Answer:
f(4) = 6
Step-by-step explanation:
Given the rule f(n) = 4f (n - 1) + 2 where f(1) = 3, f(n) is just a fancy way to name the variable y. As you've seen before, there are equations that are usually y equals x and something. For example:
y = mx + b
is the same thing as
f(n) = y = mn + b.
It might be that you have multiple of the same equation where f(n) and f(x) have two different outcomes.
The f(n) part (bolded) is the "x variable" in this equation. So in f(1), n = 1.
f(n) = 4f (n - 1) + 2
f(n) = (4fn - 4f) + 2
f(n) = (n) + 2
f(1) = 1 +2
3 = 3
Now do the same thing for f(4):
f(n) = 4f (n - 1) + 2
f(n) = (4fn - 4f) + 2
f(n) = (n) + 2
f(4) = 4 + 2
f(4) = 6
please help asap!
Which graph represents the function?
Answer:
The below right one
Step-by-step explanation:
A wading pool is being filled with water from a garden hose at a rate of
6 gallons per minute. If the pool already contains 80 gallons of water and can hold
152 gallons, after how long will the pool overflow?
Assume m minutes later, the pool would overflow. Write an equation to model this scenario. There is no need to solve it.
A wading pool is being filled with water from a garden hose at a rate of
6 gallons per minute. If the pool already contains 80 gallons of water and can hold 152 gallons, and it will take 12 minutes for the pool to overflow.
In this scenario, we have a wading pool being filled with water from a garden hose at a constant rate of 6 gallons per minute. The pool already contains 80 gallons of water, and its maximum capacity is 152 gallons. We want to find out how long it will take for the pool to overflow.
Let's use "t" as the variable representing time in minutes. After "t" minutes, the amount of water in the pool will be the initial 80 gallons plus the additional water being filled by the hose at a rate of 6 gallons per minute. We can express this mathematically as:
Amount of water in the pool after "t" minutes = 80 gallons + 6 gallons/minute * "t" minutes
Now, we want to find out when the pool will overflow. The pool's capacity is 152 gallons, so we set up an equation to represent this:
Amount of water in the pool after "t" minutes = 152 gallons
Substituting the earlier expression for the amount of water in the pool after "t" minutes:
80 gallons + 6 gallons/minute * "t" minutes = 152 gallons
Now, we have an equation to model the scenario: "80 + 6t = 152".
To find the time "t" it takes for the pool to overflow, we need to solve this equation for "t."
To solve for "t," we need to find the value of "t" that satisfies the equation we derived earlier:
80 + 6t = 152
To isolate "t," we'll perform the following steps:
Subtract 80 from both sides to move the constant term to one side of the equation.
80 + 6t - 80 = 152 - 80
This simplifies to:
6t = 72
Divide both sides by 6 to solve for "t."
t = 72 / 6
t = 12
So, it will take 12 minutes for the pool to overflow.
In summary, we have a wading pool being filled with water at a rate of 6 gallons per minute, and we want to know when it will overflow, given its current water level of 80 gallons and a maximum capacity of 152 gallons. The equation "80 + 6t = 152" models this situation, with "t" representing the time in minutes. Solving this equation will give us the time it takes for the pool to overflow.
To know more about Equation here
https://brainly.com/question/29181550
#SPJ2
Ricky made approximately 4 goal points for every 7 of his shots on goal. What is the probability that Ricky would make 2 goal points on two shots in a row during the season?
Given:
Ricky made approximately 4 goal points for every 7 of his shots on goal.
To find:
The probability that Ricky would make 2 goal points on two shots in a row during the season.
Solution:
Using the given information, the probability of a goal point on one shot is:
[tex]P(one\ goal)=\dfrac{4}{7}[/tex]
We need to find the probability that Ricky would make 2 goal points on two shots in a row during the season.
Since the both shots are independent events therefore,
[tex]P(Two\ goals)=P(one\ goal)\times P(one\ goal)[/tex]
[tex]P(Two\ goals)=\dfrac{4}{7}\times \dfrac{4}{7}[/tex]
[tex]P(Two\ goals)=\dfrac{16}{49}[/tex]
Therefore, the required probability is [tex]\dfrac{16}{49}[/tex].
Hi! I need some help on my hw! Feel free to attach a picture explaining it if that’s easier tysm!
Two angles are called complementary if their measures add to 90 degrees, and called supplementary if their measures add to 180 degrees.
1. 45 and 135
2. 45 and 45
3. know that triangles add up to 180 so:
95+40=135 either use algebra or just do 180-135 to get:
x=45
if your reading this please help meeee
Answer:
both angles are 92 degrees
Step-by-step explanation:
88+c=180
c=92
c and b are vertical angles and all vertical angles are equal
Find the volume of the sphere.
Either enter an exact answer in terms of it or use 3.14 for T.
6
units
Answer:
Volume = 904.32 units³
Step-by-step explanation:
Volume = 4/3πr³ = 4/3(3.14)(6³) = 904.32
Find the exact value of x.
Answer:
x=6.9
Step-by-step explanation:
[tex]x^{2} =6*8[/tex]
[tex]x=\sqrt{48}[/tex]
[tex]x=6.9[/tex]
[tex]hope[/tex] [tex]it[/tex] [tex]helps...[/tex]
[tex]have[/tex] [tex]a[/tex] [tex]great[/tex] [tex]day!!![/tex]
Use the drawing given. (Please answer first blank and let me know it the second blank is correct.)
Answer:
EF = 12
arc AG = 62°
Step-by-step explanation:
since ED = 13, EC = 13, so DF = 10/2 = 5
EF² + 13² - 5² = 169 - 25 = 144
EF = √144 = 12
∠AEG = 90° - 28° = 62°
arc AG = 62°
I need help quick it is due in 3 hours
Answer:
20.24
Step-by-step explanation:
Recall SOH, CAH, TOA and realize that TOA is the easiest one
we have
[tex]tan(39)=\frac{x}{25}\\tan(39)*25=x\\20.24=x[/tex]
an onion soup recipe calls for 3 2/3 cups of chopped onions. katrina has already chopped 1 1/3 cups of onions. she wants to know how many more cups she needs to chop. HELP PLS
She need 1 2/3 more cups
Hope this helped :3
Which equation matches the function shown in the graph?
A. Y= sin(x-pi)+3
B. Y= 3cos(x+pi)
C. Y= 3sin(x-pi)
D. Y= 3cos(x-pi)
Answer:
its c ! just took the test :)
Option C is correct. The equation that matches the function shown in the graph is expressed as y = 3sin(x-π)
The general formula for a sine function is expressed as;
y = Asin(x+Ф)
A is the amplitude i.e the maximum point on the curve. From the diagram, we can see that the maximum point is at 3 (factor 3 elongates the curve).
A = 3
Also, since the graph translates to the right by π, hence Ф = -π
Substituting the resulting values into the formula, we will have;
y =3sin(x+ (-π))
y = 3sin(x-π)
Hence the equation that matches the function shown in the graph is expressed as y = 3sin(x-π)
Learn more about since graph here: https://brainly.com/question/16262155
Anyone know answer ???
Answer:
C
Step-by-step explanation:
We know that ∠ 1 + ∠ 2 + ∠3 = 180 → (1)
and ∠ 3 + ∠ 4 = 180 → (2)
From (2) ∠ 3 = 180 - ∠ 4
Substitute ∠ 3 = 180 - ∠ 4 into (1)
∠ 1 + ∠ 2 + 180 - ∠ 4 = 180 ( add ∠ 4 to both sides )
∠ 1 + ∠ 2 + 180 = 180 + ∠ 4 ( subtract 180 from both sides )
∠ 1 + ∠ 2 = ∠ 4 → C
PLS HELP... 10 POINTS ASAP
Coach Jackson has a ratio of 1 girls to 3 boys in his classroom. If there are 6 girls in his class, what is the total number of students in Coach Jackson's class?
a. 18
b. 24
c. 12
d. 2
Answer:
b, 24
Step-by-step explanation:
b
1:3
6:18
6+18=24
I GOTCHU HOMIE
Answer:
The answer is 18.
Step-by-step explanation:
6 x 3 x 1 = 18
PLEASE HELP ME,!!!!!!!!!!! ALL LINKS WILL BE REPORTED!!
Which of the following indicates the subtraction property of equality when solving the equation 86 – 2 (9x + 4) = 12x + 18?
Question options:
A)
2(9x + 4) = 86 – 12x – 18
B)
–2(9x + 4) = 12x + 18 – 86
C)
x = 2
D)
86 – 18x – 8 = 12x + 18
Answer:
D
Step-by-step explanation:
Answer: D) 86 - 18x - 8 = 12x + 18
Mhanifa can you please help this is due asap!
Answer:
Step-by-step explanation:
soory i do not kno this one
Answer:
#1a. Diagonals bisect each other
SU = 108.8 cmSW = 1/2*SU = 1/2*108.8 cm = 54.4 cmb. Adjacent interior angles are supplementary
m∠TSV = 57°m∠SVU = 180° - 57° = 123°#2a. Diagonals bisect each other
FH = 2*HZ = 2*4 = 8 unitsb. Adjacent interior angles are supplementary
m∠EHG = 44°mFEH = 180° - 44° = 136°a. Adjacent
b. Linear Pair
c. Complementary
d. Supplementary
e. Vertical
NO LINKS PLEASE HELP NOW COMPLETELY ACCURATE ANSWER IMMEDIATELY PLEASE ANSWER I WILL GIVE BRAINLIEST
Answer:
got em
Step-by-step explanation:
PLEASE HELP WILL MARK U BRAINLIEST
Answer:
C) 16.97
Step-by-step explanation:
If the sides are 12, the hypotenuse is 12*(2^1/2) to the 45 - 45 - 90.
When you put 2*(2^1/2) into the calculator, you get 16.97.
Answer:
16.97
Step-by-step explanation:
Equation used: c=[tex]\sqrt{ax^{2} +bx^{2} }[/tex]
Equation filled out: c=[tex]\sqrt{12x^{2} +12x^{2} }[/tex]
Next step: c=[tex]\sqrt{288}[/tex]
Total: 16.97056 though to the hundreath place 16.97
So if both legs are 12 inches each, that mean that 12^2 +12^2 which totals out too 288, then you find the full square of 288 which leads out to 16.97!
The diameter of a spherical basketball is 10 inches.
What is the volume of the basketball?
Give the exact solution.
HELPP
Answer:
523.6
Step-by-step explanation:
Here is the equation to get that answer:
V=4/3πr3=4/3·π·53≈523.59878
Sue has to cut her grandma's grass this weekend and wants to know exactly how much area she will be cutting. Calculate the area of the polygon. Be sure to show all your work and explain your answer. Six-sided polygon that includes two isosceles right triangles, one with height and base of 25 feet, the other height and base of 8 feet, and one rectangle measuring 35 feet by 8 feet.
Answer:
Step-by-step explanation:
700.5
Solve each equation for points!!
Step-by-step explanation:
A = -7.
B = -8 x-(-6) is the same as x + 6
C = 13
D = 2
E = -3
A teepee is in the shape of a cone. The teepee is 12.5 feet high, 16 feet wide. Find the volume of air that occupies the teepee, assuming it is empty.
Answer:
837.8 ft²
Step-by-step explanation:
The formula for the volume of a cone of base radius r and height h is
V = (1/3)(base area)(height), which here is:
V = (1/3)(π·8² ft²)(12.5 ft), or
V = (π/3)(64 ft²)(12.5 ft) = 837.8 ft²
Expand the brackets. 7 ( 5 + g ) 11 ( 3s – 4 ) 4 ( 4 – x ) 8 ( 6 + 4w )
Answer:
See answers below
Step-by-step explanation:
Expand the brackets. 7 ( 5 + g ) 11 ( 3s – 4 ) 4 ( 4 – x ) 8 ( 6 + 4w )
We will expand each of the bracket using distributive property
For the expression 7(5+g)
7(5)+7g
= 35+7g
For the expression 11(3s-4)
= 11(3s)-11(4)
= 33s-44
For the expression 4(4-x)
= 4(4)-4x
= 16-4x
For the expression 8(6+4w)
= 8(6)+8(4w)
= 48+32w
When graphing c=12, would you use an closed circle or opened circle?
Answer:
closed
Step-by-step explanation:
because its = not -< or>-
first to answer these 2 questions correctly gets brainleist ! i will give 12 points :)
Answer:
5. a) 96ft²
6. c) 144ft²
Step-by-step explanation:
A race car has a average speed of 105 miles per hour. How long will it take to cover 140 miles?
Your ship sinks and you swim to a nearby island. On this island, the inhabitants do not use money. The island residents use island fruit as money.
If 60 bananas = 20 coconuts
35 figs = 15 oranges
10 coconuts = 25 figs
200 figs = 1 boat
How many bananas would you need to purchase a boat to get off the island?
Answer:
69 doritos
Step-by-step explanation:
mountain dew and 360 no scope =69 doritos
Help? which one should I pick
Answer:13
Step-by-step explanation:
the shape gets small so it cant be 52
a diameter of 120 feet. To the nearest foot, what is the minimum length of fencing he needs to buy? If the fence costs $2.10 per foot, what will be the total cost?
Step-by-step explanation:
they have 122.1 of total of cost
Answer:
It is assumed the full circular fencing is needed.
Circumference of the circle = the length of fencing:
C = πd = 3.14*120 feet = 376.8 feet ≈ 377 feetTotal cost:
377*$2.10 = $791.70A 90-foot rope from the top of a tree house to the ground forms a 45° angle of elevation from the ground. How high is the top of
the tree house? Round your answer to the nearest tenth of a foot.
Answer:
63.6 feet
Step-by-step explanation:
[tex]sin (45)=\frac{x}{90}[/tex][tex]x=90 sin (45)[/tex][tex]x=45\sqrt{2}[/tex]x = 63.6 feet