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Answer:
Step-by-step explanation:
When using the substitution method we use the fact that if two expressions y and x are of equal value x=y, then x may replace y or vice versa in another expression without changing the value of the expression.
Solve the systems of equations using the substitution method
{y=2x+4
{y=3x+2
We substitute the y in the top equation with the expression for the second equation:
2x+4 = 3x+2
4−2 = 3x−2
2=== = x
To determine the y-value, we may proceed by inserting our x-value in any of the equations. We select the first equation:
y= 2x + 4
We plug in x=2 and get
y= 2⋅2+4 = 8
The elimination method requires us to add or subtract the equations in order to eliminate either x or y, often one may not proceed with the addition directly without first multiplying either the first or second equation by some value.
Example:
2x−2y = 8
x+y = 1
We now wish to add the two equations but it will not result in either x or y being eliminated. Therefore we must multiply the second equation by 2 on both sides and get:
2x−2y = 8
2x+2y = 2
Now we attempt to add our system of equations. We commence with the x-terms on the left, and the y-terms thereafter and finally with the numbers on the right side:
(2x+2x) + (−2y+2y) = 8+2
The y-terms have now been eliminated and we now have an equation with only one variable:
4x = 10
x= 10/4 =2.5
Thereafter, in order to determine the y-value we insert x=2.5 in one of the equations. We select the first:
2⋅2.5−2y = 8
5−8 = 2y
−3 =2y
−3/2 =y
y =-1.5
Answer:
Step-by-step explanation:
Given the coordinate points (6, -3) and (7, -10), we are to find the equation of a line passing through this two points;
The standard equation of a line is y = mx+c
m is the slope
c is the intercept
Get the slope;
m = Δy/Δx = y2-y1/x2-x1
m = -10-(-3)/7-6
m = -10+3/1
m = -7
Get the intercept;
Substitute the point (6, -3) and m = -7 into the expression y = mx+c
-3 = -7(6)+c
-3 = -42 + c
c = -3 + 42
c = 39
Get the required equation by substituting m = -7 and c= 39 into the equation y = mx+c
y = -7x + 39
Hence the required equation is y = -7x + 39
Answer:
2.5 second
Step-by-step explanation:
The equation is missing in the question.
The equation is, 
, where 'h' is the height and 't' is time measured in second.
Now we know to reach its maximum height, h in t seconds, the derivative of h with respect to time t is given by :
Now the differentiating the equation with respect to time t, we get
For maximum height,
So, 
Therefore, the ball takes 2.5 seconds time to reach the maximum height.
Answer:
A. 1/5k - 2/3j and -2/3j +1/5k
Step-by-step explanation:
A. 1/5k - 2/3j and -2/3j +1/5k
B. 1/5k - 2/3j and -1/5k +2/3j
There is a change in the signs of each term
1/5k changed to -1/5k
-2/3j changed to +2/3j
Not equivalent
C. 1/5k - 2/3j and 1/5j - 2/3k
There is a change in the variables
1/5k changed to 1/5j
-2/3j changed to -2/3k
D. 1/5k - 2/3j and 2/3j - 1/5k
The is a change in the signs of each term
1/5k changed to -1/5k
-2/3j changed to +2/3j
The only equivalent expression is
A. 1/5k - 2/3j and -2/3j +1/5k
