If f(x) = 3 ^ x, prove that f(x) + f(x + 1) = 4f (x) .

Answers

Answer 1

Answer:

see explanation

Step-by-step explanation:

Given

f(x) = [tex]3^{x}[/tex] , then

f(x + 1) = [tex]3^{x+1}[/tex] = [tex]3^{x}[/tex] × 3

Then

f(x) + f(x + 1)

= [tex]3^{x}[/tex] + 3. [tex]3^{x}[/tex] ← factor out [tex]3^{x}[/tex] from each term

= [tex]3^{x}[/tex] (1 + 3)

= 4. [tex]3^{x}[/tex]

= 4f(x)


Related Questions

6. Use a one unit multiplier to convert 20 inches to centimeters.
7. Use two unit multipliers to convert 25 feet to centimeters.

Answers

Answer:

should be 15.

Step-by-step explanation:

Find the approximate side length of a square game board with an area of 194 in2.

Answers

Answer:

root 194=13.928 inches

Find the area of a triangle with legs that are: 16 m, 12 m, and 8 m.
O A. 16.4 m2
B. 54 m2
C. 46.5 m2
D. 38.2 m2

Answers

ans. 46.5m2......................

Is 3.824 a rational number?

Answers

Answer:

NopE, can’t be made into a fraction

Answer:

Yes

Step-by-step explanation:

A number is rational if it can be expressed in the form p/q, where q is not zero.

3.824 can be expressed as 3824/1000.

So, it satisfies the criteria of a rational number.

Ariana is a songwriter who collects royalties on her songs whenever they are played in a commercial or a movie. Ariana will earn $40 every time one of her songs is played in a commercial and she will earn $110 every time one of her songs is played in a movie. Ariana earned a total of $500 in royalties on 9 commercials and movies. Write a system of equations that could be used to determine the number of commercials and the number of movies on which Ariana's songs were played. Define the variables that you use to write the system.

Answers

40c+ 110m =500
c + m =9
c is variable for commercial; m is variable for movies

Ummm i know the answer isn't 4 pls help

Answers

Answer:

11

4m-28 = 16

4m = 44

m=11

Step-by-step explanation:

Bags of limes = 4

Total limes in each bag = m

Total limes = 4m

ATQ

4m - 7(4)= 16

4m = 16+28

4m = 44

m = 44/4

m = 11

Value of m = 11

Must click thanks and mark brainliest

ANSWER QUICK !!
Yuri is participating in a tund-raiser at school. She will receive donations from 2 people. A cousin will donate $0.40 for every 1/8 mile that Yuri walks.
A friend will give Yuri a one-time donation of $30
What is the minimum number of miles Yuri needs to walk to raise at least $507 Enter the answer in the box,

Answers

507 - 30 =  477

477 / 0.4 = 1192.5

1192.4 / 8 = 149.0625 miles or 150 miles

i don't know if this is right cause the answer seems so absurd

What is the circumference of the following circle?
ea
3 cm
a
t
D
cm
Show Calculator

Answers

your question is incomplete dear check it once

help me please asap it's important​

Answers

Answer:

6250cubic meters

Step-by-step explanation:

To find the volume of a square-based pyramid, use the formula V = A(h/3), where V is the volume and A is the area of the base. A=625; H=30 (given)

V= 625(30/3) = 6250

Can someone help me please !

Answers

Answer:

[tex] \sqrt{ - 256} = \sqrt{256} \times \sqrt{ - 1} = 16i[/tex]

I hope I helped you^_^

if 5^t = 0.04 ,then find the value of t

Answers

Answer:

t=-2

Step-by-step explanation:

Solve Exponent.

5t=0.04

log(5t)=log(0.04)(Take log of both sides)

t*(log(5))=log(0.04)

t=log(0.04)÷log (5)

t=−2

The probability that Jess will answer any question correctly, independently of her answer to any other
question, is p (p > 0). Let the random variable Y be the number of questions that Jess answers
correctly in any set of 25.

