Asked by Asma Amer
−2z+4=19
Answers
Answered by
Asma Amer
4(x−6)=9
Answered by
Asma Amer
−2(7x+11)=15
Answered by
Asma Amer
10y+19−2y=−125
Answered by
Asma Amer
A movie theater offers two options for membership. The first option costs $15 per ticket but an initial fee of $10. The second option costs $12.50 per ticket but an initial fee of $40 . After how many tickets are both options the same price?
____ tickets
____ tickets
Answered by
Asma Amer
There are two different vats. The first vat has 12 gallons is being filled at a rate of 3 gallons per minute. The second vat has 120 gallons and is leaking fluid at a rate of 7 gallons per minute. After how many seconds will both vats have the same amount of liquid?
____ minutes
____ minutes
Answered by
GPT 3.5
To solve for z, we need to isolate it on one side of the equation.
Starting with the equation −2z + 4 = 19, we can begin by subtracting 4 from both sides:
−2z + 4 - 4 = 19 - 4
−2z = 15
Next, divide both sides of the equation by -2:
−2z/-2 = 15/-2
z = -7.5
Therefore, the solution to the equation −2z + 4 = 19 is z = -7.5.
Starting with the equation −2z + 4 = 19, we can begin by subtracting 4 from both sides:
−2z + 4 - 4 = 19 - 4
−2z = 15
Next, divide both sides of the equation by -2:
−2z/-2 = 15/-2
z = -7.5
Therefore, the solution to the equation −2z + 4 = 19 is z = -7.5.
Answered by
GPT 3.5
To solve for x, we need to isolate it on one side of the equation.
Starting with the equation 4(x - 6) = 9, we can begin by distributing the 4 to the terms inside the parentheses:
4x - 24 = 9
Next, we can add 24 to both sides of the equation to move the constant term to the right side:
4x - 24 + 24 = 9 + 24
4x = 33
Finally, divide both sides of the equation by 4 to solve for x:
4x/4 = 33/4
x = 33/4
Therefore, the solution to the equation 4(x - 6) = 9 is x = 33/4.
Starting with the equation 4(x - 6) = 9, we can begin by distributing the 4 to the terms inside the parentheses:
4x - 24 = 9
Next, we can add 24 to both sides of the equation to move the constant term to the right side:
4x - 24 + 24 = 9 + 24
4x = 33
Finally, divide both sides of the equation by 4 to solve for x:
4x/4 = 33/4
x = 33/4
Therefore, the solution to the equation 4(x - 6) = 9 is x = 33/4.
Answered by
GPT 3.5
To solve for x, we need to isolate it on one side of the equation.
Starting with the equation −2(7x + 11) = 15, we can simplify the left side by distributing the -2 to the terms inside the parentheses:
-14x - 22 = 15
Next, we can add 22 to both sides of the equation to move the constant term to the right side:
-14x - 22 + 22 = 15 + 22
-14x = 37
Finally, divide both sides of the equation by -14 to solve for x:
-14x / -14 = 37 / -14
x = -37/14
Therefore, the solution to the equation −2(7x + 11) = 15 is x = -37/14.
Starting with the equation −2(7x + 11) = 15, we can simplify the left side by distributing the -2 to the terms inside the parentheses:
-14x - 22 = 15
Next, we can add 22 to both sides of the equation to move the constant term to the right side:
-14x - 22 + 22 = 15 + 22
-14x = 37
Finally, divide both sides of the equation by -14 to solve for x:
-14x / -14 = 37 / -14
x = -37/14
Therefore, the solution to the equation −2(7x + 11) = 15 is x = -37/14.
Answered by
GPT 3.5
To solve for y, we need to isolate it on one side of the equation.
Starting with the equation 10y + 19 - 2y = -125, we can simplify the left side of the equation by combining like terms:
10y - 2y + 19 = -125
This simplifies to:
8y + 19 = -125
Next, we can subtract 19 from both sides to move the constant term to the right side:
8y + 19 - 19 = -125 - 19
8y = -144
Finally, divide both sides of the equation by 8 to solve for y:
(8y) / 8 = (-144) / 8
y = -18
Therefore, the solution to the equation 10y + 19 - 2y = -125 is y = -18.
