Quadratic equations Questions and Answers

Solve the following formula for the specified variable L B h r k for r Simplify your answer

Solve the formula for the indicated variable S 9 vh 9 v for h h Use integers or fractions for any numbers in the expression Simplify you

The second side of a triangular deck is 6 feet longer than the shortest side and the third side is 6 feet shorter than twice the length of the shortest side If the perimeter of the deck is 64 feet what are the lengths of the three sides The shortest side of the deck is feet Simplify your answer

A rectangle has a width of 56 centimeters and a perimeter of 232 centimeters What i the rectangle s length cm

Miguel Rodriguez borrowed 200 from his brother Julio to pay for books and tuition He agreed to pay Julio in 6 months with simple annual interest at 6 2 a How much will the interest amount to b What amount must Miguel pay Julio at the end of 6 months

Calculate the number of possibilities Choosing first second and third place finishers in a race with 10 competitors

Determine whether the graph below is that of a function by using the vertical line test If it is use the graph to find a its domain and range b the intercepts if any c any symmetry with respect to the x axis y axis or the origin OA The domain is The range is Type your answers in interval notation B The graph is not a function T If the graph is that of a function what are the domain and range of the function Select the correct choice below and fill in any answer boxes within your choice A12 2 I

For the functions f x 3x 2x 1 and g x x x 3 g x would be equal to a g x 2x 3x 2 b g x 4x x 2 c g x 2x x 2 d fg x 4x 3x 4

For the functions f x 3x 5 and g x x 1 find gof x a gof x 3x 2 b gof x 3x 5 c gof x 3x 4 d gof x x 1

3 8 9 13 16 23 29 33 39 Question 34 1 point Listen C Which graph represents the function g 2 for the given graphs of f x and 9 x 6 O Od Od 654 3 3 2 14 D s x 16 12 S 2 6 12 8 2 x 18 2 2 3 1 37 Sa 8220 3855 1161

Solve the equation by using the quadratic formula Enter your answers as a comma separated list If there is no real solution enter NO REAL SOLUTION x 8x 2 a Give real answers exactly X b Give real answers rounded to two decimal places X

A function of the form f x cos x c passes through the point A 3 1 The function is a f x cos x 0 5 b f x cos x 1 c f x cos x d f x cos x 0 5

Consider the function f x cos 2x The graph of f x has the interval 0 2 a 5 b 6 Oc 2 x intercept s in

The graph given here shows the motion of a pedal on a child s bicycle as they ride down the driveway at their home Height cm 20 15 10 2 3 4 5 6 7 time s 9 10 11 12 13 14 15 What is the significance of the period of the curve a the distance covered during one full rotation of the pedal b the time needed for a full rotation of the pedal c the distance covered for the whole trip d the time needed for the whole trip A

The function f x sin kx contains the point A 1 The function is a f x sin x b f x sin 2 c f x sin 2x d f x sin 2x

Solve for x in each equation below Assume that a 0 and a is not 1 It may be helpful to convert the equation into exponential form A log a z I B log a x C log a x x D loga x

Condense ea 9 5 log a log b 5169 29 11 log 2 3 log 11 13 3log x 3log y 15 4log 6 8log2 11 4log2 5 10 log 12 logg 7 log 11 12 6log u log 4 v 14 log x log y log z 16 4log4 a 8log 4 b 4log 4 c

Expand each logarithm 1 log x y z logga x loga y logg 2 3 log4 12 log 12 1 log 4 10 y 12 5 log 114 7 log 35 75 gol gold St gol AI 2 log a b 6 4 log 4 6 y a 8 log 6 log 356

y x 3 X 1 3 5 y Write as a relation 15 Range 17 State the domain and range for each of the following a Domain b Domain 3 Range SHIM HIKIZ Fut Ay T Ho TIL X ty O Z IL 10 y 3 x TH xt X X 2 0 2 4 16 Determine whether each of the following represents a function a 2 2 3 6 1 2 b X 3 0 c y 4 3 y 3 1 5 7 d 0 6 12 18 S 10 Arsh

As a nurse part of your daily duties is to mix medications in the proper proportions for your patients For one of your regular patients you always mix Medication A with Medication B in the same proportion Last week your patient s doctor indicated that you should mix 150 milligrams of Medication A with 135 milligrams of Medication B However this week the doctor said to only use 63 milligrams of Medication B How many milligrams of Medication A should be mixed this week

Solve cos2 x 2 0 for 0 x 2 a There is no solution to this equation Od 1 1 2 d 12 212

Which of the following is an equivalent expression to 1 cos 0 sin 0 cos 0 a 2 sin 0 cos 0 Ob tan c cos 0

For which of the following is there no solution for x a cos x 0 75 b cos x 1 0 J Oc cos x 0 75 0 d cos x 2 0

Two lines A and B are represented by the following equations Line A 2x y 6 Line B x y 4 Which statement is true about the solution to the set of equations 4 points O It is 2 2 O There are infinitely many solutions O It is 4 0

Consider a point on a unit circle x y Which of the following is an equivalent way of stating that point a tan 0 cot 0 b 1 sin 0 1 cos 0 c sin 0 cos 0 d cos 0 sin 0

