The side AB measures option 2.
units long.
Step-by-step explanation:
Step 1:
The coordinates of the given triangle ABC are A (4, 5), B (2, 1), and C (4, 1).
The sides of the triangle are AB, BC, and CA. We need to determine the length of AB.
To calculate the distance between two points, we use the formula 
where (
) are the coordinates of the first point and (
) are the coordinates of the second point.
Step 2:
For A (4, 5) and B (2, 1), (
) = (4, 5) and (
) = (2, 1). Substituting these values in the distance formula, we get

So the side AB measures
units long which is the second option.
Answer:
33.75
Step-by-step explanation:
45x0.75=33.75
It always helps to draw a picture. Given the information, Segment OF is the center line that is bisecting this angle.
Since it's bisecting (cutting in half)... we can simply set the two angles equal to each other.
y+30=3y-50
-2y+30=-50
-2y=-80
y = 40
C)40.
Answer:
Logarithms are the "opposite" of exponentials, just as subtraction is the opposite of addition and division is the opposite of multiplication. Logs "undo" exponentials. Technically speaking, logs are the inverses of exponentials. On the left-hand side above is the exponential statement "y = bx
Step-by-step explanation:
Answer:
Option (B)
Step-by-step explanation:
There are two lines on the graph representing the system of equations.
First line passes through two points (-3, 1) and (-2, 3).
Slope of the line = 
= 
m = 2
Equation of the line passing through (x', y') and slope = m is,
y - y' = m(x - x')
Equation of the line passing through (-3, 1) and slope = 2 will be,
y - 1 = 2(x + 3)
y = 2x + 7 ----------(1)
Second line passes through (0, 1) and (-1, 4) and y-intercept 'b' of the line is 1.
Let the equation of this line is,
y = mx + b
Slope 'm' = 
= 
= -3
Here 'b' = 1
Therefore, equation of the line will be,
y = -3x + 1 ---------(2)
From equation (1) and (2),
2x + 7 = -3x + 1
5x = -6
x = 
x = 
From equation (1),
y = 2x + 7
y = 
= 
= 
= 
Therefore, exact solution of the system of equations is
.
Option (B) will be the answer.