Answer: Parallel lines have the same slope
y = 2x +b
Use the given point (2, 5)
5 = 2(2) +b
b = 5 -4 = 1
The equation of the line is
y = 2x +1
Note general form of the slope-intercept form of a line is y = mx +b, where m is the slope and b is the y-axis intercept
Step-by-step explanation:
Answer: 6 cm
Step-by-step explanation:
6 cm is the radius because half the diameter is the radius
Answer:
The system has one solution.
Step-by-step explanation:
We have two equations:
y = -2x - 4
y = 3x + 3
Equalling them:
y = y
-2x - 4 = 3x + 3
5x = -7
![x = -\frac{7}{5}](https://tex.z-dn.net/?f=x%20%3D%20-%5Cfrac%7B7%7D%7B5%7D)
And
![y = 3x + 3 = 3(-\frac{7}{5}) + 3 = \frac{-21}{5} + 3 = \frac{-21}{5} + \frac{15}{5} = -\frac{6}{5}](https://tex.z-dn.net/?f=y%20%3D%203x%20%2B%203%20%3D%203%28-%5Cfrac%7B7%7D%7B5%7D%29%20%2B%203%20%3D%20%5Cfrac%7B-21%7D%7B5%7D%20%2B%203%20%3D%20%5Cfrac%7B-21%7D%7B5%7D%20%2B%20%5Cfrac%7B15%7D%7B5%7D%20%3D%20-%5Cfrac%7B6%7D%7B5%7D)
Replacing in the other equation we should get the same result.
![y = -2x - 4 = -2(-\frac{7}{5}) - 4 = \frac{14}[5} - 4 = \frac{14}{4} - \frac{20}{5} = -\frac{6}{5}](https://tex.z-dn.net/?f=y%20%3D%20-2x%20-%204%20%3D%20-2%28-%5Cfrac%7B7%7D%7B5%7D%29%20-%204%20%3D%20%5Cfrac%7B14%7D%5B5%7D%20-%204%20%3D%20%5Cfrac%7B14%7D%7B4%7D%20-%20%5Cfrac%7B20%7D%7B5%7D%20%3D%20-%5Cfrac%7B6%7D%7B5%7D)
So the system has one solution.
Answer:
![x = - 4\: or \: x = 9](https://tex.z-dn.net/?f=x%20%3D%20%20-%204%5C%3A%20or%20%5C%3A%20x%20%3D%20%209)
Step-by-step explanation:
make one side equal to zero:
![{x}^{2} - 5x - 36 = 0](https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B2%7D%20%20-%205x%20-%2036%20%3D%200)
find two factors that multiply to -36 and add to -5 (-9 & 4)
![{x }^{2} - 9x + 4x - 36 = 0](https://tex.z-dn.net/?f=%20%7Bx%20%7D%5E%7B2%7D%20%20-%209x%20%2B%204x%20-%2036%20%3D%200)
factorise
![x(x - 9) + 4(x - 9) = 0](https://tex.z-dn.net/?f=x%28x%20-%209%29%20%2B%204%28x%20-%209%29%20%3D%200)
![(x + 4)(x - 9) = 0](https://tex.z-dn.net/?f=%28x%20%2B%204%29%28x%20-%209%29%20%3D%200)
solve for x
![x = - 4 \: or \: x = 9](https://tex.z-dn.net/?f=x%20%3D%20%20-%204%20%5C%3A%20or%20%5C%3A%20x%20%3D%209)
Answer:
y - 5 < 20
y < 25
Step-by-step explanation:
y - 5 < 20
y < 25