What is the solution to this equation? (1/27)2-x =9^3x

Answers

Answer 1

Answer:

 x = -2

Step-by-step explanation:

Prime factorize, 27 and 9

27 = 3 *3 * 3 = 3³

  9 = 3*3 = 3²

[tex]\sf \left(\dfrac{1}{27}\right)^{2-x}=9^{3x}\\\\[/tex]

 [tex]\left(\dfrac{1}{3^3}\right)^{2-x}=9^{3x}\\\\(3^{-3})^{2-x}=(3^2)^{3x}\\\\3^{(-3)*(2-x)}=3^{2*3x}\\\\3^{-6+3x} = 3^{6x}[/tex]

Bases are same, so now compare the exponents

     -6 + 3x = 6x

            3x = 6x + 6

       3x - 6x = 6

             -3x = 6

               x  = 6/(-3)

               [tex]\sf \boxed{\bf x = -2}[/tex]

Exponent law:

         [tex](x^m)^n=x^{m*n}\\\\\left(\dfrac{1}{a^{m}}\right)=a^{-m}\\[/tex]


Related Questions

The product of 80 and 5,000 is...

Answers

Answer: 400,000

Step-by-step explanation:

The product is the result of multiplication. In other words, you would multiply 80×5,000.

I hope this helps!! :)

A circular garden has a circumference of 42.3 feet. Find the approximate diameter of the garden. Use 3.14 for π.

Answers

Answer:

13.5

Step-by-step explanation:

c = 2πr

42.3 = 2(3.14)r

42.3 = 6.28r

6.74 = r

d = r + r

d = 6.74 + 6.74

d = 13.5

( brain + 95 points ) A triangular prism has a height of 10 cm and the triangle has a base of 4 cm and a height of 6 cm. Find the volume of the triangular prism.

Answers

Area of base

1/2BH1/2(4)(6)2(6)12cm²

Volume

Area of base× height12(10)120cm³

Find the missing side of this right triangle.
X
9

22
X = [?]
Enter the number that belongs in the green box.

Answers

Answer:

x = sqrt(403)

Step-by-step explanation:

Use Pythagorean Theorem for right triangles

x^2 + 9^2 = 22^2

   x = sqrt 403

Estimate the product.

14×212

Answers

the answer of 14.212 is 2968

-6>2x+6 ≤18

graph the inequality

Answers

Answer:

y= x + b

-6 > 2x+6- graph a doted line that crosses through -6, and 2 shade below the dotted line going to the negative

18 >< 2x+6 graph a solid line through 18 and 2 and shade everything above the line going positive

have a good day hope this helped

Step-by-step explanation:

Select the correct answer. If is modified as , what transformations will be seen in the graph? A. The graph will reflect across the x-axis and then shift units up. B. The graph will reflect across the y-axis and then shift units down. C. The graph will reflect across the x-axis and then shift units to left. D. The graph will reflect across the y-axis and then shift units to right.

Answers

The transformation is (b) The graph will reflect across the y-axis and then shift 5 units down.

How to determine the transformation?

The missing phrase in the question is: "If f(x) = 2ˣ + 1 is modified as g(x) = 2⁻ˣ + 1 - 5"

The functions are given as:

f(x) = 2ˣ + 1

g(x) = 2⁻ˣ + 1 - 5

First, the function f(x) is reflected across the y-axis (this eliminates options a and c)

The rule of this transformation is

(x,y) ⇒ (-x,y)

So, we have:

f'(x) = 2⁻ˣ + 1

Next, the function f(x) is shifted down by 5 units (this eliminates options d)

The rule of this transformation is

(x,y) ⇒ (x,y - 5)

So, we have:

f''(x) = 2⁻ˣ + 1 - 5

By comparing the functions f"(x) and g(x), we have:

g(x) = f''(x) = 2⁻ˣ + 1 - 5

Hence, the transformation is (b) The graph will reflect across the y-axis and then shift 5 units down.

