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Factor the polynomial.
7x2+16x+4
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
Please show your work
Factor the given polynomial completely. If the polynomial cannot be factored, say that it is prime.
x2 - x -56
Is this prime, if not what is it equal to? please show work
There is a set of chips of 5 different colours (there are at least 6 chips of every colour). It is necessary to put 6 of these chips in a row (from left to right) in such a way that any two adjacent chips are of different colours, and at least three colours have to be used. How many ways of doing it are there?
There are 18 boys and 35 girls in a mathematical club. For playing some game, the teacher has to distribute chips among the children (their total number is equal to k, and all of them have to be given). It is necessary that all the boys have the same numbers of chips, all the girls have the same numbers of chips, and each of the children has at least one chip. It has turned out that the teacher can distribute the chips in a single way. Determine the largest possible value of k.
The radioactive isotope gallium-67, used in the diagnosis of malignant tumors, has a biological
𝑡
half-life of 46.5 hours. The half-life of the isotope is modeled as 𝐴 = 𝐴0 (1)h , where h is the 2
half-life and t is the time in hours. If we start with 100 milligrams of the isotope, how many milligrams will be left after: 24 hours, and after 1 week?
A new pizzeria has opened near you home, the owner has decided to offer a 20% discount on
the opening day on the pizza whose original price is x dollars. The owner is offering additional
15% discount coupon to those who agree to fill a feedback form afterwards. You and your
friends have agreed to provide feedback and thus have become entitled to the additional 15%
discount coupon. Use the concept of composite functions to identify the amount that you will
pay after applying the coupon on the sale price.
Solve each of the following equations:
(i) e2x · (e2x-1)3 = 9
(ii) 2 ln x - ln(3 - 5x) = ln 2
Using the substitution u = 2x, solve the equation 23x = 2(2x+1) + 3(2x)
Consider the shuttle carrying the astronauts is dropped from 100ft. The position 𝑠 of the shuttle is given by the following function as a function of time: 𝑠(𝑡) = −16𝑡 2 + 100.s. What is the domain of this function?
