Answer:
The expression (-root3·a - a)², can be simplified into the form a² × (4 + 2·√3)
Step-by-step explanation:
The given expression can be written as follows;
(-root3·a - a)² = (-√3·a - a)²
Which can be expanded to give;
(-√3·a - a) × (-√3·a - a) = 3·a² + 2·√3·a² +a²
We collect like terms to get;
3·a² + 2·√3·a² +a² = 3·a² +a²+ 2·√3·a² = 4·a² + 2·√3·a²
We factorize out the common coefficients of the terms to have;
4·a² + 2·√3·a² = a² × (4 + 2·√3)
Which gives the initial expression (-root3·a - a)², to presented in the form a² × (4 + 2·√3).
Do you mind if I re-arrange it slightly before we solve it ?
You said 20x + 3.00y ≥ 500
Subtract 20x
from each side: 3.00 y ≥ -20x + 500
Divide each side by 3 : y ≥ -20/3 x + 500/3
Make it an equation,
and graph this line: y = -20/3 x + 500/3
The line is made out of all points where 'y' is EQUAL to
1/3 of (-20x + 500).
The inequality wants to see all the points that are equal to it
AND all the points that are greater than that.
So the graph of the inequality is the line AND every point that's
anywhere above the line. It's called the "half-infinite plane"
bounded by the line.
Answer:
7/8 > 3/4 > 1/2
Or
1/2 < 3/4 < 7/8
Step-by-step explanation:
Given 7/8, 3/4, and 1/2
We need to make the numbers in order from the least to the greatest or from the greatest to the least
The easy method is convert the rational numbers to decimal numbers
So,
7/8 = 0.875
3/4 = 0.75
1/2 = 0.5
So, the numbers form the least to the greatest are:
0.5 , 0.75 , 0.875
So,
1/2 , 3/4 , 7/8
The inequality correctly compares the numbers are:
1/2 < 3/4 < 7/8
Or can be written from the greatest to the least as:
7/8 > 3/4 > 1/2
9514 1404 393
Answer:
2
Step-by-step explanation:
Solving the given equation for y, you have ...
2x +4y = -64
4y = -2x -64
y = -1/2x -16
The coefficient of x is the slope of the given line: -1/2. The slope of the perpendicular line is the opposite reciprocal of this:
-1/(-1/2) = 2
The slope of the perpendicular line is 2.
M=3 therefore y is slanted right downwards