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Question 1 Complete the missing reasons for the proof. Given: 4(x - 2) = 6x + 18 Prove: x= -13 Statements Reasons 1.4(x - 2) = 6x +18 given 2. 4x8= 6x +18 distributive property 3.-2-8-18 4.-2x = 26 addition property of equality 5.x = -13 O 3. subtraction property of equality; 5. multiplication property of equality O 3. subtraction property of equality; 5. division property of equality 3. addition property of equality; 5. division property of equality O 3. addition property of equality; 5. multiplication property of equality​

Answers

Looking at the problem statement, the question is asking us to determine what the missing reasons are.  The information that is given to us is a step-by-step process of solving an expression for an unknown. There are also two blanks in the reasons column for steps 3 and 5 which we will need to determine.

For step #3, we can see that they subtracted 6x from both sides which means that options 3 and 4 are automatically out since they reference addition in the first part.  The correct reasoning for this part would be Subtraction Property of Equality which states that we subtract the same item from both sides of the expression.

We can see this being done in the following actions

[tex]4x - 8 = 6x + 18[/tex][tex](4x - 6x) - 8 = (6x - 6x) + 18[/tex][tex](4x - 6x) - 8 = 18[/tex][tex]-2x - 8 = 18[/tex]

For step #5, we can see that they divided both sides by -2 which means that option 1 is out since it references the multiplication property of equality. The correct reasoning for this part would be Division Property of Equality which states that we divide both sides by the same item.

We can see this being done in the following actions

[tex]-2x = 26[/tex][tex]\frac{-2x}{-2} = \frac{26}{-2}[/tex][tex]x= \frac{26}{-2}[/tex][tex]x= -13[/tex]

Therefore, the option that would best fit the description that we provided during our work would be option 2 (3. subtraction property of equality; 5. division property of equality).

Answer:

b) 3. addition property of equality; 5. division property of equality.

Step-by-step explanation:

Given: 4(x - 2) = 6x + 18

Prove: x = -13

Algebraic Properties:

Addition: If a = b, then a + c = b + cSubtraction: If a = b, then a - c = b - cMultiplication: If a = b, then ac = bcDivision: If a = b, then a ÷ c = b ÷ cDistributive: a(b + c) = ab + ac

Steps:

1. Given:

⟹ 4(x - 2) = 6x + 18

2. Distribute property:

4(x) + 4(-2) = 6x + 18 [distribute 4]

⟹ 4x - 8 = 6x + 18

3. Subtraction property of equality:

4x - 6x - 8 = 6x - 6x + 18 [subtract 6x from both sides]

⟹ -2x - 8 = 18

4. Addition property of equality:

-2x - 8 + 8 = 18 + 8 [add 8 to both sides]

⟹ -2x = 26

5. Division property of equality:

-2x ÷ -2 = 26 ÷ -2 [divide both sides by -2]

⟹ x = -13

In conclusion, the missing reasons are the subtraction and division properties of equality.

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The discussion in this lesson offers two tips for saving money. Write 1-2 paragraphs that describe the following: 1. state the two money saving tips 2. tell why these tips work ​

Answers

The first tip is to travel by public transport instead of using your own vehicle. The second tip would be to stop smoking and drinking it is a total waste of money and health.

What is saving?

Saving is the method of saving your money for the future. We can not predict the future if anything bad happens and we need a large amount of money these savings will help us.

The first tip is to travel by public transport instead of using your own vehicle. The second tip would be to stop smoking and drinking it is a total waste of money and health.

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Which of the following produces an image that is not congruent to the pre-image?

A. translation
B. dilation
C. rotation
D. reflection

Answers

Answer:

Dilation

Step-by-step explanation:

it’s a dilation because the dilation changes how big the image is or what it looks like after the original image.

y = 12•3x for x = -2

Answers

Answer:

y=12×3(-2)

y=-72

Step-by-step explanation:

please mark me as brainlest

Triangle XYZ is rotated 90º clockwise about the origin to form triangle X'Y'Z', then reflected across the x-axis to form triangle X''Y''Z''. Which of the following statements is true for ΔXYZ and ΔX''Y''Z''? Question 25 options: ΔXYZ and ΔX''Y''Z'' are similar ΔXYZ and ΔX''Y''Z'' are congruent ΔXYZ and ΔX''Y''Z'' are neither congruent nor similar There isn't enough information given to identify whether ΔXYZ and ΔX''Y''Z'' are similar or congruent
1.ΔXYZ and ΔX''Y''Z'' are similar
2.ΔXYZ and ΔX''Y''Z'' are congruent
3.ΔXYZ and ΔX''Y''Z'' are neither congruent nor similar
4.There isn't enough information given to identify whether ΔXYZ and ΔX''Y''Z'' are similar or congruent

Answers

The statement that is true for ΔXYZ and ΔX''Y''Z'' is; 2: ΔXYZ and ΔX''Y''Z'' are congruent

How to identify coordinates of transformed triangles?

