Consider the arithmetic sequence 10,12,14,16 if n is an integer, which of these functions generate the sequence?
Given:
The arithmetic sequence is:
10, 12, 14, 16, ...
To find:
The function that generates the given sequence if n is an integer.
Solution:
We have,
10, 12, 14, 16, ...
Here, the first term is 10 and the common difference is:
[tex]d=a_2-a_1[/tex]
[tex]d=12-10[/tex]
[tex]d=2[/tex]
The nth term of an arithmetic sequence is:
[tex]a_n=a+(n-1)d[/tex]
Where, a is the first term, d is the common difference and [tex]n\geq 1[/tex].
Putting [tex]a=10,d=2[/tex] in the above formula, we get
[tex]a_n=10+(n-1)2[/tex]
[tex]a_n=10+2n-2[/tex]
[tex]a_n=8+2n[/tex]
Therefore, the function [tex]a_n=8+2n, n\geq 1[/tex] generates the sequence.
Evaluate f(−3) for f(x)=2x2−x+5.
Answer: -4
Step-by-step explanation:
2(-3)*2-(-3)+5= -4
Use a permutation expression to solve.
In a race of 43 people, how many different ways can the runners place in 1st, 2nd, and 3rd?
Answer:
74046
Step-by-step explanation:
Permutations = [tex]_np_r=\frac{n!}{(n-r)!}[/tex]
where r = choice of things from a set ( in this case the 3 places ) so r = 3
and n = amount of things ( in this case the 43 people ) so n = 43
We then plug in the values of n and r in the permutations formula
[tex]\frac{43!}{(43-3)!} =74046[/tex]
Hence the answer is 74046
I know the answer can someone just help me explain it???
Step-by-step explanation:
It is Graph B. We can do this by checking the points. The equation given is d = 5t^2, where d technically is the y-coordinate and t is the x-coordinate. On Graph B, two obvious points are (1, 5) and (2, 20). We can check these points to see if they fit the equation.
(1,5): d = 5t^2
5 = 5(1)^2
5 = 5*1
5 = 5, so this point is correct.
(2, 20): = d = 5t^2
20 = 5(2)^2
20 = 5*4
20 = 20, so this point is correct.
We know that Graph A is incorrect because it doesn't follow the equation. The line goes through (1, 5), which we already know is correct, (2, 10), (3, 15), and (4, 20). We already figured out that (2, 20) is correct so (2,10) can't be correct. (3, 15) and (4, 20) are also incorrect but in this case, we only need to find one incorrect coordinate to validate our answer. Thus, as Graph A is wrong, Graph B is right.
In the right triangle shown,
m
∠
V
=
60
°
m∠V=60°m, angle, V, equals, 60, degree and
U
V
=
18
UV=18U, V, equals, 18.
60
°
60°
x
x
18
18
U
U
W
W
V
V
How long is
U
W
UWU, W?
Answer:
what
Step-by-step explanation:
Solve the equation
x^2 = -8x-7
by factoring
Answer:
x= -1,-7
Step by step:
Answer:
x = -7 and -1
Step-by-step explanation:
Move the right side of the equation over to the left;
x^2+8x+7 = 0; Factor
(x+7)(x+1)=0 ; Solve for x;
x = -7 and -1
20 minutes before 3 in the afternoon is written as _:__p.m.
Answer:
2:40 p.m.
Step-by-step explanation:
NO LINKS!
Select the correct answer from each drop-down menu.
Consider the end behavior of the function
g(x) = | x-2 | -3
As x approaches negative infinity, f(x) approaches
[BLANK] infinity
Options :
Negative, Positive
As x approaches positive infinity, f(x) approaches [BLANK] infinity
Options :
Negative, Positive
Answer: negative, positive
Step-by-step explanation:
FOR PLATO!
Positive
Positive
find cot0 given cos0=2/7 and the terminal side is in quadrant IV
Answer:
0.2985
Step-by-step explanation:
find cot0 given cos0=2/7 and the terminal side is in quadrant IV
Given
cos theta = 2/7
theta = arccos(2/7)
theta = 73.40 degrees
cot theta = cot73.40
cot73.40 = 1/tan73.40
cot73.40 = 1/3.35
cot73.40 = 0.2985
hence the required answer is 0.2985
simplify 3a - 4b - 6a +b
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\text{3a - 4b - 6a + b}[/tex]
[tex]\large\textsf{COMBINE the LIKE TERMS}[/tex]
[tex]\large\text{\underline{(3a - 6a)} + (\bf -4b + b)}[/tex]
[tex]\large\text{\underline{3a - 6a = \bf -3a}}[/tex]
[tex]\large\text{\bf -4b + b = \bf \underline{-3b}}[/tex]
[tex]\large\text{= \bf -3a - 3b}[/tex]
[tex]\boxed{\boxed{\large\text{Answer: \huge \bf -3a - 3b }}}\huge\checkmark[/tex]
[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Translate algebraic words to symbols.
