Liliana decides to crop a square photo 2 inches on each side to fit it into a frame. The area of the original photo was 121 squa
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The two intersection points are (-2.79, -0.58) and (0.79, 6.58).
<h3>How to find the points of intersection?</h3>
Here we want to solve the system of equations:
y = 2x + 5
x² + y² = 36
To solve this, we need to replace the first equation into the second one:
x² + (2x + 5)² = 36
Now we can solve this for x:
x² + 4x² + 10x + 25 = 36
5x² + 10x - 11 = 0
This is a quadratic equation, to solve it we use the general formula:
So we have two solutions for x:
x = (-10 - 17.9)/10 = -2.79
x = (-10 + 17.9)/10 = 0.79
To get the y-values of the solutions, we evaluate the linear equation in these values of x:
y = 2*(-2.79) + 5 = -0.58
y = 2*( 0.79) + 5 = 6.58
Then the two intersection points are (-2.79, -0.58) and (0.79, 6.58).
If you want to learn more about intersection points:
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Answer:
Part 1) The graph has three (3) x-intercepts and has one (1) y-intercept
Part 2) The y-value of the minimum point is -3
Part 3) f(4)=3
Part 4) f(0)=3
Part 5) f(5)=1.5
Part 6) x=-6
Part 7) The horizontal line y=-1 intersects the graph three times
Part 8) The value of the function for f(6) is equal to zero
Part 9) The function is increasing on the interval (-6,-2) and (8,11) and the function is decreasing on the interval (2,8)
Part 10) The function is positive on the interval (-3,6) and (10,11) and is negative on the interval (-6,-3) and (6,10)
Step-by-step explanation:
Part 1) Find the number of x-intercepts and y-intercepts of the graph
we know that
The<u> x-intercepts</u> are the values of x when the value of y (the function) is equal to zero
Look at the graph
The graph has 3 x-intercepts
The x-intercepts are the points (-3,0), (6,0) and (10,0)
The<u> y-intercepts</u> are the values of y when the value of x is equal to zero
Look at the graph
The graph has 1 y-intercept
The y-intercept is the point (0,3)
Part 2) The y value of the minimum point on the graph is?
we know that
Look at the picture
The minimum point is (-6,-3)
therefore
The y-value of the minimum point is -3
Part 3) f(4) is equal to?
we know that
f(4) is the value of the function when the value of x is equal to 4
Look at the graph
For x=4
The value of the function is equal to y=3
therefore
f(4)=3
Part 4) f(0) is equal to?
we know that
f(0) is the value of the function when the value of x is equal to 0
Look at the graph
For x=0
The value of the function is equal to y=3
therefore
f(0)=3
Part 5) f(5) is equal to?
we know that
f(5) is the value of the function when the value of x is equal to 5
Look at the graph
For x=5
The value of the function is about y=1.5 (see the attached figure)
therefore
f(5)=1.5
Part 6) The value of x when f(x)= -3 is?
Look at the graph
we have the point (-6,-3)
when the value of f(x)=-3
the value of x is equal to x=-6
Part 7) The horizontal line y = -1 intersects the graph _____ times?
Look at the graph
The horizontal line y=-1 intersects the graph three times (see the attached figure)
Part 8) f(6) is positive or negative?
Look at the graph
we have the point (6,0)
For x=6
The value of the function is equal to zero
Part 9) Is the graph increasing or decreasing on the interval -6?
Look at the graph
The function is increasing on the interval (-6,-2) and (8,11) and the function is decreasing on the interval (2,8)
Part 10) Is the graph positive or negative on the interval 6
Look at the graph
The function is positive (f(x) > 0) on the interval (-3,6) and (10,11) and is negative (f(x) < 0) on the interval (-6,-3) and (6,10)
