Use the equation, (1/27)^x=3^(-4x+6), to complete the following problems.
Rewrite the equation using the same base.
Solve for x. Write your answer as a fraction in simplest form.
Please show all work, and refrain from posting links, thank you!

Answers

Answer 1

Answer:

Given equation:

[tex]\left(\dfrac{1}{27}\right)^x=3^{(-4x+6)}[/tex]

27 can be written as [tex]3^3[/tex]

Also [tex]\dfrac{1}{a^b}[/tex] can be written as [tex]a^{-b}[/tex]

[tex]\implies \dfrac{1}{27}=\dfrac{1}{3^3}=3^{-3}[/tex]

Therefore, we can rewrite the given equation with base 3:

[tex]\implies (3^{-3})^x=3^{(-4x+6)}[/tex]

To solve, apply the exponent rule [tex](a^b)^c=a^{bc}[/tex]

[tex]\implies 3^{-3 \cdot x}=3^{(-4x+6)}[/tex]

[tex]\implies 3^{(-3x)}=3^{(-4x+6)}[/tex]

[tex]\textsf{If }a^{f(x)}=a^{g(x)}, \textsf{ then } f(x)=g(x)[/tex]

[tex]\implies -3x=-4x+6[/tex]

Add [tex]4x[/tex] to both sides:

[tex]\implies x=6[/tex]


Related Questions

25 % of what number is 5.

SHOW YOUR WORK!!!!

Answers

Answer:

The answer is 1.25

Step-by-step explanation:

5% of 25 = ?

5/100 × 25

1/20 × 25 = 25/20 = 5/4 = 1.25

Thus, 5% of 25 is 1.25

help. list all possible answers

Answers

Hii
Answer:

need more details?

Use the standard normal distribution to find P(-1.23 Sz<2.12).

Answers

Answer:

  (d)  0.8736

Step-by-step explanation:

Unless you have a table of the normal distribution available, this is a calculator problem. Your calculator, or any spreadsheet, can tell you the probability is ...

  P(-1.23 ≤ z ≤ 2.12) ≈ 0.8736

A bird drops of stick to the ground from a height of 95 ft. The function h= 16t^2+95 gives the sticks approximate height h above the ground, in feet, feet r seconds. At above what time does the stick hit the ground

Answers

Answer:

2.44 seconds (above 2 seconds)

Step-by-step explanation:

When the stick hits the ground it has the height of zero.

Substitute h with 0 and solve the given equation for t:

[tex]- 16t^2 + 95 = 0\\16t^2 = 95\\t^2 = 95/16\\t = \sqrt{5.93} \\t=2.44[/tex]

Can you help me with this

Answers

In the case of multiplication in exponents, if the numbers are the same, their exponents are added.

7 + 8 is written to the power of x, and 3 + 2 is written to the power of y.

Which expressions are equivalent to Tan(< g

Answers

Answer:

Can u post a picture so I can see what your talking about!?

What is the slope of the graph of this function in decimal form?
(6,1) (-6,-5)

Answers

Answer:

slope = 0.5

Step-by-step explanation:

[tex]slope=\frac{-5-1}{-6-6} =\frac{-6}{-12} =\frac{1}{2} =0.5[/tex]

Hope this helps

The slope of the graph through points (6,1) and (-6,-5) is 0.5.

What is the slope of the graph?

The slope formula can be expressed as:

[tex]Slope (m) = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Given the coordinates of the points through which the graph passes through:

Point 1 ( 6,1 )

x₁ = 6

y₁ = 1

Point 2( -6,-5 )

x₂ = -6

y₂ = -5

Plug the coordinates into the slope formula and simplify.

[tex]Slope (m) = \frac{y_2 - y_1}{x_2 - x_1}\\\\Slope (m) = \frac{-5 - 1}{-6 - 6}\\\\Slope (m) = \frac{-6}{-12}\\\\Slope (m) = \frac{1}{2}\\\\Slope (m) = 0.5[/tex]

Therefore, the slope of the line is 0.5.

