An arithmetic progression is a sequence that has a common difference between consecutive terms.
[tex]f(n) = 19 -6n[/tex] and [tex]f(0) = 19\\f(n) = f(n - 1) -6;[/tex] represent the same sequenceThe definition I will choose for f(20) is: [tex]f(20) = 19 - 6 \times 20[/tex].The 500th term is -1976.Question 6:
The recursive function is given as:
[tex]f(0) = 19\\f(n) = f(n - 1) -6;[/tex] for [tex]n \ge 1[/tex]
The definition of nth term is given as:
[tex]f(n) = 19 - 6n[/tex] for [tex]n > 0[/tex]
A proof that the functions represent the same sequence is as follows:
Set [tex]n=1[/tex] in
[tex]f(0) = 19\\f(n) = f(n - 1) -6;[/tex]
[tex]f(1) = f(1 -1) - 6 = f(0) - 6[/tex]
[tex]f(1) = 19 - 6 = 13[/tex]
Set [tex]n = 2[/tex]
[tex]f(2) = f(2 -1) - 6 = f(1) - 6[/tex]
[tex]f(2) = 13 - 6 = 7[/tex]
Set [tex]n = 3[/tex]
[tex]f(3) = f(3 -1) - 6 = f(2) - 6[/tex]
[tex]f(3) = 7 - 6 = 1[/tex]
Write out the equations
[tex]f(1) = 19 - 6 = 13[/tex]
[tex]f(2) = 13 - 6 = 7[/tex]
[tex]f(3) = 7 - 6 = 1[/tex]
Rewrite as:
[tex]f(1) = 19 - 6 = 13[/tex]
[tex]f(2) = 19 - 6 - 6 = 7[/tex]
[tex]f(3) = 19 - 6 - 6 -6= 1[/tex]
Rewrite again as:
[tex]f(1) = 19 -6\times 1 = 13[/tex]
[tex]f(2) = 19 -6\times 2 = 7[/tex]
[tex]f(3) = 19 -6\times 3 = 1[/tex]
Replace the numbers in brackets with n
[tex]f(n) = 19 -6\times n[/tex]
[tex]f(n) = 19 -6n[/tex]
Hence, it is proved that
[tex]f(n) = 19 -6n[/tex] and
[tex]f(0) = 19\\f(n) = f(n - 1) -6;[/tex] represents the same sequence
The definition I will choose for f(20) is:
[tex]f(20) = 19 - 6 \times 20[/tex]
This is gotten from [tex]f(n) = 19 -6n[/tex].
I choose the definition because it is faster to calculate f(20) directly, than using recursion
Question 7:
Given that:
[tex]T_1 = 20[/tex]
[tex]T_2 = 16[/tex]
First, we calculate the common difference
[tex]d = T_2 - T_1[/tex]
[tex]d = 16 - 20 =-4[/tex]
The 500th term is then calculated using the nth term of an arithmetic progression formula.
[tex]T_n = T_1 + (n - 1) \times d[/tex]
So, we have:
[tex]T_{500} = 20+ (500 - 1) \times -4[/tex]
[tex]T_{500} = 20+ 499 \times -4[/tex]
[tex]T_{500} = 20 -1996[/tex]
[tex]T_{500} = -1976[/tex]
Hence, the 500th term is -1976.
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Need the answers ASAP it’s due in a hour
Answer:
lunch 28 breakfast 10 n both 12
Step-by-step explanation
Hi gyes what is your favourite subject tell me.My math
Me too!
My other favourite subject is science.
Mine is also Math,lol all ot the answer and you .
I like math because it’s my best subject.
Hannah but 3.4 pounds of apples she paid $.89 per pound how much did Hana pay for apples
Answer:
3.026 $
Step-by-step explanation:
3.4 × 0.89 = 3.026 $
The table and the graph show information about students enrolled in spanish and french classes at a high school. use the graph to determine after how many years there will be equal enrollment in spanish and french classes
Answer:
after 6 years
Step-by-step explanation:
thats when the lines intersect, (6,300)
There will be equal enrollment in Spanish and French classes after 6 years from now.
The red line shows the number of students enrolled in French class each year from now and blue line shows the number of students enrolled in Spanish class each year from now.
The point of intersection of the lines is the point which lies in both the line.
So, it represents the point or time when there are same number of students enrolled in both French and Spanish classes.
From the graph, we can see that the two lines at a point [tex](6,300)[/tex]. The value on the [tex]x[/tex]-coordinate shows the years from now. So, we can say that there will be equal number of students enrolled in two classes after 6 years.