If Pr(Y > 23) = 6 x Pr(Y = 25), show that the value of p is 5/6

Answers

Answer:

I hope my answer helps :)

Step-by-step explanation:

P(Y > 23) = P(Y = 24) + P(Y = 25)

6P(Y=25) = P(Y = 24) + P(Y = 25)

6 = P(Y = 24)/P(Y = 25)+ 1

5 = (²C24××q¹)/C25×p²×q)

Since you know that q = 1 - p,

5 = 25{[p²(1 - p)]/}

1/5 = ( - )/

1/5 = p^(-1) - 1

6/5 = 1/p

p = 5/6 (shown)

I need help solving these two questions
For question 4 it also isn't D
For question 7 it also isn't B

Answers

Answer: i could be A and the next one is c

Step-by-step explanation:

Answer:

First question 8

Second question 10

Step-by-step explanation:

First question

The general formula for both secants is the entire length * the external segment.

Using an example, it is 3*(13 + 3) = 3*16

The other secant will be 4*(x + 4)

These two are equal

4(x + 4) = 3 * 16

4(x + 4) = 48                Divide by 4

x + 4 = 12                    Subtract 4 from both sides

x = 8

Second Question

8(x + 8) = 6(6 + 18)

8x + 64 = 6(24)

8x + 64 = 144            Subtract 64

8x = 80                     Divide by 8

x = 80 /8

x = 10

Express 128 1/4 in simplest radical form.

Answers

Answer:

514/4

Step-by-step explanation:

128 1/4

= (128×4+1)/4

= 514/4

[tex]\\ \sf\longmapsto 128\dfrac{1}{4}[/tex]

[tex]\\ \sf\longmapsto \dfrac{128(4)+1}{4}[/tex]

[tex]\\ \sf\longmapsto \dfrac{512+1}{4}[/tex]

[tex]\\ \sf\longmapsto \dfrac{513}{4}[/tex]

Pls help me !!! What is the area of rectangle

Answers

Answer:

B 48

Step-by-step explanation:

Ac=2AE, because AE=r, Ac=d, d=2r

Ac=2*5=10

The angle ADC is right, because it leans on the diameter AC,

find the leg DC, use the Pythagorus theorem

DC= sqrt (Ac^2-AD^2)= sqrt(100-36)=sqrt64=8

S= 6*8=48

f(x)=8−4x−x3 g(x)=x2+7x−9 Find f(x)+g(x). Select one: a. x3+x2+3x−1 b. −x3+x+3x−1 c. −x3+x2+11x−9 d. 8x2+3x−9x3

Answers

Answer:

B

Step-by-step explanation:

We are given the two functions:

[tex]f(x) = 8 - 4x - x^3\text{ and } g(x) = x^2 + 7x - 9[/tex]

And we want to find:

[tex]f(x) + g(x)[/tex]

Substitute:

[tex]= (8 - 4x - x^3) + (x^2 + 7x - 9)[/tex]

Rewrite:

[tex]= (-x^3) + (x^2) + (7x - 4x) + (8 - 9)[/tex]

Combine like terms:

[tex]= -x^3 + x^2 +3x -1[/tex]

In conclusion:

[tex]f(x) + g(x) = -x^3 + x^2 +3x -1[/tex]

Hence, our answer is B.

244 Children are on a school trip, there
are 19 seats on a coach. How many
coaches are needed?

Answers

Answer:

Totally number of coaches needed is 12

Step-by-step explanation:

If you like my answer than please mark me brainliest thanks

Use the identity property to answer the question.

Answers

Answer:

3k + 0 = 3k

Step-by-step explanation:

Identity property of addition states that the sum of 0 and the term would result in the term.

∴ in this case, 3k + 0 will result in 3k.

~

Help me in this one pls I give 15 pts

Answers

Answer:

I think option b i.e 7 is right but not sure

Samira and Sonia each have a bag containing 20 sweets. In each bag, there are 5 red, 6 green and 9 yellow sweets.
(a)
(b)
Samira chooses one sweet at random from her bag.
Write down the probability that she chooses a yellow sweet.
[1] Sonia chooses two sweets at random, without replacement, from her bag.
(i) Show that the probability that she chooses two green sweets is 3 . 38
(ii) Calculate the probability that the sweets she chooses are not both the same colour.