Learn more about slope formula here: brainly.com/question/24578307

#SPJ3


82% of £134.18
Give your answer rounded to 2 DP

Answers

82 = 0.82 = multiplier

134.18 x 0.82 = 110.0276

= £110.03 (2.d.p)

Best answer gets brainliest!

Answers

Answer: Best answer gets brainliest!

90+120= 210

Step-by-step explanation:

Add the amount of students together!

Hopefully this helps you!

-Keira

hello!

First, let's check how many 7th grade students take the bus.

On the graph, find "7th grade"

There are 90 7th grade students taking the bus.

Same with the 8th grade:-

120 students

How many 7th & 8th grade students take the bus?

The sum of the 7th grade students & the 8th grade students is your answer.

So, add:-

[tex]\sf{90+120}[/tex]

[tex]\bigstar{\boxed{\pmb{210~students}}\longleftarrow\sf{Option~B~is~correct}}}[/tex]

note:-

Hope everything is clear; if you need any explanation/clarification, kindly let me know, and I'll comment and/or edit my answer :)

solve pls brainliest

Answers

Answer:

2/5 > 1/4

Step-by-step explanation:

First convert the denominators to the LCM which will be 20

2/5 will convert to 8/20 because 5 x 4 = 20 so 2 x 4 = 8 and 1/4 will convert to 5/20 because 4 x 5 = 20 so 1 x 5 = 5

The cheetah is the fastest land animal in the world. During a sprint, the number of feet a cheetah runs y varies directly with the amount of time in seconds x as shown in the table. Write and solve a direct variation equation to determine how far the cheetah can run in 5.5 seconds.

Answers

Step-by-step explanation:

[tex] \hookrightarrow \sf y = kx [/tex]

[tex] \sf where \: k \: is \: constant[/tex]

[tex] \sf \: k = \frac{y}{x} [/tex]

[tex] \hookrightarrow \sf \: k = \frac{y}{5.5} [/tex]

Equation = [tex] \sf \: k = \frac{y}{5.5} [/tex]

In a student union election of a school, 91% of boys and 84% of girls voted. It is kwon

Answers

Answer:

If there are 350 kids for example your answers would be:

Boys: 182

Girls: 168

Step-by-step explanation:

If you add those numbers together you'll get 350 again

please help me

Select the reason that best
supports Statement 4 in the
given proof.
A. Transitive Property
B. Multiplication Property of Equality
C. Substitution
D. Given

Answers

Answer: C

Step-by-step explanation:

They are substituting PQ=25 from steps 1 and 3.

Kevin is 4 times as old as Daniel and Kevin is
also 6 years older than Daniel

Answers

Step-by-step explanation:

let kevein be x and daniel be y

x=4y (equation i)

x=6+y(equationii)

putting the value of x in equationii

4y=6+y

3x=6

x=2

what numbers between the number 7-15 make 33

Answers

11 x 3
33/3
33/11

when you subtract or add any numbers together it wouldn’t be between 33
11x3 =33
Check:
33/3=11

Please answer all three if you do i will mark brainliest

Answers

Answer:

1 positive correlation

2 A

3 negative

Step-by-step explanation:

Hope this helps!:)

A triangle has two sides of length 19 and 19. What is the largest possible whole-number length for the third side?

Answers

Answer: 37

To maximize the length of the third side, which I'll call x, it needs to be the longest side.

So by the triangle inequality theorem, 19+19>x, meaning the maximum whole number value of x is 37.

I need help, I will give brainliest

what is the value of x, round to the nearest 10th.
use sin, cos, and tan

Answers

Value of X:
10cm = Adjacent 8cm = opposite
Tan -1(8/10) = 38.7

Value of Y:
10cm = opposite 8cm = adjacent

Tan-1(10/8) = 51.3

does anyone know the answer to this question?

