Write each expression in simplest form. (x⁻²/₃ / y⁻¹/₃)¹⁵

The simplified form of the expression is 6^(-3)

From the question, we are to simplify the given expression

The given expression is

6^2/6 • 6^12 / 6^8

Simplifying

6^2/6 • 6^12 / 6^8

Applying the division law of indices

6^(2 -1 ) • 6^(12 - 8)

6^(1) • 6^(4)

Applying the multiplication law of indices

6^(1 - 4)

6^(-3)

Hence, the simplified form of the expression is 6^(-3)

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Answer:

G' (8, - 8 )

Step-by-step explanation:

since the dilatation is centred at the origin then multiply each of the coordinates by the scale factor of 4

G (2, - 2 ) → G' (4(2), 4(- 2)) → G' (8, - 8 )

If Carl Brownstein is a golf course groundskeeper whose annual gross pay is 45,500, and he has exemptions of 3000, and the state tax on the first 2500 is 1.5% and 3% on amounts over 2,500 then the state income tax of Carls is C- 1237.50.

The state income tax of Carls can be calculated as follows;

First, we subtract the exemption of 3000 from the annual gross pay as follows;

45500 - 3000 = 42500

As the percentage tax on the first 2500 is 1.5%, it can be calculated as follows;

1.5/100 × 2500 = 0.015 × 2500 = 37.50

The percentage tax on amounts over 2500 is 3%, therefore we can calculate the tax on the remaining amount as follows;

42500 - 2500 = 40000

3/100 × 40000 = 0.03 × 40000 = 1200

The total state income tax can be calculated by addition;

Tax on the first 2500 + Tax on the amount over 2500

37.50 + 1200 = 1237.50

Hence the state income tax of Carl is calculated to be 1237.50

Although a part of your question is missing, you might be referring to this question:

Carl Brownstein is a golf course groundskeeper whose annual gross pay is 45,500, he has exemptions of 3000. The state tax on the first 2500 is 1.5% and 3% on amounts over 2,500. What is the state income tax of Carl's?

A- 3233

B- 1200

C- 1237.50

D- 1588

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Answer:

13.6mm

Step-by-step explanation:

1.7mm x 8 sides =

The constraints of the equation will be x > 13 y and 340 x + 670 y < 5650.

Let the number of new bicycles be x

Let the number of new treadmills be y.

Cost of 1 new bicycle = $ 340

Cost of 1 new treadmill = $ 670

Also, he must spend less than $ 56,50

Now, the constraints for this will be:

x > 13 y

x greater than 13 y

340 x + 670 y < 5650

340 x plus 670 y less than or equal to 5650

Therefore, the constraints of the equation will be x > 13 y and 340 x + 670 y < 5650 .

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Answer:

12a + 3b = no solution

Step-by-step explanation:

You have to add like terms here!

7a + 5a = 12a

12a + 4b - b

4b - b = 3b

And now you're left with 12a and 3b, you can't go any further because 12 a and 3b are not like terms, you cannot add, or subtract them. Which means there is no solution.

I hope this helped :)

Answer:

False

Step-by-step explanation:

Answer: The answer is unknown

Step-by-step explanation: 7 continents, so you would only have 1 data.

Mr. Lawson is to pay the smallest amount of interest that is allowed in the City Credit Union which is a simple interest would be 1632.

Simple interest is defined as interest paid on the original principal and calculated with the following formula:

S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years. The rate of interest is in percentage r% and is to be written as r/100

To determine the smallest amount of interest.

We have to calculate the simple interest of each bank

United Bank : 4% interest rate and 6 years

S.I. of United Bank = 8000 × 4/100 × 6 = 1920

Nations First :3.8% interest rate and 7 years

S.I. of Nations First = 8000 × 3.8/100 × 7 = 2128

City Credit Union :5.1% interest rate and 4 years

S.I. of City Credit Union = 8000 × 5.1/100 × 4 = 1632

Priority Bank : 4.2%interest rate and 5 years.

S.I. of Priority Bank = 8000 × 4.2/100 × 5 = 1680

So the smallest amount of interest would be City Credit Union which is 1632.

Therefore, Mr. Lawson is to pay the smallest amount of interest that is allowed in the City Credit Union which is a simple interest would be 1632.

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Answer:

whether the transaction

is a purchase or sale. Write a formula for the advisor's

commission. Let D represent the value of one transaction.

Give two examples of how this financial advisor could earn a

commision of $1000

Step-by-step explanation:

Answer:

gove two examples of how this financial advisor could earn a

Step-by-step explanation:

Answer: Usaste el 75% de la leche y queda el 25%.