Answers

Step-by-step explanation:

there must be some typos here. but I try to address the right issues.

there is nothing under (a). so, really nothing to answer.

(b)

there are 20 sweets in her bag. 9 if the 20 are yellow.

so, the probability is the ratio of desired possibilities vs. total possibilities.

that is, tada! 9/20

that is the probabilty for Samira to pick a yellow sweet.

[1] (i)

again, 20 sweets to start with.

6 are green.

when she picks the first one, her probability to pick a green one is 6/20 = 3/10 = 0.3

and now, under the assumption that this came true, she picks another sweet.

this time she had only 19 left, and 5 of them are green.

so, this probabilty is 5/19

now both events need to happen for the case we are discussing. there is no overlapping, no ors, ifs and buts. it is just the product of both probabilities.

3/10 × 5/19 = 15/190 = 3/38

I think that is what the description asks for.

(ii)

that probability is

first selection is red and second is not red +

first selection is green and second is not green +

first selection is yellow and second is not yellow

so,

red and not red

5/20 = 1/4 red

15/19 not red (there are still 15 sweets of other colors in the bag, but again now only 19 total).

red and not red = 1/4 × 15/19 = 15/76 = 0.1974

green and not green

6/20 = 3/10 = green

14/19 = not green

green and not green = 3/10 × 14/19 = 52/190 = 26/95 =

= 0.2737

yellow and not yellow

9/20 = yellow

11/19 = not yellow

yellow and not yellow = 9/20 × 11/19 = 99/380 = 0.2606

so, now assuming up all 3 possibilities ("or" = sum) gives us the general possibility of selecting two different colors

= 0.7316

I"M TIMED!!! PLSSSSSSSSSS HELPPPPPPPPPPP
Drag and drop the numbers and symbols into the boxes to form an expression that represents this phrase:

8 more than quotient of 12 and 6
Which Order Do I Put It In?

Answers

12/6+8. Twelve divided by 6 then add 8

the expression is "2 + 8." To find the quotient of 12 and 6, divide 12 by 6. The result is 2.

Step 1: Add 8 to the quotient.

Now, add 8 to the quotient found. The expression is "quotient + 8."

Step 2: Write the final expression.

The final expression that represents "8 more than quotient of 12 and 6" is "quotient + 8."

So, the expression is "2 + 8."

To know more about expression:

https://brainly.com/question/12884615

#SPJ3

URGENT. Geometric Probability.

Answers

Answer:

Hello,

Step-by-step explanation:

heigth of the equilateral triangle:

[tex]h=3*\dfrac{\sqrt{3}}{2}[/tex]

Area of the triangle:

[tex]A=\dfrac{6*3\sqrt{3} }{2*2} =\dfrac{9\sqrt{3} }{2} \\\\[/tex]

Area of the disk:

[tex]S=\pi*4^2=16\pi\\\\[/tex]

Probability:

[tex]p=\dfrac{9\sqrt{3} }{2*16*\pi}=0.15506125....\approx{15.5\%}[/tex]

Answer:

Step-by-step explanation:

The height of the triangle is given as 6.5, the base is given as 6, therefore, the area of the triangle is:

[tex]A=\frac{1}{2}(6)(6.5)\\A=19.5[/tex]

The area of the circle is:

[tex]A=\pi(4)^2\\A=16\pi\\A=50.26548[/tex]

Divide the area of the triangle by the area of the circle:

[tex]\frac{19.5}{50.2654}*100=38.8[/tex]%

52°
Х
X
tycoom whoever helps with thos

Answers

Answer:

142

Step-by-step explanation:

The exterior angle of a triangle is equal to sum of the opposite interior angles

x = 52+90

x = 142

An exterior angle of a triangle is equal to the sum of its interior opposite angles.

