Which of the following numbers is divisible by 3?
a) 539
b) 85
c) 9,285
d) 640

Using exponent properties, the equivalent expression is:

[tex]\frac{y^{18}}{z^{18}}[/tex]

The original expression is:

[tex]\left[\frac{y^{-3}z^5}{z^{-4}y^6}\right]^{-2}[/tex]

When two terms that are divided have the same base and different exponents, we keep the base and subtract the exponents, hence:

[tex]\left[\frac{y^{-3}z^5}{z^{-4}y^6}\right]^{-2} = [y^{-3 - 6}z^{5 - (-4)}]^{-2} = [y^{-9}z^9]^{-2}[/tex]

The negative exponent at the numerator goes to the denominator, hence:

[tex][y^{-9}z^9]^{-2} = \left[\frac{z^9}{y^9}\right]^{-2}[/tex]

The negative outer exponent means that we have to exchange the numerator and denominator, hence:

[tex]\left[\frac{z^9}{y^9}\right]^{-2} = \left[\frac{y^9}{z^9}\right]^{2}[/tex]

Then both numerator and denominator exponents multiply by 2, hence the equivalent expression is:

[tex]\frac{y^{18}}{z^{18}}[/tex]

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Answer:

y^18/x^18

Step-by-step explanation:

Answer:

630 seconds

Step-by-step explanation:

1 minute = 60 seconds

Number of minutes × Number of seconds per minute = Number of seconds in total

60 × 10 ½ = 630 seconds

Hope this helped! ^^

Answer:

[tex]\frac{9b}{a^{2} }[/tex]

Step-by-step explanation:

[tex]\frac{a^{2} }{b}(\frac{3b}{a^{2} })^{2}[/tex]

[tex]\frac{9a^{2}b^{2} }{a^{4}b }[/tex]

[tex]\frac{9b}{a^{2} }[/tex]

The snail move at the pace in 1440in/hr.

Speed:

Speed is measured as the ratio of distance to the time in which the distance was covered.

Speed is a scalar quantity as it has only direction and no magnitude.

Given,

A snail moves at a pace of 2 ft/min.

Here we need to find how fast does the snail move in inches/hour.

We know that,

1 ft/min = 720.00 in/h

So, here we have 2 feet/minute.

That is equal to

=> 2 x 720.00 in/h

When we multiply it then we get the value of,

=> 1440 in/hr

Therefore, the snail move at the pace in 1440in/hr.

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Answer:

1. straight

2. right

3. obtuse

4. acute

Step-by-step explanation:

Answer:

5y^7x^2

Step-by-step explanation:

5y (xy^3)^2

apply product rule: xy^3

5y(x^2(y ^3)^2)

multiply exponents: (y^3)^2

5y(x^2y^6)

Add exponents: y and y^6

5y^7x^2

diamater:

[tex]d=2r \\\\d=2 \cdot 16 \\\\d=32[/tex]

circumference:

[tex]C=2 \pi r \\\\C=2 \cdot \p \cdot 16 \\\\C=32 \cdot \pi \\\\C \approx 100.48[/tex]

Hope that I helped you!

Answer:

Step-by-step explanation:

The X is equal to 1/6.

Meaning that the X is 1/6.

Answer:

x = 1/6

Step-by-step explanation:

(x - 3) = 7x - 4

x = 7x -1

-6x = -1

-x = -1/6

x = 1/6

Answer:

Step-by-step explanation:

3−4x/3 this is for x

y = -4/3x + 3 this is for why I’m not sure which one your trying to solve for

The equation -2x=3/8 is not a literal equation.

A literal equation can be defined as an equation which primarily of letters.

It is an equation  made up of several variables or letters.

Examples of literal equations are;

We can see from the examples shown that the equations or formulas have several variables or letters that could be written in terms of other variables.

Given the equation;

-2x=3/8

We can see that there is only one variable to be worked out and hence, is not a literal equation.

Thus, the equation -2x=3/8 is not a literal equation.

