Find the range of the function. Use interval notation. g(x)=log↓3(x-2)​

Answer:

y = 6(sq rt 3)

x = 18

Step-by-step explanation:

y = (0.5)(12)(sq rt 3) = 6(sq rt 3)

x = (0.866)(12)(sq rt 3) = (10.392)(sq rt 3) = sq rt 324

reduced

x = 18

The trigonometric function gives the ratio of different sides of a right-angle triangle. The value of x and y is 18 and 6√3 units respectively.

The trigonometric function gives the ratio of different sides of a right-angle triangle.

[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}\\\\\\Cosec \theta=\dfrac{Hypotenuse}{Perpendicular}\\\\\\Sec \theta=\dfrac{Hypotenuse}{Base}\\\\\\Cot \theta=\dfrac{Base}{Perpendicular}\\\\\\[/tex]

where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.

Let the side with label x be the base of the triangle and y be the perpendicular.

As the length of the base is x while the angle is 30°, and the length of the hypotenuse is 12√3, therefore, the value of x can be written as,

[tex]Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Cos (30^o)=\dfrac{x}{12\sqrt3}\\\\\\Cos (30^o) \times {12\sqrt3}={x}\\\\x = {12\sqrt3} \times \dfrac{{\sqrt3}}{2}\\\\x = 18[/tex]

Now, as we know that the length of the perpendicular side is y, therefore, the value of y can be written as,

[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Sin (30^o)=\dfrac{y}{12\sqrt3}\\\\\\Sin (30^o) \times {12\sqrt3} ={y}\\\\\\y = \dfrac{1}{2} \times 12\sqrt3\\\\\\y = 6\sqrt3[/tex]

Hence, the value of x and y is 18 and 6√3 units respectively.

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Answer:

[tex]it \: is \: \: \: \: {x}^{2} + 7x[/tex]

Step-by-step explanation:

I hope this is be useful for you ^_^

Expand x(x+7)

▶️x(x+7)

▶️x² + 7

▶️7x²

▶️7x²

Answer:

50%

Step-by-step explanation:

Answer:

z = 7/100

Step-by-step explanation:

Answer:

Step-by-step explanation:

7/100z

Answer:

4x-30=2-10

4x= 2-10+30

4x= 2-40

4x=-38

x-38/4

Answer:

1872 in

Step-by-step explanation:

156 ft x 1ft = 156ft cause if you multiply 1 with any number its what ever number you multiplied 1 with.

[tex]\tt{} {2x}^{2} - 19x + 42[/tex]

[tex]\tt{} {2x}^{2} - 7x - 12x + 42[/tex]

[tex]\tt{}x \times (2x - 7) - 6(2x - 7)[/tex]

[tex]\tt{}(2x - 7) \times (x - 6)[/tex]

Answer:

180 pounds

Step-by-step explanation:

In six months Bill's weight will be increased by 60 pounds

10 pounds*6 months=60 pounds

120+60=180

In six months Phil will lose 24 pounds decreasing his weight from 204 to 180

4 pounds*6 months=24 pounds

204-24=180

Answer:

180 lbs

Step-by-step explanation:

204-24= 180

120+60=180

multiply each by 6  

Answer:

I believe so! good luck!

Step-by-step explanation:

Answer: 16.7%

I took the k12 unit test

The inflation rate is given by the percentage error and is given by the equation A = 16.71 %

What is Percentage Error?

The difference between an exact value and an approximation to it is the approximation error in a data value. Either an absolute error or a relative error might be used to describe this error.

Percentage error is the difference between the measured value and the true value , as a percentage of the true value

Percentage Error = [ ( | Measured Value - True Value | ) / True Value ]x 100

Given data ,

Let the inflation rate of percentage error be represented as A

Let the cost of the Jolly Peanut butter be = $ 3.59

So , the original cost = $ 3.59

Let the increased rate of Jolly Peanut butter be = $ 4.19

So , the increased rate = $ 4.19

Now , the inflation rate is given by the equation

Percentage Error = [ ( | Measured Value - True Value | ) / True Value ]x 100

Substituting the values in the equation , we get

Inflation rate A = ( ( 4.19 - 3.59 ) / 3.59 ) x 100

On simplifying the equation , we get

Inflation rate A = ( 0.6 / 3.59 ) x 100

Inflation rate A = 0.16713 x 100

Inflation rate A = 16.71 %

Therefore , the value of A is 16.71 %

Hence , the inflation rate is 16.71 %

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Answer:

You know you could just look up every single one of these

Step-by-step explanation:

Answer:

The second statement.