Six times y divided by x squared
A. 6y - X2
B. 6y + 2x
C. (6 + y)/2x
D. 6y/x2
Answer:
D
Step-by-step explanation:
Answer:
D. 6y/x²
Step-by-step explanation:
6×y= 6y
x squared =x²
8c^(2)+6c-2c^(2)-5c
Answer:
6c^2 + c
Step-by-step explanation:
8^2 - 2c^2= 6c^2
6c-5c = c
What’s the quotient of 5,045 divided by 23
Answer:
219.347
Step-by-step explanation:
Answer:
93
Step-by-step explanation:
Charlie is flying a kite one afternoon and steps on the end of the string to have his
hands free to take a picture. The string is 135 feet long and forms a 68-degree angle
with the ground. How high is his kite at this time? Round to the nearest foot, and
enter the number only.
Answer:
roubd it to 20 and you will get 679.90
Can someone please help me figure out this problem. Thanks
Answer:
.6
Step-by-step explanation:
-2.1-.6=-1.5 / -1 1/2
No links! Answer please will give brainliest if I can!
answer:
i drew the graph since i couldn’t write it out
A rectangle has an area of 75.2m
One of the sides is 0.8m in length.
Work out the perimeter of the
rectangle.
Answer:
94.8
Step-by-step explanation:
Aera is : length *width
75.2 = 0.8 * x then x =94
Perimeter is : length + width =94 +0.8
i need help solving this
Answer:
y= - 2/3x + 3
i need help please help meeeehhh
Answer:
e=26
d=52
f=154
Step-by-step explanation:
theyre equal to the ones across from them, and i used a line to find the measure of d
Use the following sequence to complete the sentence below.
8, -1, -10, -19
The sequence is (a geometric/arithmetic sequence) and has a (common difference/common ratio) of ________
Answer:not sure what u talking about
Step-by-step explanation:
Answer:
Since the ratios are constant, the sequence is geometric. The common ratio is –1. Since the ratios are constant, the sequence is geometric.
How do I solve this problem?
Answer:
504
6x84= 504
The picture is too big so you're not going to get the full explanation ok
Jack can fill buckets of water four times fast as his sister Jill. They have to fill 400 buckets of
water for their village located at the bottom of a hill. Working together, Jack and Jill can complete
the job in six hours.
30. How many hours will it take Jack if he works alone?
Answer:
1.5 hour
Step-by-step explanation:
You divide 6 by 4.
Answer:
7.2 hrs
Step-by-step explanation:
Jack does 4/5 of the work in 6 hrs. He still needs to do 1/5 more if he's doing it by himself. 1/5 of 6 = 1.2 and 1.2 + 6 = 7.2 hrs
plz help with this thanks
Answer:
which one
Step-by-step explanation:
the upper answer would be 38 and lower would be
Answer:
4f = 38
Step-by-step explanation:
f(x) = 9x + 2
=
f(4) = 9(4) + 2
=
4f = 36 + 2
=
4f = 38
Does anyone know the answer for this?
Solve: 2x-4 = -(x-6)/2
Answer:
x = 14/5
Step-by-step explanation:
2x-4= -x-6/2
multiply by 2 on both sides to get rid of the fraction
4x-8= -x-6
add both sides by 8 and both sides by x to get the constants on the right and the variables on the left
4x+x=6+8
combine like terms/simplify
5x=14
divide both sides by 5 to isolate the x
x=14/5
i hope this helps :)
+ listen
19. Isabel spent $34.93 for 7 books on her
summer reading list. If the books were all the
same price, how much did each one cost?
Answer:
$4.99
Step-by-step explanation:
[tex]34.93 \div 7 [/tex]
Answer:
[tex]7 \: books = 34.93 \: dollars \\ 1 \: book = ( \frac{1}{7} \times 34.93) \: dollars \\ = 4.99 \: dollars[/tex]
PLEASE ANSWER EEEEEEEEEEEEEEEEEEE
Answer:
5 x 4 x 3 = 60
Step-by-step explanation:
Do - H x L x W
H is 5
L is 4
W is 3
Five boys namely, Abel, Ben, Carlo, Dave and Elmer made a race. They all started at 7:10 in the morning. Abel finished the race at 7:18 a.M., Ben at 7:32 a.M., Carlo at 7:38 a.M., Dave at 7:42 a.M. And Elmer at 7: 52 a.M. About how many minutes did Abel finished the race?
Answer:
8 minutes
Step-by-step explanation:
minutes Abel completed the race = time finished - time started
7:18 - 7:10 = 8 minutes
what is 6 divided by 1/4
Answer:
24
Step-by-step explanation:
6 / 1 / 4 =
6 x 4 =
24
Answer:
6 divided by 1/4 is 24
Step-by-step explanation:
Median of 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20
Answer:
10.5
Step-by-step explanation:
Find the two middle numbers, add them together and divide them by two if it is an even number. For odd numbers, your median will be the middle number.