Algebra I
Zane likes to go rock climbing in active volcanoes. One time, when he was 20 meters below the edge of a volcano, he heard some rumbling, so he decided to climb up out of there as quickly as he could. He managed to climb up 4 meters each second and get out of the volcano safely.
Graph the relationship between Zane's elevation relative to the edge of the volcano (in meters) and time (in seconds).
Your answer should be told to me in slope-intercept form.
y = 4x - 20
Two birds are flying toward a birdhouse that is halfway between them. The birds are at coordinates A (-4,4) and B (10, -2). What are the coordinates of the birdhouse?
The birdhouse is at (3,1)
Midpoint formula:
((x2 + x1)/2 , (y2 + y1)/2)
g(x) = 2x + 4
m(x) = 2x^2 - 4x
Simplify this expression:
3g(-4) - 2m(0)
2437/10 * 2431/10
81
Ishaan is 3 times as old as Christopher and is also 14 years older than Christopher.
How old is Christopher?
Christopher is 7
1. y = 3x
y = x + 14
2. 3x = x + 14
-x -x
3. 2x = 14
4. 2x/2 = 14/2
5. x = 7
The measure of an interior angle of a regular polygon is 120 degrees. How many sides does the polygon have?
6 sides
ext. angle = 60 degrees
All ext. angles of a regular polygon add up to 360 degrees
360/n = Exterior angle for regular polygon
360/ext. angle = n (number of sides)
360/60 = 6
How many solutions are there?
-2|3x+4|+22 > 23
No solutions
Which exponential expression is equivalent to sqrt[4]x?
x^1/4
Karl filled up the tank of his truck with 400 liters of fuel and set out to deliver a shipment to Alaska. The truck consumed 0.8 liters of fuel for each kilometer driven.
Graph the amount of fuel remaining in the truck's tank (in liters) as a function of distance driven (in kilometers).
y = -0.8 + 400
Barbara is building a wooden cabin. The cabin is 42 meters wide. She obtained a bunch of 27-meter-long wooden beams for the roof of the cabin.
Naturally, she wants to place the roof beams in such an angle that each pair of opposite beams would meet exactly in the middle.
What is the angle of elevation, in degrees, of the roof beams?
Round your final answer to the nearest tenth.
38.9 degrees
What is the equation of the parent function with the vertex?
f(x) = |x|
vertex: (2,2)
f(x) = |x-2| + 2
Which exponential expression is equivalent to sqrt[4]x3?
x3/4
A certain company's main source of income is a mobile app.
The company's annual profit (in millions of dollars) as a function of the app's price (in dollars) is modeled by
P(x)=-2(x-3)(x-11)
What would be the company's profit if the app price is 0 dollars?
-66 Million dollars
The people of Bridgetown wanted to build a bridge across a nearby river. Since they were poor swimmers, their master Trigonomos agreed to measure the width of the river without actually crossing it.
Trigonomos spotted a tree across the river and marked the spot directly across from it. Then he walked to another point 10 meters down the river and found that the angle between his side of the river and the line connecting him to the tree was 40 degrees.
What is the width of the river?
Round your final answer to the nearest hundredth.
The width of the river is 8.39 meters
Is the following function even, odd, or neither?
f(x)= x/(x^2+1)
Odd
x-2 * x11/9
x-7/9
Khan Academy - Unit 6
A certain company's main source of income is a mobile app.
The company's annual profit (in millions of dollars) as a function of the app's price (in dollars) is modeled by
P(x)=-2(x-3)(x-11)
Which app prices will result in $0 annual profit?
$3 and $11
An angle bisector is bisecting the right angle of a right triangle. The two legs of the triangle are 8 and 15 cm long. What are the two lengths the angle bisector bisects the hypotenuse?
136/15 or 9.067 and
119/15 or 7.93
Solve the inequality
-2|2x+4|< 4
Infinite Solutions