Solve: 3^x+1 + 3^x= 108​

Answers

Answer 1

Answer:

x = 3

Step-by-step explanation:

[tex] {3}^{(x + 1)} + {3}^{x} = 108 \\ \\ {3}^{x} .3 + {3}^{x} = 108 \\ \\ {3}^{x} (3 + 1) = 108 \\ \\ {3}^{x} (4 )= 108 \\ \\ {3}^{x} = \frac{108}{4} \\ \\ {3}^{x} = 27 \\ \\ {3}^{x} = {3}^{3} \\ \\ \implies x = 3[/tex]


Related Questions

A sphere has a radius of 15ft find the volume of the sphere

Answers

Answer:

14130= I rounded  

Step-by-step explanation:

This is the formula

4/3 x pi x r cubed

radius :15

pi = 3.14

substitue the Values

4/3 times 3.14 times 15 times 15 times 15.

3375 = 15 times 15 times 15

3375 x 3.14 = 10597.5 x  4/3

14130

Answer:

14,137.1669 ft^3

Step-by-step explanation:

1. Cube the radius: 15^3 = 3375

2. Multiply the cubed radius by 4/3: 3375*4/3 = 4500

3. Multiply the equation by 3.14159 (pi): 4/3(3.14159)(3375) = 14,137.1669 ft^3

4. Round your answer as needed.

From the equation below, where is the center of the circle located and what is the radius?
(x – 4)2 + (y + 8)2 = 16
A) Center: (4, -8) Radius = 4
B) Center: (-4, 8) Radius = 4
C) Center: (4, -8) Radius = 16
D) Center: (-4, 8) Radius = 16

Answers

Answer:

B Center: (-4, 8) Radius = 4

Step-by-step explanation:

PLSSS HELLPPPPP!!!!!!! Find the measure of the missing angle.

Answers

Answer:

86 degrees

Step-by-step explanation:

The total angles of a quadrilateral add up to 360 degrees, so if you do 360-134-50-90, you get 86, which is your answer.

Answer:

x is 86

Step-by-step explanation:

To solve we will use the equation s = (n-2) 180

s is the sum of all the angles, and n is the number of sides the shape has.

We do not know what s is yet, and since this is a 4 sided figure we will have to solve it like this:

s= (4-2) 180

s= 2(180)

s= 360

Since we now know all the angles added together will equal 360 we can now solve for x. We will solve by adding up all the angles together plus x like this:

134+ 90+ 50+x = 360

274 + x = 360  

-274         -274               360-274 = 86

X = 86

Solve for n.
n + 184 = –375

Answers

Answer:

n=-559

Step-by-step explanation:

Hope this helps and have a great day. :)

Answer:

n= -559

Step-by-step explanation:

So in order to solve this, you need to subtract 184 on both sides.

n+184=-374

   -184=-184

-----------------------

n= -559

So the answer is n= -559

Hope this helped!!! :)

The bottom of a ladder is placed 4 feet from the side of a building. The top of the ladder must be 13 feet off the ground.

What is the shortest ladder that will do the job? SHOW your work.

10 foot ladder
12 foot ladder
14 foot ladder

Answers

Answer:14

Step-by-step explanation:

Plz help this is due today NO LINKS OR GROSS PICTURES OR I Will REPORT And please show work

Answers

Answer: Trapezoid

Step-by-step explanation:

Trapezoids are parollelograms, that’s all

50 PTS for answer!! I need help! "Work this one out," said Monica to her colleague. "I drive from my home to the office every morning. At the back of my house is a short, fairly narrow driveway approximately 300 yards long. I drive my car down this driveway in a westerly direction, yet when I stop the car at the end of the driveway it is facing east."
"Does the driveway go round in a circle?" asked the colleague.

"No," replied Monica, "it is absolutely straight."

What is the explanation?

Answers

es norte sur este y oeste  es un camino completamente recto esta en circulo por ue esta la brujula que apunta al norte y al sur

9
Is the function shown in the
graph one-to-one?
Yes, there exists one
input for every output.
No, there exists
more than one output for at
least one input.
• No, there exists
more than
one input for at least one
output.
Yes, there exists one output for
every input.

Answers

Answer: Choice D

Yes, there exists one output for every input.

=======================================================

Explanation:

x = input

y = output

For any given x value, we have exactly one and only one y value that pairs up with it. Use the vertical line test. This is where we try to draw a single vertical line through more than one point on the curve. You'll find that no such line can be drawn. Any vertical line only crosses the curve exactly once (corresponding to exactly one output). We say that it passes the vertical line test, and therefore we have a function.

