Answer:
Step-by-step explanation:
<u>Given</u>
<u>Substitute and solve for n:</u>
- 42 = n² + n
- n² + 2*1/2n + 1/4 = 42.25
- (n + 0.5)² = 42.25
- n + 0.5 = √42.25
- n + 0.5 = 6.5
- n = 6
Correct option is C
Answer:
109 - -37 = 146
Step-by-step explanation:
since you are subtracting a negative, the negative number and the sign cancel each other out. So all you have to do is add.
A - False
B - True
C - True
D - False
E - True
-----
7.84 / 2 = 3.92
Answer: (-2, 5) and (2, -3)
<u>Step-by-step explanation:</u>
Graph the line y = -2x + 1 (which is in y = mx + b format) by plotting the y-intercept (b = 1) on the y-axis and then using the slope (m = -2) to plot the second point by going down 2 and right 1 unit from the first point:
y - intercept = (0, 1) 2nd point = ( -1, 1).
Graph the parabola y = x² - 2x - 3 by first plotting the vertex and then plotting the y-intercept (or some other point):
![y = x^2-2x-3\quad \rightarrow \quad a=1,\ b=-2,\ c=-3\\\\\text{axis of symmetry:}\ x = \dfrac{-b}{2a}\ \longrightarrow \ x=\dfrac{-(-2)}{2(1)}=\dfrac{2}{2}=1\\\\\text{y-value of vertex:}\ f(1) = (1)^2-2(1)-3\quad \longrightarrow \quad y = 1 - 2 - 3=-4\\\\\text{y-intercept:}\ f(0)= (0)^2-2(0)-3\ \longrightarrow \ y=0 - 0 - 3 = -3 \\](https://tex.z-dn.net/?f=y%20%3D%20x%5E2-2x-3%5Cquad%20%5Crightarrow%20%5Cquad%20a%3D1%2C%5C%20b%3D-2%2C%5C%20c%3D-3%5C%5C%5C%5C%5Ctext%7Baxis%20of%20symmetry%3A%7D%5C%20x%20%3D%20%5Cdfrac%7B-b%7D%7B2a%7D%5C%20%5Clongrightarrow%20%5C%20x%3D%5Cdfrac%7B-%28-2%29%7D%7B2%281%29%7D%3D%5Cdfrac%7B2%7D%7B2%7D%3D1%5C%5C%5C%5C%5Ctext%7By-value%20of%20vertex%3A%7D%5C%20f%281%29%20%3D%20%281%29%5E2-2%281%29-3%5Cquad%20%5Clongrightarrow%20%5Cquad%20y%20%3D%201%20-%202%20-%203%3D-4%5C%5C%5C%5C%5Ctext%7By-intercept%3A%7D%5C%20f%280%29%3D%20%280%29%5E2-2%280%29-3%5C%20%5Clongrightarrow%20%5C%20y%3D0%20-%200%20-%203%20%3D%20-3%20%5C%5C)
vertex = (1, -4) 2nd point (y-intercept) = (0, -3)
<em>see attached</em> - the graphs intersect at two points: (-2, 5) and (2, -3)
Answer:
y = 3/5 x+3
Step-by-step explanation:
two points on the graph
(-5,0) (0,3)
the y intercept is 3 (this is where it crosses the y axis)
the slope is
change in y 0 to 3 up 3
------------------ = -------------- = ------- = 3/5
change in x -5 to 0 right 5
we can tell the slope is positive because it goes from bottom left to top right
a negative slope goes from top left to bottom right
slope intercept form is
y=mx+b
y = 3/5 x+3