Quadratic equations Questions and Answers

Two numbers total 71 and have a difference of 13 Find the two numbers The larger number is and the smaller number is

Determine the domain and range of the function T 3 2 3 2 PE 4 2 3 A 20 3 4

Solve the system of equations by the substitution method 20x 4y 10 5x y 10 Select the correct choice below and if necessary fill in the answer box to complete your choice OA The solution is Type an ordered pair Simplify your answer OB There are infinitely many solutions x y 20x 4y 10 or x y 5x y 10 OC There is no solution or

The perimeter of a rectangle is the distance around the outside of the rectangle Suppose the length of a rectangle is 5 units greater than its width Find the perimeter of the rectangle A 4x 10 B None of the answers listed C 4x 5 D x x 5 x 5 E 2x 10

Homework Unit 6 MATH 0307 13 2 1 graphing by plotting po For the equation find three ordered pair solutions by completing the table Then use any two of the ordered pairs to graph the equation x y 3 Complete the table below X 3 1 y Question 5 13 2 1 Part 3 of 4 0 2 1 HW Score 63 89 5 75 of 9 points O Points 0 of 1 10 8 6 10 18 6 2 2 Ay 8 10 10

The monthly mean salaries and standard deviations of four college students are given below Student Clarissa Abi Kaila Shenika Which statement must be true Mean 345 598 812 208 Standard Deviation 12 53 8 99 15 29 7 67 O The monthly salary of Shenika is less spread out than the monthly salary of Clarissa O The monthly salary of Kaila is less spread out than the monthly salary of Abi The monthly salary of Abi is less spread out than the monthly salary of Shenika The monthly salary of Clarissa is less spread out than the monthly salary of Abi

S 12 14 14 14 9 14 21 14 2 2 0 5 7 14 0 25 49 19 5 What is the first error he made in computing the standard deviation OYuri failed to find the difference between each data point and the mean OYuri divided by n instead of n 1 0 Yuri did not subtract 9 14 correctly Yuri failed to square 2 correctly

identifying intercepts dentify the intercepts Ay A Q Part 1 of 2 Points 0 of 1 Select the correct choice below and if necessary fill in the answer box to complete your ch A x intercept s Type an ordered pair Use a comma to separate answers as needed OB There is no x intercept Sav

y 3 x 1 equation Your job is to create a visually appealing comprehensive and organised sketch of the given function Make sure to include proper terminology explanations function characteristics ie intercepts increasing decreasing intervals positive negative intervals restrictions asymptotes domain range end behaviours maxima minima values critical points concavity points of inflection etc etc You can use technology to CHECK your sketch however you need to provide a step by step hand drawn sketch as you calculate and find information about your function

graphing by plotting po Graph the linear equation X 8 GLIED Use the graphing tool to graph the linear equation Click to enlarge graph 6 12 Ay

Given the graph of f x below graph h x f 2x 4 4 2 YA 4 0 2 2 2 2 4 0 X

sin 7 x cos 7 x tan 27 x 3 3 2 T 2 sec x csc x cot 2 X 2 sin r sin x

1 Elena is paid a constant rate for each hour she works The table shows the amounts of money that Elena earned for various amounts of time that she worked Time hours 2 5 3 3 5 4 5 Amount Earned dollars 22 50 27 31 50 40 50 a Write a function that models the table of values Define your variables F BF A 1 b Determine the amount of money Elena earns if she works 7 5 hours F IF A 2

For the following equation find three ordered pair solutions by completing the table Then use the ordered pairs to graph the equation y 3x 6 Find three ordered pair solutions of the given equation X 0 y Part 1 of 4 10 AY 10 8 O 2 Points 0 of 1

finding slope given 2 p and the slope of the line if it exists in Q 1 Question 5 3 4 9 HW Score 83 33 5 of 6 points O Points 0 of 1 OA The slope is Select the correct choice below and if necessary fill in the answer box to complete your choim Type an integer or a simplified fraction Save OB The slope is undefined

The table shows some values of a polynomial function Over which interval s is the average rate of change of the function positive Select all that apply X f x 0 50 from x 0 to x 2 from x 1 to x 2 from x 0 to x 3 from x 2 to x 3 from x 0 tox 1 from x 1 to x 3 1 75 2 40 3 65

finding slope given 2 p Find the slope of the line if it exists 8 6 f2 Ay Question 6 3 4 11 Points 0 of 1 Sav Select the correct choice below and if necessary fill in the answer box to complete your c A The slope is Type an integer or a simplified fraction B The slope is undefined

5 Solve the triangle find all missing sides and angles 6 8 cm W 9 6 cm 8 7 cm F

21 1 12 O O O F 2 O G 2 y 1 4 H 3 72

There were 800 farmers markets initially in the USA in 2012 In 2013 the number of farmers markets was 1 25 times the initial number of farmers markets Then In 2014 the number of farmers markets was 1 25 times the number of farmers markets the previous year If this pattern continues which of the following graphs represents the number of farmers markets in the USA over time Farmers Markets Farmers Markets Number of Farmers Markets 2 000 1 600 1 200 800 400 0 4 1 2 4 Years since 2012 Graph W Number of Farmers Markets f x 2 000 1 600 1 200 800 400 0 1 3 4 2 Years since 2012 Graph X 5

24 If m HGK 6x 3 m HJK 4x 9 m JHK y 11 and mZGKH 3y 2 Find x and y Show work 34 2 H 0v 24 9 Y 11 4 73 6x 3 4x 9 3 6x 4x 12 un 47 2X 12 x 6 34 2 2 4 1 2 34 3y y 13 24 13 y 6 5 6x 3 G K

4 Solve the triangle find all missing sides and angles 48 7 c

5 times a number is 14 less than the square of that number Find the positive solution