Side note: the curve does not pass the horizontal line test. That means the function is not one-to-one.

Which of the following graphs shows a pair of lines that represent the equations with a solution (−2, 5)?

Answers

Answer:

The first one (top)

Step-by-step explanation:

The coordinate plane works with coordinates being x, y, and so if x is -2, then it would be to the left of 0. 5 is above 0, and you see the 2 lines intersecting at that point.

A store wants to have an end of year sale so they discount all prices by 35%. If you buy an item that originally sells for $80.00, how much are you paying for it after the discount?

Answers

Answer:

$52.00

Step-by-step explanation:

35% of $80

(35÷100) ×80

0.35× 80

$28.00

$80 -$28

$52.00

Two friends are to meet at the library. Each independently and randomly selects an arrival time within the same one-hour period. Each agrees to wait a maximum of fifteen minutes for the other to arrive. What is the probability that they will meet

Answers

Answer:

The probability that they will meet is 0.4375

Step-by-step explanation:

Let A and B be two friends who choose to meet  the same one-hour period.Since there are 60 minutes in an hour therefore n= 60

A can wait for 15 minutes

So the probability of A to meet is given by P(A)=  (15/60)= 1/4

Similarly

B can wait for 15 minutes

So the probability of B to meet is given by P(B)=  (15/60)= 1/4

The  probability  that A cannot meet is given by 1- P(A)=  1-1/4= 3/4

Similarly

The  probability  that B cannot meet is given by 1- P(B)=  1-1/4= 3/4

And

The  probability  that both  A  and B cannot meet is given by = 3/4*3/4= 9/16

So the probability that both will meet = 1- 9/16= 7/16= 0.4375

PLEASE HELPP!!
An initial amount of money is placed in an account at an interest rate of 5% per year, compounded continuously. After five years, there is $3287.11 in the
account. Find the initial amount placed in the account. Round your answer to the nearest cent.

Answers

9514 1404 393

Answer:

  $2560.00

Step-by-step explanation:

The account balance is given by the formula ...

  A = Pe^(rt) . . . . principal P invested at rate r for t years

Filling in your numbers, we have ...

  $3287.11 = Pe^(0.05·5)

  P = $3287.11e^(-0.25) = $2560.00

The initial amount was $2560.00.

The X and Y coordinates (in feet) for station Shore are 2058.97 and 6980.06, respectively, and those for station Rock are 1408.03 and 6980.06, respectively. What are the azimuth, bearing, and length of the line connecting station Shore to station Rock

Answers

Answer:

Hence, the azimuth, bearing, and length of the line connecting station Shore to station Rock are [tex]270^{\circ},90^{\circ}[/tex] and [tex]650.94[/tex] feet.

Given :

The shore station point [tex](X_1,Y_1)[/tex] in feet,

        [tex](X_1,Y_1)=(2058.97, 6980.06)[/tex]

The Rock station point [tex](X_2,Y_2)[/tex] in feet

       [tex](X_2,Y_2)=(1408.03,6980.06)[/tex]

From the figure

     [tex]x=2058.97-1408.03=650.94[/tex] feet

    [tex]y=6980.06-6980.06=0\\[/tex] feet

Length of the line [tex]L=\sqrt{x^2+y^2}[/tex]

                           [tex]\Rightarrow L=\sqrt{(650.94)^2+0}=650.94[/tex]

                            [tex]\Rightarrow L=650.94[/tex] feet

[tex]\because[/tex] [tex]\tan \theta=\frac{y}{x}=\frac{0}{x}=0[/tex]

[tex]\Rightarrow \theta=\tan^{-1}(0)=0[/tex]

Azimuth of line[tex]=270^{\circ}+\theta[/tex]

                       [tex]=270^{\circ}+0[/tex]

                      [tex]=270^{\circ}[/tex]

[tex]\therefore[/tex] Bearing [tex]=360^{\circ}-\text{Azimuth}[/tex]

                [tex]=360^{\circ}-270^{\circ}[/tex]

                [tex]=90^{\circ}[/tex]

Fay read an article that said 26% of Americans can speak more than one language. She was curious if this
figure was higher in her city, so she tested H, : p=0.26 vs. H : p > 0.26, where p represents the
proportion of people in her city that can speak more than one language.
She found that 40 of 120 people sampled could speak more than one language. The test statistic for these
results was 2 1.83.
Assuming that the necessary conditions are met, what is the approximate P-value for Fay's test?
You may round to three decimal places.
P-value

Answers

Answer:

0.0336

Step-by-step explanation:

the hint says so

According to the result of the test statistic, the approximate p-value for Fay's test is of 0.034.

