Given:
[tex]f(1)=7[/tex]
[tex]f(n)=3f(n-1)+3[/tex]
To find:
The value of f(3).
Solution:
We have,
[tex]f(n)=3f(n-1)+3[/tex] ...(i)
Substituting [tex]n=2[/tex] in (i), we get
[tex]f(2)=3f(2-1)+3[/tex]
[tex]f(2)=3f(1)+3[/tex]
Substituting [tex]f(1)=7[/tex] in the above equation, we get
[tex]f(2)=3(7)+3[/tex]
[tex]f(2)=21+3[/tex]
[tex]f(2)=24[/tex]
Now, substituting [tex]n=3[/tex] in (i), we get
[tex]f(3)=3f(3-1)+3[/tex]
[tex]f(3)=3f(2)+3[/tex]
Substituting [tex]f(2)=24[/tex] in the above equation, we get
[tex]f(3)=3(24)+3[/tex]
[tex]f(3)=72+3[/tex]
[tex]f(3)=75[/tex]
Therefore, the value of f(3) is 75.
A play is being presented on a circular stage. The two main characters are
at positions A and B at the back of the stage. What angle of view between
the main characters does an actor at position C at center stage have? *
Answer:
The angle of view between the main characters is 80°.
Step-by-step explanation:
The angle of view of the actor C between actors A and B is the measure of the angle of the central arc between A and B. Hence, the angle of view between the main characters is 80°.
What is the slope of a line perpendicular to 3x + 4y = -2?
Answer:
[tex]\frac{4}{3}[/tex]
Step-by-step explanation:
The slope of the perpendicular line will be the negative reciprocal of the original slope.
For this line, the slope is [tex]-\frac{3}{4}[/tex] , whose negative reciprocal is [tex]\frac{4}{3}[/tex]
There are 6 blue marbles, 4 green marbles, and 2 red marbles. You choose 2 marbles. What is the chance that they will be blue?
Answer:
0.0152 probability
Step-by-step explanation:
first there are 12 marbles: odds are 2/12 = 1/6
Then, there are 11 marbles: odds are 1/11
So the odds of both of them being blue are: 1/6 * 1/11 = 0.0152
Please give brainliest thanks!
Please help I will mark brainlest
Find the sum of 1+2+3+4...19
Spam answer will be reported
Answer:
190
Step-by-step explanation:
1+2+3+4......19=210-20
=190
Answer this question for me please
Answer:
9-2 = 7
8-3 = 5
[tex]\sqrt{5^{2} +7^{2} \\[/tex]
= 8.602325267
Step-by-step explanation:
Thank you show your work<3
x=
y=
Answer:
[tex]x=-5,\\y=\frac{13}{2}[/tex]
Step-by-step explanation:
[tex]\begin{cases}x+2y=8,\\x=-5\end{cases}[/tex]
Substitute the second equation into the first ([tex]x=-5[/tex]):
[tex]-5+2y=8,\\2y=13,\\y=\boxed{\frac{13}{2}}[/tex]
The second equation already denotes [tex]x=-5[/tex]. Therefore,
[tex]\boxed{x=-5,\\y=\frac{13}{2}}[/tex]
Answer:
x=-5
y=6.5
Step-by-step explanation:
if x=-5 then x+2y=8 could be rewriten as -5+2y=8 then you add 5 on both sides and you get 2y=13 then divide both sides by 2 and you get y=6.5
f(x) = x +1 g(x) = x^2 - 3
find f 3
find gf3
Pls help
A quadratic equation written in general form has a coefficient of −5 on the leading term, a coefficient of 2 on the first-degree term, and a constant of 3. What is the equation? Use x as the variable.
Answer:
f(x) = -5x² + 2x + 3
Step-by-step explanation:
f(x) = -5x² + 2x + 3
The LCM of three numbers is 360 and the GCD of the same numbers is 2.If one of the numbers is 40.Find the other 2 numbers
Answer
“The LCM of three numbers is 360“ The prime factors of 360 are 2³×3²×5¹. That means:
At least one of the numbers contains 2³ in its factorization list.
At least one of the numbers contains 3² in its factorization list.
At least one of the numbers contains 5 in its factorization list.
“One of the numbers is 40“ The factorization list of 40 is 2³×5, so 1) and 3) are satisfied.
“The GCD of the same numbers is 2“ This implies that all 3 numbers are even, and that at least one number only has one 2.
The candidates for the 2nd number, that has 3², are: 18, 12, 72 (3²×2³), 120, 180, or 360.
The candidates for the 3rd number depends on how many 2s the 2nd number has.
If more than one: 2, 6, 18, 10, 30, 90
If only 1, those plus 4, 8, 12, 36, 72, 20, 40, 120, 180, 360
Please help! I’m begging lolll
Answer:i think is C
Step-by-step explanation:
Given that cos(θ)= -√3/4 and tan(θ) > 0, find sin(θ)
Answer:
B. -√13/4
Step-by-step explanation:
cos 0 = -√3/4 => x=-√3 , h=4
tan 0 > 0
y should be on quadrant III
y= √4²-3= √16-3=√13 => -√13
so, sin 0 = y/h = -√13/4
Answer:
B. -√13/4
Step-by-step explanation:
:)
PLEASE please help me with this!! its due tonight. THANK YOU.
explaining your answer = brainliest
the area of the parallelogram is 49 square centimeters.
y = ___ cm
Answer:
[tex]y = 12.25[/tex]
Step-by-step explanation:
Area of parallelogram = [tex]49 {cm}^{2} [/tex]
∴ Side of Parallelogram = [tex]s = \frac{perimeter}{4} [/tex]
[tex]∴ \: s = y[/tex]
[tex]y = \frac{49}{4} [/tex]
[tex]y = 12.25[/tex]
Hope it is helpful...What is the output (y) if the input (x) is -10?
plz exsplain
Answer:
y = -5
Step-by-step explanation:
y = x / 2
For x = -10
Plug -10 into the equation
y = -10/2
y = -5
------------------
For the remaining values
x y
0 0
4 2
10 5
Plsss Answer 100% will mark as brainlist!!!