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A sequence is defined by f (0) = -4, f (n) = f(n − 1) – 2 for n > 1. What is a definition for the nth term of the sequence? OA)f (n) = -2-n for n > 0 OB)f (n) = -2 - 4n for n > 0 O C)f (n) = -4 – 2n for n > 0 OD)f (n) = -4 - n for n > 0
Answer: C) f(n)= -4- 2 for n>0
Step-by-step explanation:
What is the 6th term of the sequence?
Answer:
i really dont know maybe 6
Step-by-step explanation:
A and Z are both between points M and N such that MZ=AN and A is between M and Z. Given: MA=5x AZ=3x-2 AN=6(2x-1) find MN
Answer:
MN = 11
Step-by-step explanation:
M___A___Z___N
MZ =MA+AZ
MZ = 5x + 3x -2 = 8x - 2
MZ = AN
8x - 2 = 6(2x-1)
8x - 2 = 12x - 6
12x - 8x = 6 -2
4x = 4
x =4/4
x =1
MA= 5x = 5(1) = 5
AZ = 3x-2 = 3(1) - 2 = 3 -2= 1
MZ = 8x -2 = 8(1)-2= 8-2=6
AN = 12x - 6 = 12(1)-6 = 12 - 6 = 6
MN = MA + AN = 5 + 6 = 11
I hope I helped you^_^
PLEASE HELP ASAP Due in 1 day!!!
Question 1
Find(f+g)(x)
f(x)=4x−4 and g(x)=2x^2−3x
Question 2
Find(f−g)(x)
f(x)=2x^2−2 and g(x)=4x+1
Question 3
Find(h⋅g)(x)
h(x)=3x−3 and g(x)=x^2+3
Question 4
Find(f/g)(x)and state the domain restriction.
f(x)=x+4 and g(x)=x+6
Step-by-step explanation:
Q1 . (f+g)(x) = f(x) + g(x)
=4x-4 +2x^2 -3x
= 2x^2 + x -4
Q2. (f-g)(x) = f(x) - g(x)
= 2x^2−2 - (4x+1)
= 2x^2 -2 -4x -1
= 2x^2 - 4x -3
Q3. h(x)=3x−3 and g(x)=x^2+3
(h.g)(x) = h(x) × g(x)
= (3x-3) × (x^2 + 3)
=3x^3 -3x^2 + 9x -9
Q4.f(x)=x+4 and g(x)=x+6
(f/g)(x) = f(x) ÷ g(x)
= x+4 / x+6
the domain restriction is x>-6
x<-6
x doesn't equal (-6)
If the two function f(x) and g(x) are to be combined, use basic arithmetic rules,
(f + g)(x) = f(x) + g(x)
(f - g)(x) = f(x) - g(x)
[tex](\frac{f}{g})(x)=\frac{f(x)}{g(x)}[/tex]
(f . g)(x) = f(x) × g(x)
Question 1
f(x) = 4x - 4 and g(x) = 2x² - 3x
[tex](f+g)(x)=f(x)+g(x)[/tex]
Therefore, [tex](f+g)(x)=(4x-4)+(2x^2-3x)[/tex]
[tex]=2x^2+x-4[/tex]
Question 2
f(x) = 2x² - 2 and g(x) = 4x + 1
Since, (f - g)(x) = f(x) - g(x)
Therefore, (f - g)(x) = (2x² - 2) - (4x + 1)
= 2x² - 2 - 4x - 1
= 2x² - 4x - 3
Question 3
h(x) = 3x - 3 and g(x) = x² + 3
Since, (h - g)(x) = h(x) - g(x)
Therefore, (h - g)(x) = (3x - 3) - (x² + 3)
= 3x - 3 - x² - 3
= -x² + 3x - 6
Question 4
F(x) = x + 4 and g(x) = x + 6
Since, [tex](\frac{f}{g})(x)=\frac{f(x)}{g(x)}[/tex]
Therefore, [tex](\frac{f}{g})(x)=\frac{x+4}{x+6}[/tex]
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what is the answer 2(5c + 8)?
Answer:
How to solve your problem
2 ( 5 + 8 )
Simplify
Step-by-step explanation:
Distribute
2 ( 5 + 8 )
1 0 + 1 6
solution:
1 0 + 1 6
there you go
hope this helpsFind the distance between the two points P(-7,-2) and Q(-1,6).
Round your answer to the nearest 10h if necessary.
Answer:
10
Step-by-step explanation:
√(x2 - x1)² + (y2 - y1)²
√[-1 - (-7)]² + [6 - (-2)]²
√(6)² + (8)²
√(36) + (64)
√100
= 10
If a number is a whole number, then it cannot be
O an irrational number
O an integer
O a rational number
O a natural number
Answer:
The answer is "am irrational number"
What is this? I don’t know the answers plz help
Answer:
C
Step-by-step explanation:
Answer:
c.
