3. How could you adapt the rule for division by 3 to decide easily when
a number is divisible by 9?

By logarithmic differentiation, the first derivative of y = 2ˣ is y' = 2ˣ · ㏑ 2.

Logarithmic differentiation is a combination of derivative rules and logarithm properties which is useful to derive power, exponential and power-exponential functions:

y = 2ˣ

㏑ y = ㏑ 2ˣ

㏑ y = x ㏑ 2

y' / y = ㏑ 2

y' = y · ㏑ 2

y' = 2ˣ · ㏑ 2

By logarithmic differentiation, the first derivative of y = 2ˣ is y' = 2ˣ · ㏑ 2.

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The number of nights will be 8.62 when the Hotel B charge is less than A.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that hotel, A charges $179 per night with a 14% nightly room tax and free parking. Hotel B charges $169 per night with 18% nightly room tax plus a one-time $40 parking fee. The number of the nights will be calculated as below:-

From the given data from the equations:-

A = 179 + ( 0.14 x 179 ) x

A = 204.06x

B = ( 169 + ( 0.18 x 169 )x + 40

B = 199.42x + 40

Equate the two equations:-

204.06x = 199.42x + 40

4.64x = 40

x = 40 / 4.64

x = 8.62 nights

Therefore, the number of nights will be 8.62 when the Hotel B charge is less than A.

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The correct option regarding number 1 is given by:

C. The number is neither prime nor composite.

Prime numbers are numbers that have only two factors, that are 1 and itself. Examples of prime numbers are 2, 3, 5, 7, and so on...

Number 1 has only one factor, itself, hence for this reason it is neither prime(two factors are needed) nor composite, as it cannot be written as a product of two numbers both different than 1, hence option c is correct.

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Answer:

this is a vertical problem what is on one side is on the other

Step-by-step explanation:

so r is the same as 95

Answer:

C is right 20kg

Step-by-step explanation:

bec

ause the formula of force=mass ×acceleration

to find mass= force/acceleration.

Answer: A number that ends in 0 is divisible by 2, 5, and 10. 6730 is divisible by 2, 5, and 10, which means that it is in the 2, 5, and 10 times tables.

Step-by-step explanation:

Answer: 6,730

Step-by-step explanation:  A number is divisible by 10 if it ends in a 0. The number ends in a 0 and so it is divisible by 10. A number that ends in 0 is divisible by 2, 5 and 10. 6730 is divisible by 2, 5 and 10, which means that it is in the 2, 5 and 10 times table.

Answer:

$3,792

Step-by-step explanation:

$316 x 12

Answer:

0.283258167471352[tex]\sqrt[3]{k}[/tex]

Step-by-step explanation:

Based on the given conditions, formulate:

Write the equation of the function:

Substitute and calculate:

Answer:

0.456

Step-by-step explanation:

456÷1000

=0.456ml

Considering the numeric values and the range concept, we have that:

The range of the function is given by: {f(0), f(1), f(2), f(3), f(4), f(5)}.

To find the numeric value of a function, we replace each instance of the variable by the desired value.

The range of a function is the set that contains all possible output values for the function. These outputs are the numeric values for the domain of the function, which compose the input values.

For this problem, we have that:

Hence:

The range of the function is given by: {f(0), f(1), f(2), f(3), f(4), f(5)}.

The function is not given, hence this problem was solved speaking in general terms. In your problem, you will mark the numeric values of the function given.

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w = 5

Step-by-step explanation:

2+(7w)+(8w)=5

(7÷5)+(8÷5)+2

(1.4) (1.6) +2

+1.5

=3+2=5

The correct answer to this problem is an option (H) 2/3.

A sequence is a sequence of things (usually numbers) in order 3, 5, 6, 7, 8, and so on. A geometric sequence is known as a particular type of sequence ]. A sequence multiplies each term (except the first) by a constant to get the next term in the sequence. So, from the information, we can conclude that to get the next term in the geometric sequence, we need to multiply that with a specific term (known as the common ratio), and to find the last term in the sequence, we multiply that term by the same standard ratio. Just split it.

