The set of all points in a plane that are equidistant from two points is an (n):

Which methods can be used to expand (x+3)3?

Solution

Here use the Distributive Property of Multiplication Across the Addition.

The Distributive Property is a.(b + c) = a. b + a.c

Using the distributive property, we can expand the given expression.

(x + 3).3 = 3.x + 3.3

That is the expanded form.

The expression (x+3)³ can be expanded by using the binomial expansion method or by multiplying (x+3) by itself three times. This involves using binomial coefficients and combining like terms or calculating the products directly and simplifying the resulting expression.

To expand (x+3)³, we can use binomial expansion, which involves recognizing the pattern of coefficients that arise from Pascal's Triangle or using the binomial theorem. Another way is to multiply (x+3) by itself three times. In both methods, you calculate the products and combine like terms to get the final expanded form.

For cubing of exponentials, such as cubing (x+3), you must calculate each term of the binomial raised to the third power and then combine like terms. The cube of the digit term is calculated as usual, and you multiply the exponents by 3 when dealing with exponential terms.

An example of this concept applied to individual exponentials is: (5³)⁴ = 5³*⁴ = 5¹². In our case of binomial expansion, the expanded form of (x+3)³ would be x³ + 3*x²*³ + 3*x*3² + 3³, which simplifies to x³ + 9*x² + 27*x + 27.

C (third graph, the parabola); To find if it is a function or not draw a vertical line on the graph. If the vertical line could never intercept the figure more than once anywhere on the graph then it is a function.

From left to right of the pictures it's the 3rd photo. It's the 3rd photo because it passes the vertical line test witch means if a vertical line was drawn within the middle of the graph it would only pass through one line and not two. The other ones would pass through two lines instead of one. I hope this helped you!

Answer:

Step-by-step explanation:

Given a geometric sequence.

2, 6, 18, 54, …

We have to find the I and nth term.

A geometric sequence. is one where each term is multiplied by a constant value to get the next term.

In our sequence, we find the pattern as each term is multiplied by 3 to get successive terms.

Hence common ratio r = 3

First term = a = 2

For Geometric sequence nth term = a_n = ar^(n-1)

Hence we get a_1 = 2

and a_n =  2(3)^(n-1)

By substituting for n any natural number we can get that term.

9x < 54     |divide both sides by 9

x < 6

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

-4x < 12     |change the signs

4x > -12    |divide both sides by 4

x > -3

-3 < x < 12

Answer: b.

ANSWER

[tex]\frac{4x^4+34x^3+44x^2+11x-27}{x+7}=4x^3+6x^2+2x-3- \frac{6}{x+7}[/tex]

EXPLANATION

See graph in attachment.

Answer

4x³+6x²+2x-3   remainder -6

Explanation

Find the attached  file.

ratio = 12 : 48 = 1 : 4 = [tex]\frac{1}{4}[/tex] as a fraction in simplest form

[tex]i^{77}=i^{4\cdot19+1}=(i^4)^{19}\cdot i^1=1^{19}\cdot i= i[/tex]

i^77 = (i^4)^19 * i

= 1^19  * i

= 1 * i

= i

Answer is   i

Answer:

x=-0.688

Step-by-step explanation:

-2496-3744x+36 = -759x-414-10x

-2460-3744x = -769x-414

-2975x = 2046

Answer: The correct option is (D) (5, -2).

Step-by-step explanation:  We are given to use the method of substitution to solve the following system of equations :

[tex]3x+7y=1~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\y=x-7~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]

Substituting the value of y from equation (ii) in equation (i), we get

[tex]3x+7y=1\\\\\Rightarrow 3x+7(x-7)=1\\\\\Rightarrow 3x+7x-49=1\\\\\Rightarrow 10x=50\\\\\Rightarrow x=\dfrac{50}{10}\\\\\Rightarrow x=5,[/tex]

and from equation (ii) again, we get

[tex]y=x-7=5-7=-2.[/tex]

Thus, the required solution is (x, y) = (5, -2).

Option (D) is CORRECT.

12x - 3y

Put the values of x = -14 and y = 3 to the expression:

12(-14) - 3(3) = -168 - 9 = -177

Answer:

Domain is the set of all real numbers

Range is the set of all real numbers.

Step-by-step explanation:

Given a graph with curve which has y intercept -5, and x intercept 5.

