Use the sequence below to answer parts a and b (8,17,26,35,44,53,...) Create an explicit formula to determine the 12th term of the sequence Create a recursive formula to prove the 7th term is 62.
Answers
The explicit formula for the sequence (8, 17, 26, 35, 44, 53, ...) is 8 + (n-1) * 9, and the 12th term can be found by substituting n = 12. The recursive formula for the sequence is a1 = 8 and an = an-1 + 9. Using this recursive formula, we can verify that the 7th term is indeed 62.
Explanation:To create an explicit formula for the sequence (8, 17, 26, 35, 44, 53, ...), we notice that the difference between each term is 9. So, the explicit formula for the sequence is 8 + (n-1) * 9, where n represents the position of the term in the sequence. Using this formula, we can find the 12th term by substituting n = 12: 8 + (12-1) * 9 = 89.
To create a recursive formula to prove that the 7th term is 62, we observe that each term is the previous term plus 9. So, the recursive formula for the sequence is:
a1 = 8an = an-1 + 9Using this recursive formula and starting with a1 = 8, we can find the 7th term as follows:
a1 = 8a2 = a1 + 9 = 8 + 9 = 17a3 = a2 + 9 = 17 + 9 = 26a4 = a3 + 9 = 26 + 9 = 35a5 = a4 + 9 = 35 + 9 = 44a6 = a5 + 9 = 44 + 9 = 53a7 = a6 + 9 = 53 + 9 = 62Therefore, the 7th term in the sequence is indeed 62.
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Related Questions
Doug got 8 out of 10 questions correct on a math quiz. If each question was worth the same number of points, and the test was worth 50 points total, what was Doug's score?
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There is 10 questions, which equal 50 points so, 50/10 = 5. And he got 8 of those 10 right so multiply 8 * 5 = 40 and that's how you get your answer
estimate the square root of 25
to the nearest integer
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The outside temperature was 73°f at 1.p.m and decreases at a rate of 1.5°f each hour. What expression can be used to determine the temperature h(h is the variable) hours after 1.p.m?
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The expression to represent the temperature 'h' hours after 1 p.m. given an initial temperature of 73°F and a decrease rate of 1.5°F per hour is 73 - 1.5h. This allows us to calculate the temperature at any given hour where 'h' is the number of hours after 1 p.m.
Explanation:The problem involves dealing with linear equations, specifically those representing changes over time. In this situation, the temperature starts at 73°F at beginning of the time, i.e., at 1 pm and then decreases at a steady rate of 1.5°F per hour.
So, the decrease in temperature can be represented by 1.5h, where h is the number of hours elapsed since 1 p.m. As the temperature starts at 73°f, we subtract this decrease from the initial temperature. Therefore, the expression to determine the temperature after h hours is 73 - 1.5h.
This equation tells us that for each hour after 1 p.m., we simply subtract 1.5 from 73 and this would give the temperature at that time. For example, at 2 p.m., h equals 1, and the equation 73 - 1.5(1) gives us 71.5°F.
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to package and ship an item, it cost $5.75 for the first pound and $0.75 for each additional pound. Find the 12th term and explain what it represents.
Answers
The 12th term represents the cost of packaging and shipping a 12-pound item, which is $14.
To find the 12th term in this sequence, we first need to understand what the sequence represents. In this case, it's the cost of packaging and shipping items based on their weight.
Let's break down the formula:
For the first pound, the cost is $5.75.
For each additional pound beyond the first, the cost is $0.75.
So, the sequence represents the cost of packaging and shipping items weighing 1 pound, 2 pounds, 3 pounds, and so on.
To find the 12th term:
[tex]\[ \text{Cost} = \$5.75 + (n - 1) \times \$0.75 \][/tex]
Where ( n ) is the weight of the item.
For the 12th term:
n = 12
[tex]\[ \text{Cost} = \$5.75 + (12 - 1) \times \$0.75 \][/tex]
[tex]\[ \text{Cost} = \$5.75 + 11 \times \$0.75 \][/tex]
[tex]\[ \text{Cost} = \$5.75 + \$8.25 \][/tex]
[tex]\[ \text{Cost} = \$14 \][/tex]
So, the 12th term represents the cost of packaging and shipping a 12-pound item, which is $14.
△EFG≅△JKL. What is m∠K? Enter your answer in the box. ° Two same size triangles. Triangle L J K and triangle E F G. angle F is 62 degrees. Angle G is 53 degrees.
