The equation of the directrix of the parabola given is x = 6, Option D is the correct answer.
<h3>What is Directrix of a Parabola ?</h3>
A parabola is a U shaped curve whose all point are at same distnace from a point called as focus and a line called as Directrix .
The equation of the parabola given is
y² = -24x
When the standard equation of parabola is
(y - k)² = 4p (x - h),
where the focus is (h + p, k) and the directrix is x = h - p.
here h = 0
p = -24/4 = -6
x = 0 - (-6)
x = 6
Therefore Option D is the correct answer.
To know more about Directrix
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5y - 2x + 1 = 0.
5y = 2x-1.
y = 2/5 x - 2/5
this tells us that tan(theta) = 2/5
sin(theta)/sqrt(1-sin^2(theta)) = 2/5
x/sqrt(1-x^2)=2/5
x^2/(1-x^2)=4/25
25x^2=4-4x^2
29x^2=4
x^2=4/29
x = -2/sqrt(29) because quadrant III
cos(x) = sqrt(1-4/29) = -5/sqrt(29)
tan(theta)=2/5
cos(theta)=-5/sqrt(29)
sin(theta)=-2/sqrt(29)
cot(theta)=5/2
sec(theta)=-sqrt(29)/5
csc(theta)=-sqrt(29)/2
Step-by-step explanation:
y + 4 = -2x + 2
2x + y = -2
2x = -2 - y
x = -2 -y/2
Set up a proportion that looks like 5/12 = 13/x with X being the actual distance between the cities if they are 13 inches apart on the map.
Then cross-multiply to get 5x = 156. Divide by 5 to isolate the X and get X = 31.2
The cities are a distance of 31.2 miles apart.
I'm guessing your question cut off where you put to the nearest... and you mean to round to the nearest whole number in which case your answer would be just 31 miles apart.
Answer:
First expression 8y +4x +10
Second expression 7x-3y +6
If you want to combine both expressions: 5y +11x +16
Step-by-step explanation:
Like terms are the terms which have same variables and powers/roots.
Example: 7x and 2x are like terms because the variables are both "x". So we can combine in 9x
In an expression, only like terms can be combined. We combine like terms to shorten and simplify algebraic expressions, so we can work with them more easily. To combine like terms, we add the coefficients and keep the variables the same
10y + 3x + 10 + x -2y
10y-2y=8y 3x+x=4x
so 8y +4x +10
3x - y + 4x + 6 - 2y
3x+4x=7x -2y -y = -3y
so 7x-3y +6