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The answer to this question is:

Ratio 344:109 represents the ratio of the total votes to Jocelyn's votes.

A ratio in mathematics shows how frequently one number is contained in another. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of orange to lemon is eight to six (that is, 8:6, which is equal to the ratio of 4:3).

According to the question,

No. of votes Rosalia got = 124

No. of votes Jocelyn got = 109

No. of votes Danny got = 111

No. of votes received by all candidates =

= 124 + 109 + 111

= 344

So, the ratio 344:109 is the ratio of the total votes to Jocelyn's votes.

Therefore, Ratio 344:109 represents the ratio of the total votes to Jocelyn's votes.

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Answer:

The variable is x and the constant is 6.  The coefficient of the variable is 3.

Step-by-step explanation:

The solution to the fraction expression -2 1/3 + (-1 3/4) is -4 1/12

The fraction expression is given as

-2 1/3 + (-1 3/4) =

Express the terms of the expression as an improper fraction

So, we have

-2 1/3 + (-1 3/4) = -7/3 + (-7/4)

Remove the bracket in the above expression.

So, we have

-2 1/3 + (-1 3/4) = -7/3 - 7/4

Take the LCM in the above expression.

So, we have

-2 1/3 + (-1 3/4) = (-7 * 4 - 7 * 3)/12

Evaluate the difference

-2 1/3 + (-1 3/4) = -49/12

Express the fraction as a mixed fraction

-2 1/3 + (-1 3/4) = -4 1/12

Hence, the solution to the fraction expression -2 1/3 + (-1 3/4) is -4 1/12

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Answer:

−[tex]x^{2}[/tex] + 9x + 1

Step-by-step explanation:

Answer:

1. = 96

2. = -158

Step-by-step explanation:

When you multiply two negatives the answer is positive, and when you multiply one negative and one positive the answer is negative

[tex]2(x-3)\geqslant -3(-3+x)\implies 2x-6\geqslant 9-3x\implies 2x\geqslant 15-3x \\\\\\ 5x\geqslant 15\implies x\geqslant \cfrac{15}{5}\implies x\geqslant 3[/tex]

This shows that a reasonable domain for this function is x > -5/6

The domain of a function is a value of the independent variable of the function for which it exists.

Given the equation below:

f(x) = 12x + 10

Since the function represents the expression used calculate a person's daily paycheck, then the function f(x) must be greater than zero;

12x + 10 > 0

12x > -10
x > -10/12
x > -5/6

This shows that a reasonable domain for this function is x > -5/6

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The required GCF is 8.

The greatest common factor is that greatest number from the factors which divides the number completely.

For example take numbers 12 and 16.

The factors of 12 are 2×2×3.

And the factors of 16 are 2×2×2×2.

We can clearly see that the common factors are 2×2 which gives 4. So, 4 is the greatest common factor which divides both 12 and 16.

Here it is given to find the greatest common factor of 16 and 40.

Factors of 16 = 2×2×2×2

Factors of 40 = 2×2×2×5

We can see clearly the common factors are 2×2×2 which gives 8.

So, 8 is the greatest common factor.

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Number of shoes needed to wrap around the equator = 7.57 x10⁷

The length of a size 7 shoe = 1.4 x 10-¹ m

The circumference of the Earth around the equator =  1.06 x 10^7 m

We know that here, the circumference around the equator will be equal to the number of shoes times the length of each shoe.

So to find the number of shoes, we should divide the circumference of the Earth by the length of one shoe.

Hence, number of shoes end-to-end needed to wrap around the equator = 1.06 x 10⁷ / 1.4 x 10-¹

             = 7.57 x10⁷

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Answer:

7. Slope = -5

Y-intercept = -3/4

8. Slope = 1/4

Y-intercept = 5

Step-by-step explanation:

y = mx + b

Slope = m

Y-intercept = b

An example of a systematic random sample will be selecting 4 balls from a bag containing. The correct option is B.

