1. Construct 5 real life problems invloving rational function or equation. Write the step-by-step solution for each problem. 2. Construct 5 examples of Rational Equation, Rational Function, Rational Inequality.
Q: r believes that the profit P, in dollars, from selling x tickets is given by P(x)= 35x − 0.25x2.…
A: Given P(x) = 35x - 0.25x2 → 1For maximum profit put P'(x) = 0⇒ P'(x) = 35 - 0.25(2x)⇒ P'(x) = 35 -…
Q: Suppose that your friend solved the equation (x + 3)2 = 25 as follows:(x + 3)2 = 25x2 + 6x + 9 =…
A: The approach used for solving the equation is correct. We can solve the equation using the approach…
Q: Without graphing what is the vertex of the quadratic function 2x^2-8x+8
A: Topic = Functions
Q: 5. Find two positive numbers whose sum is 10 and the sum of their squares is as small as possible.
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Q: 11. Solve for the value of x. 3 1.2V3
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Q: Use a graphing utility to solve x3 - 3x2 - 4x + 8 = 0.Round answers to two decimal places.
A: x3 - 3x2 - 4x + 8 = 0.
Q: Write the equation for each graphed rational function. YA 8- 8- 4- 4- -8 -4 -4 YA yA 8- 8- -4- -12…
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Q: 1.Find the minimum or maximum value of the quadratic function. f(x) = −2x2 + 12x − 5 ?
A: Note- As per our policy we can answer only 1st question. If you want solutions for other, then you…
Q: State the circumstances that cause the graph of a quadratic function f(x)= ax2+bx+c to…
A: An x-intercept is a value at which the graph of the quadratic equation function intersects the…
Q: 12. If the x-term is missing, then the quadratic equation cannot be used.
A: We are authorized to answer one question at a time, since you have not mentioned which question you…
Q: The profit function,in dollars, for a product is given by Π(x) = −x^3 + 76x^2 − 380x − 2800, where…
A: (a) Consider the provided profit function,
Q: 1. Solve for x. X + 10 18 3
A: NOTE-Since you have asked multiple question, we will solve the first question for you. If youwant…
Q: I. Find the solution to the following rational equations. (Show your solutions) 1.+=2 5x x-2 8 х-5…
A: As per our guidelines we are only supposed to solve 3 subparts. So we will solve 4,5 and in test 2…
Q: Use the graph of the rational function to solve the inequality: 1/4(x + 2) > - 3/4(x - 2)
A: Given inequality is 14x+2>-34x-2.
Q: 14. Solve for x. 2¯¾ = 8(x-3)
A: Given, 2-x2=8x-3
Q: Analyze the graph of the rational function
A: To analyse the rational fraction, the asymptotes and the intercepts of the graph are to be found.…
Q: Solve the following rational inequality for x^2-5x+4/x-6
A: Consider the inequality
Q: What is the equation of a quadratic function y=f(x) with two irrational zeros, negative square root…
A: The equation of a quadratic function y=f(x) with two irrational zeros, negative square root of h and…
Q: * = 22. Solve for x. x +3 4 8.
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Q: Q1) A: Proof that <- where x & y E to the rational numbers. B: Solve the following inequalities and…
A: 1(A) prove that 1x<1y where x,y∈ℚ solution we have 1x<1y that is 1x-1y<0⇒y-xxy<0 as we…
Q: 5. a) Solve x4 +x3 - 12x² = 0 b) Use your solutions to part a) to sketch the graph of f(x) = x +x³ –…
A: To solve the equation and draw the graph
Q: billions of dollars) for the years 2010 to 2015 can be approximated by the following quadratic…
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Q: 12.What are the zeros of the function represented by the quadratic equation 9 (x) = (x+ 3) +3?,
A: Solution: The objective is to find the zeros of the given quadratic equation
Q: Graph the rational function. 2x-6 S(x) = -x+4
A: Given function fx=2x-6-x+4
Q: Determine the quadratic function whose graph is given below. AY 20- 10- -10 -5 K0,-3) 10 (-2, 70…
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Q: Show that the equation √ (3 − x) = x^3 has a solution in the interval [−1, 2].
