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.
From point A, draw a line segment at an angle to the given line, and about the same length. The exact length is not important. Set the compasses on A, and set its width to a bit less than one fifth of the length of the new line. Step the compasses along the line, marking off 5 arcs. Label the last one C. With the compasses' width set to CB, draw an arc from A just below it. With the compasses' width set to AC, draw an arc from B crossing the one drawn in step 4. This intersection is point D. Draw a line from D to B. Using the same compasses' width as used to step along AC, step the compasses from D along DB making 4 new arcs across the line. Draw lines between the corresponding points along AC and DB. Done. The lines divide the given line segment AB in to 5 congruent parts.
Answer:
5
6 ---
9
Step-by-step explanation:
Answer:
0.56457
Step-by-step explanation:
log 3 with base 7 = (Log 3)/ (Log 7) = 0.47712125 / 0.845098040014
(Log 3) / (Log 7) = 0.56457
Subtract x from both sides:
(3x - x) + 7 = (x - x) - 1
3x - x = 2x:
2x + 7 = (x - x) - 1
x - x = 0:
2x + 7 = -1
Subtract 7 from both sides:
2x + (7 - 7) = -7 - 1
7 - 7 = 0:
2x = -7 - 1
-7 - 1 = -8:
2x = -8
Divide both sides by 2:
2x / 2 = -8 / 2
2 / 2 = 1:
x = -8 / 2
The gcd (greatest common denominator) of 8 and 2 is 2:
-8 / 2 = 2(-4) / 2x1 = 2/2 x - 4 = -4
x = -4
