Answer:
x = 5/39
, y = 539/39
Step-by-step explanation:
Solve the following system:
{y - 2.5 x = 13.5
12.25 x - y = -12.25
In the first equation, look to solve for y:
{y - 2.5 x = 13.5
12.25 x - y = -12.25
y - 2.5 x = y - (5 x)/2 and 13.5 = 27/2:
y - (5 x)/2 = 27/2
Add (5 x)/2 to both sides:
{y = 1/2 (5 x + 27)
12.25 x - y = -12.25
Substitute y = 1/2 (5 x + 27) into the second equation:
{y = 1/2 (5 x + 27)
1/2 (-5 x - 27) + 12.25 x = -12.25
(-5 x - 27)/2 + 12.25 x = 12.25 x + (-(5 x)/2 - 27/2) = 9.75 x - 27/2:
{y = 1/2 (5 x + 27)
9.75 x - 27/2 = -12.25
In the second equation, look to solve for x:
{y = 1/2 (5 x + 27)
9.75 x - 27/2 = -12.25
9.75 x - 27/2 = (39 x)/4 - 27/2 and -12.25 = -49/4:
(39 x)/4 - 27/2 = -49/4
Add 27/2 to both sides:
{y = 1/2 (5 x + 27)
(39 x)/4 = 5/4
Multiply both sides by 4/39:
{y = 1/2 (5 x + 27)
x = 5/39
Substitute x = 5/39 into the first equation:
{y = 539/39
x = 5/39
Collect results in alphabetical order:
Answer: {x = 5/39
, y = 539/39
(n - 4) - 3 = 3 - (2n + 3)
Let's first start by removing the parenthesis.
(n-4) = +(n-4) so we just remove the parenthesis without changing the signs. So the first part of the equation will be n - 4 - 3.
Before (2n+3), we can notice a minus sign (-) which means that to remove the parenthesis, we need to change the signs of the numbers and variables inside.
-(2n+3) = -2n-3
So the second part of the equation becomes 3 -2n - 3
(n-4) - 3 = 3 - (2n+3)
n - 4 - 3 = 3 - 2n - 3
n - 7 = -2n
Now we need to put the variables apart and the constants apart. So we subtract n from each side:
n - n - 7 = -2n - n
-7 = -3n
Divide both sides by -3
(-7)/(-3) = (-3n)/-3
7/3 = n
In the equation (n-4) - 3 = 3-(2n+3), the value of n is n=7/3
Hope this helps! :)
Answer:
Three days at the most.
Step-by-step explanation:
First you must see how much money he spends on driving, 75 x 0.10 = 7.5. Subtract that from 120 to get 112.5. He has that much money left. Now you will divide 112.5 by 30.05. 112.5/30.05 = 3.74376039933. Simplify to get 3.
(also, he will have 22.35 dollars left)
To factor x^2 + 2x - 8 follow these steps
1) Write to factors, with x as the first term, this way:
(x )(x )
2) The sign to the right of the x in the first factor is the same sign of the coeficient of x in the polynomial.
That is +.
The sign to the right of the x of the second factor is the product of the sign of the coefficent of x (this is +) and the sign of the independent term (this is - ).
So that is (+).(-) + -.
Now the two factors have this form:
(x + ) (x - )
3) Now find two numbers whose product is - 8 and whose difference is +2
Those numbers are + 4 and -2.
Then the two factors are:
(x + 4) (x - 2).
So the answer if that the correct factorization is (x + 4) (x - 2)
Answer:
The area of the larger is 36 units^2
Step-by-step explanation:
The scale factor is 6/3 = 2
When we work with areas, it is scale factor squared
scale factor ^2 = area of larger / area of smaller
2^2 = area of larger / 9
4 =area of larger / 9
Multiply each side by 9
4*9 = 36
The area of the larger is 36 units^2