Given GP is 9/2,3,2,4/3

Common ratio = Second number / first number

= 3/ (9/2) =2/3

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The "0.004" is the constant of proportionality, in this particular case, that value represents the height if a single sheet of paper.

We know that the height, in inches, of s sheets of paper can be described by the equation:

h = 0.004*s

So, if we have a single sheet, the height is:

h = 0.004*1 = 0.004

The height of a single sheet if 0.004 inches.

If instead we have two, then s = 2, we will have:

h = 0.004*2 = 0.008

The height is 0.008 inches.

So, the given equation:

h = 0.004*s

Is a proportional relation.

The "0.004" is the constant of proportionality, in this particular case, that value represents the height if a single sheet of paper.

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Answer:

last one is right

Step-by-step explanation:

multiply 8 by X is 8x and 8 multiplied by 8 is 64

Hope it helps

Answer: 8x+64=8x(x+8)

Step-by-step explanation:

8 is a common of 8 so 8x8=64

Answer:

2.712

Step-by-step explanation:

2.712

5x+3y=15 is the equation for the standard form of the line .

What is in slope-intercept form?

We are given two coordinates (3,0) (0,5)

Start by finding slope

y2-y1/x2-x1=  5-0/0-3= -5/3 this is your slope m.

y=mx+c

y= -5/3x+c (but remember standard line is ax+by=c) so we have to switch sides

5/3x + y=5 (remember standard form has no fraction so multiply by 3 on all sides)

5x+3y=15

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The probability of the spinner's point landing on yellow is 30.56%.

A pie graph is a type of chart which displays data in the form of a circular graph.

We understand that the total value of the pie is always 100%. It is also understood that a circle will have a circumference of 360°. As a consequence, the total of all data points equals 360°. There appear to be two main pie chart formulas based on these:

When a circle is completely rotated, it forms a 360-degree angle in the center.

The overall percentage of all colors is 100%.

Because 360 degrees / 100 percent = 3.6, divide the valuation of yellow by 3.6.

The total percentage of yellow displayed by the spinner's pointer is 110%.

P (probability of landing on yellow) = 110/3.6

P (probability of landing on yellow) = 30.555... = 30.56 (approx.)

As a result, the probability of the pointer landing on the yellow is 30.56%

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Answer:

[tex]x^4y^2-6x^3y^3 = x^3y^2(x - 6y)[/tex]

Step-by-step explanation:

to pick out common factors, you have to find the highest common denominator. We start by listing units and variables:

we can divide the x^4y^2 by up to x^4 and up to y^2, cannot divide by non-variable numbers

we can divide 6x^3y^3 by up to x^3 and up to y^3, and by 6 if we needed to.

This means that for units, we're not dividing (because we can't simplify x^4y^2 dividing by a bare number.

For x, we can divide both by x^3, because we can divide both by x^3, but cannot divide 6x^3y^3 by x^4 or more.

For y, we can divide both by y^2, because we can divide both by y^2, but cannot divide x^4y^2 by x^3 or more.

We take the x^3y^2 and bring it in front of the brackets.

Disclaimer: when I say "cannot divide" I mean "cannot divide without introducing fractions or negative exponents".

The 10th term of the given arithmetic sequence 2,8,14,20, ........... is ( a₁₀ = 56.)

The difference between two mathematical orders is a fixed value in Arithmetic Progression (AP). Arithmetic Sequence is another term for it.

We'd come across a few key words in AP which have been classified as:

The AP can also be viewed in terms of common differences, as illustrated below.

Now, the sequence given in the question is;  2,8,14,20, ...........

Define the first term as 'a₁' = 2.

Define 'a₂' = 8 is the second term.

Define the third term as 'a₃' = 14.

Evaluate the common difference;

d = a₂ - a₁  

Put the values in the obtained equation;

d = 8 - 2 = 6

Now, to evaluate the value of the 10th term imply the formula of nth term.

an = a + (n − 1) × d , n = total number of terms = 10.

