Answer:
5 (x - 2)
Step-by-step explanation:
1. Factor by grouping
5 (x - 2)
This is the answer.
I hope this helps :)
A geometric sequence is given by the recursive rule $a_1=\frac{2}{3},\ a_n=3a_{n-1}$ . Give an explicit rule for the nth term of the sequence $b_1,\ b_2,\ b_3,\ \dots\ ,$ given that $b_1=a_1,\ b_2=a_3,\ b_3=a_5,\ \dots$ .
Answer:
[tex]b_n = \frac{2}{27} (9^n)[/tex]
Step-by-step explanation:
Given
[tex]a_1=\frac{2}{3},\ a_n=3a_{n-1}.[/tex]
Required
An explicit rule for [tex]b_1,\ b_2,\ b_3,\ \dots[/tex]
Where [tex]b_1=a_1,\ b_2=a_3,\ b_3=a_5,\ \dots[/tex]
We have:
[tex]a_1=\frac{2}{3},\ a_n=3a_{n-1}.[/tex]
Calculate a2
[tex]a_2 = 3a_{2-1}[/tex]
[tex]a_2 = 3a_1[/tex]
[tex]a_2 = 3 * \frac{2}{3}[/tex]
[tex]a_2 = 2[/tex]
Calculate a3
[tex]a_3 = 3a_{3-1}[/tex]
[tex]a_3 = 3a_2[/tex]
[tex]a_3 = 3 *2[/tex]
[tex]a_3 = 6[/tex]
Calculate a4
[tex]a_4 = 3a_{4-1}[/tex]
[tex]a_4 = 3a_3[/tex]
[tex]a_4 = 3*6[/tex]
[tex]a_4 = 18[/tex]
Calculate a5
[tex]a_5 = 3a_{5-1}[/tex]
[tex]a_5 = 3a_4[/tex]
[tex]a_5 = 3*18[/tex]
[tex]a_5 = 54[/tex]
So:
[tex]b_1=a_1,\ b_2=a_3,\ b_3=a_5,\ \dots[/tex]
[tex]a_1=\frac{2}{3}[/tex] [tex]a_3 = 6[/tex] [tex]a_5 = 54[/tex]
The above sequence form a geometric sequence.
Calculate common ratio (r)
[tex]r = \frac{b_3}{b_2}[/tex]
[tex]r = \frac{a_5}{a_3}[/tex]
[tex]r = \frac{54}{6}[/tex]
[tex]r = 9[/tex]
So, the explicit formula is:
[tex]b_n = b_1 * r^{n-1[/tex]
[tex]b_1=a_1[/tex], so:
[tex]b_n = a_1 * r^{n-1[/tex]
[tex]a_1=\frac{2}{3}[/tex], so:
[tex]b_n = \frac{2}{3} * 9^{n-1[/tex]
Split:
[tex]b_n = \frac{2}{3} * \frac{9^n}{9}[/tex]
[tex]b_n = \frac{2}{3*9} (9^n)[/tex]
[tex]b_n = \frac{2}{27} (9^n)[/tex]
The explicit rule is: [tex]b_n = \frac{2}{27} (9^n)[/tex]
Mr. Hoosier has gathered all these data about his finances.
Salary $159,000
Taxable interest $5600
Municipal Bond interest $15,000
Total Itemized deductions $9500
The personal exemption is $4700. The standardized deduction for a single filer is 5000.
Answer:
1. His tax is $37,490.
2. His average effective tax rate is 22%
3. His average tax rate is 24.93%
4. His marginal tax rate is 35%.
5. His tax liability will fall by $170
6. His tax liability will fall by $500.
Step-by-step explanation:
Note: This question is not complete. See the attached pdf file for the complete question.
The explanation of the answer is now given as follows:
1. What is his tax?
Note: See the attached excel for Mr. Hoosier's Tax Computation Based on the Tax Table in the question.
From the attached excel file, the Net tax is $37,490 which is his tax.
Therefore, his tax is $37,490.
2. His average effective tax rate
His average effective tax rate = Tax / (Taxable income + Tax exempt income) = Tax / (Taxable income +Municipal Bond interest) = $37,490 / ($150,400 + $20,000) = 0.2200, or 22%
3. His average tax rate
Average tax rate = Tax / Taxable Income = $37,490 / $150,400 = 24.93%
4. His marginal tax rate
His marginal tax rate is 35% as in the tax computation used based on the tax table.
5. Assume he discovers that he is eligible for a 500 tax deduction. How much does his tax liability fall with that addition?
