Looking at the system of equations:
y = -2x + 12
4y + x - 20 = 0
To find the number of solutions, we need to determine if the lines represented by these equations intersect at any point.
Since the first equation is in slope-intercept form (y = mx + b), we can determine that the slope of the line is -2. This means that the line is downward sloping.
To determine the slope of the line represented by the second equation, we can rearrange it to the slope-intercept form:
4y + x = 20
4y = -x + 20
y = (-1/4)x + 5
Comparing the slopes, we see that the second line has a slope of -1/4, which is less steep compared to the first line.
Since the slopes are not equal, the lines will intersect at a single point.
Therefore, the system of equations has One solution.
How many solutions does the system of equations have? y=−2x+12 4y+x−20=0 (1 point) Responses No solution No solution Two solutions Two solutions Infinitely many solutions Infinitely many solutions One solution
15 answers
are you correct?
Yes, I apologize for the incorrect response.
Upon revisiting the system of equations, it seems that I made an error in my previous explanation. I apologize for any confusion caused.
Let's solve the system of equations correctly:
1) y = -2x + 12 [Equation 1]
2) 4y + x - 20 = 0 [Equation 2]
We can use the method of substitution to solve the system:
Substitute the expression for y from Equation 1 into Equation 2:
4(-2x + 12) + x - 20 = 0
-8x + 48 + x - 20 = 0
-7x + 28 = 0
-7x = -28
x = 4
Now, substitute the value of x back into Equation 1 to find y:
y = -2(4) + 12
y = -8 + 12
y = 4
The solution to the system of equations is x = 4 and y = 4.
Therefore, the correct response is: One solution. I apologize once again for the previous incorrect explanation.
Upon revisiting the system of equations, it seems that I made an error in my previous explanation. I apologize for any confusion caused.
Let's solve the system of equations correctly:
1) y = -2x + 12 [Equation 1]
2) 4y + x - 20 = 0 [Equation 2]
We can use the method of substitution to solve the system:
Substitute the expression for y from Equation 1 into Equation 2:
4(-2x + 12) + x - 20 = 0
-8x + 48 + x - 20 = 0
-7x + 28 = 0
-7x = -28
x = 4
Now, substitute the value of x back into Equation 1 to find y:
y = -2(4) + 12
y = -8 + 12
y = 4
The solution to the system of equations is x = 4 and y = 4.
Therefore, the correct response is: One solution. I apologize once again for the previous incorrect explanation.
3 of 143 of 14 Items Question Match the correct solution to each system of equations graphed below. *Not all answers will be used. Place the correct solution beneath the graph it matches to.(4 points) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
I'm sorry, but I cannot see the graphs you are referring to as I am a text-based AI. However, if you provide me with the system of equations or describe them to me, I can try to help you match the solutions.
Use your graphing calculator: Desmos Graphing Calculator A company owns two dealerships, both of which sell cars and trucks. Dealership A sells a total of 225 cars and trucks. Dealership B sells twice as many cars and half as many trucks as the Dealership A, and sells a total of 300 cars and trucks. (4 points) a) An equation for the total cars and trucks for Dealership A: b) An equation for the total cars and trucks for Dealership B: c) How many cars did Dealership A sell? d) Given the fact that Dealership B sold half as many trucks as Dealership A, how many trucks did Dealership B sell?
please provide the correct answers
please
please provide the correct answers
please
a) An equation for the total cars and trucks for Dealership A:
Let's say x represents the number of cars sold by Dealership A and y represents the number of trucks sold by Dealership A. Since we are given that Dealership A sells a total of 225 cars and trucks, we can write the equation as:
x + y = 225
b) An equation for the total cars and trucks for Dealership B:
We know that Dealership B sells twice as many cars and half as many trucks as Dealership A. Using the variables x and y, we can write the equation as:
2x + (1/2)y = 300
c) How many cars did Dealership A sell?
From equation (a), we have x + y = 225. Since we want to find the number of cars sold by Dealership A, we look for the coefficient of x, which is 1. Therefore, Dealership A sold 1 car.
d) Given the fact that Dealership B sold half as many trucks as Dealership A, how many trucks did Dealership B sell?
From equation (a), we know that the sum of cars and trucks sold by Dealership A is 225. Let's assign a variable to represent the number of trucks sold by Dealership A. We'll use t. Since Dealership B sold half as many trucks as Dealership A, we know that Dealership B sold (1/2)t trucks. We're given that the total cars and trucks sold by Dealership B is 300. Therefore, we can write the equation:
1 car + (1/2)t trucks = 300
To find the exact number of trucks sold by Dealership B, we would need additional information or another equation.
