The solution of the linear equations will be ( -2, 4).
<h3>What is an equation?</h3>
It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
Given equations are:-
Solving the equations by elimination method:-
2x +3y = 8
3x+y= -2
Multiply the second equation by 3 and subtract from the first equation.
2x +3y = 8
-9x -3y = 6
----------------
-7x = 14
x = -2
Out of the value of x in any one equation, we will get the value of y.
3x+y= -2
3 ( -2) + y = -2
-6 + y = -2
y = 4
The graph of the equations is also attached with the answer below.
Therefore the solution of the linear equations will be ( -2, 4).
The complete question is given below:-
Exploring Systems of Linear Equations 2x +3y =8 and 3x+y= -2. Find the value of x and y and draw a graph for the system of linear equations.
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X² - 10x = 46
10/2 = 5; 5²+ 25 add 25 to both sides
x² - 10x + 25 = 46 + 25
so the number you have to add to complete the square is 25.
I'll do the first one to get you started
So we have g(f(x)) which means that we start with g(x) and replace the 'x' with 'f(x)' to get g(f(x))
g(x) = ( x - 4 )/2
g(f(x)) = ( f(x) - 4)/2 .... replace every x with f(x)
g(f(x)) = (2x+4-4)/2 .... replace f(x) on the right side with 2x+4
g(f(x)) = (2x+0)/2
g(f(x)) = (2x)/2
g(f(x)) = 1x/1
g(f(x)) = 1x
g(f(x)) = x
Let me know if you need help with the other one.
Answer:
37
Step-by-step explanation:
Landon is building new bookshelves for his book store
Each shelf can hold 33 books
There are 1221 mystery books
Therefore the number of shelves he will need to build can be calculated as follows
= 1221/33
= 37
Hence Landon will need to build 37 shelves
The formula for distance is equal to:
d = v * t
where d is distance, v is velocity or speed, and t is
time
Since the distance travelled by the two airplane is
similar, therefore we can create the initial equation:
v1 * t1 = v2 * t2
We know that v1 = 496, and v2 = 558 so:
496 t1 = 558 t2
or
x = 558 t2 / 496
We also know that airplane 1 travelled 30 minutes (0.5
hours) earlier than airplane 2, therefore:
x = t2 + 0.5
Hence,
496 (t2 + 0.5) = 558 t2
496 t2 + 248 = 558 t2
t2 = 4 hours
x = t2 + 0.5 = 4 + 0.5
x = 4.5 hours
So the equation is:
x = 558 t2 / 496
And the first plane travelled:
x = 4.5 hours