Taxable income = 150400 - 500 = $149,900
Based on the tax table in the question, we have:
Tax = 8850 + (149900 - 55000) * 30% = $37,320
Reduction in tax liability = $37,490 - $37,320 =$170
Therefore, his tax liability will fall by $170
6. Now he discovers that he is eligible for a $500 tax credit. How much does his tax liability fall due to this credit?
The purpose of the tax credit is to make tax liability reduced dollar by dollar.
Therefore, if he discovers that he is eligible for a $500 tax credit, his tax liability will fall by $500.
Joaquin walked exactly 3 _ 4 of a mile. According to the line plot, what is the difference between the distance Joaquin walked and the least distance any of the other students walked to school?
Answer:
The difference is [tex]\frac{3}{8}[/tex] mile
Step-by-step explanation:
The question is incomplete, as the line plot is not attached.
I will answer this question with the attached line plot.
From the question:
[tex]Joaquin = \frac{3}{4}[/tex]
From the attached line plot:
[tex]Least = \frac{3}{8}[/tex]
The difference (D) is:
[tex]D = Joaquin - Least[/tex]
[tex]D = \frac{3}{4} - \frac{3}{8}[/tex]
Take LCM
[tex]D = \frac{6 - 3}{8}[/tex]
[tex]D = \frac{3}{8}[/tex]
Hence: The difference is [tex]\frac{3}{8}[/tex] mile
Plz help !! 7th grade math !
can u guys give me kobe faimley fun facts PLZZ
Answer:
His father spent eight seasons playing in the NBA and an additional eight years playing professional basketball
Step-by-step explanation:
Factorise this pleasee
x2+ 11x+ 18
Answer:
[tex](x +9)(x+2)[/tex]
Step-by-step explanation:
Given the problem,
[tex]x^2 + 11x + 18[/tex]
Factor the problem. Find factors of (18) such that when added the result is (11).
[tex](x +9)(x+2)[/tex]
Test by distributing, multiply each term in one parenthesis by every term in the other parenthesis,
[tex](x+9)(x+2)\\\\x^2 + 2x + 9x + 18\\\\x^2 + 11x + 18[/tex]
Answer:
(x+9)(x+2) is your answer
Step-by-step explanation:
x2+ 11x+ 18
x²+9x+2x+18
x(x+9)+2(x+9)
(x+9)(x+2)
The largest three-digit multiple of 6 ?
Answer:
Step-by-step explanation:
100 is the smallest three-digit number. 999 is the highest three-digit number. 102 is the smallest three-digit number divisible by six. 996 is the largest three-digit number divisible by six.
Answer:
744Step-by-step explanation:
The largest 3-digit multiple of 6 that uses digits 4 and 4.
The multiple of 6 is an even number which is divisible by 3.
Numbers are only divisible by 3 if the sum of the digits is divisible by 3.
We have 4 + 4 = 8 and the largest digit to add is 7.
744 is the largest possible number.Proof:
744/6 = 124Which of the following equations has infinitely many real solutions?
A. 2(x - 7) = 2x + 14
B. 2(x - 7) = 2x – 14
C. 2x + 1 = 2x - 1
D. 2x + 1 = x - 1
Answer:
B - 2(x -7) = 2x - 14
Step-by-step explanation:
If you expand this equation, you get 2x-14 = 2x-14. This means that the equation will be true for any x, and has infinitely many solutions
Hopefully this helps! Let me know if you have any questions
I need help I would appreciate it if u would help me with this problem :)
Answer:
The answer is letter A.
Step-by-step explanation:
The amount that each company charges per hour on the pool is known, however the amount of hours they will be working is not, and is needed to distinguish which company is cheaper. Therefore, the number of hours is substitued by x and it is right next to the amount they charge for each hour. To find what each company charges, you must sum up what they charge and what they charge per hour, times the hours they will have to work on it( which is unknown and by x).
Dr. McCoy, a veterinarian, noticed that she only had about 12 ounces of cat treats left. So, she bought a new 3-pound jar. If she uses about 6 ounces of cat treats every week, in how many weeks will she run out?
what is 80% of 25 help me
When an equation in one variable is solved using a system of equations, the solution is always the
of each intersection.
Answer:
When an equation in one variable is solved using a system of equations, the solution is always the x-coordinate of each intersection.
Step-by-step explanation:
Answer:
1st part: X Coordinate
2nd part: A and C
Step-by-step explanation:
See image for question.
Please show workings and diagrams.