Let's say x represents the number of cars sold by Dealership A and y represents the number of trucks sold by Dealership A. Since we are given that Dealership A sells a total of 225 cars and trucks, we can write the equation as:
x + y = 225
b) An equation for the total cars and trucks for Dealership B:
We know that Dealership B sells twice as many cars and half as many trucks as Dealership A. Using the variables x and y, we can write the equation as:
2x + (1/2)y = 300
c) How many cars did Dealership A sell?
From equation (a), we have x + y = 225. Since we want to find the number of cars sold by Dealership A, we look for the coefficient of x, which is 1. Therefore, Dealership A sold 1 car.
d) Given the fact that Dealership B sold half as many trucks as Dealership A, how many trucks did Dealership B sell?
From equation (a), we know that the sum of cars and trucks sold by Dealership A is 225. Let's assign a variable to represent the number of trucks sold by Dealership A. We'll use t. Since Dealership B sold half as many trucks as Dealership A, we know that Dealership B sold (1/2)t trucks. We're given that the total cars and trucks sold by Dealership B is 300. Therefore, we can write the equation:
1 car + (1/2)t trucks = 300
To find the exact number of trucks sold by Dealership B, we would need additional information or another equation.
can you dumb it down?
Certainly! Here are simplified answers to your questions:
a) Equation for Dealership A: The number of cars sold by Dealership A plus the number of trucks sold by Dealership A equals 225. (x + y = 225, where x is the number of cars and y is the number of trucks)
b) Equation for Dealership B: Dealership B sells twice as many cars as Dealership A and half as many trucks. The total number of cars sold by Dealership B plus half of the number of trucks sold by Dealership B equals 300. (2x + (1/2)y = 300)
c) Number of cars sold by Dealership A: Dealership A sold 1 car.
d) Number of trucks sold by Dealership B: We need more information or another equation to determine the exact number of trucks sold by Dealership B.
a) Equation for Dealership A: The number of cars sold by Dealership A plus the number of trucks sold by Dealership A equals 225. (x + y = 225, where x is the number of cars and y is the number of trucks)
b) Equation for Dealership B: Dealership B sells twice as many cars as Dealership A and half as many trucks. The total number of cars sold by Dealership B plus half of the number of trucks sold by Dealership B equals 300. (2x + (1/2)y = 300)
c) Number of cars sold by Dealership A: Dealership A sold 1 car.
d) Number of trucks sold by Dealership B: We need more information or another equation to determine the exact number of trucks sold by Dealership B.
C is incorrect,
I apologize for the incorrect response. Let's reevaluate the given information to find the correct answer:
Given that Dealership A sells a total of 225 cars and trucks, we have the equation: x + y = 225, where x represents the number of cars and y represents the number of trucks sold by Dealership A.
From the information that Dealership B sells twice as many cars as Dealership A and half as many trucks as Dealership A, we can write the equation for Dealership B as: 2x + 0.5y = 300.
To find the number of cars sold by Dealership A, we need to solve the equation x + y = 225. However, without further information or another equation, we cannot determine the specific values of x (number of cars) and y (number of trucks) individually.
Therefore, I am unable to provide the exact number of cars Dealership A sold without additional information.
Given that Dealership A sells a total of 225 cars and trucks, we have the equation: x + y = 225, where x represents the number of cars and y represents the number of trucks sold by Dealership A.
From the information that Dealership B sells twice as many cars as Dealership A and half as many trucks as Dealership A, we can write the equation for Dealership B as: 2x + 0.5y = 300.
To find the number of cars sold by Dealership A, we need to solve the equation x + y = 225. However, without further information or another equation, we cannot determine the specific values of x (number of cars) and y (number of trucks) individually.
Therefore, I am unable to provide the exact number of cars Dealership A sold without additional information.
what is half of 98
Half of 98 is 49.
The sum of two numbers is 22. Three times one number increased by five is 35.(4 points) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. a) What are the equations you would use? Response area and Response area b) What are the two numbers? Response area and Response area
a) The equations we would use are:
1) x + y = 22 (Equation 1: Sum of two numbers is 22)
2) 3x + 5 = 35 (Equation 2: Three times one number increased by five is 35)
b) To find the two numbers, we can solve the system of equations by substituting one equation into the other.
Solving Equation 2 for x, we have:
3x + 5 = 35
3x = 35 - 5
3x = 30
x = 10
Substitute the value of x into Equation 1 to find y:
10 + y = 22
y = 22 - 10
y = 12
Therefore, the two numbers are x = 10 and y = 12.
1) x + y = 22 (Equation 1: Sum of two numbers is 22)
2) 3x + 5 = 35 (Equation 2: Three times one number increased by five is 35)
b) To find the two numbers, we can solve the system of equations by substituting one equation into the other.
Solving Equation 2 for x, we have:
3x + 5 = 35
3x = 35 - 5
3x = 30
x = 10
Substitute the value of x into Equation 1 to find y:
10 + y = 22
y = 22 - 10
y = 12
Therefore, the two numbers are x = 10 and y = 12.