Solve the following system of equations using matrices(row operations). If the system has no solution, say that it is inconsistent.

x - 3y + 4z = 10

2x + y + z = 6

-3 + 4y - 2z =. -15

If csc x = 2 and x is in Q I, determine the exact values of sin x and cos x.

Which of the following polynomials is guaranteed by the Intermediate Value Theorem to have a zero on the interval [−3,−2] ?

Select the correct answer below:

a) f(x)= x 2 −2x g

b) (x)=3 x 2 +3x−7 h

c) (x)=− x 2 +3x−3 j

d ) (x)=4 x 2 −2x−1

Please help explain how to get the answer..? and which one is the correct answer?

in the second half of the 20th century, the city of phoenix, Arizona exploded in size. between 1990 and 2000 the population of phoenix increased exponentially. in 1990 the population was 928,000 people, and in 2000. the population was 1,377,000.

a) what is the 1 decade (10 year) growth factor for the population of phoenix since 1990?

b) write a function f(d), that determines the population of phoenix in terms of the number of decades, d, that have elapsed since the beginning of 1990.

c) what Is the 5-year growth factor for the population of phoenix since 1990?

d) write a function g(x), that determines the population of phoenix in terms of the number of 5-year periods, x, that have elapsed since the beginning of 1990

A factory that makes statuettes is trying to maximize its income. Their two primary products are the Liberty and Colossus statuettes. Each Liberty requires 36 minutes of machine time to rough cut the shape and 60 minutes of artist time to finish the details. The Colossus requires 48 minutes on the machines and 30 minutes with the artist's hand. The factory is limited each day to 432 minutes of machine time and 600 minutes of artist time. Both use 22 kilograms of stone, and the factory has 242 kilograms of stone available per day. If each Liberty brings in a profit of ninety-six dollars, and each Colossus brings in ninety-one dollars, how many statuettes of each type should the factory make each day?

Liberty:

Colossus:

A spherical ball of radius 3 in is dropped into a conical vessel of depth 8 in and radius of base 6 in. what is the area of the portion of the sphere which lies above the circle of contact with the cone?

What are the most important things to consider when identifying a model to fit a set of data? Be sure to list as many characteristics as you can, but don't be afraid to share any thoughts, ideas, or uncertainties you may have about a particular model. If you're unsure about something, just ask some clarifying questions to help you get a better idea of what the model's key features are. Your post must have a minimum of 5 sentences.

Descartes' Rule of signs Use Descartes' Rule positive and how of Signs to determine how many negative real zeros of the polynomial can have. Then determine the possible total number of real zeros.

P(x) = x^3 - x^2 - x - 3

P(x) = 2x^3 - x^2 + 4x -7

P(x) = 2x^6 + 5x^4 - x^3 -5x -1

P(x) = x^4 + x^3 + x^2 + x + 12

P(x) = x^5 + 4x^3 - x^2 + 6x

P(x) = x^8 - x^5 + x^4 - x^3 + x^2 - x + 1

*** Please explain to me very detaily***

Thank you very much.

solve the given equation. 7 sin²(θ) − 22 sin(θ) + 3 = 0

question 11 a, b, and c

a. Find the equation of the hyperbola satisfying the given conditions.

Vertices at (-12, 0) and (12, 0); focus at (3squareroot 17, 0)

b. Determine whether the given function is one-to-one. If it is one-to-one, find a formula for the inverse

f(x)=6x-3/6x+3

c. Solve.

How long will it take for $1600 to grow to $14,000 at an interest rate of 3.7% if the interest is compounded continuously? Round the number of years to the nearest hundredth.

Based upon market research, the Hawthorne Company has determined that consumers are willing to purchase 139 units of their portable media player each week when the price is set at $34.50 per unit. At a unit price of $10.40, consumers are willing to buy 380 units per week.

(a) Determine the weekly demand equation for this product, assuming price, p, and quantity, x, are linearly related.
p =

(b) Determine the weekly revenue function.
R(x) =

(c) Determine the number of units consumers will demand weekly when the price is $30.30 per portable media player.
units

(d) Determine the number of units consumers will demand weekly when the revenue is maximized.
units

(e) Determine the price of each unit when the revenue is maximized.
dollars

the figure shows the graph of f(x) = e^x. in the exercise 1 to 4, use transformation of this graph to graph each function. be sure to give equation of this the asymptotes. use the graph to determine each function's domain and range. if applicable, use a graphing utility to confirm your graph

1). g(x) = e^x-1

2). g(x) = e^x+2

3) h(x) = e^-x

4) g(x) = 2e^x

a broadway theatre has 600 seats, divided into orchestra, main, and balcony seating. orchestra seats sell for 50 main seats for 35 and balcony for 25. if all seats are sold the revenue to the threatre is 20900. if all the main and balcony seats are sold but only half the orchestra seats are sold the gross revenune is 17900 how many are there of each kind of seat