Answer:
y = 3/2x + 2
Step-by-step explanation:
Step 1: Write original equation into slope-intercept form
3y = -2x + 3
y = -2/3x + 1
Step 2: Find slope of perpendicular line
Take the negative reciprocal of the other slope.
m = 3/2x
Step 3: Find <em>b</em>
y = 3/2x + b
-4 = 3/2(-4) + b
-4 = -6 + b
b = 2
Step 4: Rewrite perpendicular equation
y = 3/2x + 2
This is all a bit complicated so try and stick with me on this one!
This one is the first problem in the first picture! a + 2 / a^2 + a - 1 / a + 1/ -a^2 - 2a - 1
= a^4 + a^3 - a^2 - a / -a^5 - 3a^4 - 3a^3 - a^2
= -a^3 - a^2 + a + 1 / a^4 + 3a^3 + 3a^2 + a
= -a^3 - a^2 + a + 1/ a^4 + 3a^3 + 3a^2 + a
= (-a - 1) (a + 1) (a - 1) / a(a+ 1) (a + 1) (a + 1)
= -a + 1 / a^2 + a
The second problem in the first picture! 3x / y + 3x - y^2 / 3xy - 9x^2 + y^2 + 9x^2 / y^2 - 9x^2
= -81x^4y + 18x^2y^3 - y^5 / 243x^5 - 54x^3y^2 + 3xy^4
This one is for the last picture! 4y^2 + 4y + 1 / 4y - 8y^2 - 4y^2 + 1 / 4y + y
= 16y^3 + 24y^2 / -32y^3 + 16u^2
= 16y + 24 / -32y + 16
= 2y + 3 / -4y + 2
I hope this was helpful!!!
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Y-intercepts always have 0 as the x-coordinate, so it's (A)
Answer:
<em>The plane landed after 9.4 minutes.</em>
Step-by-step explanation:
<u>Function Modeling</u>
The initial altitude of a plane arriving at JFK International Airport is 30,000 ft.
It then began its descent at a rate of 3,200 feet per minute.
Let's call t the number of minutes since the descent started. If each minute the plane descends 3,200 feet, then after t minutes it descends 3,200t.
This must be subtracted from the initial altitude, thus the altitude H is written as:
H = 30,000 - 3,200t
When the plane landed, its altitude was H=0, thus:
0 = 30,000 - 3,200t
Adding 3,200t:
3,200t = 30,000
Dividing by 3,200:
t = 30,000/3,200
t = 9.375 minutes
Rounding to the nearest tenth:
The plane landed after 9.4 minutes.
Option 1: Graph both equations to see where they intersect. If they do not intersect at lattice points, then use the substitution method.
Option 2: Use substitution method of system of equations
Equation of a circle: (x-h)² + (y-k)² = r²
Choose one of the equations and solve for one of the variables
(I am choosing to solve for y)::
(y-k)² = r² - (x-h)²
|y - k| = √(r² - (x-h)²)
y - k = +/- √(r² - (x-h)²)
y = k +/- √(r² - (x-h)²)
Now, substitute k +/- √(r² - (x-h)²) for y into the other equation to solve for x.
Substitute those x values into y = k +/- √(r² - (x-h)²) to solve for y.
Hope this makes sense!