A probability sampling technique called systematic sampling involves picking people from the population at regular intervals, such as every 15th person on a list of the population. This can mimic the advantages of straightforward random sampling if the population is arranged in random order.

Here we have two options a.) selecting all the students in a class of 30.

b.) Select 4 balls from a bag containing 30 balls.

Out of the two options, a systematic random sample will be Select 4 balls from a bag containing 30 balls.

Therefore, the correct option is B.

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When x = -2:

f(-2) = -3 (-2) + 1

f(-2) = 6 +1

f(-2) = 7

y = 7

When x = 0:

f(0) = -3 (0) + 1

f(0) = 0 +1

f(0) = 1

y = 1

When x = 3:

f(3) = -3 (3) +1

f(3) = -3 (3) + 1

f(3) = -9 +1

f(3) = -8

y = -8

So, the Range is {7, 1, -8}

Answer:

Step-by-step explanation:

1/144

hope this helps :)

I'm assuming the equation is

[tex]\frac{3}{4}y - \frac{2}{4}y+7 = \frac{2}{4}y-1[/tex]

Let me know if the equation is different so I can update the solution.

-----------------

Fractions are a pain to deal with, so it's best to eliminate them whenever we can. In equations like this, we can multiply both sides by 4 since this is the LCD (which stands for "lowest common denominator").

If we multiply both sides by 4, then all the denominators of 4 will cancel.

We'll have these steps:

[tex]\frac{3}{4}y - \frac{2}{4}y+7 = \frac{2}{4}y-1\\\\4\left(\frac{3}{4}y - \frac{2}{4}y+7\right) = 4\left(\frac{2}{4}y-1\right)\\\\3y - 2y + 28 = 2y - 4 \ \ \text{ ... denominators cancel after distributing}\\\\y + 28 = 2y - 4\\\\y- 2y =- 4-28\\\\-y = -32\\\\y = \frac{-32}{-1}\\\\y = 32\\\\[/tex]

Answer:

[tex]y=32[/tex]

Step-by-step explanation:

Given the following question:

[tex]\frac{3}{4}y-\frac{2}{4}y+7=\frac{2}{4}y-1[/tex]
[tex]\frac{3}{4}y-\frac{2}{4}y+7-7=\frac{2}{4}y-1-7[/tex]
[tex]\frac{3}{4}y-\frac{2}{4}y=\frac{y}{2}-8[/tex]
[tex]\frac{3}{4}y-\frac{2}{4}y-\frac{y}{2}=\frac{y}{2}-8-\frac{y}{2}[/tex]
[tex]-\frac{y}{4}=-8[/tex]
[tex]4\left(-\frac{y}{4}\right)=4\left(-8\right)[/tex]
[tex]\frac{-y}{-1}=\frac{-32}{-1}[/tex]
[tex]y=32[/tex]

Therefore "y = 32."

Hope this helps.

One of the boards is 30 inches long and the other board is 12 inches longer so it has to be 42 inches long. The sum of the lengths of the two boards is 72 cm and one of the boards is 12 inches longer than the other.

Here,

A board is 72 cm in length and must be cut so that one piece is 12 cm longer than the other piece .

We have to find the leg of each piece.

What is Length, Width and height?

The length, width and  height of an object are the different dimensions in linear units. length is the longest side of a shape, width is the shorter side, and height is the vertical dimension of the shape.

Now,

If you're going to cut the 72 inch board into two pieces, you can call one of the pieces x units long.

And, since the other piece is 12 inches longer than your first piece, its length is x + 12.

And, when you place these two pieces back together, their lengths should add up to be 72 inches.

You can write this last statement about adding the two pieces together to get a 72 inch piece

In equation form as:

x + (x+12) = 72

2x + 12 = 72

To solve this begin by subtracting 12 from both sides;

2x = 60

Now just divide both sides by 2 to find that:

x = 30

So, one of the boards is 30 inches long and the other board is 12 inches longer so it has to be 42 inches long. The sum of the lengths of the two boards is 72 cm and one of the boards is 12 inches longer than the other.

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