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MSBSHSE Solutions For SSC Maths Part 2 Chapter 3- Circle

A tan? You can solve this problem either 1 by simplifying the numerator and denominator separately and then simplifying the result or 2 by using the distributive property. For this problem, we will use the first method. To simplify the expression, first factor the numerator and the denominator.

By the trial-and-error method, the numerator can be factored into two binomials as follows. Thus, the factored form of the expression is Notice that there is a common factor, x � 4which is in both the numerator and the denominator. Therefore, you can further simplify the expression by cancelling it.

To solve, first factor the polynomial. Notice that the greatest common factor GCF of the terms is 2x. Factor this expression out and then use trial-and-error to factor the resulting trinomial. These values divide the number line into four intervals. Choose a test number from each interval and determine whether the product 10th class algebra practice set 1.2 error positive or negative.

For this problem, we will use -5, -1, 1, and 2 as test numbers. Substitute these values into the original polynomial. The baseball will hit the ground when its height is zero. Therefore, we need to set the given function equal to zero. Now solve the resulting equation. Factor the left side 10th class algebra practice set 1.2 error use the zero-product property to solve for t. The answer only makes sense when t is positive, so we can discard the negative value.

Thus, the calculator will hit the ground 3 seconds after it is thrown. Check this value on your own by substituting it into the original equation to make sure that the result is a true statement. The numerator can be factored by grouping as follows. Notice that there is a common factor, x-3which is in both the numerator and the denominator.

Use a unit circle to 10th class algebra practice set 1.2 error the value of cosine. In a right triangle, the cosine function is cos?

Using the Pythagorean Theorem, we find that the length of the second leg is. Since the tangent function is tan? Therefore, tan? All of the choices involve two transformations of the given expression: factoring out either 2 or 2x and changing the radical to an exponent.

First factor out the greatest common factor GCF of the terms. In this case, the GCF is 2. Find f x. Solve the inequality for x. Select all that apply. A baseball is thrown up in the air from an initial height of 6 feet. How long will it take in seconds for the baseball to hit the ground?

Solve the equation for x. Suppose that angle? Find tan?. 10th class algebra practice set 1.2 error You can solve this problem either 1 by simplifying the numerator and denominator separately and then simplifying the result or 2 by using the distributive property. D To simplify the expression, first factor the numerator and the denominator. A and C To solve, first factor the polynomial. D The baseball will hit the ground when its height is zero.

C nly: The logarithm of a number is the exponent that the base must to be raised to in order to get that number. Then use these values to calculate the average rate of change.

C Use a unit circle to model the value of cosine. B All of the choices involve two transformations of the given expression: factoring out either 2 or 2x and changing the radical to an exponent.

Main points:

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The mean of the tests are , and the standard deviation is. What is the student's z-score? Write the formula for z-score where is the data, is the population mean, and is the population standard deviation. The z-score is:. Suppose Bob's test score is Determine the z-score if the standard deviation is 3, and the mean is Write the formula for z-scores. This tells how many standard deviations above the below the mean. The answer is:.

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Hanley Rd, Suite St. Louis, MO Subject optional. Home Embed. Email address: Your name:. Example Question 1 : Z Scores. Possible Answers:. Correct answer:.

Explanation : If the mean 10th Class Algebra Practice Set 1.2 Quota of a normally distributed set of scores is and the standard deviation is , then the -score corresponding to a test score of is From a -score table, in a normal distribution, We want the percent of students whose test score is 85 or better, so we want.

This is or about 5. Report an Error. We want to determine the probability that X is between 69, and 78, To approximate this probability, we convert 69, and 78, to standardized values z-scores.

We then want to determine the probability that z is between 1. Example Question 3 : Z Scores. Explanation : The z-score is a measure of an actual score's distance from the mean in terms of the standard deviation.

The formula is: Where are the mean and standard deviation, respectively. If we plug in the values we have from the original problem we have which is approximately. Example Question 4 : Z Scores. Explanation : The z-score can be expressed as where Therefore the z-score is:. Example Question 5 : Z Scores. Explanation : Use the formula for z-score: Where is her test score, is the mean, and is the standard deviation.

Example Question 6 : Z Scores. Example Question 7 : Z Scores. Explanation : Write the formula to find the z-score. Substitute the values into the formula and solve for the z-score. Example Question 8 : Z Scores. Explanation : Write the formula for z-score where is the data, is the population mean, and is the population standard deviation. Substitute the variables. Example Question 9 : Z Scores. Explanation : Write the formula for z-scores.

Substitute the known values into the equation. Example Question 10 : Z Scores. Find the z-score if the result of a test score is 6, the mean is 8, the standard deviation is 2. Explanation : Write the formula to determine the z-scores. Substitute all the known values into the formula to determine the z-score.

Simplify this equation. Copyright Notice. Find the differences between consecutive square numbers. Explain what you notice.

