Answer:
a. Parallel
b. Not parallel
Step-by-step explanation:
Systems which have no solutions are parallel lines. These lines do not intersect and therefore have no solution. Remember, parallel lines have the same slope. Compare the slope in each equation when in y=mx+b format to see if they are parallel.
a. y= 2x + 3 y-2x=-3 becomes y = 2x - 3
m = 2 m= 2
The slopes are the same so these are parallel lines.
b. 3x + y = 2 becomes y= -3x + 2 y = 1/3 x + 1/2
m = -3 m= 1/3
The slopes are different so this is not parallel.
Since -3 and 1/3 are the negative reciprocals of each other. These lines are actually perpendicular.
Answer:
5 months
Step-by-step explanation:
Equation A: 15+30x
Equation B: 35x
In 5 months Gym a will cost 15+30(5) or $175 and Gym B will also cost $175.
Basically all you have to do is apply reasonable numbers until you find out where the costs will meet up.
9514 1404 393
Answer:
(x, y, z) = (-1, 0, -3)
Step-by-step explanation:
We notice that the coefficients of z are such that elimination of the z term from the equations is made easy.
Adding equations 1 and 2:
(2x -3y -2z) +(x +3y +2z) = (4) +(-7)
3x = -3
x = -1
Adding equations 2 and 3:
(x +3y +2z) +(-4x -4y -2z) = (-7) +(10)
-3x -y = 3
Substituting for x, we get ...
(-3)(-1) -y = 3
0 = y . . . . . . . . . . . add y-3 to both sides
Then z can be found from any equation. Substituting for x and y in the second equation gives ...
-1 +2z = -7
2z = -6 . . . . . add 1
z = -3 . . . . . .divide by 2
The solution is (x, y, z) = (-1, 0, -3).
Answer:
<em>The scale factor is 1:125</em>
Step-by-step explanation:
<u>Scaling</u>
Objects can be represented in a reduced or augmented size by using scaling which consists of multiplying or dividing by a constant factor. We use scaling when representing geographic locations on a map.
On a scale drawing, a distance of 5 meters = 500 cm is represented by 4 centimeters. The scale factor is usually represented as a ratio of the smallest to the biggest magnitude:
The scale factor is 1:125