Step-by-step explanation:
Starting with the multiplications, first the multiply matrix A by -4, so we multiply every value in the matrix by -4 and we get
16 16 -4
-4 -16 -28
-8 -12 -12
Then we do the next multiplication which is 8 by matrix B, so once again we multiply every value in the B matrix by 8
16 72 -72
64 64 -16
32 80 8
Now that we did both multiplications, just need to sum the results, so we sum each value of matrix A with the value on the matrix B that's on the same spot
16 + 16 16 + 72 -4 + (-72)
-4 + 64 -16 + 64 -28 + (-16)
-8 + 32 -12 + 80 -12 + 8
And the final result is
32 88 -76
60 48 -44
24 68 -4
So it's option c
solve the equation simultaneously:
y = 2-2x
y = -16 + 2(x-3)^2
Answer:
y = -26
Step-by-step explanation:
[y = 2 - 2x] + [y = -16 + 2(x - 3)^2]
y = -16 + 2x - 6^2
y = -16 + 2x - 6^2 + 2 - 2x
y = (+2x - 2x) - 16 - 6^2 + 2
y = -16 - 6^2 + 2
y = -16 - 12 + 2
y = - 28 + 2
y = -26
6 + 2 ÷ 4 × 3 - 7 + 6 + 5 ÷ 3 - 1 × 1
Answer:
7.16666666667
Step-by-step explanation:
Carson buys eggs and lemons at the store.
He pays a total of $39.62.
He pays $6.74 for the eggs.
He buys 8 bags of lemons that each cost the same amount.
Which equation could be used to determine xx, how much each bag of lemons costs?
Answer: 8x = $39.62 - $6.74
Step-by-step explanation:
Cost of 1 bag of lemons = $x
Cost of 8 bags of lemons = 8*x = 8x
Cost of 8 bags of lemons = Total cost - cost of the egg
8x = $39.62 - $6.74
What is the product of (7/8 ) (-16) (-7) (-1/14)
A . -7
B . - 9/16
C . -1/7
D . 23/12
Answer:
I believe its A.
Step-by-step explanation:
Tom drives at a steady speed covering 1 mile every minute. He comes to a
section of road where the speed limit is 50 mph.
Is he over the speed limit? Give a reason for your answer.
Answer:
Yes he is over the speed limit.
Step-by-step explanation:
1 mile per minute * 60 minutes (1 hour) = 60 miles per hour
60 > 50
Solve for b.
7
10b+ 18 = 28
Answer: 6
Submit Answer
Answer:
False B=1
Step-by-step explanation:
10b+18=28
Subtract 18 both sides.
10b=10
Divide 10 both sides.
b=1
abc is a triangle in which ab=5cm, ca=13cm and bc=12 cm. calculate sina, cosc, tana, cotc, seea and cosec
Evaluate y4 + 2x When x =1, y = 7
Answer:
30
Step-by-step explanation:
y4 + 2x
(7)4 + 2(1)
28 + 2
30
Help I'll give you 100 points
✏ Answer:
[tex]y=-9[/tex]
Step-by-step explanation:
[tex]2-\frac{1}{8}y=11+\frac{7}{8}y[/tex]
➠ Subtract 2 from both sides:-
[tex]2-\frac{1}{8}y-2=11+\frac{7}{8}y-2[/tex]
[tex]-\frac{1}{8}y=\frac{7}{8}y+9[/tex]
➠ Subtract 7/8y from both sides:-
[tex]-\frac{1}{8}y-\frac{7}{8}y=\frac{7}{8}y+9-\frac{7}{8}y[/tex]
[tex]-y=9[/tex]
➠ Divide both sides by -1:-
[tex]\frac{-y}{-1}=\frac{9}{-1}[/tex]
[tex]y=-9[/tex]
OAmalOHopeO
✎--------------------------
[tex] \huge \boxed{\mathfrak{Question} \downarrow}[/tex]
[tex] \tt \: 2 - \frac { 1 } { 8 } y = 11 + \frac { 7 } { 8 } y \\ [/tex][tex] \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}[/tex]
[tex] \tt \: 2 - \frac { 1 } { 8 } y = 11 + \frac { 7 } { 8 } y \\ [/tex]
Subtract [tex]\tt\frac{7}{8}y[/tex] from both sides.
[tex] \tt \: 2-\frac{1}{8}y-\frac{7}{8}y=11 \\ [/tex]
Combine [tex]\tt-\frac{1}{8}y[/tex] and [tex]\tt-\frac{7}{8}y[/tex] to get -y.
[tex] \tt \: 2-y=11 [/tex]
Subtract 2 from both sides.
[tex] \tt \: -y=11-2 [/tex]
Subtract 2 from 11 to get 9.
