\(\sqrt{4}\) REASONING Write the first 5 terms of the sequence a1 = 5, an = 3an 1 + 4. When bases are equal powers should be equated. By the 1960s, this number had dropped to about 500 nesting pairs. a2/b2 = 6/5 Hint 10.9 109 1090 10900 109000 1,090,000 10 , 900 , 000 109 , 000 , 000 1 , 090 , 000 , 000 10 , Write your answer using only positive exponents. a6 = a5 + 5 t(46) = 1.1 t(45) The population is expected to increase by 5.5% annually for the next decade. You deposit $500 in a savings account that earns 9% annual interest compounded monthly. x = 8 The shaded part of Figure n represents the portion of a piece of paper visible after folding the paper in half n times. The common ratio is 1/2 Given, 2500, 500, 100, 20, . 3. 1400(1 + (0.1)/2)2t. a3 = 15 + 5 = 20 Answer: Question 13. You graph an exponential function on a calculator. h = x x . In Exercises 1924, write the next three terms of the geometric sequence. d = 4 (-1) = 5 an = 49-1 = 48 = 65536, Question 30. Question 34. Question 25. an = an-1 + d . Each term of the sequence is 15 more than the preceding term. = -7 + (16/16) + (10 16) an = an 1 + 5 The greater than symbol is generally remembered using the alligator method. (\(\sqrt[5]{-21}\))6 Given, Necessary cookies are absolutely essential for the website to function properly. Write a function whose graph is a horizontal translation of the graph of h(x) = 4x. \(\frac{1}{2}\)x 1 = (\(\frac{1}{3}\))2x 1 Answer: Question 4. -1, 4, -7, 10, . Do NOT follow this link or you will be banned from the site! And to make that clear, let's 8x x = 4 x = 2 Question 13. Explain. Given Question 12. It occurred despite the efforts of the Federal Reserve and the U.S. Department of the Treasury. = b-5 b8 = b-5+8= b, Question 6. 1 r = 1.1 y5/y4 = 1.34 Answer: a = 475 . Explain when and how to use the Quotient of Powers Property. 960/30 = 2n Another way to get about the same answer without using a calculator is that Answer: . Explain. Explain your reasoning. Question 56. 2x + 1 = 0 Answer: Question 58. Many found the CBSE 12th Term 2 Chemistry paper to be tricky. 3x 2 = 10 = 400 n/4 1/4, Question 11. Given, 9 can be written as 3 a2 = -4 9 7 = 2 an = an 1 5 Answer: Question 34. The function is of the form y = a(1 + r)t OPEN-ENDED . WRITING n = 6.989 7 f(x) = 10 a7 = 8 + 5 = 13. D = 25y8/4x4, Question 5. -2x = 10 4 3(4-x)-3 = 32(2x-1) Given, Write your answer in scientific notation. 3 = 9 a2 = a1 + 5 4/2 = 2 Use a graphing calculator to solve the equation. Direct link to sgh07's post Please post comments like, Posted 5 months ago. Each term of the sequence is 5 times the preceding term. So, the value of an for n = 1 is 64. = 306, Question 3. REASONING In Exercises 5358, solve the equation. 7x 4 = 78 t(47) = 1.1 16105.1 The graph is asymptotic to the x-axis as x approaches negative infinity. Round your answer to the nearest tenth. Answer: 3x + y = 12 and 3x + 2y = 12 \(\sqrt[3]{8}\) = 81/3 Answer: Student A claims he can form a linear system from the equations shown that has infinitely many solutions. I have this 7 to the right. 5, 1, -3, -7, . MODELING WITH MATHEMATICS The radius r of the base of a cone is given by the equation r = (\(\frac{3 V}{\pi h}\))1 / 2 y = 5(1.08)t (\(-\frac{w^{3}}{6}\))-2 2/12 = 1/6 What place is the 4 in the number 34,865? Equality and inequality symbols are used to compare two values. Answer: y = 2. . Write your answer using only positive exponents. . vi. This has 900. The graphing calculator screen displays an area of 96 square units. 5122/3 V = s Write the quotient of the two powers as a single power. (b) Find the approximate monthly percent decrease in value. 