Answer:
12-9
Step-by-step explanation:
If 'x' value is 2
Then x*6 - 9
Then x*6 = 12
Then x*6-9 = 12-9
23:8 is the simplest form. However, you can put 5.75:2 or even 2.86/1 if you are looking for the absolute simplest
There is one solution:
use elimination method
5x - 7y = 12
5y - 2x = -7 ---> change equation around
5x - 7y = 12
-2x + 5y = -7
2 x ( 5x - 7y) = 2 x (12) multiply both sides by 2
5 x (-2x +5y) = 5 x (-7)
this give you
10x - 14y =24
-10x+25y = -35 add down
-----------------------------
11y = - 11 x is eliminated to find y value
y = -1 input to one of the original equations
5(-1) - 2x = -7
-5 - 2x = -7
+5 +5 add 5 to both sides
----------------------------
-2x = -2
x = 1
your coordinates for when they intersect is at (1, -1)
one solution
we have
we know that
The absolute value has two solutions
Subtract
both sides
Step 1
Find the first solution (Case positive)
![-[+(x-12)]=-0.75](https://tex.z-dn.net/?f=-%5B%2B%28x-12%29%5D%3D-0.75)

Subtract
both sides


Multiply by
both sides

Step 2
Find the second solution (Case negative)
![-[-(x-12)]=-0.75](https://tex.z-dn.net/?f=-%5B-%28x-12%29%5D%3D-0.75)

Adds
both sides


<u>Statements</u>
<u>case A)</u> The equation will have no solutions
The statement is False
Because the equation has two solutions------> See the procedure
<u>case B)</u> A good first step for solving the equation is to subtract 0.5 from both sides of the equation
The statement is True -----> See the procedure
<u>case C)</u> A good first step for solving the equation is to split it into a positive case and a negative case
The statement is False -----> See the procedure
case D) The positive case of this equation is 0.5 – |x – 12| = 0.25
The statement is False
Because the positive case is
-----> see the procedure
case E) The negative case of this equation is x – 12 = –0.75
The statement is True -----> see the procedure
<u>case F)</u> The equation will have only 1 solution
The statement is False
Because The equation has two solutions------> See the procedure
Answer:
92
Step-by-step explanation:
Since the sum of the two numbers is 5, we can represent one of them by x and the other by 5-x. Then the desired product is ...
x²(5-x)³
A graphing calculator can show the extreme values of this on the interval 1 ≤ x ≤ 4. The maximum is 108 at x=2; the minimum is 16 at x=4.
The difference between the maximum and minimum is 108-16 = 92.
_____
If you like, you can take the derivative and set it to zero.
f(x) = x²(5 -x)³
f'(x) = 2x(5 -x)³ +x²(-3)(5-x)² = x(5 -x)²(2(5-x) -3x)
f'(x) = 5x(5-x)²(2-x)
This will be zero for x=0, x=5, and x=2. The points at x=0 and x=5 represent minima in the product. The values x=0 and x=5 are not in the domain of interest. The point at x=2 represents a maximum.
To find the function extremes on an interval, we need to evaluate the function where the derivative is zero, and also at the ends of the interval. So, the function values of interest are ...
f(1) = 1²·4³ = 64
f(2) = 2²·3³ = 108 . . . . product maximum
f(4) = 4²·1³ = 16 . . . . . . product minimum
The difference between the maximum and minimum is 92.