Answer:
x²^2 + 4x + 4 - 9y²=(x+2-3y) (x+2-3y)
Step-by-step explanation:
hello :
x²+4x+4 = x²+2(2x)+2²=(x+2)² use identity : (a+b)² = a²+2ab+b²
( x² + 4x + 4) - 9y² = (x+2)²-(3y)² = (x+2-3y) (x+2-3y) use identity :
a²-b² =(a-b)(a+b)
Answer:
M = - 19/2 or in decimal form - 9.5
Step-by-step explanation:
1. Subtract
4 from both sides.
M/3 = 5/6 - 4
2. Simplify
5/6
− 4 to −19/6
3. Multiply both sides by
3.
M = - 19/6 x 3
4. Simplify 19/6 × 3 to 57/6
M = -57/6
5. Simplify 57/6 to 19/2
M = - 19/2
I believe this question should be a multiple choice question as there are numerous solutions.
Some of these solutions are:
4/3x+ 4 2/3 = <span>4/3x+ 8/3
</span>4/3x+ 4 2/3 = <span>8/6x+ 4 4/6
</span>4/3x+ 4 2/3 = 12/9x + 4 2/3
This can be explained as:
For 8/6x+ 4 4/6, divide the numerator by 2 and the denominator by 2 in each of the terms, the output will be the original expression.
For 12/9x + 4 2/3 , divide the numerator by 3 and the denominator by 3 in the first term (12/9x), the result will be the original expression.
F(x)=sqrt(x)
D(x)=sqrt((f(x)-0)^2+(x-4)^2) [distance of (4,0) from any point on graph]
=sqrt((√x-0)^2+(x-4)^2)
=sqrt(x+(x-4)^2)
To minimize distance, we equate D'(x)=0, or equivalently, we equate the derivative of D(x)^2 to zero.
The latter is easier to derive, and gives the same results.
We will do both.
D'(x)=(1/2)(2(x-4)+1)/sqrt(x+(x-4)^2) [using chain rule]
D'(x)=0 => (2(x-4)+1)=0 => x-4=-1/2 => x=7/2
d(D²(x))/dx
=d(x+(x-4)^2)/dx
=2(x-4)+1
=> 2(x-4)+1=0 => x=7/2
So the point on the graph is (sqrt(7/2),7/2)=(1.8708,3.5) approx.
Answer:
x = 100
Step-by-step explanation:
350x + 22,000 = 410x + 16,000
-350x -350x
22,000 = 60x + 16,000
-16,000 -16,000
6,000 = 60x
6,000 / 60
x = 100
