What is the next step?

Original: y = 3^x

---To find the inverse, switch the x and y, then solve for y.

Inverse: x = 3^y

---Take the log base 3 of both sides to get y by itself

Answer: [tex]log_{3}(x) = y[/tex]

[tex]y = log_{3}(x)[/tex]

Hope this helps!

Answer:

Your answer is A.

Step-by-step explanation:

Absolute values of any number are positive.

|4| = 2

|-2| = 2

2 = 2 and 4 > -2

C and D can be true, but they are not since less than or greater than doesn't apply if they were less than/greater than or equal, then yes.

The terms a1, a2 and a3 do not have a common difference, and the value of a1 in the geometric sequence is 10/9

The arithmetic sequence is given as:

a₁, a₂ and a₃

The geometric sequence is given as:

a₄, a₇ and a₁₂

The common ratio of a geometric sequence is:

[tex]r = \frac{T_2}{T_1}[/tex]

So,we have:

[tex]\frac{a_7}{a_4} = \frac{a_{12}}{a_7}[/tex]

Cross multiply

[tex]a_{12} * a_4 = a_7 * a_7[/tex]

Given that a7 = 30, the equation becomes

[tex]a_{12} * a_4 = 30 * 30[/tex]

Evaluate the product

[tex]a_{12} * a_4 = 900[/tex]

Rewrite as:

[tex]a_{4} * a_{12} = 900[/tex]

Express 900 as 10 * 90

[tex]a_{4} * a_{12} = 10 * 90[/tex]

By comparison, we have:

a₄ = 10 and a₁₂ = 90

This means that the geometric sequence is:

10, 30, 90 ---- it has a common ratio of 3

The nth term of a geometric sequence is:

[tex]a_n = ar^{n-1}[/tex]

So, we have:

[tex]a_7 = ar^6[/tex]

[tex]a_4 = ar^3[/tex]

Substitute values for a7 and 14

[tex]ar^6 = 30[/tex]

[tex]ar^4 = 10[/tex]

Divide both equations

[tex]r^2 = 3[/tex]

Take the cube of both sides

[tex]r^6 = 27[/tex]

Substitute [tex]r^6 = 27[/tex] in [tex]ar^6 = 30[/tex]

[tex]a * 27 = 30[/tex]

Divide both sides by 27

[tex]a = \frac{10}{9}[/tex]

Hence, the value of a1 in the geometric sequence is 10/9

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Answer:

Yes

Step-by-step explanation:

Because when you draw it u get a right angle

Using proportions, it is found that the dimensions of the reception area of of 12 feet by 20 feet.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, the scale factor is of 1 inch = 4 feet, meaning that each inch on the drawing represents a dimension of 4 feet.

The drawing is of 3 inches by 5 inches, hence the real dimensions are given by;

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Because this is a right triangle, we can use a trigonometric function to solve for the missing side.

Remember: SOH-CAH-TOA

We are given an angle, as well as the adjacent side and hypotenuse. Therefore, we should use the cosine function to solve for x.

cos(67) = x / 15

x = cos(67) * 15

x = 5.9

Answer: 5.9

Hope this helps!

Answer:

7

Step-by-step explanation:

21 = 3 x 7

35 = 7 x 5

70 = 2 x 5 x 7

The greatest common factor of 21, 35 and 70 is 7.

Note : -

The greatest common factor ( GCF ) of a set of numbers is the largest factor that all the numbers share.

Answer:

35 square feet

Step-by-step explanation:

Area of the rug :

Answer:

Daniel =Were you thinking of perpendicular lines?

Oris= It seems like you've got the basic idea, but your definition could be more precise.

Kaoris= Yes well done...

Answer:

2 outliers

Step-by-step explanation:

(1,9) and (10,7) both are outliers.

There are 2 outliers in the given scatter plot. Therefore, option B is the correct answer.

An outlier is a data point that does not fit the rest of the data. It lies outside of a cluster and does not follow the same pattern. Scatter plots can have many outliers, just one outlier, or no outliers.

From the given graph, we can see that coordinates (1, 9) and (10, 7) are not in the cluster.

These two points lies out side the cluster, so these points are outliers.

Therefore, option B is the correct answer.

