Answer:
The equation of the line is y = -3/7x - 23/7
Step-by-step explanation:
To start we need to find the slope of the original line. We can do this by solving the equation for y.
3x + 7y = 21
7y = -3x + 21
y = -3/7x + 3
Now we know the slope to be -3/7. Since parallel lines have same slopes, we know the new line also will have a -3/7 slope. We can now use that along with the given point in point-slope form to find the equation.
y - y1 = m(x - x1)
y + 5 = -3/7(x - 4)
y + 5 = -3/7x + 12/7
y = -3/7x - 23/7
Are the two middle ones minus or negatives
Answer:
12 units
Step-by-step explanation:
The lactus rectum for a parabola is equal to 4 times the length of the focus from the vertex. Therefore, we need to determine the focus 
by using the equation 
for a vertical parabola.
We can deduce that 
, 
, and 
. Therefore, the focus of the parabola is 
or 
.
Because the focus is , then it is 3 units away from the vertex 
, making the length of the latus rectum 3*4=12 units.
Answer:
3) 67/441
Step-by-step explanation:
Comparing the given equation to the expressions you need to evaluate, you find there might be a simplification.
3x² +5x -7 = 0 . . . . . given equation
3x² +5x = 7 . . . . . . . add 7
x(3x +5) = 7 . . . . . . . factor
3x +5 = 7/x . . . . . . . . divide by x
Now, we can substitute into the expression you are evaluating to get ...
1/(3α +5)² +1/(3β +5)² = 1/(7/α)² +1/(7/β)² = (α² +β²)/49
__
We know that when we divide the original quadratic by 3, we get
x² +(5/3)x -7/3 = 0
and that (α+β) = -5/3, the opposite of the x coefficient, and that α·β = -7/3, the constant term. The sum of squares is ...
α² +β² = (α+β)² -2αβ = (-5/3)² -2(-7/3) = 25/9 +14/3 = 67/9
Then the value of the desired expression is ...
(67/9)/49 = 67/441
8.61 x 10^-8 = 0.0000000861 in standard form