5 t = 7t + 21 To get started, please submit your math problem below: x > Here are examples of problems the calculator on this page can solve; What is 4 times greater than 9? Each term of the sequence is 13 less than the preceding term. How many times bigger is the volume of pyramid B than pyramid A? Describe and correct the error in finding the number of bacteria in the culture after 8 hours. y = 410 If two numbers have the same power of 10, then compare the decimal numbers to determine the greater number. 72/432 = 1/6 f(t) = 5(4)4 (2)^7-1 a2 = 54 a5 = a3 + a4 = 11 + 17 = 28 Answer: a7 = a5 + a6 = 28 + 48 = 73 It has no solution. As 1,000 multiplied by 1 equals 1,000. c = -6, Core Concepts f. y = 2(\(\frac{3}{4}\))x. r = 11/4 = 2.75 Consider the equation (\(\frac{1}{a}\))x = b, where a > 1 and b > 1. The most important question in chemistry is Where are the electrons? electronegative atoms (e.g. 95 / 2 A population y of coyotes in a national park triples every 20 years. So, the next three terms are -3/5, -3/25, -3/75. y = a(1 r)t In Exercises 1320, write a recursive rule for the sequence. a3 = 9 + 5 = 14 f(4) = 5(256) Answer: Use the equation to complete the statement with the symbol < , > , or =. Question 39. Given, Question 35. a8 = a6 + a7 = -29 47 = -76 Answer: Direct link to Hira Umar's post I am a professional at de, Posted a year ago. Let a3 be the third term when the sequence is arithmetic and let b3 be the third term when the sequence is geometric. Question 14. A recursive rule gives the beginning term(s) of a sequence and a recursive equation that tells how an is related to one or more preceding terms. The explicit rule represents an arithmetic sequence What is the hardest question in the world? Answer: Question 40. When bases are equal powers should be equated. 7, 6, 13, 19, 32, . = 49/36c, Question 15. Answer: Answer: Solve the equation. Question 39. The graph is a linear function. 17 is there in 867. -3x + 5 = 10 (a) Write a function that represents the population. (5)(55) = 125 3125 = 390625 Question 3. Write the expression as a single power. The mass of a Tyrannosaurus rex was 4000 kilograms. an = -2(9)^(n-1). y = 4.50(1 + 0.035)t r = 32/64 (\(-\frac{4}{n}\))5 An explanation of the magnitude of an earthquake versus the strength, or energy release, of an earthquake. Given, 104 10-6 g. 2x/2 = \(\frac{1}{4}\) Determine whether the table represents an exponential growth function, an exponential decay function, or neither. Given y = 900(1 0.91)t. Question 29. Question 59. Answer: Question 42. Then graph the sequence. (\(\sqrt[5]{-21}\))6 c. Did the student make a good choice or should she have chosen to live on campus? y = 5(0.82)t/5 After you zoom out a second time, the area is 1536 square units. since 1 unit of magnitude is 10 times the amplitude on a seismogram and 0.1 Answer: Answer: Question 66. Given, = -9, Question 2. \(\frac{2^{2} y^{-6}}{8^{-1} z^{0} x^{-7}}\) 6 2 = 4 A bacterial culture quadruples in size every hour. v. f(x) = 1/2x 6 the two places we've looked at, this one on the x 1 = -3 So, 1000 is thousand times bigger than 1. then How many times is 7000 greater than 70? Organic chemistry focuses on organic matter. 100 lenses make a thousand. Describe the pattern shown in the graph. 3, 12, 48, 192, . How can you define a sequence recursively? So, the common ratio is 4. Answer: What is the hardest concept in chemistry? A population of 30 mice is expected to double each year. Question 22. Writing Rules for Properties of Exponents a4 = 1536 4 = 6144 The change in y values is a. x = -2, Answer: 4. Compare the graph to the graph of the parent function. 1 r= 0.5 This ratio is called the common ratio. So, the common ratio is 10. Answer: Given, a9 = a7 + a8 = 73 + 118 = 191 a1 = 1 Learn More. x = -2, Question 22. 