In triangle ABC, cevians AD and CF are bisectors. Find area ABC / area AFD if AB = 21, AC = 28, and BC = 20.
In: Math
A doll sold for ?$215 in 1975 and was sold again in 1989 for $488. Assume that the growth in the value V of the? collector's item was exponential.
?a) Find the value k of the exponential growth rate. Assume Vo=215.
?(Round to the nearest? thousandth.)
?b) Find the exponential growth function in terms of? t, where t is the number of years since 1975
?V(t)=
?c) Estimate the value of the doll in 2015.
?(Round to the nearest? dollar.)
?d) What is the doubling time for the value of the doll to the nearest tenth of a? year?
?(Round to the nearest? tenth.)
?e) Find the amount of time after which the value of the doll will be ?$3037
?(Round to the nearest? tenth.)
In: Math
Give a paragraph for each to explain.
1. Allie says that are parallel because they do not intersect. How do you respond?
2. Rajesh named the line below as . How do you respond?
3. A student says that because starts at A and ends at B and starts at B and ends at A. How do you respond?
4. Henry claims that a line segment has a finite number of points because it has two endpoints. How do you respond?
5. A student claims that if any two planes that do not intersect are parallel, then any two lines that do not intersect should also be parallel. How do you respond?
6. A student says that it is actually impossible to measure an angle, since each angle is the union of two rays that extend indefinitely and therefore continue forever. What is your response?
7. Maggie claims that to make the measure of an angle greater, you just extend the rays. How do you respond?
8. A student says that there can be only 360 different rays emanating from a point since there are only in a circle. How do you respond?
9. A student asks why an angle is not defined as the union of two half-lines and a common point. How do you respond?
In: Math
a) The point at which a company's costs equal its revenues is the break-even point. C represents the cost, in dollars, of x units of a product and R represents the revenue, in dollars, from the sale of x units. Find the number of units that must be produced and sold in order to break even. That is, find the value of x for which C=R.
C=15x+32,000 and R=17x.
How many units must be produced and sold in order to break even?
b) A bicycle travels at a speed of 55 miles per hour for x hours. Find an expression for the distance that the bicycle travels.
c) The price per unit, p, and the demand, x, for a particular material is related by the linear equation p =140 -7/8 X, while the supply is given by the linear equation
p=7/8x. At what value of p does supply equal demand?
d) Suppose that a cyclist began a 476 mi ride across a state at the western edge of the state, at the same time that a car traveling toward it leaves the eastern end of the state. If the bicycle and car met after
8.5 hr and the car traveled 32.2 mph faster than the bicycle, find the average rate of each.
The car's average rate is
The bicycle's average rate is
e) A baseball team has home games on Thursday and Saturday. The two games together earn $4640.00 for the team. Thursday 's game generates$300.00 less than Saturday 's
game. How much money was taken in at each game? How much money did Thursday 's game generate? How much money did Saturday 's game generate?
In: Math
A and B are any positive numbers, write equations and sketch graph. A>0, B>0
|
Circle Write your Equation and draw the graph. Mark on the graph x-intercepts and y- intercepts |
Circle Equation and graph. Mark on graph x-intercepts and y- intercepts |
Circle Equation and graph. Mark on graph x-intercepts and y- intercepts |
Spiral Equation and graph. |
|
r = A |
r = A sin(θ) |
r = A cos(θ) |
r = Aθ |
|
r= - A |
r = - A sin(θ) |
r = - A cos(θ) |
r = -Aθ |
Limazons A>0, B>0
|
Equation and graph. Mark on graph x- and y-intercepts. r = A + B sin(θ) r = A - B sin(θ) |
Equation and graph Mark on graph x- and y-intercepts. r = A + B cos(θ) r = A - B cos(θ) |
|||||
|
A < B |
Equation: Graph: |
|||||
|
A = B |
||||||
|
A > B |
||||||
|
A ≥ 2B |
||||||
|
Rose Curves |
r = A sin(B*θ) |
r = A cos(B*θ) |
||||
|
B is even B=2 |
||||||
|
B=4 |
||||||
|
B=6 |
||||||
|
B is odd B=1 |
||||||
|
B=3 |
||||||
|
B=5 |
||||||
|
B=7 |
||||||
|
Lemniscates |
r2 = A2 sin(2 θ) |
r2 = A2cos(2 θ) |
||||
In: Math
8,500 people were surveyed about their recent electronics purchases. 3,149 of those surveyed have bought a cell phone in the last year, 1,508 have bought a tablet in the last year, and 925 have bought both.
a) How many people bought at least one of the two?
b) How many people didn’t buy a cell phone or a tablet?
In: Math
10- Explain what it means to have a fractal dimension between 1 and 2.
In: Math
Find the area of a regular octagon of side 10 cm. (NOTE: Do not use the directed formula of the area of the polygon)
In: Math
Question: Describe the various methods of solving linear systems. With which method of solving linear systems are you most comfortable, and why?
Hint: First, define a linear system, and give an example. Then, discuss the methods, and show the steps to solve your example. Finally, talk about advantages and drawbacks of each method.
"Real-Life" Relationship: Any relationship where we have a fixed cost and variable cost can be represented by a linear equation.
For instance, the cost of a rental car from Hertz might be $100 plus $0.70 per mile, while Enterprise might charge $80 plus $0.80 per mile. We can solve the following system to find out when the cost is the same (c = cost, m = miles driven)
c = 0.7m + 100 (Hertz)
c = 0.8m + 80 (Enterprise)
It turns out that they are equal when the mileage is m = 200.
Challenge 1: Given two lines in standard form, how can you quickly decide if they have the same slope, simply by using ratios of y and x coefficients?
Challenge 2: What is a quick way (without finding the slope or solving for y) to decide whether the following system has a solution?
2x + 3y = 4
2x + 3y = 5
In: Math
Determine the vertex, focus, and directrix for the following parabola.
A. y=4(x+2)^2-21
B. y-7=1/8(x-3)^2
C. x=1/4y^2
In: Math
1. Identify what they are given and what they need to find;
2. Identify the type of problem they have been given and the tools necessary to solve the problem;
3. Correctly apply the tools to the information given to set up the problem;
4. Perform mathematically correct calculations to determine a solution;
5. Interpret their results in terms of the original problem.
Use the internet and find the Medicare expenditures in the year 2000 and the Medicare expenditures in 2015. Use the exponential growth function and develop a model. Let t = 0 in the year 2000. If the model remains accurate, estimate Medicare expenditures for the year 2017.
In: Math
Prove that the diagonals of a square meet at a point half way from each opposing set of corners.
In: Math
Write the augmented matrix of the system and use it to solve the system. z.
x − 2 y − z = − 6
x − y − 2 z = − 4
− x − y + 2 z = − 4
In: Math
In: Math
the following statements are given (A) a parallelogram with a right angle is a rectangle (B) a rhombus eith equal diagonals is a square (C) a kite with equal diagonals is a square (D) A TRAPEZIUM WITH BOTH PAIRS of opposite sides parallel is a rhombus (E) a quadriateral with equal diagonals is a rectangle. Which of the following is correct? [1] A and B [2] A,C AND E [3] B,C and D [4] E and C [5] B and E
In: Math