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Answer:

C) 75.36 cubic feet

Step-by-step explanation:

Volume of a cone: ⅓hπr²

Given:

Substitute the given values to find the volume:

V = (⅓)(8)(3.14)(3)²

V = (⅓)(8)(3.14)(9)

V = (⅓)(226.08)

V = 75.4 ft³ (nearest tenth)

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Correct option is A)

Consider the given equation,

3

2x

+10.3

x

−9=0

Let ,y=3

x

Now ,

y

2

−10y+9=0

y

2

−9y−y+9=0

y(y−9)−1(y−9)=0

(y−9)(y−1)=0

When,

x−9=0

x=9

Now ,

9=3

x

3

2

=3

x

x=2

When,

y−1=0

y=1

3

x

=1

3

x

=3

0

x=0

x=0,x=2

This is the answer

Answer:

2513 miles

Explanation:

[tex]\sf Length \ of \ arc = \dfrac{\theta}{360} * 2\pi r[/tex]

Here given:

∅ = 36°

radius = 4000 miles

Insert following:

[tex]\sf \rightarrow \dfrac{36}{360} * 2\pi (4000)[/tex]

[tex]\sf \rightarrow 800\pi \ \ \ (in \ terms \ of \ \pi )[/tex]

[tex]\sf \rightarrow 2513.3 \ \ (rounded \ to \ nearest \ tenth)[/tex]

[tex]\sf \rightarrow 2513 \ \ (rounded \ to \ nearest \ mile)[/tex]

Your answer is B.

Vertical goes straight up and down.

Horizontal lines go side to side

A diagonal line is slanted.

Answer:

Ib = $16 per lb

Step-by-step explanation:

Answer:

$8,051.62

Step-by-step explanation:

Compound interest formula

[tex]\sf A=P(1+\frac{r}{n})^{nt}[/tex]

where:

Given:

Substituting given values into the formula:

[tex]\implies \sf A=5000(1+\frac{0.06}{4})^{4 \times 8}[/tex]

[tex]\implies \sf A=5000(1.015)^{32}[/tex]

[tex]\implies \sf A=8051.62\:(nearest\:hundredth)[/tex]

Rate of interest

So

Compound ineterest formula to be used

To multiply 64 × 8.32 use the logarithm equation 2)㏒64 + ㏒8.32

To answer the question, we need to know what logarithm of a number is

The logarithm of a number x is the power to base 10 of that number.

So, logarithm of x to base 10 is written as ㏒x.

Since we want to multiply 64 × 83.2, we convert this to logarithmic equation using the addition rule of logarithm.

㏒ab = ㏒a + ㏒b

So, 64 × 8.32 to logarithm is ㏒(64 × 8.32) = ㏒64 + ㏒8.32

So, to multiply 64 × 8.32 use the logarithm equation 2)㏒64 + ㏒8.32

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Answer:

im not really sure what that means im so sorry

Step-by-step explanation:

Answer:

4 bulbs

Step-by-step explanation:

Answer:

−x^2+10x−21

Step-by-step explanation:

Hope this helped you! If this is wrong, please tell me and have a good day!

Answer:

6

Step-by-step explanation:

b+4=10

  -4 .-4

b=6

Answer:

b= 6

Step-by-step explanation:

subtract the answer (10) by the remaining 4, (so 10-4) which equals 6

Answer:

Picture Below :)

Step-by-step explanation:

*ta da*

- Have a great day -

The product and the sum of the functions will be 3x² - 6x - 24 and 4x + 2. The value of the function (f - g) at x = 4 is negative 18.

In mathematics, functions are everywhere and are necessary for constructing physical connections. A function is a statement, rule, or law that establishes the connection between two variables.

The functions are given below.

f(x) = x - 4

g(x) = 3x + 6

Then the product of the functions will be

(f × g)(x) = (x - 4)(3x + 6)

(f × g)(x) = 3x² -12x + 6x - 24

(f × g)(x) = 3x² - 6x - 24

Then the sum of the functions will be

(f + g)(x) = x - 4 + 3x + 6

(f + g)(x) = 4x + 2

Then the difference in the functions at x = 4 will be

(f - g)(4) = (x - 4) - (3x + 6)

(f - g)(4) = x - 4 - 3x - 6

(f - g)(4) = -2x - 10

(f - g)(4) = -2 (4) - 10

(f - g)(4) = -8 -10

(f - g)(4) = -18

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Answer:

6.15 × 10⁵

Step-by-step explanation:

When converting a number of scientific notation, we need to move the decimal point until the number is greater than 1 and less than 10, then multiply this by 10 to the power of the number of places we moved the decimal point (negative when moving it forwards, positive when moving it backwards).