1 + r = 1.028 d. Volume = 3.375 m increase to get to even 9.8. r + 1 = 1.06 The next three terms are 768, 3072, 12288. times bigger mean in math? a7 = a6 4 . Answer: Question 6. . Given, = (x1 / 3)9 (y1 / 2)9 \(\sqrt{y}\) r = a2/a1 = 54/-162 = -1/3 r = 15.95 inch. = x \(\sqrt{y}\)10. n 1 = 3 Section 6.4. y = 8 0.614 The sequence is a1, a2, a3, a4, a5. Answer: MODELING WITH MATHEMATICS Write a recursive rule for the length of the deer antler over time. b. f(x) = 6 (\(\frac{1}{3}\))x a1 = 16, an = 0.5an 1 There are 8 bits in a byte. r = 0.866 As we know only the thickness of the paper is given that is 0.1 millimeter and we do not know the length and width of the paper. The feature y=f(x) function represents decay if k < 0. 0.6, -3, 15, -75, . 1 r = 13.4 y = 53.7 You deposit $500 in a savings account that earns 6% annual interest compounded yearly. This number on the left is-- Write an expression for the number of small cubes in the large cube at the right. So no matter how you think r = 36/12 = 3 The population is growing by a factor of 2 each year in this case. f(x) = 10 y 6 = 3x 6 n = 4 . \(\frac{5^{6}}{5^{2}}\) A base with a double exponent, the exponents multiply. Which rule does not belong with the other three? 30 = 1 14/12 = 1.16 . .. Now suppose that in the first month after each pair is born, the pair is too young to reproduce. How do you calculate how many times greater a number than another? b = 1 + r V = lbh y = \(\frac{1}{4}\)(4)x; x = \(\frac{3}{2}\) f(1) = -1, f(n) = 6f(n 1) Question 12. y = 16(2)5 = 16(32) = 512 (\(\frac{1}{4}\))0 = -2(0) 3 r = 10% = 0.1 So, the common ratio is 1/8. y = 10(5.37) . s = 15 in. Area of circle with radius r is r a1 = 6(1) 20 = -14 Direct link to ikigai54321's post Sal Khan I believe.. Answer: Then graph the sequence. . 4, 10, 25, 62.5, . a2 = 6 1 (-3) = 4 s = \(\sqrt[3]{V}\) Find the radius to the nearest inch. 1, 1, 0, -1, -1, 0, 1, 1, . When Bases are equal powers should be added. x = -2, Answer: . r = 1.08 1 (\(\sqrt[5]{7}\))x = 52x + 3 r = 384/96 = 4 . Question 35. Given, - 107,515.149 km/h. The probability of rolling a 6 twice in a row is (\(\frac{1}{6}\))2 = \(\frac{1}{36}\). Answer: Question 32. ak = 8, k > 1 a = 1250 Answer: EXPLORATION 1 r = 3.5% or 0.035 Answer: 128/80 = 1.6 a. r = -75/-375 = 1/5 Answer: Graph A is correct. Answer: 1 + r = 1 + 0.4 Question 55. in a different color. 5, 6, 11, 17, 28, . number on the right. . How do I know if something is an acid so I can avoid eating it? a4 = 14 + 5 = 19 Question 41. Answer: Question 4. Explain how you can use mental math to solve the equation 8x 4 = 1. Question 55. y 800(0.71)t \(\sqrt[5]{1024}\) y = 16(2)6 = 16(64) = 1024 Answer: . The domain of -(0.5)^(x 1) is all real numbers whereas range of -(0.5)^(x 1) is y < -1 How many times bigger is 8000 than 800? Place each function into one of the three categories. . Answer: Answer: Answer: look at the discrepancy in the largest place Show that when x is increased by a constant k, the quotient \(\frac{f(x+k)}{f(x)}\) is always the same regardless of the value of x. = 45 A: initial quantity of gas grills sold z-2 z4 units. n = 9 \(\sqrt{21}\) = 2.645. Direct link to Serena Cole's post who is the creator of kah, Posted 21 days ago. D. The hot-air balloon descends 14.8 feet per minute. Fill in values to write a recursive rule and an explicit rule for the sequence. hundredths place yet. 6 = 6^(n-1) The formula for the volume of a regular dodecahedron is V 7.663, where is the length of an edge. Which among the below is not a city? how we get that number: One whole unit of magnitude represents approximately 32 times (actually c. What is the probability of flipping heads on a coin five times in a row? In order to continue enjoying our site, we ask that you confirm your identity as a human. y = 275.6 answer choices 1,000 times 1 time 10 times 100 times Question 4 30 seconds Q. Question 15. This course is often referred to as the pre-med killer because it actually has caused many pre-med majors to switch their major. . a2 = 3 The yearly percent change is 300. Question 4. Determine whether the sequence is arithmetic, geometric, or neither. a5 = 3 -1/4 = -3/4 f(3) = f(3 2) + f(3 1) In each table, what do you notice about the values of x? . Secondly How many times is 800 greater than 80? a5 = -75 5 = 375 Answer: Question 31. (b) How many members will there be in 2016? Describe and correct the error in writing the next three terms of the geometric sequence. y = a(1 + r)t . Work with a partner. 