Prove the polynomial identity in part b. Prove the polynomial identity is true by showing that the simplified expressions for the left and right sides are the same. Essential Question How can you use the factors of a cubic polynomial to solve a division problem involving the polynomial? Match each division statement with the graph of the related cubic polynomial f x.

Use the results of Exploration 1 to find each quotient. Write your answers in standard form. Check your answers by multiplying. How can you use the factors of a cubic polynomial to solve a division problem involving the polynomial? Use an example in your explanation. Provide examples to support your claim.

In Exercises 25�32, use synthetic division to evaluate the function for the indicated value of x. Draw the figure and label its dimensions. Write a function for the average attendance per team over this period of time.

Is there an easier method? What is the value of k? Find an expression for the missing dimension. What is the dividend? How did you find it? Match each polynomial equation with the graph of its related polynomial function. Use the x-intercepts of the graph to write each polynomial in factored form. Use the x-intercepts of the graph of the polynomial function to write each polynomial in factored form.

What information can you obtain about the graph of a polynomial function written in factored form? Then factor f x completely. In Exercises 45�50, show that the binomial is a factor of the polynomial. Then factor the polynomial completely. Determine the values of x for which the model makes sense. If not, factor completely. What lesser number of T-shirts could the company produce and still make the same profit? What lesser number of shoes could the company produce and still make the same profit?

You use the Factor Theorem and synthetic division and your friend uses direct substitution. Whose method do you prefer? Your friend concludes that f x cannot be factored.

Use the graph to write an equation of the cubic function in factored form. Can you use the Factor Theorem to factor f x? Rewrite each equation of a circle in standard form.

Identify the center and radius of the circle. Then graph the circle. Write an algebraic expression for the volume of each of the three solids. Leave your expressions in factored form.

Core Vocabulary. Core Concepts 10th Class Algebra Practice Set 1.2 Ios Section 4. Section 4. Describe the entry points you used to analyze the function in Exercise 43 on page Describe how you maintained oversight in the process of factoring the polynomial in Exercise 49 on page Write an expression for the area and perimeter for the figure shown.

What was the average rate of change in the price of stamps from to ? Essential Question How can you determine whether a polynomial equation has a repeated solution? Some cubic equations have three distinct solutions. Others have repeated solutions.

Match each cubic polynomial equation with the graph of its related polynomial function. Then solve each equation. For those equations that have repeated solutions, describe the behavior of the related function near the repeated zero using the graph or a table of values.

Determine whether each quartic equation has repeated solutions using the graph of the related quartic function or a table of values.

Write a cubic or a quartic polynomial equation that is different from the equations in Explorations 1 and 2 and has a repeated solution. Then find all real zeros of the function. In Exercises 41�46, write a polynomial function f of least degree that has a leading coefficient of 1 and the given zeros. Each mold is a rectangular prism with a height 3 centimeters greater than the length of each side of its square base.

Each mold holds cubic centimeters of glass. What are the dimensions of the mold? Write a polynomial equation that you can use to find the value of x. Identify the possible rational solutions of the equation in part a. Use synthetic division to find a rational solution of the equation. Show that no other real solutions exist. What are the dimensions of the cube? What are the dimensions of the block? List the possible whole-number solutions of the equation in part a.

Consider the domain when making your list of possible solutions. The sides and bottom of the basin should be 1 foot thick. Its outer length should be twice its outer width and outer height.

What should the outer dimensions of the basin be if it is to hold 36 cubic feet of water? Use the information in the graph to answer the questions. What are the real zeros of the function f? Write an equation of the quartic function in factored form. The left ramp is twice as long as the right ramp. If cubic feet of concrete are used to build the ramps, what are the dimensions of each ramp?

You are making an ice mold for a school dance. It is to be shaped like a pyramid with a height 1 foot greater than the length of each side of its square base. The volume of the ice sculpture is 4 cubic feet. If a n has r factors and a 0 has s factors, what is the greatest number of possible rational zeros of f that can be generated by the Rational Zero Theorem? Then find all solutions.

Make a conjecture about how you can use a graph or table of values to determine the number and types of solutions of a cubic polynomial equation. Use the graph of the related quartic function, or a table of values, to determine whether each quartic equation has imaginary solutions. Is it possible for a cubic equation to have three imaginary solutions? Find all zeros of the polynomial function. Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros.

Determine the possible numbers of positive real zeros, negative real zeros, and imaginary zeros for the function. In Example 5, what is the tachometer reading when the boat travels 20 miles per hour? Degree: 4 Answer:. Degree: 5 Answer:. Degree: 2 Answer:. Degree: 3 Answer:. In Exercises 21�28, write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros. Explain why the third zero must also be a real number.

In Exercises 33�40, determine the possible numbers of positive real zeros, negative real zeros, and imaginary zeros for the function.

In which year did the population first reach ,? In which year did the number of infested inland lakes first reach ? Who is correct?

What is the value of x? Label each x-intercept. Then write the function in standard form. Does the function contradict the Fundamental Theorem of Algebra? The graph represents a polynomial function of degree 6.