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m∠E = m∠J , m∠F = m∠K , and m∠G = m∠L.
m∠K = 62°
Problems 7and 8 50 POINTS
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Answer:
To find the area of a rectangle, you do Length times width. 11 times 8 equals 88, so the width would have to be 8. To find the perimeter, you add up all of the sides. If the width is 8, and the perimeter is 46, 8+8=16 and 48-16 = 30 then the length is 15.
Solve the equation. 2x + 4 = 3x – 2 6 7 3 –2
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-x=-6
x=6
x will be 6
The sum of two consecutive even integers divide by four is 189.5
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The sum of a number and 14 is less than or equal to three times the number
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***
the sum means add....so the sum of a number and 14 is 14 + x
is less then or equal....< =
3 times the number....3x
in order to solve
subtract x on both sides
14≤2x
divide by 2 on both sides
7≤x
Write an expression that shows how to multiply 7 ×256 using expanded form and distributive property
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The distributive property is a property of multiplication that states that if you have two terms a and (b+c) multiplied together, their product is the same as ab+ac; the a is distributed multiplicatively to the b and the c.
Putting 2 and 2 together, this question wants us to take the expanded form of 256 (200+50+6), and use the distributive property to find:
[tex]7 \times(200+50+6)[/tex]
Can you use the definition of the distributive property above to find the product?
I don't understand this. Please help!:::: Provide an answer for a, b, c, and d.
Answers
The reason why we know that angle A and angle D are congruent is because they are both right angles. By the right angle congruence theorem (the reason just below the blank for part A), we can say that angle A = angle D. They are both 90 degree angles.
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Answer for the blank in part B is "Given" without quotation marks of course. This is the first "given" while the second given is coming up in part C
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For part C, the other given is [tex]\angle C \cong \angle F[/tex] so that's what will go in the blank. It may seem silly, but all we're doing is repeating verbatim what is given to us. With any proof, you always start with what you are given and somehow connect it with what you're trying to prove
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Finally, the answer for the blank in part D is "AAS Congruence Theorem" (without quotes)
The AAS congruence theorem allows us to prove two triangles congruent if we know if two pairs of angles are congruent plus if we know two sides are congruent as well.
The angle portions are covered by part A and part C. The side portions are part B's territory. Combining A, B, & C allows us to use the AAS theorem
Note: It is NOT the ASA theorem because the two angles do not sandwich the sides. In other words, the side AB is not between the two angles A and C. Similarly, DE is not between the two angles D and F. The order is very important as ASA is slightly different than AAS.
how many 1/8 cups are there in 1/4 cup?
Answers
To figure out how many 1/8 cups are in a 1/4 cup, we execute a division of fractions. This problem can be rewritten as 1/4 divided by 1/8, then inverted to 1/4 multiplied by 8/1, which equals 2. Therefore, there are 2 1/8 cups in a 1/4 cup.
Explanation:To find out how many 1/8 cups are there in 1/4 cup, you need to understand concept of fractions and their division. In this case, we want to know how many times 1/8 goes into 1/4.
We could write this as a division problem, 1/4 ÷ 1/8. Division of fractions involves flipping the second fraction (1/8) and multiplying instead. So, 1/4 divided by 1/8 becomes 1/4 multiplied by 8/1.
This results in the fractions giving us 2.
Therefore, there are 2 1/8 cups in a 1/4 cup.
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If 3 pieces of candy costs $2.10 how much would four pieces cost?
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Hope this helps.
Each Piece costs .07 cents. Found this out by dividing 2.10 by 3. Then add .07 to 2.10 :)
1. How is the valuation of current assets affected if the company follows IFRS?
a. Valuation is based on historical cost.
b. Valuation is based on market adjustments.
c. Valuation is based on LCM accounting.
d. Assets are expensed immediately.
2. Many of the accounting standards in GAAP for current asset accounts are _________ with the international standards.
a. converged
b. accordant
c. accrued
d. converted
3. Unearned subscription revenue occurs on the balance sheet as a
a. long term asset
b. long term investment
c. current asset of long term investment
d. current liablity of long term liablity
4. Interest payable is shown on the
a. income statement
b. balance sheet as a long term liablity
c. balance sheet as a current liablity
d. balance sheet as a long term asset
Answers
Many of the accounting standard in GAAP for surrent assets account are converted with the international standards. The answer is D.
Unearned subscription account usually occur on the balance sheet as a current liability of long term liability. The answer is D.
