This problem can be readily solved if we are familiar with the point-slope form of straight lines:
y-y0=m(x-x0) ...................................(1)
where
m=slope of line
(x0,y0) is a point through which the line passes.
We know that the line passes through A(3,-6), B(1,2)
All options have a slope of -4, so that should not be a problem. In fact, if we check the slope=(yb-ya)/(xb-xa), we do find that the slope m=-4.
So we can check which line passes through which point:
a. y+6=-4(x-3)
Rearrange to the form of equation (1) above,
y-(-6)=-4(x-3) means that line passes through A(3,-6) => ok
b. y-1=-4(x-2) means line passes through (2,1), which is neither A nor B
****** this equation is not the line passing through A & B *****
c. y=-4x+6 subtract 2 from both sides (to make the y-coordinate 2)
y-2 = -4x+4, rearrange
y-2 = -4(x-1)
which means that it passes through B(1,2), so ok
d. y-2=-4(x-1)
this is the same as the previous equation, so it passes through B(1,2),
this equation is ok.
Answer: the equation y-1=-4(x-2) does NOT pass through both A and B.
Answer:
Step-by-step explanation:
Total number of red disk=6
Total number of yellow disk=2
Total disk=6+2=8
Odd number=1,3,5,7=4
Odd number on red disk=1,3,5=3
Probability,
Using the formula
The probability of getting odd number disk=
The probability of getting odd numbered red disk=
The probability of selecting a red disk,given that an odd numbered disk is selected=
Using conditional probability
Answer:
the mean for the data set is 129.3
Answer:
105
Step-by-step explanation:
Theorem:
If parallel lines are cut by a transversal, then same-side interior angles are supplementary.
Lines AB and CD are parallel, and angles 3 and 6 are same-side interior angles, so by the theorem above, angles 3 and 6 are supplementary. That means that the sum of their measures is 180 deg.
m<3 + m<6 = 180
m<3 + 75 = 180
Subtract 75 from both sides.
m<3 = 105
Answer: 105 degrees