The graph is  continuous at all points of x and y

We find that the graph is a straight line with positive slope of the form

x/5 +y/-5=1

Or x-y =5

The graph is defined for all values of x and y.

The domain is the set of values x can take  

In the graph horizontal axis is x axis.

Hence from the graph we see that x can take values from -infinity to + infinity

Hence domain is x = R

For range, we consider the values of y as per graph.

WE find that y is  taking values in the interval (-infinity, infinity)

Hence Range =R

The term 'domain' in mathematics refers to the complete set of possible values of the independent variable in a function. The 'range' on the other hand, represents the possible results of the function after an experiment or survey. These values are not always numerical but could be a set of words or phrases.

The domain of a function is the complete set of possible values of the independent variable. In the context of your question, it can be a list such as X = {English, Mathematics,...} representing all the majors offered at a university, or it can be a numerical set, for example Y = {0, 1, 2,...} representing the integers from zero up to the upper limit of classes. Even functions like Z where the domain includes any amount of money from zero upwards can exist.

Similarly, the range of a function is the set of all possible values that the function can take after the experiment is performed or the question is answered. For instance, if a function has a domain of hair color, its range would be the different hair colors like black, blond, gray, green, orange, etc. This shows that the domain and range of a function are not necessarily numerical.

The specific value x the function takes only becomes known after performing the experiment or survey. However, there might be certain values that are outside the domain of the function and as such, would not give a reliable prediction, just like 90 in the dataset from 65 to 75. Such an occurrence doesn't fall within the domain of the function and can't be accurately predicted.

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The answer would be B. x^2+8x+15

Answer:

y  = 1.00+0.10 x

Step-by-step explanation:

Given that a taxi has a minimum charge of 1 dollar upto 1/10 mile and adds 0.10 for every additional 1/10 mile.

If a person travels <=1/10 miles his charges are 1 dollar

If he travels >1/10 miles charges are 1 dollar +0.10(extra miles 1/10)

Let y be the charges and x be the no of 1/10 miles.

Then the equation for y in terms of x would be

y =1.00 +1/10(x)

y  = 1.00+0.10 x

Answer: D. Yes because it passes the vertical line test.

Step-by-step explanation

A function cannot have duplicate x-coordinates.

When given a table or a set of coordinates, if there is an x-coordinate that is paired with two different y-coordinates then it is not a function.

When given a graph, the simplest way to determine if it is a function is to use the vertical line test.  If you can draw a vertical line anywhere through the graph and it passes through two points, then it is not a function.

In the given graph, it passes the vertical line test so it IS a function.

If you are F years old and your brother is B years older, then your brother is F+B years old. Add your age (F) and your brother's age (F+B) and you get F+(F+B) = 2F+B

The sum of your ages is 2F+B

where F and B are placeholders for numbers.

The number 12079 could be said two ways in terms of hundreds, tens, and ones. It can be 'twelve thousand, seventy-nine' or 'one hundred and twenty hundred, seven tens and nine ones'

The number 12079 can be said in two different ways using hundred, tens and ones. First, you could say it as 'twelve thousand, seventy-nine.' This is because 12 is the thousands component (consisting of hundreds and thousands), and 79 is the ones and tens components. Secondly, you could say it as 'one hundred and twenty hundred, seven tens and nine ones'

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Divide 5 pages by 3 hours to fins how many pages he wrote in 1 hour:

5 pages /  3 hours = 1 2/3 pages per hour.

Multiply 1 2/3 pages per hour by total hours to find total pages.:

1 2/3 x 8 = 13 1/3 pages (13.33)

The complete solution is in image attached.

Answer:

Step-by-step explanation:

We convert into decimals and then multiply

Otherwise we can convert everything into one unit and then multiply.

10 hg = 1 kg and 100x1000 cg = 1kg

Using this

a. 9 kg 3 hg 1 cg × 9 = 9.300001x9=83.700009 kg

b.  11 dg 4 cg × 12 = 11.400004x12 =16.8000048kg

c. 10 g 5 dg × 6 = 10.5x6 =63.0 kg

d. 5 g 3 dg 4 cg × 8 =5.300004x8 = 42.400032

      700a + 1200r = 1,000,000

700(1000) + 1200r = 1,000,000

700,000  + 1200r = 1,000,000

                    1200r = 300,000

                           r = [tex]\frac{300,000}{1200} = \frac{3000}{12} = 250[/tex]

Answer: 250 pounds of robusta beans