Algebra Questions

Determine the equation s of the vertical asymptote s if any of the graph of p Also determine the I value s if any where the graph of p has a hole If either does not exist enter DNE P 1 21 19 The equation s of the vertical asymptote s of p are The 7 value s where the graph of p has a hole is are

0 027t The 495 million exponential model A 420 8e describes the population A of a country in millions t years after 2003 Use the model to determine when the population of the country will be The population of the country will be 495 million in Round to the nearest year as needed

p x x 8x 19x 19x 13x 24

Express log b OA log b 35 pq 4 7 m b Choose the correct answer below 3 5 pq O D log b 4 7 m b 35 pq OB log b log 3p log5q log4m 7 4 7 m b 3 5 pq OC log b 4 7 m b 35 p q in terms of sums and differences of logarithms 4 7 mb 3 log op 5 logb 4logm 7 log53 5log pq log 4 log bm logb 3 log pq 5 4 logpm 7 logb

Find fog x and gof x and the domain of each 2 f x x 1 g x 6x 5x 1 fog x Simplify your answer The domain of fog x is Type your answer in interval notation gof x Simplify your answer The domain of gof x is Type your answer in interval notation

The given graph is a graph of a one to one function f Sketch the graph of the inverse 1 function f OA Q O B G O C 10 3 6 10 1 16 Q 5 O D G bns

20 Solve the linear system of equations using the elimination addition multiplication method 6x 2y 6 5x 5y 5 x 2 y 3 Ox 3 y 12 x 4 y 3 x 3 y 6

22 How many solutions does the following system have 1x 2y 11 3x 6y 33 O two O one O infinite

pq Express log b 5 9 m b OA log b 46 OB log b 46 pq 5 9 mb 46 pq mb 4 log p 6log bq 5logm 9 log 4 6 logpq log 5 logbm log9 5 9 46 pq OC log 5 9 m b in terms of sums and differences of logarithms 46 p q OD log 5 9 mb log 4p log6q log 5m 9 4 logpq 6 5 logbm 9 logb

Graph the equation on paper and then choose the correct graph on the right y X Choose the correct graph www O A O C Ay Ay G 5 O B O D Ay Q

9 Solve the inequality set Graph the solution on a numberline 2 3 1 or 9 2 0x 7 2 x 2 or 7 x 2 or 7 all real numbers no solution

Graph both functions using the same set of axes f x 3 f x log 3x Choose the correct graph f x 3 is the solid red line f x log 3x is the dashed blue line O A O C Ay Ay Q O O B O D

Write the expression as a single function of a cos 90 x Choose the correct answer below O A cos x OB sin x O C OD sin a cos a

Simplify the expression by using an appropriate identity Do not use a calculator cos21 cos69 sin21 sin69 cos21 cos69 sin21 sin69 1

Use identities to reduce the expression to a function of a cos x 90 Choose the correct function for cos x 90 OA A sin a OB cos x O C cos OD sin a

Completely factor and find all roots of the following polynomial Use the given partial graph of f identify a root of f f x 15x 73x 37x 129x 36

Find the exact value of the expression given below cos 105 Rewrite the expression using a sum or difference formula Choose the correct answer below A cos 105 cos 60 45 sin 60 cos 45 cos 60 sin 45 B cos 105 cos 60 45 cos 60 cos 45 sin 60 sin 45 C cos 105 cos 60 45 sin 60 cos 45 cos 60 sin 45 OD cos 105 cos 60 45 cos 60 cos 45 sin 60 sin 45 The exact value of cos 105 is Simplify your answer including any radicals Use integers or fractions for any numbers in the expression Rationalize all denominators

27 The larger of two numbers is 25 more than the smaller When added together the sum of the larger number and five times the smaller number is 127 What are the two numbers larger number smaller number