Answers

Answer:

c = 2.5 , d = - 3

Step-by-step explanation:

f(x) = cx + d

f(4) = 7 ( substitute x = 4 into the equation and equate to 7 )

f(10) = 22 ( substitute x = 10 into the equation and equate to 22 )

4c + d = 7 → (1)

10c + d = 22 → (2)

subtract (1) from (2) term by term to eliminate d

(10c - 4c) + (d - d) = 22 - 7 , that is

6c = 15 ( divide both sides by 6 )

c = 2.5

substitute c = 2.5 into (1) and solve for d

4(2.5) + d = 7

10 + d = 7 ( subtract 10 from both sides )

d = - 3

Answer:

c = 2.5

d = - 3

Step-by-step explanation:

f(x) = cx + d

f(4) = 7

f(10) = 22

4c + d = 7

10c + d = 22

(10c - 4c) + (d - d) = 22 - 7

6c = 15

---    ----

6      6

c = 2.5

4(2.5) + d = 7

10 + d = 7

-10       -10

d = - 3

I need this for a geometry assignment........please help

Answers

All three are similar

In ∆SUT and ∆VWX

Two sides are similar and one angle is similar

So by SSA they are similar

In ∆PRQ and rest two

All angles are.

80,80,20°

So

They are similar by AAA congruence

Select the true statement about trend lines.
O A. A trend line should be as close as possible to the points.
O B. A trend line connects the points.
O C. A trend line goes through the first and last points.
D. A trend line is always horizontal.
SUBMIT

Answers

The statement that is true about trend lines is: A. A trend line should be as close as possible to the points.

What is a Trend Line?

A trend line, which can also be called the line of best fit, is a straight line that represents the pattern of a data, which can be positive or negative.

A trend line does not necessarily need to connects all the points, but goes through some points to show the pattern. It may not even be necessary to go through any of the points, what's improtant is for the trend line to be close to as many points as possible.

Therefore, the statement that is true about trend lines is: A. A trend line should be as close as possible to the points.

Learn more about trend lines on:

https://brainly.com/question/2589459

Mr. Jones and Mr. Griebel each bought new shoes, Mr. Jones used a 20% off coupon and paid $82. Mr. Griebel used a $20 off coupon. How much Mr Griebel pay for his shoes?

Please help meee

Answers

Answer:

Assuming they bought the same shoes, $82.5

Step-by-step explanation:

80% of Original Shoe price = $82

Divide by 0.8 to find the original price.

82 / 0.8 = 102.5

102.5-20=82.5

A straw is placed inside a rectangular box that is 3 inches by 6 inches by 8 inches, as shown. If the straw fits exactly into the box diagonally from the bottom left corner to the top right back corner, how long is the straw? Leave your answer in simplest radical form.

Answers

The straw is placed diagonally in the rectangular prism, therefore, the length of the straw is √109 inches

How to find the diagonal of a rectangular prism?

Diagonal of a rectangular prism = √(l² + w² + h²)

Where,

l = lengthw = widthh = height

Therefore,

l = 6 inches

w = 3 inches

h = 8 inches

diagonal = √(6² + 3² + 8²)

diagonal = √36 + 9 + 64

diagonal = √109 inches

learn more rectangular prism here:https://brainly.com/question/21888893

Find the surface area
8in
3in
6in

Answers

Answer:

Area of a Rectangular prism is

A = 2lh + 2lw + 2hw

Step-by-step explanation:

See picture above

A boy yells in a narrow valley. the sound reflects off of a boulder that is 80 m away. how long will it take to hear the echo if the speed of a sound wave is 320 m/s? (speed = ) 0.25 seconds 0.50 seconds 2.0 seconds 4.0 seconds

Answers

Answer:

  0.50 seconds

Step-by-step explanation:

The time it takes for an echo to return is the time it takes for the sound to make the round trip between the source and the reflecting object.

The boulder is 80 m away from the source, so the round-trip distance is 2×80 m = 160 m. At a speed of 320 m/s, it takes sound ...

  (160 m)/(320 m/s) = 0.50 s

to make the round-trip.

It will take 0.50 seconds to hear the echo.

The time it will take to hear the echo, when the speed of a sound wave is 320 m/s is 0.50 seconds.

What is the speed of sound?

Speed of sound is the rate by which the sound wave travels. The speed of sound depends on the medium by which the sound wave is travelling.

The speed of the wave can be found out using the following formula.

[tex]s=\dfrac{d}{t}[/tex]

Here, (d) is the distance travelled by the wave and (t) is time taken by the wave to cover that distance.

