Answer:
Equation 1: No solution
Equation 2: Infinity
Equation 3: One solution
Equation 4: Infinity
Equation 5: No solution
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The zero of a function is the x-value at which the function value is zero. That is, the value of the function that intersects the x-axis. From the picture, the zero is -5
Answer: (-4,-8)
Step-by-step explanation: I got a 100% on the quiz
Answer:
The required equation is:
![y = -\frac{3}{2}x+9](https://tex.z-dn.net/?f=y%20%3D%20-%5Cfrac%7B3%7D%7B2%7Dx%2B9)
Step-by-step explanation:
To find the equation of a line, the slope and y-intercept is required.
The slope can be found by finding the slope of given line segment. A the perpendicular bisector of a line is perpendicular to the given line, the product of their slopes will be -1 and it will pass through the mid-point of given line segment.
Given points are:
![(x_1,y_1) = (8,10)\\(x_2,y_2) = (-4,2)](https://tex.z-dn.net/?f=%28x_1%2Cy_1%29%20%3D%20%288%2C10%29%5C%5C%28x_2%2Cy_2%29%20%3D%20%28-4%2C2%29)
We will find the slope of given line segment first
![m = \frac{y_2-y_1}{x_2-x_1}\\= \frac{2-10}{-4-8}\\=\frac{-8}{-12}\\=\frac{2}{3}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%5C%5C%3D%20%5Cfrac%7B2-10%7D%7B-4-8%7D%5C%5C%3D%5Cfrac%7B-8%7D%7B-12%7D%5C%5C%3D%5Cfrac%7B2%7D%7B3%7D)
Let m_1 be the slope of perpendicular bisector then,
![m.m_1 = -1\\\frac{2}{3}.m_1 = -1\\m_1 = \frac{-3}{2}](https://tex.z-dn.net/?f=m.m_1%20%3D%20-1%5C%5C%5Cfrac%7B2%7D%7B3%7D.m_1%20%3D%20-1%5C%5Cm_1%20%3D%20%5Cfrac%7B-3%7D%7B2%7D)
Now the mid-point
![(x,y) = (\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2})\\= (\frac{8-4}{2} , \frac{10+2}{2})\\=(\frac{4}{2}, \frac{12}{2})\\=(2,6)](https://tex.z-dn.net/?f=%28x%2Cy%29%20%3D%20%28%5Cfrac%7Bx_1%2Bx_2%7D%7B2%7D%20%2C%20%5Cfrac%7By_1%2By_2%7D%7B2%7D%29%5C%5C%3D%20%28%5Cfrac%7B8-4%7D%7B2%7D%20%2C%20%5Cfrac%7B10%2B2%7D%7B2%7D%29%5C%5C%3D%28%5Cfrac%7B4%7D%7B2%7D%2C%20%5Cfrac%7B12%7D%7B2%7D%29%5C%5C%3D%282%2C6%29)
We have to find equation of a line with slope -3/2 passing through (2,6)
The equation of line in slope-intercept form is given by:
![y = m_1x+b](https://tex.z-dn.net/?f=y%20%3D%20m_1x%2Bb)
Putting the value of slope
![y= -\frac{3}{2}x+b](https://tex.z-dn.net/?f=y%3D%20-%5Cfrac%7B3%7D%7B2%7Dx%2Bb)
Putting the point (2,6) to find the y-intercept
![6 = -\frac{3}{2}(2)+b\\6 = -3+b\\b = 6+3 =9](https://tex.z-dn.net/?f=6%20%3D%20-%5Cfrac%7B3%7D%7B2%7D%282%29%2Bb%5C%5C6%20%3D%20-3%2Bb%5C%5Cb%20%3D%206%2B3%20%3D9)
The equation is:
![y = -\frac{3}{2}x+9](https://tex.z-dn.net/?f=y%20%3D%20-%5Cfrac%7B3%7D%7B2%7Dx%2B9)
<span>The find step is to find C which is the vertical shift. This is the average between the maximum and minimum. So its 30+70=100/2= 50. the amplitude (A) take the average of the difference between max. temp. and min. value So 70-30= 40/2= 20, but it becomes -20 because the graph is shifted up 50 degrees and decreases to 30 at 4a.m. Then the period is 2pi/B which is 2pi/24, which equals pi/12. A=-20 B= pi/12 C=50</span>