the point (-2, 3) and a slope "m" of -3. Plugging these values into the point-slope form, we get:
(y - 3) = -3(x - (-2))
(y - 3) = -3(x + 2)
(y - 3) = -3x - 6
y = -3x - 3 - 6
y = -3x - 9
Therefore, the point-slope form of the equation is (y - 3) = -3(x + 2). So the answer is B.
Moving on to the next question.
4. The slope-intercept form of an equation of a line is given by the equation y = mx + b, where "m" is the slope and "b" is the y-intercept.
In this question, we are given the point (3, 5) and a slope of 6. Plugging these values into the slope-intercept form, we get:
y = 6x + b
To find the value of "b," we can substitute the coordinates of the given point:
5 = 6(3) + b
5 = 18 + b
b = 5 - 18
b = -13
Therefore, the slope-intercept form of the equation is y = 6x - 13. So the answer is B.
Moving on to the last question.
5. The domain of a function are the possible x-values for which the function is defined. In the given function y = 3/x, we need to find the values of x that are allowed.
For this function, the only restriction is that x should not be equal to 0 since division by zero is undefined. So, the domain of the function is x ≠ 0.
Therefore, the answer is A. D: x ≠ 0.
I hope that helps! Let me know if you have any other questions.