How to find the p-value of a test?

It depends on the test statistic z, as follows.

For a left-tailed test, it is the area under the normal curve to the left of z, which is the p-value of z.For a right-tailed test, it is the area under the normal curve to the right of z, which is 1 subtracted by the p-value of z.For a two-tailed test, it is the area under the normal curve to the left of -z combined with the area to the right of z, hence it is 2 multiplied by 1 subtracted by the p-value of z.

In this problem, we are testing if the proportion is greater than a value, hence it is a right-tailed test.

The test statistic is z = 1.83, which has a p-value of 0.966.

1 - 0.966 = 0.034.

Hence, the approximate p-value for Fay's test is of 0.034.

You can learn more about p-values at brainly.com/question/13873630

The ratio of blue cars to red cars in a garage is 7:6. If there are
28 blue cars in the garage then how many red cars must be in the garage?

Answers

Answer:

24 Red Cars

Step-by-step explanation:

Step 1 : Create a ratio

7:6 = 28:x

Step 2 : Find the relation between the two.

28/7 = 4

Step 3 : Multiply 6 by 4 to find x

6 * 4 = 24

Edit : Reread question

Answer:

24

Step-by-step explanation:

7/6=28/x

7x=28*6

7x=168 ...both divide by 7

x=24

red cars in garage 24

finding the slope to points​

Answers

can you please put the points

QUESTION: WHATS BETTER

APPLE JUICE OR ORANGE JUICE

Answers

Answer:

orange juice is better than Apple Juice

15) Find the product. Show all your work.
Reduce all your answers into simplest
form
3 - x
5
л |N

Answers

Answer:

[tex]\frac{3}{2}[/tex]

Step-by-step explanation:

3 [tex]\frac{3}{4}[/tex] x [tex]\frac{2}{5}[/tex]

[tex]\frac{15}{4}[/tex] x [tex]\frac{2}{5}[/tex]

[tex]\frac{30}{20}[/tex] = [tex]\frac{3}{2}[/tex]

or another way

[tex]\frac{15}{4}[/tex] x [tex]\frac{2}{5}[/tex]

[tex]\frac{3}{2}[/tex] x [tex]\frac{1}{1}[/tex] = [tex]\frac{3}{2}[/tex]


I'm thinking of two numbers: a and b.
The sum of my numbers (a + b) is 6.7, and their
difference (a - b) is 4.3.
What are my two numbers?

Answers

Answer:

5.5 and 1.2

Step-by-step explanation:

Answer:

a = 5.5

b = 1.2

Step-by-step explanation:

5.5 + 1.2 = 6.7

5.5 - 1.2 = 4.3

The price of a cell phone is usually $240 Ella mom buys one of these cell phones when the discount is 25 how much did Ella mom save?

Answers

Answer:

$60

Step-by-step explanation:

$240 = 100%

Discount = 25%

100% - 25% = 75%

75% as a decimal is 0.75

Multiply:

240(0.75) = 180

You could also do 3/4 of 240 because 0.75 is 3/4

To find out how much she saved, let's subtract the sale price from the original price:

240 - 180 = 60

Ella's mom saved $60 from the discount

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

[tex]24x^{2}+bx^{2} =25x^{2}[/tex]

Answers

Answer:

x = 0

Step-by-step explanation:

Subtract 25x^2 from both sides

24x^2 + bx^2 - 25x^2 - 25x^2

Simplify

bx^2 - x^2 = 0

Factor bx^2 - x^2: x^2(b - 1)

bx^2 - x^2

Factor out common term x^2

= x^2 (b - 1)

x^2(b - 1) = 0

Using the Zero Factor Principle: If ab = 0 then a = 0 or b = 0

x^2 = 0

Apply rule x^n = 0   x = 0

x = 0

NEED HELP ASAP WILL GIVE BRAINLIEST REAL ANSWERS ONLY PLZ WILL REPORT FAKE ANSWERS

Answers

Answer:

The graph has a domain of {x|0 < x < infinite} and approaches 0 as x decreases

The graph has a domain of {y| -infinite < y < infinite} and decreases as x approaches 0.