Answer:
a) 16.4 m, 101°b) 6.22 m, 51 m²Step-by-step explanation:
Find the measure of angle Q:
50° + (180° - 130°) = 100°a) Find PR using the law of cosines:
PR = √(8² + 13² - 28*13*cos 100°) = 16.4 m (rounded)Find ∠P using law of sines:
16.4/sin 100° = 13/ sin Pm∠P = arcsin (13 sin 100° / 16.4) = 51° (rounded)The bearing of R from P is:
50° + 51° = 101°b)
Find the measure of h, the distance from Q to PR:
h/ PQ = sin Ph = PQ sin Ph = 8 sin 51° = 6.22 mFind the area of ΔPQR:
A = 1/2PR*hA = 1/2(16.4)(6.22) = 51 m²I don't really understand this
please answer asap!!!!
first answer will get brainliest
Answer:
The answer is C
Step-by-step explanation:
Answer: )D
Step-by-step explanation:
45% of c is 72. Find the value of c.. PLEASE IT IS DUE IN 5 MINUTES
Answer:
160
Step-by-step explanation:
72x100/45. Hope this helps
what is 30 = –5d – 5
Answer:
-7
Step-by-step explanation:
30=-5d-5
-5d=30+5
-5d=35
d=35/-5
d=-7
Carl Lock took out a simple interest loan at 12.75% interest for 12 months. His previous balance is $942.36.
What is his final payment if the loan is paid off with the next payment?
Answer:I believe it is $955.11
Step-by-step explanation:
Divide the interest by 12 (number of months) which comes to about $1.07 (rounded) multiply that by 12 which give you with how much the total interest is, add it by the total and boom
Franco earns $8 per hour at his after-school job. Last week, he received a paycheck of more than $168. If he worked for h hours that week, find all the inequalities that represent this situation.
a.) 8 x h > 168
b.) 8 > 22 x h
c.) 8 x h < 168
d.) h > 21
e.) h < 21
Answer: A and D
Step-by-step explanation:
if he earns $8 an hour and he got $168 and h= the hours then
h=8 x 21 = 168
Answer:
The other person is correct.
Step-by-step explanation:
The table and the graph below each show a different relationship between the same two variables, x and y:
How much more would the value of y be on the graph than its value in the table when x = 12?
150
300
450
600
y=360
Step-by-step explanation:
y goes up by 30 everytime and would start at 30 if X =1, so X x 30= y. 12 x 30= 360=y
Answer:
300 or B
Step-by-step explanation: give the other person brainliest
How can you tell if a pattern is quadratic or linear?
Answer: By finding the differences between the y-values, we can determine the degree of the model for the data.
If the first difference is the same value, the model will be linear.
If the second difference is the same value, the model will be quadratic.
Step-by-step explanation:
plzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz help i only need number 3
very urgent need help asap
Mrs. Williams has 7 gallon of juice left in a bottle. She pours an equal amount of
juice into 5 glasses to empty the bottle. Which model represents the fractional
amount of the gallon of juice in each glass?
20
LLLL
Answer:
1/20 of a gallon
Step-by-step explanation:
If she divides 1/4 into 5 glasses, the answer would be 0.05, or 1/20 gallons.
hii pls help i’ll give brainliest
Answer:
Disagree, Disagree, Agree
Step-by-step explanation:
Hope this helps! BTW I am in 6th grade doing 8th grade math so trust me if u want.
Given the following exponential function, identify whether the change represents
growth or decay, and determine the percentage rate of increase or decrease.
y = 70(0.96)
Answer:
it is a decay, it's value drops by 4%
Step-by-step explanation:
0.96 is less than 1 so it is a decay function.
1-0.96 = 0.04 so it drops at the rate of 4%
Can someone help me with this one problem!!!!
Answer: No
Step-by-step explanation: No because y is not the same as x.
Is 1/10 closer to 0 or 1/2 ?
Answer:
its much closer to 0
Step-by-step explanation:
1/2 is more 5/10 and 0 is 0/10
0 is one away from one and 5 is 4 away
help pls, fast to, thx
Answer:
∠b = 64°
Step-by-step explanation:
We know that a complete rotation is 360°, so:
∠b + 57° + 239° = 360°
∠b = 360° - 57° - 239°
∠b = 64°
Sierra has enough fencing to make three chicken coops shown each has the same perimeter which has the greatest area?
Answer:
Top left triangle has the greatest area
Step-by-step explanation:
Area of a triangle:
area = base × height / 2
a = bh/2
Top Left Triangle:
a = 6 × 5.2 / 2
a = 31.2 / 2
a = 15.6
Top Right Triangle:
a = 8 × 2.9 / 2
a = 23.2 / 2
a = 11.6
Bottom Left Triangle:
a = 2 × 7.9 / 2
a = 15.8 / 2
a = 7.9
Compare areas:
15.6 > 11.6 > 7.9
Find the value of x .
Answer:
98
Step-by-step explanation:
x+30+52=180
x+82=180
x=180-82
x=98