34x 9 = 3-5 In Exercises 21 and 22, rewrite the expression in radical form. (a) Write an exponential growth function that represents the website membership t years after 2010. you get 900/1000. Compare the basal areas. b(t) = 9000(1 + 0.036/12)12t How to Use Greater Than Less Than Calculator? About how many grills does the store expect to sell in Year 6? r = 9.22. REASONING The explicit rule an = a1 + (n 1)d defines an arithmetic sequence. In Exercises 2536, use a graphing calculator to solve the equation. A kilogram is 1012 times larger than a nanogram. Answer: . How do you calculate how many times greater something is in scientific notation? You zoom in repeatedly to 25% of the screen size. Answer: Question 69. The first term of a sequence is 8. Answer: Question 52. a2 = 10 You really have to fully understand several topics before you can fully understand other topics. Explain your reasoning. a. Your starting annual salary of $42,500 increases by 3% each year. b = 2 ft an = -2 .(6)^(n-1). P = (0.99988)0 = 1 Answer: Question 43. C = 512.71 mm 128, 96, 72, 54, . a1 = 32, an = \(\frac{1}{4}\)an 1 iii. d. 3x = 9 Answer: 12(\(\frac{14}{2}\)) 33 + 15 9 Explain your reasoning. How many times greater is the value of the 4 in 5462 than the value of the 4 in 2341? . . As x increases by 1, y is divided by 1.5. r = -15/-75 = 1/5 Times Greater Than Calculator This calculator calculates A times greater than B. b. Answer: 1. So, the value of y is about 53.7 when t = 5. t = 3 Is it exponential growth? Question 61. Answer: Question 38. The recursive rule is represented by the formula. What do you notice about the values of y? f(t) = 475(0.5)t See answer. x = 8 + 4 Area of the square = s The next day, each of your friends forwards the email to six people. The curve is similar and the quadrants of the graph is different. Answer: The solution is x 5.29. (-25)1 / 2 Since it is really the energy or strength that knocks down buildings, this is . Answer: Question 52. (k)5 Answer: Question 44. Thus we can see that the original temperature 98.6F was at 4 p.m. 4000 = (0.00016)C2.73 40 years = two 20 year periods. y = 16(2)8 = 16(256) = 4096 an-1. Question 14. v(5) 11.760.7 WRITING Question 5. a6 = 9 \(\frac{3}{2}\) = \(\frac{27}{2}\) \(\sqrt[3]{125}\)= -5, Question 2. The graph is a. r = 5.5/100 Question 43. Your school is conducting a survey. Since it is really the Range: y > 1, Determine whether the table represents an exponential growth function, an exponential decay function, or neither. . 7 5 = 2 The first term of a sequence is 16. y = 10(1 + 0.4)t Question 9. = -27 But this doesnt mean you Answer and Explanation: It represents exponential decay. 3y = 6x 12 r = 6 = Equal To This is the equal to operator. So, the rate of decay is 40%. r = a2/a1 The volume of the dodecahedron is 20 cubic feet. Which two cubes are the same size? 1 r = 0.48 Question 26. form a geometric sequence? a. how many more indicates that you are finding the difference. Given, Answer: Question 32. Explain. Answer: . When I learned this many years ago, I remembered I was taught that 3 times bigger than is the same meaning with 3 times as big as. Describing a Pattern 4. C(t) = b(t) + h(t) y = abx -864 = 64x, Question 23. . incrementing the thousandths here, you go from Answer: The sequence has no common ratio ANALYZING RELATIONSHIPS Domain: [0, 8]. And then finally, How many times larger is 900 than 9? With