How many positive real zeros does the function have? Compare the graphs when n is even and n is odd. Describe the relationship between the sum of the zeros of a polynomial function and the coefficients of the polynomial function. Describe the relationship between the product of the zeros of a polynomial function and the coefficients of the polynomial function. The table shows the value of your deposits over the four-year period.

Copy and complete the table. Write a polynomial function that gives the value v of your account at the end of the fourth summer in terms of g. What growth factor do you need to obtain this amount?

What annual interest rate do you need? Then graph each function. Section 2. Write a function g whose graph represents the indicated transformation of the graph of f. Sections 1. The graph of each cubic function g represents a transformation of the graph of f.

Write a rule for g. The graph of each quartic function g represents a transformation of the graph of f. Then graph g. Write a rule for g and then graph each function. Describe the graph of g as a transformation of the graph of f. Write a rule for W. Find and interpret W 7. In Exercises 3�6, describe the transformation of f represented by g. In Exercises 11�16, describe the transformation of f represented by g.

In Exercises 17�20, write a rule for g and then graph each function. Find and interpret W 5. Your friend claims that when you divide the volume in half, the volume decreases by a greater amount than when you divide each side length in half.

Then describe two transformations where the order is not important. The hummingbird feeds each time it is at ground level. At what distances does the hummingbird feed? A second hummingbird feeds 2 meters farther away than the first hummingbird and flies twice as high. Write a function to model the path of the second hummingbird. Determine the real zeros of each function. Then describe the transformation of the graph of f that results in the graph of g.

Then write a function W that gives the volume in cubic yards of the cone when x is measured in feet. Find and interpret W 3. Find the minimum value or maximum value of the function. Describe the domain and range of the function, and where the function is increasing and decreasing. Essential Question How many turning points can the graph of a polynomial function have?

A turning point of the graph of a polynomial function is a point on the graph at which the function changes from. Then use a graphing calculator to approximate the coordinates of the turning points of the graph of the function.

Round your answers to the nearest hundredth. Is it possible to sketch the graph of a cubic polynomial function that has no turning points? Identify the x-intercepts and the points where the local maximums and local minimums occur.

Determine the intervals for which the function is increasing or decreasing. In Exercises 23�30, graph the function. In Exercises 31�36, estimate the coordinates of each turning point. State whether each corresponds to a local maximum or a local minimum. Then estimate the real zeros and find the least possible degree of the function.

Use a graphing calculator to graph the function. At what time during the stroke is the swimmer traveling the fastest? Then describe how the public school enrollment changes over this period of time. WRITING Why is the adjective local, used to describe the maximums and minimums of cubic functions, sometimes not required for quadratic functions? Find the zeros, local maximum, and local minimum values of the function.

The box will be formed by making the cuts shown in the diagram and folding up the sides. You want the box to have the greatest volume possible. How long should you make the cuts? What is the maximum volume? What are the dimensions of the finished box? You have square feet of material to build a quonset hut.

Write an equation that gives V as a function in terms of r only. Find the value of r that maximizes the volume of the hut. Is there a maximum degree that such a polynomial function can have?

Write an equation for the volume of the cylinder as a function of h. Find the value of h that maximizes the volume of the inscribed cylinder. What is the maximum volume of the cylinder?

The distance a baseball travels after it is hit depends on the angle at which it was hit and the initial speed. Recall that when data have equally-spaced x-values, you can analyze patterns in the differences of the y-values to determine what type of function can be used to model the data. If the first differences are constant, then the set 10th Class Algebra Practice Set 1.2 Note of data fits a linear model. If the second differences are constant, then the set of data fits a quadratic model.

Find the first and second differences of the data. Are the data linear or quadratic? Use a graphing calculator to draw a scatter plot of the data. Do the data appear linear or quadratic? Use the regression feature of the graphing calculator to find a linear or quadratic model that best fits the data. A blow of feet shows exceptional power, as the majority of major league players are unable to hit a ball that far.

Anything in the foot range is genuinely historic. How well does the model you found in Exploration 1 b fit the data? Do you think the model is valid for any initial speed? Use finite differences to determine the degree of the polynomial function that fits the data. Then use technology to find the polynomial function.

In Exercises 7�12, use finite differences to determine the degree of the polynomial function that fits the data. Show that this function has constant second-order differences. Use the model to estimate the age in human years of a cat that is 3 years old. Find a polynomial model for the data. Estimate the average speed of the pontoon boat when the engine speed is RPMs.

The graph shows typical speeds y in feet per second of a space shuttle x seconds after it is launched. What type of polynomial function models the data?

Which nth-order finite difference should be constant for the function in part a? Find a polynomial function that fits the data. Determine the total number of diagonals in the decagon shown. Then write the function using the A, B, and C values you chose. Then show that the third-order differences are constant. Explain how understanding the Complex Conjugates Theorem allows you to construct your argument in Exercise 46 on page

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