When the product of 6 and the square of a number is increased by 5 times the number, the result is 4. Which equation represents
2 answers:
Answer:
The equation that represents this situation is given by:
Step-by-step explanation:
Let " x " be any number.
Square of this number is: x²
and the product of 6 and square of a number is given by: 6x²
Now if this quantity is increased by 5 times the number; then the result is 4.
( 5 times the number x is given by: 5x )
This means that the expression could be given by:
On subtracting both side of the equality by 4 we obtain the equation as:
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Answer:
Ok, we have a system of equations:
6*x + 3*y = 6*x*y
2*x + 4*y = 5*x*y
First, we want to isolate one of the variables,
As we have almost the same expression (x*y) in the right side of both equations, we can see the quotient between the two equations:
(6*x + 3*y)/(2*x + 4*y) = 6/5
now we isolate one off the variables:
6*x + 3*y = (6/5)*(2*x + 4*y) = (12/5)*x + (24/5)*y
x*(6 - 12/5) = y*(24/5 - 3)
x = y*(24/5 - 3)/(6 - 12/5) = 0.5*y
Now we can replace it in the first equation:
6*x + 3*y = 6*x*y
6*(0.5*y) + 3*y = 6*(0.5*y)*y
3*y + 3*y = 3*y^2
3*y^2 - 6*y = 0
Now we can find the solutions of that quadratic equation as:
So we have two solutions
y = 0
y = 2.
Suppose that we select the solution y = 0
Then, using one of the equations we can find the value of x:
2*x + 4*0 = 5*x*0
2*x = 0
x = 0
(0, 0) is a solution
if we select the other solution, y = 2.
2*x + 4*2 = 5*x*2
2*x + 8 = 10*x
8 = (10 - 2)*x = 8x
x = 1.
(1, 2) is other solution
Answer: x= 8.
Step-by-step explanation: Given equation -3(2x-3)=25-8x.
Step 1: We have -3 in front of (2x-3). We always simplify a parenthesis first.
Therefore, applying Distributive property in first step, we get
-6x +9 = 25-8x.
Step 2: We need to get rid 9 from left side to get constant numbers on right side.
9 is being added on left side.
So, we would apply reverse operation of addition.
Therefore, applying Subtraction property of equality, we get
-6x +9-9 = 25-8x-9
-6x =16 -8x.
Step 3: We need to get rid 8x from right side.
The reverse operation of subtraction is addition.
Therefore, applying Addition property of equality, we get
-6x+8x =16 -8x+8x
2x = 16.
Step 4: We need to isolate it for x.
So, applying Division property of equality, we get