Step-by-step explanation:

Once it gets to 10, if you keep multiplying by 2 it will always end in 0.

Answer:

800 cm

Step-by-step explanation:

x = height of lamp post

set up a proportion:

90/160 = 450/x

cross-multiply:

90x = 72000

x = 800

Answer:

Since you did not want the answer the things you need to solve this question are below.

Step-by-step explanation:

In order to solve this, you will need to read about the scale factor. Here is a picture telling about it briefly.

Answer:

55%

Step-by-step explanation:

1/4 - Micah will only have a 25% chance of selecting a blue pencil.

1/5 - Micah will only have a 20% chance of selecting a red pencil.

So, to conclude this, Micah only has a 55% chance of selecting a yellow pencil.

Answer:

36

Step-by-step explanation:

100% - 36% = 64%

This answer is correct 101% trust me!

Answer:

7

Step-by-step explanation:

They only have to 2 factors for example: 2,3,5,7,11

Answer:

h.7

Step-by-step explanation:

2 is the lowest prime # and the sum of 2 and 5 is 7

Answer:

D&E

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

2*radius

Answer:4

Step-by-step explanation:

2*2=4

Answer:

volume = 261.79938779915 m3

Step-by-step explanation:

And rounded to nearest number is 261.8 mi3 or answer b.

Answer:

D

Step-by-step explanation:

If something is not constant we know it is non-linear. We know this is not constant because when graphed, the line is not straight.

Answer:

D.

Step-by-step explanation:

Here the rate of change is not constant. For example:

10-5 / 20-17 = 5/3

13-10/23-20 = 3/3 = 1

Answer:

the answer is 2/5

Step-by-step explanation:

The graph that looks like this

Answer: D

Step-by-step explanation:

I think

answer for the first one

1) [tex]6 {y}^{2} - 24y[/tex]

[tex] = > 6y(y - 4)[/tex]

2) [tex]6pq - 4q + 6 - 9p[/tex]

[tex] = > (6pq - 4q) + ( - 9p + 6)[/tex]

[tex] = > [2q(3p - 2)] + [- 3( 3p - 2)] [/tex]

[tex] = > 2q(3p - 2) - 3(3p - 2)[/tex]

[tex] = > (3p - 2)(2q - 3)[/tex]

3) [tex] {x}^{2} + 14xy + 49y[/tex]

[tex] = > {x}^{2} + 2 \times x \times 7y + {(7y)}^{2} [/tex]

[tex] = > {(x + 7y)}^{2} [/tex]

[tex] = > (x + 7y)(x + 7y)[/tex]

4) [tex]25 {y}^{2} - 16[/tex]

[tex] = > {(5y)}^{2} - {4}^{2} [/tex]

[tex] = > (5y + 4)(5y - 4)[/tex]

5) [tex]9 {x}^{2} - 30x + 25[/tex]

[tex] = > {(3x)}^{2} - 2 \times 3x \times 5 + {(5)}^{2} [/tex]

[tex] = > {(3x - 5)}^{2} [/tex]

[tex] = > (3x - 5)(3x - 5)[/tex]

6) [tex] {p}^{2} + 2p - 15[/tex]

[tex] = > {p}^{2} + 5p - 3p - 15[/tex]

[tex] = > p(p + 5) - 3(p + 5)[/tex]

[tex] = > (p + 5)(p - 3)[/tex]

7) [tex] {y}^{2} + 8y + 12 = 0[/tex]

[tex] = > {y}^{2} + 2y + 6y + 12[/tex]

[tex] = > y(y + 2) + 6(y + 2)[/tex]

[tex] = > (y + 2)(y + 6)[/tex]

Answer:

1.6

Step-by-step explanation:

Find the number in the tenth place

6

and look one place to the right for the rounding digit

2

. Round up if this number is greater than or equal to

5

and round down if it is less than

5

.

1.6

Answer:

I had it before and it is 15 ft²

Answer:

y = 13√2

x = 13

Step-by-step explanation:

y: The sine of an angle is equal to the ratio of the opposite side to the hypotenuse.

x: Find the last side of the triangle using the Pythagorean theorem.

good luck, i hope this helps :)

Answer:

C

Step-by-step explanation:

Answer: It's C.

Step-by-step explanation:

Answer:

Step-by-step explanation: