Answer:
The y-variable will be eliminated when adding the system of equations.
There is only one solution to the system of equations.
Step-by-step explanation:
-x + 6y = 16 (1)
8x - 6y = -2 (2)
Add the equations to eliminate y
-x + 8x = 16 +(-2)
7x = 16 -2
7x = 14
x = 14/7
x = 2
Substitute x = 2 into (1)
-x + 6y = 16 (1)
-2 + 6y = 16
6y = 16 + 2
6y = 18
y = 18/6
y = 3
(x, y) = (2, 3)
Answer:
y = 8x + 14
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - 
x + 6 ← is in slope- intercept form
with slope m = -
Given a line with slope m then the slope of a line perpendicular to it is
= - 
= - 
= 8 , then
y = 8x + c ← is the partial equation
To find c substitute (- 3, - 10 ) into the partial equation
- 10 = - 24 + c ⇒ c = - 10 + 24 = 14
y = 8x + 14 ← equation of perpendicular line
Answer:
x = 3
Step-by-step explanation:
In this piece-wise function, there are three defined sections, each for a different range of x. To find an x where y is -9, we have to set all parts of it equal to -9.
-x, x < -3
So, we can start by setting -x equal to -9 and solve for x:
-x = -9
x = 9
Our domain for this piece of the function is supposed to be x < -3. x = 9 does not fit into this range, meaning, in this range, there is no x for y = -9.
2x, -3 ≤ x ≤ -2
We can set the value 2x equal to -9 and, again, solve for x:
2x = -9
x = -4.5
The solution x = -4.5 does not fit into the defined domain of -3 ≤ x ≤ -2, therefore it is not a solution.
-x^2, x > -2
One last time, we can set -x^2 equal to -9 and solve for x:
-x^2 = -9
x^2 = 9
x = 3, x = -3
We are looking for a solution that fits into the domain, x > -2, x = -3 does not work, but x = 3 does.
In conclusion, the only solution where it fit the domain was x = 3
Answer:
Step-by-step explanation:
Separate into two shapes with
then use fomula length * width * height
shape 1: 7*8*10=560cm^3
Shpe 2: 5*8*6 =240cm^3
Add the two shapes 560+240=800cm^3
Answer:
Step-by-step explanation:
The late but fast train traveled for 2 hours while the slow but early train traveled for 6 hours.
SPEED TIME DISTANCE
SLOW EARLY r 6 d
FAST LATE r+124 2 d
Catchup means each train traveled equal distance