Step-by-step explanation:

I was confused at first because I was like "There is 2 answers" and I reread the question again and found my mistake.

And sorry for the wait because "I am in class"

What is the value of x, the side length of the smallest square (please show work) Thanks!

Answers

Answer:

8 cm

Step-by-step explanation:

Ok lets on the biggest square we have 17 cm

17cm is the hypotenuse for the right triangle

The second largest's area is 225 cm^2

Sq root of 225 cm^2, is 15

To find x, lets plug the info we have to the pythagorean theorom

[tex]a^2 + b^2 = c^2\\a^2 + 15^2 = 17^2\\a^2 + 225 = 289\\\\289 - 225 = a^2\\64=a^2\\a = 8 cm[/tex]

The side length of the smallest Square is 8 cm

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Plz help this is due today NO LINKS OR GROSS PICTURES OR I Will REPORT And please show work

Answers

Answer:

The volume of Kuron Pool is 600ft³.

Step-by-step explanation:

Rectangular prisms are basically cuboids.

So using the formula to calculate volume of the cuboid i.e.

V = length x breadth(width) x height

= 15 x 8 x 5

= 600ft³

x^2+ 6x + 8
Vertex:
Axis of symmetry:
Y-intercept:
X-intercept:

Answers

Answer:

( + 2 ) ( + 4 )

Step-by-step explanation:

Answer:

See below for answers and explanations (along with a graph)

Step-by-step explanation:

To calculate the vertex, we can transform the expression into an equation in the form of y=a(x-h)²+k and take (h,k) as our vertex. By completing the square, we see that y=x²+6x+8 is the same as y=(x+3)²-1, implying that our vertex is (-3,-1)

To calculate the axis of symmetry, it is defined as the vertical line that passes the x-axis, defined as x=h, therefore the axis of symmetry is x=-3

To calculate the y-intercept, it is defined as the y-value when x=0, therefore the y-intercept would be y=(0)^2+6(0)+8=8, so y=8 or (0,8)

To calculate the x-intercepts, which are the x-values when y=0, we can factor the expression and set it equal to 0 so we can use the Zero Product Property. Therefore, if x²+6x+8=0, then (x+2)(x+4)=0, implying that x+2=0 and x+4=0 are solutions. This means that our x-intercepts are x=-2 and x=-4 or (-2,0) and (-4,0).

Note that there are different ways to achieve these answers. See the graph for a visual reference (you may need to click on it to zoom in).

Find the area of an equilateral triangle with sides of length 24 inches in simplest
form?

Answers

Answer:

B. 144√3 in².

Step-by-step explanation:

Given the following data;

Sides of length = 24 inches

Mathematically, the area of an equilateral triangle is given by the formula;

A = √3 * s²/4

Where, s represents the sides of length.

Substituting into the formula, we have;

A = √3 * 24²/4

A = √3 * 576/4

A = √3 * 144

A = 144√3 in²

In ΔPQR, the measure of ∠R=90°, RP = 7.6 feet, and QR = 5 feet. Find the measure of ∠Q to the nearest degree.

Answers

Answer:

15.9454=15.9

Step-by-step explanation:

A bank loaned out $28,500, part of it at the rate of 14% annual interest, and the rest at 4% annual
interest. The total interest earned for both loans was $2,640.00. How much was loaned at each rate?
$
was loaned at 14% and
was loated at 4%.

Answers

Answer:

$15,000 was invested at 14% per year, and $13,500 was invested at 4% per year.

Step-by-step explanation:

Given that a bank loaned out $ 28,500, part of it at the rate of 14% annual interest, and the rest at 4% annual interest, and the total interest earned for both loans was $ 2,640.00, to determine how much was loaned at each rate you must perform the following calculations:

28,500 x 0.14 + 0 x 0.04 = 3,990

20,000 x 0.14 + 8,500 x 0.04 = 3,140

15,000 x 0.14 + 13,500 x 0.04 = 2,640

Therefore, $ 15,000 was invested at 14% per year, and $ 13,500 was invested at 4% per year.

True or False
72 - ( - 100) is negative.

Answers

Answer:

false

Step-by-step explanation:

72 - (-100) --> two negatives turn into a positive

72 + 100

True is the correct answer

someone help me wiht this geomtry problem asap!!!

Answers

Answer:

if you ant to find the area of the traporziord prism you have to multiply the height and with to find the area

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