Substitute all the values;

a₁₀ = 2 + (10 - 1) × 6

a₁₀ = 2 + 9 × 6

a₁₀ = 2 + 54

a₁₀ = 56.

Therefore, the value of the 10th term is found as a₁₀ = 56.

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Equation of line is 5y = -3x + 9 .

What is equation of line?

A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept.

3x+5y-4=0

5y = -3x + 4

y = -3/5 x + 4/5

since it is parallel, its slope, m is -3/5

2x-3y-6=0

3y = 2x - 6

y = 2/3x - 2

at x-intercept, y is zero

2 = 2/3x

x = 3

therefore

y = mx + c

0 = (-3/5  * 3 ) + c

c = 9/5

equation is

y = -3/5x + 9/5

5y = -3x + 9

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Answer:

Khan academy could really help it has videos and lessons so start there.

Step-by-step explanation:

Answer: 1/4

Step-by-step explanation:

3^2 / 6^2 =

(3/6)^2=

(1/2) ^ 2=

1^2 / 2^2 = 1/4

The possible coordinates of point G on the number line is -15 and 7.

On the number line, point E has the coordinates of - 4, and EG = 11 .

The possible coordinates of point G are as follows:

A number line is a horizontal straight line with numbers placed at equal distances from each other along that line.

Negative numbers are on the left side while the positive numbers are on the right side.

Therefore, the possible coordinates of G is when we go left or right side of E on the number line.

Hence,

Let's go left E to G on the number line

Let's go right E to G on the number line

Therefore, the possible coordinates of point G on the number line is -15 and 7.

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For given polynomial 1/2a^4 + 3a³ + a

1) There is no coefficient for the third term.

2) The constant term is 0.

In this question, we have been given a polynomial 1/2a^4 + 3a³ + a

We need to determine the coefficient of the third term and the constant term.

we can rewrite given polynomial as 1/2a^4 + 3a³ + 0a² + a + 0

The general form of the fourth degree polynomial is:

a_0 + a_1x + a_2x^2 + a_3x^3 + a_4x^4

where a_0 is the constant term

Comparing given polynomial with above general form.

a_0 = 0

a_1 = 1

a_2 = 0

a_3 = 3

a_4 = 1/2

So, the constant term is a_ 0 = 0

And there is no coefficient for the third term.

Therefore, for given polynomial 1/2a^4 + 3a³ + a

1) There is no coefficient for the third term.

2) The constant term is 0.

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The coordinates of P' is (-3,2).

Given that P(-3, 6) is translated 4 units up and 8 units down.

The translation of a point involves moving it a certain distance horizontally and/or vertically. You can find the address of a translated point like this:

The point P(-3,6) is shown in blue above.

Travel 4 unit to the up and 8 units down from point P, and you arrive at point P'(-3,2), shown in red.

Hence, the coordinates of P' when P(-3, 6) is translated 4 units up and 8 units down is P'(-3,2).

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Using the given information, the equation of the circle with center located at point (6 , 4) and passes through the point (2 , 1) is (x - 6)^2 + (y - 4)^2 = 25.

Using the distance formula, get the radius of the circle by solving for the distance between the center (6 , 4) and the point (2 , 1).

radius = distance = √(x2 - x1)^2 + (y2 - y1)^2

radius = √(2 - 6)^2 + (1 - 4)^2

radius= √16 + 9

radius = √25

radius = 5

The standard form of the equation of the circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.

Given the radius and center of the circle, substitute these values to the standard form of the equation of the circle.

(x - h)^2 + (y - k)^2 = r^2

where (h , k) = (6 , 4)

r = 5

(x - 6)^2 + (y - 4)^2 = 5^2

(x - 6)^2 + (y - 4)^2 = 25

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Answer:

42

Hope this helps :)

Step-by-step explanation:

1. Substitute x with 6 since x is 6. When a variable is next to a number multiply them. Also, multiply when number is next to parenthesis.

7(6)

2. Solve by multiplying.

7(6) = 42

Check:

42 ÷ 7 = 6 ✓