Use graphing to find the solutions to the system of equations.
{−x2−y=−42x+y=−1
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(1 point)
Responses
my teacher just graded and for the first questions with the writing i got a 100 on all of them just rember to edit it
To graphically find the solutions to the system of equations, we need to plot the two equations on a graph and find the point(s) where they intersect.
The first equation is -x^2 - y = -4.
To graph this equation, we can rearrange it to y = -x^2 + 4 and plot the graph.
The second equation is 2x + y = -1.
To graph this equation, we can rearrange it to y = -2x - 1 and plot the graph.
After plotting both graphs, we can see that they intersect at the point (-3, -5).
Therefore, the solution to the system of equations is x = -3 and y = -5.
To find the solutions to the system of equations {−x^2 − y = −4, 2x + y = −1}, we can use graphing.
Step 1: Solve each equation for y:
First equation: −x^2 − y = −4
y = −x^2 + 4
Second equation: 2x + y = −1
y = −2x − 1
Step 2: Graph the two equations on the same coordinate plane.
Step 3: Find the points of intersection on the graph. These points represent the solutions to the system of equations.
To find the solutions to the system of equations using graphing, we can plot the equations on a coordinate plane and find the points where they intersect.
First, let's rewrite the given system of equations in slope-intercept form (y = mx + b):
Equation 1: -x - y = -4
Solving for y, we get: y = -x + 4
Equation 2: 2x + y = -1
Solving for y, we get: y = -2x - 1
Now, we can start graphing these equations:
1. Equation 1: y = -x + 4
Choose some x-values and substitute them into the equation to find the corresponding y-values. For example:
For x = 0, y = -0 + 4 = 4
For x = 1, y = -1 + 4 = 3
For x = -1, y = -(-1) + 4 = 5
Plot these points on the coordinate plane and draw a line through them.
2. Equation 2: y = -2x - 1
Similarly, choose some x-values and substitute them into the equation to find the corresponding y-values. For example:
For x = 0, y = -(0) - 1 = -1
For x = 1, y = -2(1) - 1 = -3
For x = -1, y = -2(-1) - 1 = 1
Plot these points on the coordinate plane and draw a line through them.
The solutions to the system of equations are the points where the lines intersect on the graph. In this case, the lines intersect at the point (3, -7).
Therefore, the solutions to the system of equations are x = 3 and y = -7.
An object is launched into the air from a height of 5 feet.
Using the graph, determine which of the following would most likely represent the time it would take the object to hit the ground.
(1 point)
Responses
Approximately -0.15 seconds
Approximately -0.15 seconds
Approximately 0.94 seconds
Approximately 0.94 seconds
Approximately 19.1 seconds
Approximately 19.1 seconds
Approximately 2.03 seconds
To determine the time it would take the object to hit the ground, we need to look for the x-coordinate on the graph where the object's height is equal to 0.
Since the object is launched from a height of 5 feet, we need to find the x-coordinate where the height is -5 on the graph.
Looking at the graph, we can see that the height becomes -5 at approximately 0.94 seconds.
Therefore, the most likely time it would take the object to hit the ground is approximately 0.94 seconds.
A football is punted into the air. After 1 second, the ball is 48 feet in the air. After 2 seconds, the football reaches its maximum height of 64 feet. Write the equation of the parabola in vertex form.(1 point)
Responses
y=−16(x−2)2+64
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y is equal to negative 16 times open paren x minus 2 close paren squared plus 64
y=(x−2)2+64
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y is equal to open paren x minus 2 close paren squared plus 64
y=−0.01(x−64)2+2
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y is equal to negative 0 point 0 1 times open paren x minus 64 close paren squared plus 2
y=−2(x−1)2+48
To write the equation of the parabola in vertex form using the given information, we need to determine the vertex and the value of a.
The vertex form of a parabola equation is given as y = a(x-h)^2 + k, where (h,k) represents the coordinates of the vertex.
From the given information, we can determine the following:
At t = 1 second, the ball is 48 feet in the air. This gives us the point (1, 48).
At t = 2 seconds, the ball reaches its maximum height of 64 feet. This gives us the vertex of the parabola as (2, 64).
Now, we can substitute these values into the vertex form equation:
y = a(x-h)^2 + k
Using the vertex coordinates (2, 64), we get:
y = a(x-2)^2 + 64
Next, we need to determine the value of a. We can use the other given point (1, 48) to solve for a:
48 = a(1-2)^2 + 64
48 = a(-1)^2 + 64
48 = a + 64
a = -16
Substituting the value of a back into the equation, we get:
y = -16(x-2)^2 + 64
Therefore, the equation of the parabola in vertex form is y = -16(x-2)^2 + 64.
Please read the following carefully.
Any number in the form of a+bi
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are real numbers and b≠0
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(1 point)
Responses
True
True
False
True
Please read the following statement carefully.
The minimum value of a function is the smallest x-value of the function.
(1 point)
Responses
True
True
False
False
False
i2=−1
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(1 point)
Responses
True
True
False
True
All complex numbers can be graphed on the real xy coordinate plane.(1 point)
Responses
True
True
False
False
A rock is thrown upward at a speed of 85 ft/sec from the top of a 100-foot-high cliff overlooking the ocean. The rock's height above the ocean can be modeled by the function f(x)=−16x2+85x+100
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where f(x) represents the height of the rock as a function of time, x.
Match each question below with the characteristic of the function that is necessary to answer it.
(3 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.
What is the maximum height of the rock?
After how many seconds does the rock reach its maximum height?
After how many seconds would the rock hit the ocean?
The x-value of the maximumThe y-value of the maximumThe x-intercept
What is the maximum height of the rock? - The y-value of the maximum
After how many seconds does the rock reach its maximum height? - The x-value of the maximum
After how many seconds would the rock hit the ocean? - The x-intercept