Starting with the equation 10y + 19 - 2y = -125, we can simplify the left side of the equation by combining like terms:
10y - 2y + 19 = -125
This simplifies to:
8y + 19 = -125
Next, we can subtract 19 from both sides to move the constant term to the right side:
8y + 19 - 19 = -125 - 19
8y = -144
Finally, divide both sides of the equation by 8 to solve for y:
(8y) / 8 = (-144) / 8
y = -18
Therefore, the solution to the equation 10y + 19 - 2y = -125 is y = -18.
Answered by
GPT 3.5
Let's represent the number of tickets as "x".
For the first option, the cost is $15 per ticket plus an initial fee of $10. The total cost will be (15x + 10).
For the second option, the cost is $12.50 per ticket plus an initial fee of $40. The total cost will be (12.50x + 40).
To find out when both options are the same price, we need to set up an equation and solve for x:
15x + 10 = 12.50x + 40
Subtracting 12.50x from both sides:
15x - 12.50x + 10 = 12.50x - 12.50x + 40
2.5x + 10 = 40
Subtracting 10 from both sides:
2.5x + 10 - 10 = 40 - 10
2.5x = 30
Dividing both sides by 2.5 to solve for x:
(2.5x) / 2.5 = 30 / 2.5
x = 12
Therefore, after purchasing 12 tickets, both options will be the same price
For the first option, the cost is $15 per ticket plus an initial fee of $10. The total cost will be (15x + 10).
For the second option, the cost is $12.50 per ticket plus an initial fee of $40. The total cost will be (12.50x + 40).
To find out when both options are the same price, we need to set up an equation and solve for x:
15x + 10 = 12.50x + 40
Subtracting 12.50x from both sides:
15x - 12.50x + 10 = 12.50x - 12.50x + 40
2.5x + 10 = 40
Subtracting 10 from both sides:
2.5x + 10 - 10 = 40 - 10
2.5x = 30
Dividing both sides by 2.5 to solve for x:
(2.5x) / 2.5 = 30 / 2.5
x = 12
Therefore, after purchasing 12 tickets, both options will be the same price
Answered by
GPT 3.5
Let's represent the number of minutes as "m".
For the first vat, it is being filled at a rate of 3 gallons per minute. The total amount of liquid in the first vat can be represented as 12 + 3m.
For the second vat, it is leaking fluid at a rate of 7 gallons per minute. The total amount of liquid in the second vat can be represented as 120 - 7m.
To find out when both vats have the same amount of liquid, we need to set up an equation and solve for m:
12 + 3m = 120 - 7m
Adding 7m to both sides:
12 + 3m + 7m = 120 - 7m + 7m
10m + 12 = 120
Subtracting 12 from both sides:
10m + 12 - 12 = 120 - 12
10m = 108
Dividing both sides by 10 to solve for m:
(10m) / 10 = 108 / 10
m = 10.8
Therefore, after 10.8 minutes, both vats will have the same amount of liquid.
To convert this to seconds, we multiply by 60:
10.8 minutes * 60 seconds/minute = 648 seconds
Therefore, after 648 seconds, both vats will have the same amount of liquid.
For the first vat, it is being filled at a rate of 3 gallons per minute. The total amount of liquid in the first vat can be represented as 12 + 3m.
For the second vat, it is leaking fluid at a rate of 7 gallons per minute. The total amount of liquid in the second vat can be represented as 120 - 7m.
To find out when both vats have the same amount of liquid, we need to set up an equation and solve for m:
12 + 3m = 120 - 7m
Adding 7m to both sides:
12 + 3m + 7m = 120 - 7m + 7m
10m + 12 = 120
Subtracting 12 from both sides:
10m + 12 - 12 = 120 - 12
10m = 108
Dividing both sides by 10 to solve for m:
(10m) / 10 = 108 / 10
m = 10.8
Therefore, after 10.8 minutes, both vats will have the same amount of liquid.
To convert this to seconds, we multiply by 60:
10.8 minutes * 60 seconds/minute = 648 seconds
Therefore, after 648 seconds, both vats will have the same amount of liquid.