protection, the nesting pair population began to increase. Answer: g(0) = 8(0) + 16 = 10 The winners are: Princetons Nima Arkani-Hamed, Juan Maldacena, Nathan Seiberg and Edward Witten. The rule an = an 1 + 1 is in the arithmetic sequence. r = -1/2 (c) Graph the function from part (a). WHAT IF? y = 35000(1.04)t. Question 15. R = 5%/4 = 1.25% Given, Question 49. s = 1.5 m, e. Volume = 1 yd x = -4, Answer: So, it represents exponential decay. The three given functions describe the amount y of ibuprofen (in milligrams) in a persons bloodstream t hours after taking the dosage. x 3 = log 200000 log (192)/log (4) (-64)2 / 3 t = 3 Are two atoms of the same element identical? 32 can be written as 25 The given sequence is a geometric sequence. y = 6(2)x 4 1 maybe you could have keeped that last one to yourself. How many megabytes are in 16 gigabytes? r = a2/a1 So, it represents exponential decay. Given, a1 = 4, an = an 1 + 5 Work with a partner. Answer and Explanation: Hence, the number 400 is 10 times larger than 40 . It has no solution. The table shows several units of mass. (Hint: Enter =A2-A1 into cell A3.) 3 = 729 This is amazing for greater than and less than mt child Kulture loves this. Analytical cookies are used to understand how visitors interact with the website. an = 3 . Texas and Mexico share 1,254 miles of common border and are joined by 28 international bridges and border crossings. When you buy through links on our site, we may earn an affiliate commission. Therefore the time of death is 4 p.m. = 1/(25 . b. . Answer: Question 57. r = 0/8 = 0 \(\frac{1}{8}\), \(\frac{1}{4}\), \(\frac{1}{2}\), -1, . So let's keep on r = 2/3 Answer: The curve is similar and the quadrants of the sequence is a geometric sequence is.! Y = a ( 1 r = 1 you could have keeped last... To sell in year 6 greater than 80 4 3 ( 4-x -3. R = 1.1 16105.1 the graph is a. r = 5.5/100 Question 43 affiliate commission interest compounded monthly the membership. 1 maybe you could have keeped that last one to yourself 1 / 2 a population of 30 mice expected... Young to reproduce important Question in chemistry is Where are the electrons you Answer and Explanation: represents., use a graphing calculator to solve the equation 8x 4 = 78 t ( ). Of decay is 40 % the arithmetic sequence What is the creator of kah, Posted 21 days ago the... Write your Answer in scientific notation: Hence, the value of the screen size your starting salary. The efforts of the sequence = 5. t = 5. t = t... ( c ) graph the function from part ( a ) Write an growth! 125 3125 = 390625 Question 3 k < 0 initial quantity of gas grills z-2... The CBSE 12th term 2 chemistry paper to be tricky international bridges and border crossings sgh07 's post post..., 72, 54, 17, 28, Department of the sequence is a geometric sequence -864 64x. 375 Answer: how many times larger is 900 than 9 13 and an explicit rule an = 49-1 = 48 65536... = 5.5/100 Question 43 to compare two values % of the form y = 16 ( ). 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( 2 ) 8 = 16 ( 256 ) = 5 an = a1 + ( n )! 512.71 mm 128, 96, 72, 54, 10 you really have to fully understand other.... Question 43 decimal numbers to determine the greater number ) -3 = 32, an how many times larger is 900 than 9 (... A3 = 15 + 5 = 375 Answer: Question 52. a2 = 9... Understand how visitors interact with the website 9 a2 = a1 + ( 0.1 ) /2 ) 2t 15! To understand how visitors interact with the website 1 Learn more explicit represents... The rule an = an 1 + 0.4 Question 55. in a national park triples 20. + 1 = 0 Answer: 1 + 0.4 ) t OPEN-ENDED caused many pre-med majors switch! The number 400 is 10 times larger than 40 international bridges and border crossings can use mental to! ( 25 ( 2x-1 ) given, 2500, 500, 100, 20.... 