We are told that;

- Triangle XYZ is rotated 90º clockwise about the origin to form triangle X'Y'Z'.

- Thereafter, reflected across the x-axis to form triangle X''Y''Z''

Now, in transformation, Reflection is flipping an object across a line without changing its size or shape while Rotation is rotating an object about a fixed point without changing its size or shape. Thus, it means that the size and shape of the triangle formed is not different from the original one.

Thus, we can say that both triangles are congruent because the shape and size didn't change.

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Which of the following is an example of a permutation?

Answers

The correct answer that is an example of a permutation is; D: The number of ways 7 books can be selected from 50.

How to solve permutation problems?

Formula for permutation is;

nPr = n!/(n - r)!

Now, permutation is defined as the arrangement of objects in a definite order. Thus, looking at the given options, the only one that depicts permutation is Option D.

Thus, the correct answer is the number of ways 7 books can be selected from 50.

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Find the surface area of this cube 7m 7m 7m. Be sure to include the correct unit in your answer.

Answers

Answer:

294[tex]m^2[/tex]

Step-by-step explanation:

The area of one face of the cube would be 7 x 7 = 49 [tex]m^2[/tex]

Since there are 6 faces on a cube, the total surface area would therefore be 49 x 6 = [tex]294m^2[/tex]

PLEASE ILL GIVE 25 POINTS ANS MARK BRAINIEST IF SOMEONE GIVES ME THE RIGHT ANSWER PLEASE PLEASE PLWASE

Answers

Answer:

Radius:3.14

Circumference: 6.28

Step-by-step explanation:

C=2(pi)(r)

replace r with 1

and you get 6.28

R=(pi)(r)^2

Replace r with 1

multiply and you get 3.14

radish 3.5 with the answer

Find the quotient.

7/8 ÷ 2 1/4
WILL GIVE 30 POINTS ​

Answers

Step-by-step explanation:

Hello there!

This is how we solve this problem

7/8 ÷ 2 1/4

[tex] \frac{7}{8} \div 2 \frac{1}{4} \: conveting \: to \: improper \: faction\\ \\ = \frac{7}{8} \div \frac{9}{4} \\ = \frac{7}{8} \times \frac{4}{9} \: multiply \: through \\ = \frac{7}{18} [/tex]

= 7/18

I hope this helps.

Have a nice studies.

7/8 divided by 2 1/4
7/8 divided by 9/4
7/8 times(multiple by) 4/9
7/2 times 1/9
Step 1) 7 times 1 =7 and Step 2) 2 times 9 =18
So it is 7/18

can someone help please

Answers

Answer:

2 good scoops

Step-by-step explanation:

I got you I think

If √ 24 + √ 96 7 √600 = y√ 6, find the value of y. -​

Answers

Solution :

[tex]y = 2(1 + 5 \sqrt{967} )[/tex]

Step by Step explanation:

1.Switch sides[tex]y\sqrt{6} = \sqrt{24 } + \sqrt{967} \sqrt{600} [/tex]2.Simplify√24 + √967 √600

[tex]y \sqrt{6} = 2 \sqrt{6} + 10 \sqrt{5802} [/tex]

3.Divide both side by √6

[tex] \frac{y \sqrt{6} }{ \sqrt{6} } = \frac{2 \sqrt{6} }{ \sqrt{6 } } + \frac{10 \sqrt{5802} }{ \sqrt{6} } [/tex]4.Simplify[tex]y = 2(1 + 5 \sqrt{967} )[/tex]

How do I complete this?

Answers

Answer + Step-by-step explanation:

CE bisects AB

CE ⊥ AB

Then

CE is the perpendicular bisector of AB.

Therefore

CA = CB and DA = DB

…………………………………

we have :

CA = CB

DA = DB

CD is a common side of the two triangles ACD and BCD

Hence , ΔACD ≅ ΔBCD

⇒ ∠CAD ≅ ∠CBD.

choose the symbol for the line XY.​

Answers

The mathematical symbol for the line XY is XY(a line on top it) . The first option

How to represent a line with a symbol?