15 Convert to standard form y 7x 17 x 16 Solve the inequality set Graph the solution on a numberlin x 13 3 and x 8 4 O 4 O2 10 and x 4 O 10 and x 4 Ox 10 O all real numbers

26 Determine whether the inequality shown below matches the graph y 2 11 no yes 11 x

8 Solve the systems of linear equations using the substitution method x y 2 7y 4x 1 O 5 3 O 7 9 O 5 7 O 7 5 29 Use substitution to solve the system for f Do not round e 0 0 25e f 10

VAV IT The xy plane above shows a portion of the graph of which of the following functions O y 3 cos 2x Oy 3 cos 2x Oy 3 cos x Oy 3 cos x

Use negative and fractional exponents to put every answer in the following format constant if any simplified as much as possible multiplied by x raised to an exponent Example 4x3 2x 2 6 x 3x 3x 1 3 3 5 4x4 x 3 4 81 1 3x6 63 2 3x 2x 3x8 3

The radioactive element carbon 14 has a half life of 5750 years A scientist determined that the bones from a mastodon had lost 61 1 of their carbon 14 How old were the bones at the time they were discovered The bones were about years old Round to the nearest integer as needed

For the given functions find fog x and gof x and the domain of each 3 1 7x f x g x 1 X fog x 0 5 Simplify your answer

14 Choose the correct graph for the inequality y24 c

13 Given the formula V Ah solve for A V 03 2 3h O V 09 O 3Vh

Find fog x and gof x and the domain of each f x x 17 g x x 17 fog x Simplify your answer

9 Convert the following equation to its alternate form standard to slope intercept or vice versa y x 7 O 8x 9y 63 Ox y 7 8x 9y 63 Ox y 7

6 Given the formula M r solve for r O T Or O r 8T 5M BM 5T 8M O r 5 7 Given the formular x txp i solve for the variable p Hint click the button next to the answer box to make sure your answer is formatted correctly Use parentheses if needed P x

Using addition and or subtraction with multiplication solve the following for x and y 3x 4y 9 2x 4y 6 O 0 2 O 5 4 O 1 2 3 0 Ono solution O infinite solutions

The demand for lumber is increasing exponentially The amount of timber N in billion cubic feet consumed t years after 1997 can be approximated by N t 65 1 018 where t corresponds to 1997 How much lumber was consumed in 1998 billion cubic feet Round to the nearest hundredth

Completely factor and find all zeros of the following polynomial f x x 10z 192 30 Write f as the product of linear factors each with a leading coefficient of 1 f x Find all zeros of f

An nth degree polynomial p satisfies the following conditions p is of degree 4 is a root of P 7i is a root of p p 3 2900 Determine an nth degree polynomial that satisfies the aforemention P x

ST H E A J 17 23 88 9 F 11 13 33 325 F 90 W 19 7 25 97 75 W 16 7 v 15 2 15 3 8 x 50 18 3 16 9 k 21 d 15 crico B 24 x 30 100 9 19 8 12 t 5 22 3 n 25 2m 7 m 40 27 The sum of the angle measures of any triangle is 180 If one angle of a triangle measures 35 and another angle measures 72 what is the measure of the third angle 7 28 63 17 10 q 3 6 5 20 43 7 x 16 0 23 3 b 1 12 26 0 3y 10 4y 28 The perimeter of this quadrilateral is 100 in What is the length of the side not given 27 in 23 in 32 in

the new test score to the test scores given in the table and then divid ing by 5 Put the new average in the hotspot of the table below Desmos Scientific Calculator Student Test scores Current Avg New test score Algebert 80 72 95 57 76 82 Bee Bee 40 55 57 84 59 82

1 n 3 10 4 d 16 5 7 18 k 1 10 11 x 44 2 y 8 15 5 6 u 22 8 7 p 12 11 5 m 92 13 In 3 way light bulbs the highest wattage is the sum of the two lower ones If the lowest is 60 watts and the highest is 150 watts what is the middle wattage 3 9 x 2 6 a 11 14 9 3 b 60 12 y 27 4 14 It was an extremely cold day on the mountain The temperature dropped 22 to 13 F What was the temperature before the drop