The interest payable is always shown on the balance sheet as a current liability. The answer in this question is C.
The wildflowers at a national park have been decreasing in numbers. There were 300 wildflowers in the first year that the park started tracking them. Since then, there have been one fourth as many new flowers each year. Create the sigma notation showing the infinite growth of the wildflowers and find the sum, if possible.
Year
New flowers
1
1200
2
300
3
75
Answers
The sigma notation would be:
∑ (from n=1 to ∞) 4800 * (1/4)ⁿ , where n is the year.
Remember that this notation should give us the sum of all new flowers from year 1 to infinite, and the values of new flowers for each year should match those given in the table for years 1, 2, and 3
This means the total number of flowers equals:
Year 1: 4800 * 1/4 = 1200 ]
+
Year 2: 4800 * (1/4)² = 300
+
Year 3: 4800 * (1/4)³ = 75
+
Year 4: 4800 * (1/4)⁴ = 18.75 = ~19 (we can't have a part of a flower)
+
Year 5: 4800 * (1/4)⁵ = 4.68 = ~ 5
+
Year 6: 4800 * (1/4)⁶ = 1.17 = ~1
And so on. As you can see, it in the years that follow the number of flowers added approaches zero. Thus, we can approximate the infinite sum of new flowers using just Years 1-6:
1200 + 300 + 75 + 19 + 5 + 1 = 1,600
The sales tax rate is 8.2%. Estimate the sales tax on a computer that costs $550.
about $40
about $36
about $32
about $44
Answers
The sales tax on the computer is $45.10.
Explanation:The sales tax (x) on the computer can be expressed by the equation:
x=550×8.2100
x=5.5×8.2
x=45.1
Can you give me some problem that’s as to do with slope or rise over run as many as you want plz I need to study for a test that is tomorrow
Answers
Answer:
hi im also doing it
Step-by-step explanation:
some 4 u to do
tell me answer after ur done
could someone help me please
Answers
________________________________________________________
Explanation:
______________________________________________________
V = (4/3) * [tex] \pi [/tex] * r³ ;
Given: [tex] \pi [/tex] = 3.14 ;
r = 9 cm ;
____________________________
Solve for "V" ;
V = 3.14 * (9 cm)³ ;
= 3.14 * 729 cm³ ;
= 2289.06 cm³ ; which is: Answer choice: [D]: "2289.06 cubic centimeters" .
___________________________________________________________
441 is 63% of what number????????????????????????????? help
Answers
Which of the following statements could be true when a transversal crosses parallel lines? Select all that apply.
Several congruent angles are formed.
Vertical angles are formed.
Complementary angles are formed.
Supplementary angles are formed.
Obtuse angles are formed.
Answers
Answer:
Several congruent angles are formed. Vertical angles are formed. Supplementary angles are formed. Obtuse angles are formed.
Step-by-step explanation:
Final answer:
When a transversal crosses parallel lines, several congruent angles and vertical angles are formed, and supplementary angles can occur; whereas complementary angles are not a necessity, and obtuse angles depend on the transversal's orientation.
Explanation:
When a transversal crosses parallel lines, several geometrical properties are observed that result in certain types of angles being formed. Let's explore these in detail:
Several congruent angles are formed because when a transversal cuts through parallel lines, corresponding angles are congruent, as are alternate interior angles and alternate exterior angles.
Vertical angles are also formed at the points where the transversal intersects the parallel lines. These vertical angles are always congruent.
Supplementary angles are formed when two angles add up to 180 degrees. This is often true for consecutive interior angles on the same side of the transversal.
However, complementary angles, which add up to 90 degrees, are not necessarily formed when a transversal crosses parallel lines. The formation of obtuse angles is possible depending on the orientation of the transversal.
could you please find what x=
for both of them please
thank you
Answers
Add 23 to both sides
8x=3x+45
Subtract 3x from both sides
5x=45
Divide both sides by 5
X=9
X+10+x+14=22
Add like terms
2x+24=22
Subtract 24 from both sides
2x=-2
Divide both sides by 2
X=-1
What is three fourths plus two thirds?