Therefore, 615000 = 6.15 × 10⁵

Answer:

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

Step-by-step explanation:

[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]

From inspection of the diagram:

[tex]\implies \textsf{P(landing on a pawn)} \sf = \dfrac{\textsf{Total number of pawns}}{\textsf{Total number of squares}}[/tex]

[tex]\implies \textsf{P(landing on a pawn)} \sf = \dfrac{16}{64}=\dfrac{1}{4}[/tex]

[tex]\sf probability : \bf 0.25[/tex]

[tex]\sf Probability = \dfrac{favorable \ outcomes}{total \ outcomes}[/tex]

[tex]\dashrightarrow \ \sf probability : \ \bf \dfrac{16}{64}[/tex]

[tex]\dashrightarrow \ \sf probability : \ \bf \dfrac{1}{4} \ \ \approx \ \ 0.25 \ \ (as \ a \ decimal)[/tex]

Answer:

a = 6

Step-by-step explanation:

Given information:

Slope = 6

Coordinates: (-9, 0) and (-8, a)

Slope formula = y2 - y1 / x2 - x1

Substitute the given values into the formula.

6 = a - 0 / -8 - (-9)

6 = a - 0 / 1

6 = a - 0

a = 6

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Let the price of an adult ticket is x and a child ticket is y .

from the question ,

[tex]6x + 2y = 124 \: \: ...(i) \\ \\ 3x + 5y = 100 \: \: ...(ii)[/tex]

Multiply 2 in eq (ii)

[tex]6x + 10y = 200 \: \: ...(iii)[/tex]

On adding eq (iii) and (i)

[tex]6x + 10y = 200 \\ \\ 6x + 2y = 124[/tex]

we get ,

[tex]8y = 76 \\ \\ y = \frac{76}{8} \\ \\ y = 9.5[/tex]

putting y in eq (i)

[tex]6x + 2y = 124 \\ \\ 6x + 2 \times 9.5 = 124 \\ \\ 6x + 19 = 124 \\ \\ 6x = 124 - 19 \\ \\ 6x = 105 \\ \\ x = \frac{105}{6} \\ \\ x = 17.5[/tex]

The value of x = 17.5 and y = 9.5

The area of the composite figure is 1152 square meters

A rectangular prism and 2 triangular prisms. The rectangular prism has a length of 20 meters, width of 6 meters, and height of 8 meters. The triangular prisms each have 2 triangular sides with a base of 6 meters and height of 8 meters. The rectangular sides are 20 meters by 6 meters, 20 meters by 10 meters, and 20 meters by 8 meters.

The composite figure shown is made up of 2 triangular prisms and one rectangular prism. If the area of each triangle base of the triangular prisms has an area of 24 m2, what is the total surface area of the composite figure?

The given parameters are:

Rectangular prism :

Length = 20 meters; Width = 6 meters; Height = 8 meters

Triangular prism :

The area of the rectangular prism is:

Area = 2 * (Length * Width + Length * Height + Width * Height)

So, we have:

Area = 2 * (20 * 6 + 20 * 8 + 6 * 8)

Area = 656

The area of the triangular prism is:

Area = 2 * Base Area + Areas of Rectangular sides

So, we have:

Area = 2 * 24 + (20 * 6 + 20 * 10 + 20 * 8)

Area = 528

The common area between the prisms is:

Common area = 8 * 4

Common area = 32

Subtract the common area from the sum of the areas of the triangular prism and the rectangular prism to get the area of the composite figure

Composite figure = 656 + 528 - 32

Evaluate the sum

Composite figure = 1152

Hence, the area of the composite figure is 1152 square meters

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Answer: D, 1152 m2

Step-by-step explanation: I got it correct

B. chair no costume also whips