Look at this diagram:If KM and NP are parallel lines and m

The powers of the imaginary number i have four possible values: 1, i, -1, and -i. Let's see some examples:

i⁰ = 1 (any number with the exponent 0 equals 1)

i¹ = i (any number with the exponent 1 is the number itself)

i² = -1 (this follows from the definition of the imaginary number, the square root of -1)

i³ = i² * i = -1 * i = -i

Now, the results start to repeat from 1 to -i:

i⁴= i² * i² = (-1) * (-1) = 1

i⁵ = i⁴ * i = 1 * i = i

i⁶ = i * i⁵ = i * i = i² = -1

i⁷ = i⁶ * i = -1 * i = -i

From that, we can follow the steps below to find the value of a power of i:

• divide the exponent by 4;

• if the rest of the division is 0, then the power equals ,i⁰ = 1,;

• if the rest of the division is 1, then the power equals ,i¹ = i,;

• if the rest of the division is 2, then the power equals ,i² = -1,;

• if the rest of the division is 3, then the power equals ,i³ = -i,.

So, for the power i⁶⁴⁹, the exponent is 649. Following the steps above, we find:

• 649/4, has a quotient of 162 and the, rest 1,. Therefore:

i⁶⁴⁹ = i¹ = i

Thus, i⁶⁴⁹ equals i.

Answer:

the value of pi is 3.14159

Thus, the final answer is 34.9.

2.

The Total cost of x small and y large greeting cards is; 1.25x + 4.50y.

An equation is an expression that shows the relationship between two or more numbers and variables.

Given that the Cost of the small greeting card = is $1.25 .

The Cost of the large greeting card =$4.50.

We need to determine the Total cost of 5 small and 4 large greeting cards and the total cost of x small and y large greeting cards.

The Cost of 5 small greeting cards = 6.25

The Cost of 4 large greeting cards = 18

Then the Total cost = $6.25+ $18 =$24.25

Therefore, the Total cost of 5 small and 4 large greeting cards is; $24.25.

Now, the total cost of x small and y large greeting cards will be;

Cost of x small greeting cards = 1.25x

Cost of y large greeting cards = 4.50y

Total cost = 1.25x + 4.50y

Therefore, the Total cost of x small and y large greeting cards is; 1.25x + 4.50y.

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The graph of the equation y = –12x – 6 is attached in the solution.

We can find the x and y intercept of the line to find make the graph.

Putting x = 0 in the given equation, we get:-

y = -12(0) - 6 = 0 - 6 = -6

Hence, the x -intercept is (0,-6).

Putting y = 0 in the given equation, we get:-

0 = -12x - 6

6 = -12x

x = 6/(-12)

x = -1/2

Hence, the y -intercept is (-1/2,0).

We can find another point on the line.

Putting x = -1 in the given equation, we get:-

y = -12(-1) - 6

y = 12 - 6 = 6

y = 6

Hence, another point on the line is (-1,6).  

Plotting these points we can graph the equation of the line.

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Answer:

slope = -1/9

Step-by-step explanation:

Hope this helps!!!

Answer :- Constant term

In p(x) = x - 12, 1 is the coefficient of x and -12 is the constant term.

Answer:

994

Step-by-step explanation:

work inside the parenthesis first. 8+2 = 10 then raise 10 to the power of 3 which is 1000. subtract 6 from 1000 & you get 994

Answer:

994

Step-by-step explanation:

PEDMAS

Do the math inside the parentheses first

8+2 = 10         Now do the exponent    10^3 = 1000   Now subtract 6  = 994

Answer:

G

Step-by-step explanation:

the domain is the interval or set of all valid x values.

we see x starts at -3 and goes up to +1.

but x = 1 has the be excluded (the hollow point tells us that, a filled point says "include").

therefore, the -3 <= x < 1 answer is correct

Option C and Option D are the appropriate measurements of center and spread for the dataset.

The mean, median, and mode are three examples of center-of-data measurements.

Included in the spread measurements are range, mean deviation, variance, and standard deviation.

The given data is displayed as a box plot with the minimum, maximum, median, Q1 and Q3 values.

The median is the most accurate measurement of the middle of the data.

The interquartile range is the appropriate way to measure spread.

In conclusion, the median and interquartile range, respectively, are the most suitable measures of the data set's center and dispersion.

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Answer:

9 inches

Step-by-step explanation:

Set it up like a fraction ratio and solve for x.  as the price (denominator) and amount (numerator) have a set ratio, you can cross-multiply for your answer.

[tex]\frac{13}{52} =\frac{x}{36\\}\\[/tex]

13*36 = 468

468/52 = 9

Another way would be to divide 13 by 52 and multiply by 36, but then you end up with decimals and cross multiplication will be easier in the long run.

We are given a set of coordinates which are;

And the slope which is;

The equation of a line in slope-intercept form is;

Note that in this equation, the variable m is the slope (that is, the coefficient of x). we can now substitute for x, y and m into the equation above and we'll have;

We now have the values of the slope and the y-intercept as

The equation now can be written as;

ANSWER:

The values are given as;

1. - 2a - 9 = 6a + 15,  a = -3

2. 14 + 3n = 5n - 6, n = 10

An algebraic expression can simply be described as a mathematical expression that composed of arithmetic operations, such as;

They are also known to be made up of terms, variables, constants, factors and coefficients.

Given the algebraic expression;

- 2a - 9 = 6a + 15

Let's take the following steps;

collect like terms

- 2a - 6a = 15 + 9

add or subtract like terms

-8a = 24

Make 'a' the subject

a = 24/-8

Find the quotient

a = -3

14 + 3n = 5n - 6

collect like terms

3n - 5n = -6 - 14

-2n = -20

Make 'n' the subject of formula

n = 10

Hence, the values are -3 and 10

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To make a poster you have to keep the ratio between lenght and height (otherwise it will look weird)

This is:

The most appropriate choice for perimeter of a shape will be given by-

UT = 19 ft

ST = 19 ft

RS = 19 ft

UR = 19 ft

What is perimeter of a shape?

Perimeter of a shape is the length of the boundary of the shape.

It is obtained by taking the sum of all the length of the boundary.

Here,

UT = (25 - x) ft

ST = (3x + 1) ft

RS = (13 + x) ft

UR = (4x - 5) ft

Perimeter = UT + ST + RS + UR

                = (25 - x + 3x + 1  + 13 + x +4x -5) ft

                = (7x + 34) ft

By the problem,

[tex]7x +34 =76\\7x = 76 -34\\7x = 42\\x = \frac{42}{7}\\x =6[/tex]

UT = [tex]25 - 6[/tex] = [tex]19[/tex] ft

ST = [tex]3 \times 6 + 1[/tex] = [tex]19[/tex] ft

RS = [tex]13 + 6 = 19[/tex] ft

UR = [tex]4\times 6 - 5[/tex] = 19 ft

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Applying the distributive property and precedence of operations, the results to each side of the expression is of 2/5, hence they property holds.

The left-hand side of the expression is defined as follows:

2/5(4/3-1/3)

Applying the distributive property, 2/5 multiplies each term as follows:

2/5(4/3-1/3) = 8/15 - 2/15

(multiplication of fractions -> multiply numerators and denominators with themselves).

They have common denominator, then the subtraction of the fractions is calculated as follows:

2/5(4/3-1/3) = 8/15 - 2/15 = 6/15

6 and 15 are divisible by 3, hence the fraction is simplified as follows:

6/15 = 2/5.

The right-hand side of the expression is given as follows:

2/5 x 4/3 - 2/5 x 1/3

We have two operations, subtraction and multiplication. The multiplication has higher precedence, hence:

2/5 x 4/3 - 2/5 x 1/3 = 8/15 - 2/15

Then the procedure is the same as the left-hand side, obtaining an equal result, and so the distributive property holds.

2/5(4/3-1/3)=2/5*4/3-2/5*1/3

We need to solve:

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Answer:

Q4) 20

Q5) 48%

hope this helps

approximately 7 years old

Step-by-step explanation:

Answer:

f(1) = 15

f(-9) = -65

f(0) = 7

Step-by-step explanation:

f(1) = 8(1) + 7

f(1) = 8 + 7

f(1) = 15

f(-9) = 8(-9) + 7

f(-9)  = -72 + 7

f(-9) = -65

f(0) = 8(0) + 7

f(0) = 7

The reminder of 2 to the 100th power divided by 5 is 1

2 to the 100th power is:

[tex]2^{100}[/tex]  = 1,267,650,600,228,229,401,496,703,205,376

Then dividing 2 to the 100th power by 5:

1,267,650,600,228,229,401,496,703,205,376 / 5 = 253,530,120,045,645,880,299,340,641,075  (without considering the decimal value)

This tells us how many times 5 can divide 2 to the 100th power.

Next, we need to multiply the answer obtained from the division by 5 (since we used 5 to divide):

253,530,120,045,645,880,299,340,641,075 x 5 = 1,267,650,600,228,229,401,496,703,205,375

Lastly, subtracting our last answer from the value of 2 to the 100th power will give us the reminder:

1,267,650,600,228,229,401,496,703,205,376 - 1,267,650,600,228,229,401,496,703,205,375 = 1

Therefore, the reminder when 2 raised to the power of 100 is divided by 5 is  1.

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Explanation

To answer the question, we have to understand the different parts of an algebraic expression

An expression containing variables, numbers, and operation symbols is called an algebraic expression. is an example of an algebraic expression. Each expression is made up of terms. A term can be a signed number, a variable, or a constant multiplied by a variable or variables.

We are given the algebraic expression:

For the given question

The difference means the result of subtracting one number from another or How much one number differs from another, so we have

Then

The coefficient is is a number or any symbol representing a constant value that is multiplied by the variable of a single term or the terms of a polynomial, so we have

Also

A quotient is a number resulting from the division of one number by another, so we have

Finally,

A product is the result of multiplication or an expression that identifies factors to be multiplied.

Thus, we have

Answer: (52,72) (52 adults and 72 children)

Step-by-step explanation:

1) Create 2 formulas that show the information show above, 2.5x+2y=274 showing how the x is how many adults paid for a ticket and y is how many children paid for a ticket. The second formula being x+y=124 meaning the combination of children and adults equal 124 people.

2) Take those formulas and input them into a graph as shown in the picture (Graph 1)

3) Find the common point shown on the graph (should be the middle grey dot if on Desmos as shown (Graph 2)

4) The common point is (52, 72)

And if you plug these numbers in by replacing the x's and y's i shown in step 1 they bring an output of 274 and 124

Hope this helps :)

A. Addition

Explanation

PEMDAS is an acronym for the words parenthesis, exponents, multiplication, division, addition, subtraction. Given two or more operations in a single expression, the order of the letters in PEMDAS tells you what to calculate first, second, third and so on, until the calculation is complete

Step 1

so, firts calculate the parenthesis

the operation in parenthesis is an addition

i hope this helps you

Scientific notation the

Answer:

-29.8

Step-by-step explanation:

4 (-1.2-4-4.75) +1+(-3)²

4 (-1.2-4-4.75) +1+(-3)²

4 (-9.95) +1+9

4 (-9.95) +1+9

-39.8 +1+9 = -29.8

Answer:120 dollars

Step-by-step explanation:

Answer:

x+1/3

Step-by-step explanation:

Add the terms together (3x+1), then divide by how many terms there are (3), to get the average of the expressions

The highest cut-off interest rate is 2.66%

Given that,

Standard deviation (sigma) = 0.37

Mean percentage (Mu) = 2.28 %

P(Z > 1.04) = 0.15

z = 1.04

Using the z-score formula,

x = (z × sigma) + mu

x =  (1.04 × 0.37 )+ 2.28 = 2.66 %

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There is sufficient evidence at the 0.10 level of significance that the percentage is not 33%.

According to the newsletter publisher that 33% of their readers own a Rolls Royce.

The testing firm says that this is an inaccurate issue and performs a test to dispute the publisher's claim, after performing the test at the 0.10 level of significance the results are as follows,

Null hypothesis:

H₀ : p = 0.33

Alternative hypothesis:

H₁ : p ≠ 0.33

We reject H₀ at the 0.10 level of significance.

Therefore, There is sufficient evidence at the 0.10 level of significance  that the percentage is not 33%.

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