Answers
hope this helpes
1 [tex] \frac{5}{12} [/tex]
Explanation:
[tex] \frac{3}{4} [/tex] + [tex] \frac{2}{3} [/tex]
Make the denominators equal by finding the least common factor:
([tex] \frac{3}{3}[/tex] • [tex] \frac{3}{4} [/tex]) + ([tex] \frac{4}{4}[/tex] • [tex] \frac{2}{3} [/tex])
[tex] \frac{9}{12} [/tex] + [tex] \frac{8}{12} [/tex]
9 + 8 = 17
[tex] \frac{17}{12}[/tex] can be simplified to 1 [tex] \frac{5}{12} [/tex]
On Thursday after work, the number of cars in a parking lot decreased at a steady rate of 13 cars every 2 minutes. Which rational number describes the number of cars per minute?
Answers
Answer:
Required ration which represent the situation = [tex]\frac{-13}{2}[/tex]
Step-by-step explanation:
Given: Cars in parking lot decreases at rate of 13 cars every 2 minutes.
To find: Rational Number which represent given information
Rational Number is a number in form of [tex]\frac{p}{q}[/tex] where p be any integer and q is non zero integer.
So from given information
No of cars decreases in 2 minutes = 13 cars
So, No of cars decreases in 1 minute = [tex]\frac{13}{2}[/tex]
Therefore rate at which cars decreasing in parking lot is [tex]\frac{13}{2}[/tex] cars/min.
Since it is decreasing, ration which represent it must be equal to [tex]\frac{-13}{2}[/tex]
Therefore, Required ration which represent the situation = [tex]\frac{-13}{2}[/tex]
An amusement park sells child and adult tickets at a ratio of 8:1. On Saturday, they sold 147 more child tickets that adult tickets. How many tickets did the amusement park sell on Saturday?
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Calculate the surface of the cube.
Answers
Select all the expressions that are equivalent to the polynomial below.
(4x+5)(-3x-1)
A (-16x2 + 10x - 3) + (4x2 - 29x - 2)
B 3(x - 5) - 2(6x2 + 9x + 5)
C 2(x - 1) - 3(4x2 + 7x + 1)
D (2x2 - 11x - 9) - (14x2 + 8x - 4)
E (-15x2 + 9x - 10) + (3x2 - 10x - 5)
F (4x2 - 13x - 7) - (16x2 + 9x - 5)
Answers
Answer:
Options A,C and D
Step-by-step explanation:
(4x+5)(-3x-1) = -12x²-19x-5
Option A:
(-16x² + 10x - 3) + (4x² - 29x - 2) = -12x²-19x-5
Option A is correct.
Option B:
3(x - 5) - 2(6x² + 9x + 5) = -12x²-15x-25
Option B is wrong.
Option C:
2(x - 1) - 3(4x² + 7x + 1) = -12x²-19x-5
Option C is correct.
Option D:
(2x² - 11x - 9) - (14x² + 8x - 4) = -12x²-19x-5
Option D is correct.
Option E:
(-15x² + 9x - 10) + (3x² - 10x - 5) = -12x²-x-15
Option E is wrong.
Option F:
(4x² - 13x - 7) - (16x² + 9x - 5) = -12x²-22x-2
Option F is wrong.
Find the equation of a line that intersects with y=2x-1 on the y-axis and is parallel to y=-x.
Please explain.
Answers
The equation of the required line is: y=-x-1.
y=2x-1 is in slope intercept form. So the y-intercept = -1.
Given that the line intersects with y=2x-1 on the y-axis. It means the required line also has y-intercpt =b= -1.
Given that: The line is parallel to y=-x.
The slope of y=-x is -1. By comparing with y=mx+b.
Since the lines are parallel. So the required line will also have slope = m= -1.
So the equation of the required line is: y=mx+b or y = -1x + (-1) or y=-x-1.
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I would only like help with these two questions can someone please help me? :)
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x is the numbers across the bottom and Y is the numbers on the sides
coordinates are written (x,y)
so for 1. A is at (1,3) B is (0,5) you can find the rest
for number 2
(2,1) is D, (3,1) is F you can find the rest.
Help me please
If you help me I would appreciate it a lot
Answers
7. 4(8)-2(3)= 26
8. (3/4) (8) (6) ÷ 3= 12
9. 2 (3/4) (6) + 8= 17
10. 6 (1/2) + 8 (3/4)= 9
17. 5(6) + 8(1/2)= 34
18. 2 ( 3×8+6) ÷ ( 10*3)= 2
19. (8+6) ÷ 1/2= 7
20. 3(6) - 2(8)= 2
Please vote my answer brainliest. thanks!
Plsss helppppppp plsssss
Answers
h 24 ft 4
----- = ---------- = ---
4 6 ft 1
Cross multiplying the 1st and 3rd fractions, we get h=16 ft (answer)