2 The position of end effector is given with respect to refrence frame Find the jacobian with respect to zero coordinate system Find singular points ac d s PORG 0

Find an equation for the graph sketched below 5 4 3 f x 9 Q SON 16 n 439 8 5 S 3 hay kj 2 on 3 In

The hole of the function f x a 1 1 b 1 0 c there is no hole d 1 0 2x 7x 8x is at x 1

Use a calculator to evaluate the expression 17P

The function f x 0 00001x 0 009x 0 2x 8 15 models the number of annual physician visits f x by a person of age x Graph the function in a 0 100 5 by 0 40 2 viewing rectangle What does the shape of the graph indicate about the relationship between one s age and the number of annual physician visits Use the TRACE or minimum function capability to find the coordinates of the minimum point on the graph of the function What does this mean Choose the correct graph below O A Q B All graphs have viewing window 0 100 5 by 0 40 2 O C Q G D OU

If f x x 1 and g x 2x find the domain of fo g x Oa 2ER Ob 0 1 R Oc xx x R II d x x TER

An open box is to be constructed from a square piece of sheet metal by removing a square of side 5 feet from each corner and turning up the edges See the figure on the right If the box is to hold 500 cubic feet what should be the dimensions of the sheet metal What is the length of a side of the square piece of sheet metal BEEXEE

Solve the triangle For the following exercises assume a is opposite side a is opposite side b and y is opposite side c Solve each triangle if possible Round each answer to the nearest tenth 24 OC 120 a 23 1 c 34 1 OC 125 a 25 1 c 34 1 OC 140 a 28 1 c 34 1 O C 136 a 22 1 c 34 1 a C C 36 16

Exercise Given f x Find the following a f x b f x 5x 4x 9

Simplify Write the answer using positive exponents 5 3 X Use La D For any numbers a and b and any integer n 9 b X a bn 5 3 to start simplifying the expression X Simplify the exponents x 5 3 y4 3 5 3 4 3 X y 15 12 5 Now rewrite the expression using only positive exponents 15 X bn b 0

Solve for X A 16 B 48 C 24 D 72 0 R 5x X 0 4x S 2x T P 3x

Simplify Write the answer using positive exponents Use X 8 X 4 5 X Simplify the exponents bn 4 5 20 4 5 y4 5 X to start simplifying the expression 20 X 4 5 JA X y 20 Now rewrite the expression using only positive exponents 20 5

The graph and equation of the function f are given a Use the graph to find any values at which f has a relative maximum and use the equation to calculate the relative maximum for each value b Use the graph to find any values at which f has a relative minimum and use the equation to calculate the relative minimum for each value a Select the correct choice below and if necessary fill in the answer boxes to complete your choice OA The function f has a relative maxima maximum at and the relative maxima maximum are is Use a comma to separate answers as needed OB The function has no relative maxima f x 2x 6x 18x 6 E QO 5 5 1 by 60 60 10

If f z 22 and g x 4 then g z Oa f g z 20 20 Ob f g x 220 1 Oc f 9 2 24 Od f 9 z 2 1

Use a graphing utility to graph the function Use a 5 5 1 by 24 24 3 viewing rectangle Then find the intervals on which the function is increasing decreasing or constant f x x 3x29x 4 Choose the correct graph below O A AA G OB 9 G O C G D

Graph the set of numbers given in interval notation Then write the inequality statement in x describing the numbers graphed 1 Choose the correct graph below O A O C 0 0 Write the inequality statement in x describing the numbers graphed SECCOU B D This question 1 point s possible 1 1 0 0 Su

20 1 point Use the given point on the terminal side of angle to find the value of the trigonometric function indica sin 0 C 4 15 15 X

The domain of f x is x x 1 x R what is the domain of g x 2f x 3 1 Oa x x 3 x R Ob xx 4 x R Oc x x 2 x R d xx 1 x R

Express the vector 1 2 3 on R as the sum of the vector on the plane passing through the origin and perpendicular to 1 2 1 and the two vectors perpendicular to it

Haley pays a monthly fee of 20 for her cell phone and then pays 5 cents per minute used The total cost of Haley s monthly cell phone bill can be expressed by the function C m 0 05m 20 where m is the number of minutes used What are the domain and range of the function C m 80 8 8 60 20

Given the graph of an exponential function identify the end behavior 10 8 6 4 2 10 8 6 2 4 6 do 8 10 2 6 8 10 Asx co f x As x o f x A A

Let f x log10x State the coordinates of the points on g that are images of the points 1 0 and 10 1 of the graph of f 4 marks g x 2log 10l 2 x 2

Consider a log63 64x log62 63 x log61 62 xx log2 3 Given that a E Z find the value of a E

Homework Unit 5 MATH 0307 9 4 2 applications w 2 unkno Question 1 9 4 9 Part 1 of 3 A35 inch piece of steel is cut into three pieces so that the second piece is twice as long as the first piece and the third piece is three inches more than five times the length of the first piece Find the lengths of the pieces What is the length of the first piece 2x

Match the steps used to solve the equation 4 51x X Drag and drop options on the right hand side and submit For keyboard navigation SHOW MORE Identify the LCD What is the equation that results after clearing fractions State the solution set III 445x x 4 1 4x 5x 1 1 4

Identify the intercepts What are the intercepts Select the correct choice below and if necessary fill in the answer box to complete your choice O A Type an ordered pair Use a comma to separate answers as needed OB There is no intercept GEIXID Av Q

8 A newly hatched frog weighs 1 5 kg This weight increases by 13 percent each day for the next 3 weeks of its life Write an exponential equation that models the growth of the frog and approximate the weight of the frog after 3 weeks Round to the nearest hundredth y kg