P(x) = x6 − 7x3 − 8

(a) Find all zeros of P, real and complex.

(b) Factor P completely.

In many cities and towns across the United States, the numbering system of the roads is based on a grid, similar to the latitude and longitude lines on a globe. Suppose the green lines in the following graph represent two east-west and two north-south running roads in a Midwestern town.

Write equations for the two horizontal and two vertical lines that represent roads in the town.






2. The Willis Tower (formerly known as the Sears Tower) in Chicago, Illinois, is the tallest building in the United States. Measuring 1,450 feet, the tower contains 110 stories filled with a combination of office and retail space. The base of the tower is made up of nine 75’ × 75’ squares. Suppose the square graphed on the coordinate plane below represents the base of the Willis Tower.

Write equations for the two horizontal and two vertical lines that pass through the square.



3. Think of another real-world situation that might involve horizontal and vertical lines. Write a description of the situation and draw the graph of a coordinate plane with two horizontal and two vertical lines to represent your situation. Draw the lines so that two of them pass through positive values and the other two pass through negative values on the coordinate plane. Then write equations for all four of the lines on your graph.

Did you drive to work or school today? When you are driving at a constant speed, the amount of gas left in the tank can typically be modeled by a linear equation. The equation y = -2x + 15 would represent a car that has a full 15-gallon tank and burns 2 gallons of gas an hour when x is the number of hours driven and y is the amount of gas in the tank. Find a linear relationship (equation) that you would use or rely on in your field when you receive your degree, and explain what it is and how it is used. Identify the initial condition, such as the full tank of gas above, and the rate of change. For a linear equation, the rate of change (slope) needs to be constant. If you can’t find one in your field, broaden your research to include any real-world application.

What color is the sky? What color are the clouds?

Under certain water​ conditions, the free chlorine​ (hypochlorous acid,​ HOCl) in a swimming pool decomposes according to the law of uninhibited decay. After shocking a​ pool, the pool​ boy, Geoff, tested the water and found the amount of free chlorine to be 2.4 parts per million​ (ppm). ​ Twenty-four hours​ later, Geoff tested the water again and found the amount of free chlorine to be 2.1 ppm. What will be the reading after 2 days​ (that is, 48 ​hours)? When the chlorine level reaches 1.0​ ppm, Geoff must shock the pool again. How long can Geoff go before he must shock the pool​ again?

Discussion 3 Solve and write an essay.

1111 réponses non lues.1111 réponses.

Essay: 2 [ x - (4 + 2x) + 3 ] - 2x - 2 = 4 [2x - (3 - x) + 5] + 6x + 28

Students, you have to do an essay for this discussion. The essay is consist of a introduction, a body, and a conclusion. You have write this essay like you are teaching your children, co-worker, or a stranger how to work this problem. The introduction is where you will define all of the terms of the problem and list all the rules. In which, you tell me what type of problem it is, if it's an equation and linear, if it has parenthesis and bracket, which have to be defined and what you would to solve the problem. The body is where you will work the problem, write out in sentence structure how you work the problem. Make sure you put the problem in your essay and everything that you did to work the problem. Lastly, the conclusion is where you will explain what the person should get for working the way that you worked it, and what they should learn

Maximize objective function P=3x+4y

subject to: x + y ≤ 7 x ≥ 0

x+4y ≤ 16 y ≥ 0

A recipe calls for 1 1/5 cups of flour for every 1/2 teaspoon of salt. Suppose you put 4 cups of flour in a mixing bowl. How much salt should you add?

Find the relation between the Euclidean radius and the spherical radius of spherical circle.
Include a picture.

Find the real zeros of the function f(x) = -(x+1)^3(x-2)^2 and their corresponding multiplicities. Use the information along with a sign chart (diagram) and then the end behavior to provide a rough sketch of the graph of the polynomial.

How many different ways can you solve a quadratic equation? List them.

Create a trinomial that can be factored and write it in standard form.

Factor x^2 – 7x + 10, 4x^2 – 81 and p (x) = 3x^3 – 12x

What key features of a quadratic graph can be identified and how are the graphs affected when constants or coefficients are added to the parent quadratic equations? Compare the translations to the graph of linear function. Create examples of your own to explain the differences and similarities.

A ball is kicked into the air and follows the path described by h(t)= – 4.9t^2 + 6t + 0.6, where t is the time in seconds and h is the height in meters above the ground. Find the maximum height of the ball. What value would you have to change in the equation if the maximum height of the ball is more than 2.4 meters?

(8) How can geometry be used to promote responsible stewardship?PLEASE TYPE

You can sell 70 pet chias per week if they are marked at $1 each, but only 20 each week if they are marked at $2/chia. Your chia supplier is prepared to sell you 10 chias each week if they are marked at $1/chia, and 60 each week if they are marked at $2 per chia.

(a) Write down the associated linear demand and supply functions.

(b) At what price should the chias be marked so that there is neither a surplus nor a shortage of chias?

We can experiment with two parallelepipeds (boxes) that are similar in shape. The dimensions of the smaller box are 2 in. x 4 in. x 3 in. The larger box has twice the dimensions of the smaller . Draw and label the large box

1. Surface area (SA) of a box is the sum of the areas of all six sides. Compare the SAs of the two boxes.

Ratio: SA of the large box is ___ times the SA of the small box

2. Compare the volumes (V) of the two boxes, measured in cubic inches. Pretend that you are filling the boxes with 1-inch cubes. The volume of each cube is 1 cubic inch (cu. in.).

Small box ____ cubes fill one layer, and ___ layers fill the box. The box holds ___ 1-inch cubes. Volume= ____ cu. in. Large box ___ cubes fill one layer, and ___ layers fill the box The box holds ____ 1-inch cubes. Volume= ___ cu. in. Ratio: The volume of the large box is ___ times the volume of the small box.

3. Show your work to compare a 3inch cube with a I-inch cube.

Think about this: 1. Look at your estimate for the amount of thatch for the kibo Art Gallery. Do you agree with it? Explain.

2. Two cylinders (cans) have similar shapes. One has four times the dimensions of the other. Show how you can compare their surface areas and volumes without the use of formulas. What conclusions do you expect? Use another sheet, if necessary.