A boy yells in a narrow valley. The sound reflects off of a boulder that is 80 m away.

For the echo, distance travelled will be doubled as it come back.Thus, the distance travelled by sound wave is,

[tex]d=2\times80\\d=160\rm\; m[/tex]

The speed of sound is 320 m/s. Put these value in the above formula as,

[tex]320=\dfrac{160}{t}\\t=0.5\rm\; s[/tex]

Thus, the time it will take to hear the echo, when the speed of a sound wave is 320 m/s is 0.50 seconds.

Learn more about the speed of sound here;

https://brainly.com/question/95976

The height of a building in a drawing is 15 inches if the actual height of the building is 165 feet find the scale factor of the Drawing

Answers

Answer:

The scale is 11 feet per one inch.

Step-by-step explanation:

[tex]\frac{165feet}{15inches} = 11feet / inch[/tex]

Hey y’all! Can I please have some help??? :)

Answers

Answer:

Rhombi and Squares

Step-by-step explanation:

1) KY (pythagorean Thm) 5² + x² = 13²    ...= 12

2) PK Diagonals bisected. also = 12

3) Diagonals of rhombi are perpendicular. <YKZ = 90

4) 67. Alternate interior angles are congruent.

5) 3. Diagonals are bisected and congruent for squares.

6) 45° . Angles are bisected by diagonals.

7) 90° . All angles of squares are right angles.

8) 6. Diagonals are bisected. So 3 is doubled to 6.

9) I need graph paper.. hol'up

Solve each equation.

5/6x = 35

A. 42
B. 29.16 (continued)
C. 35 5/6
D. 36

[ Please help me!! :( ]

Answers

[tex]\huge\fcolorbox{blue}{aqua}{Answer:}[/tex]

═════════════════════

The answer is A.42

Solution:

[tex] \frac{5}{6}x = 35[/tex]

[tex]x=35\times \left(\frac{6}{5}\right) [/tex]

[tex]x=\frac{35\times 6}{5} [/tex]

[tex]x=\frac{35\times 6}{5} [/tex]

[tex]x=\frac{210}{5} [/tex]

[tex]x=42 [/tex]

══════════════════════

Step-by-step explanation:

#Carry on learning

A circle has (-1, -1) and (-25,-11) as endpoints of a diameter.
Find the center and radius of the circle.
Write the standard equation of the circle.

Answers

well, since we know the diameter points, half-way in between is the center

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{-1}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{-25}~,~\stackrel{y_2}{-11}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ -25 -1}{2}~~~ ,~~~ \cfrac{ -11 -1}{2} \right)\implies \left(\cfrac{-26}{2}~~,~~\cfrac{-12}{2} \right)\implies (-13~~,~~-6)[/tex]

and its radius will be half the length of the diameter

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-1}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{-25}~,~\stackrel{y_2}{-11})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[-25 - (-1)]^2 + [-11 - (-1)]^2}\implies d=\sqrt{(-25+1)^2+(-11+1)^2} \\\\\\ d=\sqrt{(-24)^2+(-10)^2}\implies d=\sqrt{676}\implies d=26~\hfill \stackrel{half~that}{r=13}[/tex]

[tex]\rule{34em}{0.25pt}\\\\ \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{-13}{ h},\stackrel{-6}{ k})\qquad \qquad radius=\stackrel{13}{ r} \\\\[-0.35em] ~\dotfill\\\\\ [x-(-13)]^2~~ + ~~[y-(-6)]^2~~ = ~~13^2\implies (x+13)^2~~ + ~~(y+6)^2~~ = ~~169[/tex]

What is 9 5/9-2 5/27?​

Answers

Answer:

[tex]=7\frac{10}{27}[/tex]

Decimal: 7.37

Step-by-step explanation:

[tex]9\frac{5}{9} -2\frac{5}{27} =\frac{81+5}{9} -\frac{54+5}{27} =\frac{86}{9} -\frac{59}{27}[/tex]

[tex]\frac{258}{27} -\frac{59}{27} =\frac{199}{27}[/tex]

[tex]=7\frac{10}{27}[/tex]

Hope this helps

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