[tex] \tt \: -y=9 [/tex]
Multiply both sides by -1.
[tex] \boxed{\boxed{ \bf \: y=-9 }}[/tex]
Find the 7th term in the geometric sequence 3, 6, 12, ... Show your solution.
a + (n-1) b
= 3 + (7-1) 3
= 3 + 6(3)
= 3 + 18
= 21
Answer:
192
Step-by-step explanation:
given the geometric sequence : 3, 6, 12, ...
T1 = 3
r = 6/3 = 2
T7 =?
T7 = T1. r^(7-1)
= 3 . 2^(7-1)
= 3. 2^6
= 3. 64
= 192
(06.02 LC)
Simplify (4x - 6) + (5x + 1).
O9x + 5
O 9x - 5
Ox-5
O-x-5
Answer:
9x - 5 (second option)
Step-by-step explanation:
[tex](4x - 6) + (5x + 1)[/tex]
[tex]4x - 6 + (5x + 1) = 4x - 6 + 5x + 1[/tex]
[tex]4x + 5x = (4 + 5)x = 9x[/tex]
[tex]9x - 6 + 1 = 9x - 5[/tex]
[tex] = 9x - 5[/tex]
Please help me i’m lost
==============================================
Explanation:
The degree of separation from the two cities is 30-7 = 23 degrees.
Let's say the point C is at the center of the earth. This would mean angle BCA is 23 degrees.
Any longitude line helps form what is known as a great circle or orthodrome. This is a math term that describes a circle that is centered at the same location as the sphere's center. Imagine that you can wrap a string around the earth and this string only follows this particular longitude line. This string is effectively a vertical equator in a way. The question is: what is the length of this string?
Well that would be the circumference of the circle with radius 3960 miles because the longitudinal circle has the same radius as the sphere.
That approximates to...
C = 2*pi*r
C = 2*pi*3960
C = 24,881.4138164311
C = 24,881.41
So a bit less than 25 thousand miles. I used the calculator's stored version of pi rather than something like 3.14 to get the best accuracy possible. This is the full string's length if we want to travel the entire distance around the globe but stay entirely on this particular longitude line
We don't want the full string's length. Instead, we want just a fractional portion of it. Specifically, we want 23/360 of it because of the central angle of 23 degrees. This will give us the distance between the two cities.
So (23/360)*24,881.4138164311 = 1,589.64588271642
This then rounds to 1589.65 when rounding to the nearest hundredth.
The distance between the two cities is approximately 1589.65 miles
This is comparable to the driving distance from Los Angeles, CA to Houston, TX (approximately 1547 miles).
what is 9.58333333333 as a fraction?
Answer:
If you pacifically asking for the fraction 115/12
Step-by-step explanation:
I also looked on mathw it helps
Find the perimeter. Simplify your answer.
4y-5
10y-4
7y+8
74-5
(10y - 4) + (7y + 8) + (7y - 5) + (4y - 5) =
= 10y - 4 + 7y + 8 + 7y - 5 + 4y - 5 =
= 10y + 7y + 7y + 4y - 4 + 8 - 5 - 5 = 28y - 6
evaluate each expression for x=3 and y=2
x+7
8-y
Step-by-step explanation:
1)x+7
3+7102)8-y
8-26hope it helps.stay safe healthy and happy...please help me! will mark brainliest
k = -2
√-72k = √(-72 · (-2)) = √144 = √12² = 12
Fast help for this one
Answer:
a. -5
b. 6254
c. - 1881
d. -1200
Step-by-step explanation:
Sorry,I think you can use your calculator to solve your problem but remember don't forget to follow the rules of numeral operation.
CMIIW
[tex]( - 32) \div 8 \times 2 + 2 - ( - 1) \\ = ( - 32) \div 8 \times 2 + 2 + 1 \\ = - 4 \times 2 + 2 + 1 \\ = - 8 + 2 + 1 \\ = - 8 + 3 \\ = - 5[/tex]
[tex]53 \times ( - 9) - ( - 109) \times 53 \\ = 53 \times ( - 9) + 109 \times 53 \\ = 53( - 9 + 109) \\ = 53 \times 100 \\ = 5300[/tex]
[tex] - 19 \times 99 \\ = - 1881[/tex]
[tex]( - 63) \times 12 + 12 \times ( - 37) \\ = 12( - 63 - 37) \\ = 12 \times ( - 100) \\ = - 1200[/tex]
Hope you could understand.
If you have any query feel free to ask.
Find the range of the of the function y= 2/3x -1 when the domain is {-6, -3, 0, 3}
Answer:
(- ∞,0) (0,∞)
Step-by-step explanation:
To find the domain by finding where the equation is defined. The range is the set of values that correspond with the domain...
