Q and A for the topic: General

How would I write quadratic fx: 3x^2-18x+25 in vertex form? Please list steps.

Suppose that the functions r and s are defined for all real numbers x as follows R(x)=x+3 S(x)=4x+1 Write the expressions for (r+s)(x) and r•s)(x) and evaluate (r-s)(3)

The weight of a person is given by the equation: -125+7x -4x +5(x+1)=7(x+5)+15 where x is the exact weight of this person and for his health the doctor recommended he lose 30% of his weight How many kg do you have to lose? If you manage to lose 30% of your weight, what would your current weight be?

x+y+z=2100 15x+25y+45z=600 30x+35y+45z=1000

example of a number that is divisible by 2,3 and 4, and that is formed by five non-zero digits.

A preimage of 53 in the function f whose criterion is given by f(x)=x2+4x+8 is

Find the value of m-5 when m=16

Find the equation of the slant asymptote Y=X^2-4x+1 OVER X-4

X^4-10x^2+9=0 1. Factor the expression. State your factors 2. State the solutions to the equation. If necessary use “sqrt” for radicals; do NOT provide a decimal approximation

P(x)=-0.004x^3+.025x^2+0.55x+8 1 . Use the model to predict the hourly number of items produced in a 4 hour shift 2. According to the model, how many hours makes the most productive shift m? That is, at how many hours is the hotly production at a maximum? 3. At the shift length found in part B, how many items are produced per hour?

Use root method to solve : 4x^3 -500=0

The future value of an investment of $7500 at interest rate r (in decimal form), compounded annually for 7 years, is given by: S=7500(1+r)^7 Use the root to find the rate r that will give a future value of $12900. Round to three decimal places as needed. Do NOT provide r as a percent!

Suppose I tell you that one root of a polynomial function, f(x), is 4+3i . What must also be a root of f(x)?

Is (X+4) a factor of y=x^3-13x+12? Explain how you know.

Consider the rational function and answer the questions below: f(x)=x+2 OVER x^2-1 1. Hole(s) = 2. Vertical asymptote(s) = 3. Horizontal asymptote(s)=

The size P of a certain insect population at time t (in days) obeys the function P(t)=900e^0.02t A. Determine the number of insects at t=0 days. B. What is the growth rate of the insect population? C. What is the population after 10 days? D. When will the insect population reach 1350? E. When will the insect population double?

1. There are 4 airlines to travel south and 7 land lines. Find the probability of: a) Travel by plane b) Travel by bus AND plane

2. In the month of July, 21 days went to the gym and 23 days to work. Find the probability of: a) The days that only work was done b) the days you worked and went to the gym c) The days we went to the gym

Solve the following problems: I. 30 people gather, including men, women and children. It is known that men and women double the number of children. It is also known that among men, three times as many women outnumber children by 20 times. Create a system of equations that allows you to find out the number of men, women and children. Write the augmented matrix of the system. Solve the proposed system of equations using the Gauss Jordan method. ll. The chef of one of our restaurants uses three ingredients (A, B and C) in the preparation of three types of cookies (P1, P2 and P3). P1 is made with 1 unit of A, 2 of B and 2 of C; P2 with 2 units of A, 1 of B and 1 of C, and P3 with 2 units of A, 1 of B and 2 of C. The selling price is $7.2 for P1, $6.15 for P2 and $7.35 for P3. Knowing that the commercial margin (profit) is $2.4 in each of them, how much does each unit of A, B and C cost the chef? Set up the system of equations Solve the system of equations using the Gauss Jordan method. III. Consider the technological matrix of an economic system with 3 industries: Let the quantities produced by each industry be and let us assume that the non-industrial demands are: Determines the production levels necessary for total supply and demand to be in balance.

Find dy/dx in terms of x and y when x^3+xy^2=5x