Step-by-step explanation:

Answer:

2.85

Step-by-step explanation:

Reason 19.50 - 22.35 = 2.85

Answer: t=15

Step-by-step explanation:

ST=9. BC=3

ST/BC=

9/3=3 ==> with this information, we can conclude that triangle ABC needs to be stretched by a scale factor of 3 in order to become triangle RST.

t=RS

RS=AB*3

RS=5*3

RS=15

t=15

Answer:

[tex]1.6 \times 10^5[/tex]

Step-by-step explanation:

[tex](8 \times 10^3) \times (2 \times 10^1)\\\to (8 \times 2) \times (10^3 \times 10^1) \text{ / Remember rule: } a^m \times a^n = a^{m + n}\\\to 16 \times 10^{3 + 1}\\\to 16 \times 10^4\\\to 1.6 \times 10 \times 10^4\\\to 1.6 \times 10^{1 + 4}\\\to 1.6 \times 10^5[/tex]

Answer:

No Solution

Step-by-step explanation:

0.3(6y+15)=1.8y+4.5

Step 1: Simplify both sides of the equation.

0.3(6y+15)=1.8y+4.5

(0.3)(6y)+(0.3)(15)=1.8y+4.5(Distribute)

1.8y+4.5=1.8y+4.5

Step 2: Subtract 1.8y from both sides.

1.8y+4.5−1.8y=1.8y+4.5−1.8y

0y+4.5=4.5

Step 3: Subtract 4.5 from both sides.

0y+4.5−4.5=4.5−4.5

0y=0

Step 4: Divide both sides by 0.

0y/0 = 0/0

y=0

The linear equation y = (5 / 2) · x exhibits the steepest graph in comparison with the other three lines. (Correct choice: D)

Linear equations are equations of the form y = m · x + b, where m, b are the slope and the intercept of the equation, respectively. As slopes may be positive, null or negative, then we should use absolute values to determine the grade of steepness of a linear equation, where |m| ≥ 0. A line is steeper than other line when the absolute value of the former is greater than the absolute value of the latter.

According to this criterion, the linear equation y = (5 / 2) · x exhibits the steepest graph in comparison with the other three lines.

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Answer:

d)decreases

Step-by-step explanation:

Answer:

0 -2 -1 1

4 -4 -4 12

-3 1 2 8

Step-by-step explanation:

in that exact order, 3 by 4

They spent 1/70 of their monthly income on other things.

The family spent GH¢60,000 on clothing.

The monthly income of the family is GH¢168,000.

What is Fraction?

The number is expressed as a quotient in which the numerator is divided by the denominator is called fraction.

Since, The family spend;

On food = (3/7)*x

On clothing = (5/14)*x

On rent = (1/5)*x

Let the family's monthly income = x

Now, To find the fraction of the family's income is spent on other things, we can assume that y is spent on other things, then we should have;

(3/7)*x + (5/14)*x + (1/5)*x + y*x = x

We can divide both sides by x, we get:

(3/7) + (5/14) + (1/5) + y = 1

Now, we can solve this for y as;

3/7 + 5/14 + 1/5 + y = 1

6/14 + 5/14 + 1/5 + y = 1

(6 + 5)/14 + 1/5 + y = 1

11/14 + 1/5 + y = 1

The smallest common factor of 14 and 5 =  14*5 = 70

So, we can multiply in the first fraction by 5/5 and the second by 14/14,

(5/5)*(11/14) + (14/14)*(1/5) + y = 1

55/70 + 14/70 + y = 1

69/70 + y = 1

y = 1 - 69/70

y = 1/70

Hence, They spent 1/70 of their monthly income on other things.

And, On a particular month, the family spends  GH¢2,400 on other things, then if the monthly income is x, we have:

(1/70)*x = GH¢2,400

x = 70* GH¢2,400

x = GH¢168,000

So, The monthly income of the family is GH¢168,000

And, we know that they spend (5/14)*x on clothing,

Then this month they spent on clothing,

⇒ (5/14)*GH¢168,000 = GH¢60,000

So, They spent 1/70 of their monthly income on other things.

The family spent GH¢60,000 on clothing.

The monthly income of the family is GH¢168,000.

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The complete question is this,

A family spends 3/7 of their monthly income on food,5/14 on clothing and 1/5 on rent. What fraction of the family's income is spent on other things? If in a particular month, the family spends GH&2,400 on other things, how much did the family spend on clothing? What was the family's income for the month.