[tex]\large\bf{{\purple{ \longrightarrow \:\large\rm \: x \: = \: 52 \degree \: + \: 90 \degree }}} \\ [/tex]

[tex]\large\bf{{\purple{ \longrightarrow \:\large\rm \: x \: = \: 142 \degree }}} \\ [/tex]

(10x²+19x+6) ÷(5x+2)​

Answers

Answer:

2x + 3

Step-by-step explanation:

(10x² + 19x + 6) ÷ (5x + 2)​ =

= (10x² + 15x + 4x + 6) ÷ (5x + 2)​

= [5x(2x + 3) + 2(2x + 3)] ÷ (5x + 2)​

= [(5x + 2)(2x + 3)] ÷ (5x + 2)​

= 2x + 3

Answer:

2x+3 is your answer

please help me!!!!!!

Answers

Answer:

5 I think

Step-by-step explanation:

Since -2 is less than -1, then we'll choose the first equation, f(x) = + 1

f(-2) = (-2)² + 1

= 5

I want to rearrange the formula of 3+x=ax to find out what x is equal to. I already know the answer via the answer sheet but I want to know how to get that answer.

Answers

Answer:

See below.

Step-by-step explanation:

[tex]3+x=ax[/tex]    (Given)

[tex]x=ax-3[/tex]    (Subtracted 3 on both sides)

[tex]x-ax=-3[/tex]    (Subtracted ax on both sides)

[tex]x(1-a)=-3[/tex]    (Factor out x from x - ax)

[tex]x=-\frac{3}{1-a}[/tex]    (Divided 1 - a on both sides)

8³ x 2⁷= •••
a.4¹⁶
b.2¹⁶
c.4⁸
d.2⁸​

Answers

Answer: B:2^16

Step-by-step explanation:2^16=65536 and 8^3 x 2^7 = 65536

[tex]\boxed{\huge\text{Hey there!}}[/tex]

[tex]\huge\boxed{\mathsf{8^3 \times 2^7= \boxed{?}}}[/tex]

[tex]\huge\boxed{8^3}\\\huge\boxed{= 8\times8\times8}\\\huge\boxed{= 64 \times8}\\\huge\boxed{= \bf 512}[/tex]

[tex]\huge\boxed{2^7}\\\huge\boxed{= 2\times2\times2\times2\times2\times2\times2}\\\huge\boxed{= 4\times4\times4\times2}\\\huge\boxed{= 16\times8}\\\huge\boxed{= \bf 128}[/tex]

[tex]\huge\boxed{512 \times 128}\\\huge\boxed{= \bf 65,536}[/tex]

[tex]\huge\boxed{\textsf{ORIGINAL answer: \bf 65,536} \mathsf{\ and\ the}}\\\huge\boxed{\mathsf{EXPONENTIAL \ answer: \bf 2^{\mathsf{\bf 16}}}}\huge\checkmark[/tex]

[tex]\huge\boxed{\mathsf{Therefore, your\ answer \ is: Option\ B. 2^{16}}}\huge\checkmark[/tex]

[tex]\huge\boxed{\textsf{Good luck on your assignment \& enjoy your day!}}[/tex]

~[tex]\huge\boxed{\frak{Amphitrite1040:)}}[/tex]

Decrease 4,500 by 18%.

Answers

Answer:

5,310.

Step-by-step explanation:

Answer:

3690

Step-by-step explanation:

Simplify 18% to 0.18

4500-(4500×0.18)

4500-810

=3690

Write and solve a word problem that can be modeled by addition of two negative integers.

Answers

Answer:

Step-by-step explanation:

Question:

Max needs to purchase a car and  withdraws $100 from his bank. In a few days he withdraws another $50 to make same repairs. In total what is the change in his bank balance from theese two costs?

Solution:

(-100) + (-50) =

-150

Answered by G a u t h m a t h

2. Find the measure of eº.

Answers

D is a vertical angle to the given 159 degrees.

E + D need to equal 180 degrees.

E = 180 - D

E = 180 - 159

E  = 21 degrees

Answer: 21 degrees.

Answer: e = 21°

Step-by-step explanation:

Angle d will be 159° because alternate exterior angles are equal.

Now angle e + angle d = 180 because they form linear pair

e + d = 180

e + 159 = 180

e = 180-159

e = 21

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