In the following figure ABCD, find the value of x
Answer:
80°
because its diagnol so the one in the top corner is the same as x
Answer:
x = 140°
Step-by-step explanation:
Sum of exterior angles of polygon is 360°
That is, x + 70 + 80 + 70 = 360
x + 220 = 360
x = 360 - 220 = 140°
25x + 22x + 9 = 180.......
[tex]\sf\purple{The\:value\:of\:x\:is\:3.638.}[/tex] ✅
Step-by-step explanation:-
[tex]25x + 22x + 9 = 180 \\ ⇢ 47x = 180 - 9 \\ ⇢ 47x = 171 \\ ⇢ x = \frac{171}{47} \\ ⇢ x = 3.638[/tex]
To verify:-
[tex]25 \times 3.638 + 22 \times 3.638 + 9 = 180 \\ ⇢ 90.95 + 80.036 + 9 = 180 \\ ⇢ 180 = 180 \\ ⇢ L.H.S.=R. H. S[/tex]
Hence verified. ✔
[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{♡}}}}}[/tex]
If 2 to the power of x is 1/32. Find the value of x...
Step-by-step explanation:
2 to the power x =1/32
2 to the power x =1/2 to the power 5
2 to the power x = 2 to the power -5
then,
x = -5
pls help pls help pls help
Find the missing side
Answer:
x = 54.40883769
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp /adj
tan 37 = 41/x
x tan 37 = 41
x = 41/ tan 37
x = 54.40883769
which of the following statement is true?
if x2+1/x2=27 find the value of x3+1/x3can anyone answer this, please
Step-by-step explanation:
x2+1/x2=27
x2+1=27x2
1=26x2
x2 = 1/26
x = √(1/26)
x3+1/x3 = (√(1/26))^3 + 1 / (√(1/26))^3
x3+1/x3 = 134
Please find attached photograph for your answer
Which expression gives the measure of angle ABC?
Answer: 1/2 (110 degree + 20 degree)
Step-by-step explanation:
Select all of the true statements about the sides of a right triangle.
A. The legs are the sides next to the 90 (right) angle.
B. The hypotenuse is the longest side
C. Side “a” is always longer than side “b”.
D. The hypotenuse is opposite the 90 (right) angle.
Answer:
It should be options B and D
Cary sets up a checking account with an initial balance of $27,700, and the rent for her
apartment is deducted every month for a year. After a year the balance is $7900
(Assume no other transactions occur on the account)
Answer:
$1,650
Step-by-step explanation:
First, we need to find how much she paid the whole year. 27,700-x=7900. If we subtract 7900 from each side and add x to each side, we get 19,800=x. Therefore, she paid $19,800 in rent the whole year. Since there are 12 months in a year, and each month she paid the same, she paid $1,650 in rent each year, for 19800/12=1650
Please help me to do the other answers
Answer:
in = - 9.5
Step-by-step explanation:
- 9.5 × 2 = -19
-19 - 1 = -20
Eighty percent of students surveyed said they feel more focused after exercising. Nine hundred fifty students were surveyed.
Students Who Feel More Focused after Exercise
20%
20%
20%
20%
20%
How many students said they feel more focused after exercising?
Answer:
760
Step-by-step explanation:
Find the value of x. Round your answer to the nearest tenth.
Answer:
9.30
Step-by-step explanation:
Using SOHCAHTOA
tan=opposite/adjacent
tan25°=x/20
tan 25°=0.4663
0.4663=x/20
cross multiply
x=0.4663*20
x=9.326
to the nearest tenth=9.30
Which of the following is an example of a quadratic equation?
Answer:
C) any eqaution that has a variable or number squared is a qaudratic equation
The product of two 2-digit numbers is 3774. What is the smaller of the two numbers?
Please help quick
Answer:
In factored form: 3774 = 2 · 3 · 17 · 37
Creating two two-digit numbers: 3 · 17 = 51 and 2 · 37 = 74.
So, the two numbers are: 51 and 74.
find the eighth term of an arithmetic sequence if the first term is 5 and the common difference is 6
Answer:
47
Step-by-step explanation:
Formula for finding nth term of an arithemetic sequence is:
tn = t1 + (n-1) d
Where t1 is the first term, n is the specific term, and d is the common difference.
Plug numbers into the formula and solve:
t8 = 5 + (8-1)6
t8 = 47
What is the slope of (6,-2) and (-3,1)
Answer:
slope = 1
Step-by-step explanation:
We have two points which are (6,-2) and (-3,1).
and we need to find slope
use the slope formula
m = ( y² - y1 ) / ( x² + x¹)
Where,
m is the slope( y² - y1 ) = ( 1 - 6 )( x² + x¹) = ( -3 -2)substitute the values
m = ( 1 - 6 ) / ( - 3 -2)
m = -5 / -5
divide we get
m = 1
Answer:
slope = - [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (6-2) and (x₂, y₂ ) = (- 3, 1)
m = [tex]\frac{1-(-2)}{-3-6}[/tex] = [tex]\frac{1+2}{-9}[/tex] = [tex]\frac{3}{-9}[/tex] = - [tex]\frac{1}{3}[/tex]