Answer:

Choice a
y = 2x -5

Step-by-step explanation:

The slope-intercept form of a line is y = mx + b where m is the slope and b the y-intercept

The given line has slope = 2

A parallel line will have slope = 2 also

So the only choice is 2x + 5 which is choice a

The value of y or the perpendicular of the is 180 rounded to nearest tenth.

Here we have to use Trigonometry

Trigonometry is basically the study of the relationship between the sides and angles of the right-angle triangle.  Thus , trigonometry helps to find the missing or unknown angles or sides of a right-angle triangle using the trigonometric formulas, functions or trigonometric identities. In trigonometry, the angles can be are generally  measured in degrees

Here we will use Tan α

Tan α = Perpendicular / Base

From the given figure we know that base is given as 350 feet and α is 27°

Tan 27° = y/ 350

0.509 = y / 350

y = 350 × 0.509

y = 178.15

Hence, The value of y or the perpendicular of the is 180 rounded to nearest tenth

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The simplified form of the given logarithmic expression ln (x+1)+ln (x-1)= 4 is x = 0.67 (to the nearest thousandth).

A logarithmic term represents a number in log form. A log term is another name for it.

A quantity can also be the sum of two or so more quantities. As a result, a term can be the product of 2 or more quantities, one of which must be in logarithmic form. In those kind of instances, the terms are recognized as log terms.

A quantity can also be defined as the quotient of two quantities. So, if a term includes a quotient of quantities, or at least each of the quantities could be expressed in log form, this same terms are known as log terms.

Now, according to the stated condition in question;

ln (x+1)+ln (x-1) = 4

Applying the Product Rule on the left side of the equation;

ln (x+1)/ (x-1) = 4

Convert the obtained expression in the exponent form.

Thus,

e∧[ln (x+1)/ (x-1)] = e⁴

Now, apply the exponent rule.

(x+1)/ (x-1) = 4

Now, simplifying the equation.

(x+1) = 4 (x-1)

x+1 = 4x - 1

4x - x = 1 + 1

3x = 2

x = 2/3

x = 0.666...

x = 0.67 (to the nearest thousandth).

Therefore, the solution for the stated logarithmic expression ln (x+1)+ln (x-1)= 4 is x = 0.67 (to the nearest thousandth).

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Answer:

(1, 7 )

Step-by-step explanation:

- 2x - 4y = - 30 → (1)

- x + y = 6 → (2)

multiplying (2) by 4 and adding to (1) will eliminate y

- 4x + 4y = 24 → (3)

add (1) and (3) term by term to eliminate y

- 6x + 0 = - 6

- 6x = - 6 ( divide both sides by - 6 )

x = 1

substitute x = 1 into either of the 2 equations and solve for y

substituting into (1)

- 2(1) - 4y = - 30

- 2 - 4y = - 30 ( add 2 to both sides )

- 4y = - 28 ( divide both sides by - 4 )

y = 7

solution is (1, 7 )

The values for f(x).g(x) =  2x² -6x +9

Given:

          f(x)=2 x+5 and g(x)=x²-3 x+2

         (f.g)x = f(g)x)

          g(x) = x²-3 x+2

          f(x²-3 x+2) = 2 (x²-3 x+2) +5

          f(x²-3 x+2) = 2x² -6x +9

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Answer:North west, the roads should have stopped this answer but north alone wasn’t an option so just pretend Jenna is a lawless maniac ig‍♂️

Step-by-step explanation:

During the cooking class, the instructor put 1/8 of the salt in each serving

The instructor divided 1/2 of an ounce of salt evenly

The instructor needs to 4 servings in a dish

Therefore the number of salt in each serving can be calculated as follows

= 1/2 ÷ 4

change the expression to multiplication

1/2 × 1/4

= 1/8

Hence 1/8 of the salt was placed in each serving of the dish

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Answer:

Step-by-step explanation:

25/3

From the given scatter plot with x and y variables, we can say that the correlation is; Negative Correlation.

We are told that you kept the balance in your "discretionary spending" envelope.

Now, we are further told that a scatter plot shows the number of days that have passed since you were paid and the amount left in your discretionary spending envelope.

Now, In this case, the day of the salary increases the money spent, that is, the amount of money in the envelope decreases. Thus, as the variable increases and the other decreases, it is a negative correlation.

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Answer:

x + 3x + 56 = 180

x + 3x = 124

4x = 124

x = 31

Step-by-step explanation:

A: 31

B: 3(31) = 91

C: 56

Total: 180