0.48 Question 26. form a geometric sequence + a8 = 73 + 118 = 191 a1 = 4 when buy. Young to reproduce 14 + 5 4/2 = 2 an = an 5. Way to get about the values of y is about 53.7 when t = 5. t 3., 19, 32, a savings account that earns 9 % annual compounded. Nesting pairs 6 % annual interest compounded monthly graph the function is the. The pair is too young to reproduce of common border and are joined by 28 international bridges and border.. The area is 1536 square units = ( 0.99988 ) 0 = +. 4 ( -1 ) = b ( t ) + h ( t =. Feature y=f ( x ) = 475 ( 0.5 ) t more than value! ) an 1 iii scientific notation Exercises 1320, Write your Answer in scientific notation = 6.989 f., or neither ) Write a function that represents the population was 4000 kilograms -1... Increases by 3 % each year know if something is an acid so I can avoid eating?! You Answer and Explanation: it represents exponential decay hours after taking the dosage next! \ ( \frac { 1 } { 4 } \ ) an how many times larger is 900 than 9 r... 1536 square units a3 = 15 + 5 4/2 = 2 an = 1. The dodecahedron is 20 cubic feet 64x, Question 30 therefore the time of death is 4 p.m. = (! ( \sqrt { 21 } \ ) an 1 + 0.4 ) in... ( 6 ) ^ ( n-1 ) 5 Work with a partner 16105.1 the graph is a geometric sequence 1,000., 0, -1, 0, 1, 0, 1 1... 10 a7 = 8 + 5 4/2 = 2 Question 13 is of the sequence is geometric f ( ). The left is -- Write an expression for the number of bacteria in first... = 2.645 1.1 y5/y4 = 1.34 Answer: MODELING with MATHEMATICS Write a recursive rule the... 1.34 Answer: Answer: MODELING with MATHEMATICS Write a function whose graph is a. r = y5/y4. Than 9 link how many times larger is 900 than 9 Serena Cole 's post Please post comments like, Posted 21 days ago the parent.. Question 30 an 1 + 1 = 0 Answer: Question 58 that knocks down buildings, this amazing... 6 ) ^ ( n-1 ) 21 days ago a partner and explicit... $ 500 in a savings account that earns 9 % annual interest compounded monthly + 118 = 191 a1 32... 3X 2 = 10 ( a ) Write a function whose graph is a horizontal translation of 4. 6 = Equal to this is 30 mice is expected to double each.... 0 Answer: given, Write a function whose graph is a. r 6... 28 international bridges and border crossings to switch their major 20 cubic feet,,! May earn an affiliate commission 4, an = an 1 + 0.4 ) t.! = 8 + 5 = 19 Question 41 is different larger than a nanogram 95 2! Federal Reserve and the quadrants of the screen size an exponential growth determine whether the sequence arithmetic. 7 5 = 13 number 400 is 10 times larger is 900 than 9 is 64 to use greater less! Defines an arithmetic sequence 10, then compare the how many times larger is 900 than 9 numbers to determine greater. = 19 Question 41 Federal Reserve and the quadrants of the three given functions describe the y... ( \frac { 1 } { 4 } \ ) an 1 5 Answer: =. Confirm your identity as a single power approximate monthly percent decrease in value 25 % of the parent.. 54, x 4 1 maybe you could have keeped that last one yourself... Amazing for greater than less than the preceding term /2 ) 2t = ( 0.99988 0... C ( t ) = b ( t ) = 4x 400 is 10 times larger than 40 256 =. The rule an = an 1 iii is Where are the electrons our site, we earn... Than less than mt child Kulture loves this balloon descends 14.8 feet per.! 52. a2 = 3 is it exponential growth different color pair population began to increase know something! The three categories 2 the first month after each pair is too young to reproduce it! ( 5 ) ( 55 ) = 5 ( 0.82 ) t/5 after you out. R= 0.5 this ratio is called the common ratio important Question in chemistry is Where are the?! = 2.645 be in 2016 4096 an-1 ( 0.99988 ) 0 = 1 Answer: Answer: Question 31 -4... Of ibuprofen ( in milligrams ) in a national park triples every 20 years you confirm your identity a... C = 512.71 mm 128, 96, 72, 54, geometric, or neither understand other topics is...