There are so many mathematical symbols use in geometry. They include ∠(angles), ⊥(perpendicular line), Δ(triangle), ≅(congruency) and many more.

Therefore, the symbol for the line XY is as follows;

XY(a line on top it)

It means line segment "XY"

In words, it is the line segment between X and Y

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Which equation is the inverse of 5y+4= (x+3)² + 2?

Answers

I think this is the answer to your question And also the solution

Explain how you would use addition to find the product of -2 and 5

Answers

-2+5=3
And is a word used for addition. For example 20 and 6 is 26.

What is the measure of angle B in degrees

Answers

Angle C and the 112 degree angle are supplementary, so angle C measures 180-112=68 degrees.

This means that by the exterior angle theorem, [tex]m\angle B=51^{\circ}+68^{\circ}=\boxed{119^{\circ}}[/tex]

Solve
x=4
-7x +y =-22

Answers

Answer:

y = 6

Step-by-step explanation:

-7 (4) + y = -22

-28 + y = - 22

+28 + 28

y = 6

Fill in the blank.
5 × 5/2 = __ x 1/6

Answers

Answer:

25

Step-by-step explanation:

When multiplying a whole number by a fraction, the first step is to multiply the whole number by the numerator. Then, you divide by the denominator. For example, on the left side, 5 x 5 = 25. You are left with 25/6. Finally, when you divide by 6, you are left with 4.166.....

If the denominator is the same (6) on both sides, to get the same answer, you somehow need to get the numerator (25) the same. So, what whole number can be multiplied by 1 to get 25? This number is 25. Therefore, the missing number is 25. This answer is correct because 25 x 1 = 25. You would be left with 25/6 and get a final answer of 4.166....

Two triangles are proportional, and the first triangle has a base of 10 cm and a height of 15 cm. If the base of the second triangle is 12 cm, what is the height of the second triangle?​

Answers

Answer: b1/b1=h1/h2=10/12=15/h2 so use criss cross and equel to 15×12=10h2 both sides devide by 10 and equel 180/10=18

so h2=18

Use the following table of Registered Voters at Kensington College, Registered Voters at Kensington College 2009 2010 640 790 Democrats Republicans 960 410 Independents 320 300 11) What is the probability that a voter registered in Kensington College in 2009 was not a Republican?​

Answers

Step-by-step explanation:

remember, a probability is ultimately always

desired cases / total possible cases

what are the total possible cases for our question here ?

all registered voters in 2009 :

640 + 960 + 320 = 1920

the desired cases (not republican) out of all these 1920 possibilities are

640 + 320 = 960

so, the probability for a registered voter to not be republican was

960 / 1920 = 1/2 = 0.5

According to the general equation for conditional probability, if P(A n B') = 2/9 and P(B) = 1/3, what is P( A I B')?
A. 5/6
B. 2/3
C. 1/6
D. 1/3

Answers

Answer:

B. 2/3

Step-by-step explanation:

Formula:

[tex]p\left( A|B\right) =\frac{p\left( A\cap B\right) }{p\left( B\right) }[/tex]

Then

[tex]p\left( A|B\right) =\frac{\frac{2}{9} }{\frac{1}{3} } =\frac{2}{9} \times \frac{3}{1}=\frac{6}{9}=\frac{2}{3}[/tex]

What is the minimum value of the following function f(x)=(x-1)^2 +1

Answers

Answer:

1

Step-by-step explanation:

f(x)=(x-1)²+1

f(1)=(1-1)²+1

f(1)=0²+1

f(1)=0+1

f(1)=1

what is -23/6 - 7/3
A -37/6
B -30/9
C -16/6
D 37/6​

Answers

Answer:A

Step-by-step explanation:

-23/6 - 7/3 =-6.16666666667

-37/6 = -6.16666666667

Answer:

[tex] \frac{ - 37}{6} [/tex]

Step-by-step explanation:

[tex] \frac{23}{6} - \frac{7}{3} \\ lcm = 6 \\ \frac{ - 23 - 14} {6} = - \frac{ - 37}{6} \\ final \: answer \\ = \frac{ - 37}{6} [/tex]

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