In the parallelogram AXYZ, line segment AT = 4y – 2, line segment TY = 6x -12, line segment TX = 14, line segment ZT = 2x + 12.
Find the value of x and y.
1 answer:
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1.
(a) The variables are:
→ y is the total cost
→ x is the number of ride tickets
→ c is the price of the fair admission
(b) The linear equation that can be used to determine the cost for
anyone who only pays for ride tickets and fair admission is
y = 1.25 x + c
(c) Because the equation is linear which means the value of y depends on
the value of x and the value of c = 5 does not change so the equation
can be used to determine the cost for anyone who only pays for ride
tickets and fair admission
2.
(a) The slope of the line is
(b) The equation of the line in point-slope form is:
y - 3 = (x + 4)
(c) The equation of the line in slope-intercept form is:
y = x + 6
3.
The inequality that model the problem is:
20x + 10y ≥ 2000
Step-by-step explanation:
1.
The given is:
1. The county fair charges $1.25 per ticket for the rides.
2. Jermaine bought 20 tickets for the rides and spent a total of $35.00
at the fair
3. Jermaine spent his money only on ride tickets and fair admission
4. The price of the fair admission is the same for everyone
Use y to represent the total cost and x to represent the number of
ride tickets
∵ The price of a ticket = $1.25
∵ The number of tickets = x
∵ y represents the total cost
∵ The total cost = the cost of a ticket × the number of tickets + the price
of the fair admission
∴ y = 1.25 x + c, where c is the fair admission
∵ Jermaine bought 20 tickets
∴ x = 20
∵ Jermaine spent a total of $35.00 at the fair
∴ y = 35
- Substitute these values in the equation in step b
∴ 35 = 1.25(20) + c
∴ 35 = 25 + c
- Subtract 25 from both sides
∴ c = 5
∵ c represents a constant term (y-intercept) in the linear equation
∴ The price of the fair admission for any one is $5
(a)
The variables are:
→ y is the total cost
→ x is the number of ride tickets
→ c is the price of the fair admission
(b)
The linear equation that can be used to determine the cost for
anyone who only pays for ride tickets and fair admission is
y = 1.25 x + 5
(c)
Because the equation is linear which means the value of y depends on
the value of x and the value of c = 5 does not change so the equation
can be used to determine the cost for anyone who only pays for ride
tickets and fair admission
2.
A line goes through the points (-4 , 3) and (4 , 9)
The rule of the slope of a line is
∵ = -4 and
= 4
∵ = 3 and
= 9
∴
(a)
The slope of the line is
(b)
The point-slope form of the equation is
∵ = 3 and
= -4
∵ m =
∴ y - 3 = (x - -4)
∴ y - 3 = (x + 4)
The equation of the line in point-slope form is:
y - 3 = (x + 4)
(c)
The slope-intercept form of the equation is y = mx + c, where c is the
y-intercept
∵ m =
∴ y = x + c
- To find c substitute x and y by the coordinates of one of the two
given points
∵ x and y are the coordinates of point (4 , 9)
∴ 9 = (4) + c
∴ 9 = 3 + c
- Subtract 3 from both sides
∴ c = 6
∴ y = x + 6
The equation of the line in slope-intercept form is:
y = x + 6
3.
Jacob and Sarah are saving money to go on a trip
The given is:
1. They need at least $2000 in order to go
2. Jacob mows lawns and Sarah walks dogs to raise money
3. Jacob charges $20 each time he mows a lawn and Sarah charges
$10 each time she walks a dog
4. x representing the number of lawns mowed and y representing the
number of dogs walked
∵ x representing the number of lawns mowed
∵ Jacob charges $20 each time he mows a lawn
∴ Jacob can earn $20x
∵ y representing the number of dogs walked
∵ Sarah charges $10 each time she walks a dog
∴ Sarah can earn 10y
∵ They need at least $2000 in order to go to the trip
∴ 20x + 10y ≥ 2000
The inequality that model the problem is:
20x + 10y ≥ 2000
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