The solution s to sin x sin x for 0 x 2 is are a 0 7 37 and 2 b and 37 2 c 0 2 and 2 d

Which expression is equal to tan 0 1 tan 0 O a sin 8 csc 8 cos 0 2 cot 0 O O b sin 0 tan 0 tan 8 sin 8 c sec 0 cot 0 d 1 tan 0

Which function describes this graph 10 10 10 Click here for long description O A y x 2 x 6 B y x 8x 12 O c y x 2x 6 10 D y x 4 x 4

Rewrite and simplify log as a logarithm with base ten 10 a 1 2log10 b 2 log10 Oc 2log10 d 2x ty

The distance a cart rolling down a hill travels can be modelled by the exponential function D t 2 5 With D in metres and tin seconds What is the cart s instantaneous speed at 6 seconds a 11 10 m s b 0 090 m s c 0 090 m s d 11 10 m s

Listen to this page a y x 1 b y x Oc x 1 12 10 8 6 4 dy x 1 d y x 1 2 of y 8 6 2 AN 2 fou Using deductive reasoning which of the following is most likely the oblique asymptote for the following graph 6 8 10

After eating something that contains sugar the acid level in your mouth changes and can be modelled by the function A t 15 6t 6 t 30 Where A is the acid level and t is the time in minutes What is the vertical asymptote of this function a x 0 b x 15 6 c x 6

Question 26 1 point Listen a x 1 b x 3 Oc y 1 2 5 5 4 3 2 1 In the graph below what is the equation of the horizontal asymptote 2 3

A linear revenue function is R 80x Assume R is measured in dollars a What is the slope m b What is the marginal revenue MR MR What does the marginal revenue mean If the number of units sold is increased by this amount the revenue increases by 1 O Each additional unit sold decreases the revenue by this many dollars If the number of units sold is increased by this amount the revenue decreases by 1 Each additional unit sold yields this many dollars in revenue c What is the revenue received from selling one more item if 50 are currently being sold What is the revenue received from selling one more item if 100 are being sold

In the equation for P x the profit in dollars is represented by P and the number of items produced and sold is represented by x Therefore to find the profit when 343 items are sold we substitute 343 for in the equation P x 300x 3 900 Find P 345 items Step 4 P x 300x3 900 P 343 300 343 99000 343 3 900 99 000 Fantastic job That is if 343 items are produced and sold the total profit is 99000 c How many items must be sold to avoid losing money F The manufacturer makes money if the profit is positive profit is 0 99 000 Great work and loses money if the profit is positive We can find the break even quantity by solving the equation P x O When the manufacturer breaks even the So to avoid losing money the manufacturer must produce and sell the break even quantity which is the number of items that results in a profit equal to 0

Suppose a ceiling fan manufacturer has the total cost function C x 31x 2070 and the total revenue function R x 77x a What is the equation of the profit function P x for this commodity P x b What is the profit on 25 units P 25 Interpret your result The total costs are less than the revenue The total costs are more than the revenue The total costs are exactly the same as the revenue c How many fans must be sold to avoid losing money fans

A manufacturer sells belts for 15 per unit The fixed costs are 2000 per month and the variable cost per unit is 11 a Write the profit function P x P x b Set profit equal to zero and solve for x X Compare this x value with the break even point www This x value Select the break even point greater than A

Exercise Find the market equilibrium point for the following demand and supply functions Demand p 3q 287 Supply p 7q 2 Step 1 Write the condition for market equilibrium in the form Demand Supply 3q 287

Suppose a calculator manufacturer has the total cost function C x b What is the profit on 2800 units 24x 6400 and the total revenue function R x 66x a What is the equation of the profit function P x for the calculator P x

2 Is the triangle below a right triangle Explain Show how you know

Show that I Kirt Ief dady 120 e dx I 2TC 101

LAPLACE TRANSFORM DUHAMEL INTEGRAL Need step by step solution to given task and result Task in the left result in the right t 0 0

Find the mean X of the data 16 31 38 24 36 x Mean

Question 8 Solve the rational inequality Give the answer in interval notation 5 3x 2 IV SI5 X

Find the following for the function f x 2 X 1 a f 0 e f x X b f 3 f f x 4 c f 3 g f 2x a f 0 Simplify your answer Tyne an integer or a simplified fraction d f x h f x h

Find the following for the function f x a f 0 e f x b f 5 f f x 1 g f 3x X 2 x 1 X h f x h Simplify c f 5 g f 3x 24 Simplity your answer Use integers or tractions for any numbers in the expression d f x h f x h 3x 2 9x 1 Simplify your answer Use integers or fractions for any numbers in the expression answer Use integers or fractions for any numbers in the expression

Question 5 1 point Listen The function f x 2x x 1 x 4 is O a quartic b cubic c quadratic d linear

4 Listen The following graph is most likely which of the given types of functions 6 4 a quadratic b linear 2 2 4 4 6

Solve for x 2x 7x 3x 0 X a x 0 b x b x 1 2 c x 3

can be modeled by a function s t 3 t 5 2 3 The instantaneous rate of change 3 seconds is a negative b zero c undefined