EG bisects ZFEH and ZFGH Complete the proof that AEGH AEGF F 1 2 E Statement G EG bisects ZFEH EG bisects ZFGH ZFEGZGEH 3 4 ZEGF ZEGH EG EG AEGHAEGE H Reason Given Given Definition of angle bisector Reflexive Property of Congruence

An nth degree polynomial p satisfies the following conditions p is of degree 3 1 is a zero with multiplicity 1 of p 5 is a zero with multiplicity 1 of p is a zero with multiplicity 1 of p p 2 84 T Determine an nth degree polynomial that satisfies the aforementioned conditions P T

An nth degree polynomial p satisfies the following conditions p is of degree 3 6 is a zero with multiplicity 2 of p 4 is a zero with multiplicity 1 of p p 3 162 Determine an nth degree polynomial that satisfies the aforementioned conditions P x

Use the Rational Zero Theorem to list all possible rational zeros of the given polynomial Then use various methods to determine the actual roots of the given polynomial p z 1 1 17z 15 Enter the possible rational zeros of p using a comma separated list Using synthetic division or other various methods determine the actual zeros of p

Use the Rational Zero Theorem to list all possible rational zeros of the given polynomial p z 101 17x 2x 12 Enter the possible rational zeros using a comma separated list

In a survey conducted at a pet store 150 customers were asked if they owned birds or fish The survey data are shown in the relative frequency table Own fish Do not own fish Total Own a bird O A 10 OB 6 O C 0 1 OD 4 0 04 0 02 Do not own a bird 0 06 0 88 What percentage of the people surveyed own fish Total

Consider the polynomial p x 3x 18x 33x 18 and the completed synthetic division exercise below 2 3 18 33 6 24 3 12 9 18 18 0 The above result indicates that what value is a zero of p Based on the above result p can be factored as p x

ATVX is equilateral Complete the proof that ATUV AXWV X W 1 3 V Statement ATVX is equilateral ZVXW LUTV ZWVX TVU VR TV ATUV AXWy T Reason Given Given Vertical Angle Theorem Definition of equilateral triangle AAS

14 refer to the following information In 2006 180 million pounds of crab were sold In 2011 80 million pounds were sold In 2006 the price of king crab was 8 per pound at the beginning of the year and dropped to 7 per pound toward the end of the year If 60 of the king crab supply was sold at the higher price per pound and the rest was sold at the lower price per pound what was the total revenue generated in millions of dollars from the sales of king crab in 2006 gridded response Your answer In 2011 the price of king crab was 17 per pound In 2012 x million pounds of king crab were sold at 16 per pound If the total money generated from sales each year was the same what is the value of x

The amount of protein supplied by five different food products A B C D and E costs are 2 00 2 20 2 50 4 00 5 00 respectively for 10 grams of product Which of the five food products supplies the most protein per dollar O A OB

A zoologist is studying the reproduction rates of two different breeds of chinchillas in country Y He discovered that the Eastern chinchillas in his study produced 30 percent more offspring than the Western chinchillas did Based on the zoologist s observation if the Eastern chinchillas in his study produced 143 offspring how many offspring did the Western chinchillas produce 100 103 110 186

The specific heat capacity of substance K in calories per gram cal g is approximately 30 less than that of methyl alcohol The specific heat capacity of methyl alcohol is 0 60 cal g Which of the following is closest to the specific heat capacity in cal g of substance K

Boyd grows only tomatoes and raspberries in his garden Last year he grew 140 pounds of tomatoes and 60 pounds of raspberries This year the production by weight of tomatoes decline by 20 percent and the production by weight of raspberries declined by 50 By what percentage did the total yield by weight of Boyd s garden decline O29 percent 30 percent O 35 percent 70 percent