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Q: The solution set for x2 - 4x - 37 = 0 is {2 ± √41}. With a calculator, we found a rational…
A: Given: The quadratic equation 4x2-6x+1=0 . The solution of the given quadratic equation is given…
Q: Use the graph of the rational function to solve the inequality: 1/4(x + 2) ≤ -3/4(x - 2)
A: Given: 14x+2≤-34x-2 for finding solution of given inequality by using graph method, we draw graph of…
Q: 1. Find the solution of the following rational equations and inequalities. x2 – 4 - 1. х — 2 x + 4 -…
A: Topic:- simplification Note:- as per our guideline if more than one question uploaded than only one…
Q: Follow the seven step strategy to graph the rational function
A: To graph of the rational function f(x)=3x2/x2-4 with seven step strategy. Now, first calculate the…
Q: 4. The height h (in metres) of a certain section of a roller coaster is modelled by the equation…
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Q: At the height of COVID-19 Outbreak, the price of every box of facemask is P720.00. It is P210.00…
A: The new price of the box of facemask is P720. Now, we are given that the new price is P210 more than…
Q: The graph of a quadratic function, y=x2, is reflected over the x-axis. Which if the following is the…
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Q: A tour operator believes that the profit P, in dollars, from selling x tickets is given b
A: Given relation - P(x) = 50x-0.25x2where,P(x) = Profitx = number of ticketsDifferentiating P(x) with…
Q: If f is a polynomial or rational function, explain how the graph of f can be used to visualize the…
A: Given that f is a polynomial function or a rational function. f(x) < 0 That is, y < 0
Q: 2. The sum of the roots of the quadratic equation x²-x-6=0 is given by 2 O
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Q: 1. The sum of two nonnegative numbers is 20. Find the numbers if the product of the square of one…
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Q: Solve the given polynomial and rational function inequalities using a sign chart. Write your answers…
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Q: 2. The square of an imaginary number: A. Can never be negative. B. Can never be positive. C. Might…
A: Given that square of an imaginary number.
Q: Given the quadratic function y = x2 + 8x + c , where c is some real number constant, answer the…
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Q: Solve for x. 6 2 + х 5 15 19 2 13 15
A: Here we find the value of x.
Q: 4 The value of x that satisfies the equation x+10 is 15 - 3 O -6 O 5 10 O 30
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Q: golden rectangle
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Q: 13. Find the equation of a quadratic function where the vertex is (1, 2) and another point on the…
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Q: 2. Suppose U(x1, x2) X1X2 + X1 + x2 +1, and the budget is described by x1 + 2x2 = 30, solve for x;…
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Q: Solve the problem. 41) Decide which of the rational functions might have the given graph. 4 5X -2+
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Q: We reject any proposed solution of a rational equation that causes a denominator to equal__________.
A: Rational Function: We reject any proposed solution of a rational equation that causes a denominator…
Q: A(n) ______ number is a real number that cannot be expressed as a ratio of two integers
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- Write the steps you would use to explain solving rational inequalities to your little brother.]Explain critical points and how they are used to solve quadratic inequalities algebraically.Observe the surroundings and try to create 3-word problems involving rational functions, equations, and inequalities and show also the solutions to the problems that you created
- What are the distinct features of rational function, rational equation and rational inequality? 3-4 sentencesA student attempted to solve the inequality x+4/x-3< 0 by multiplying both sides of the inequality by x-3 to get x+4< 0. This led to a solution of x|x<-4. Is the student correct? Explain. (b) Make up an inequality (polynomial or rational) that has no solution.Ms. Love Reyes, a Mathematics teacher introduces a new project to teach her students the values of helpfulness and sharing through peer tutoring while learning Math. She believes that her students will be more comfortable and open when interacting with a peer. To teach a short cut technique in solving rational equations and inequalities, she demonstrates the strategy to one of her students and requires this student to do the same to two of his classmates, with a condition that each student who undergoes the peer tutorial will repeat the process until everyone in the class will be able to learn the short cut technique. Also, each student is required to submit a reflection paper of their experienced while doing the peer tutoring and learning with classmates, for her to assess if she is successful to attain her objectives. Based on the situation above, complete the table below. Tutorial Stage 0 1 2 3 4 5 6 Number of student who undergo the tutorial…
- 3. What is the difference between the two formats of quadratic functions when do we use one and not the other?3.Suppose a ceiling fan manufacturer has the total costfunction C(x) = 43x + 1850 and the total revenuefunction R(x) = 80x.(a) What is the equation of the profit function for thiscommodity?(b)What is the profit on 30 units? Interpret your result.(c) How many fans must be sold to avoid losing money?Profit occurs when revenue exceeds cost. If the revenue R in dollars from producing and selling x Hugo Boss polo shirts is R= 26x dollars and the cost C is C= 6x+3660 dollars, what production level produces a profit?
- Solve the problem.If the price charged for a candy bar is p(x) cents, then x thousand candy bars will be sold in a certain city, where p(x)=49-x/20. How many candy bars must be sold to maximize revenue?To strengthen your skills in determining rational functions, rational equations and rational inequality, construct five examples of each category.The total cost, in dollars, to produce bins of cat food is given by C(x)=15x+10582 The revenue function, in dollars, is R(x)=−2x^2+375x 1. Find the profit function. 2. At what quantity is the smallest break-even point?