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The given algebraic expression can be simplified as 6+9i.

A complex number is represented by the following form: a+bi, where a and b are real numbers.  The variables: a is the real part and bi imaginary part. See an example: 7 + 14i , then:

Regarding operations math, the same properties used for real numbers can be applied to complex numbers. And for solving the operations math with these numbers, it is important to know that i²= -1. Thus, 2i² = 2*(-1)= -2.

When you subtract or sum complex numbers, you can only subtract or sum: the real part with the real part of each complex number and the imaginary part with the imaginary part of each complex number. Here, you can see examples:

(5 + 2i) + (5 + 2i) = 10+4i

(4 + 9i) - (1 + 5i) = 1+4i

Therefore, the result for the  6 + √− 81 will be:

6+  √81i²

6+9i

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Answer:

true

Step-by-step explanation:

5^ -2

(1/5)^2

1/25

Answer:

That's true :

5^-2= 1/5^2= 1/25

so yes : 5^-2=1/25

Step-by-step explanation:

By the concept of percentage, 41 is [tex]10\frac{1}{4}[/tex] % of the number 400.

The percentage is a comparative figure denoting one-hundredth of any quantity. One percent (symbolized as 1%), being the hundredth component, is represented as 100 percent, while 200 percent signifies twice the amount specified. Percent is derived from the Latin word per centum, which means "by the hundred." In the 16th century, the Latin expression was adopted by English. Later, it was shortened to % with a period in the end. The present one-word form % was created after the period was eliminated and the two elements were combined. In essence, percentages are fractions with a denominator of 100. The percent symbol (%) is placed next to a number to indicate that it is a percentage.

Let the number be x.

Then, according to the question

[tex]10\frac{1}{4}[/tex] can be written as 41/4

So,

41/400 × x = 41

41 x = 41 ×100

x =400

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The expression as a power is 2^10 and 2^9

Index form of a number can be defined as the number that is written in the form of an exponential expression.

It is also described as a single number that is raised to another variable or number.

It is important to note the following index forms with base of 2, we have;

We have the expression as;

8•2^7

Substitute the values

2^3 . 2^7

Add the powers

2^3 + 7

2^10

16•32

Substitute the values

2^4 . 2^5

Add the powers

2^ 4 + 5

2^9

The expression is written as; 2^ 10 and 2^9

Hence, the values are 2^10 and 2^9

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Answer:

i know i know its is 8.78 pounds it is easy

Step-by-step explanation:

what you do is that i am smart

The required total cost of the 11 kg of potatoes and 1½ kg of carrots is $7.72.

Given that,
The cost of 5 kg of potatoes is £3.40 the cost of 2 kg of carrots is 32p working out the total cost of 11 kg of potatoes and 1½ kg of carrots.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Cost of potatoes per kg = 0.68
Cost of 11 kg of potatoes = 0.68×11 = $7.48
Cost of the carrots per kg = 0.16
Cost of 1.5 kg carrot = 0.24
Total cost of the 11 kg of potatoes and 1½ kg = 7.48 + 0.24= $7.72.

Thus, the required total cost of the 11 kg of potatoes and 1½ kg of carrots is $7.72.

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Step-by-step explanation:

i marked where to put them

Answer:

k = - 8

Step-by-step explanation:

- 268 = - 6(- 6 - 6k) + 2k ← distribute parenthesis by - 6

- 268 = 36 + 36 k + 2k ( subtract 36 from both sides )

- 304 = 38k ( divide both sides by 38 )

- 8 = k

Answer:1/2

Step-by-step explanation:

The unit rate of the plant growth is 5cm per hour

The unit rate refers to amount the plant will grow 1 hour

from the relationship

15 cm = 3 hours

? cm = 1 hour

cross multiplying

3 * ? = 15 * 1

? = 15 / 3

? = 5 cm

The plant's unit rate of growth is 5cm per hour

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The way that zeros of a polynomial function is related to the equation and graph of a function because they act as solutions to the equation and also x-intercepts of a graph.

When the quadratic equation's graph crosses the x-axis, those points are known as the zeros of the equation.

The graph's x-intercepts and a function's zeros are the same thing. If the zero of f has an odd multiplicity, the graph of f will cross the x-axis at that x value. The x-axis will be touched by the graph of f if it has an even multiplicity zero.

Hence, A polynomial's zeros are the answers to any equation such as p(x) = 0, where p(x) stands for the polynomial. Since the values of x where y = 0 if we graph this polynomial as y = p(x). In other words, these are the graph's x-intercepts.

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The total change in yards where the team started is 3x

The given parameters in the question are:

Yards per play = unknown

Number of plays = 3 consecutive plays

Represent the yards per play with x

So, we have

Yards per play = x

The total change in yards is the amount of yard per play multiplied by the number of plays

This is represented as

Total change = Yards per play * Number of plays

Substitute the known values in the above equation So, we have the following equation

Total change = x * 3

Evaluate

Total change = 3x

Hence, the total change is 36 yards

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answer:

$245.70

why?:

1 year = 52 weeks

52/2= 26

26*3 = 78 times

78*3.15= 245.70

Answer: The missing values in the ratio table will be 0.666 and 5.33 inches.

Step-by-step explanation:

As the ratio of the terms is equal. The value of x and y is ,

2/3 = x/1

x=2/3

x=0.66 inches

In order to obtain y,

2/3 = y/8

y=2×8/3

y=16/3

y=5.33 inches.

Step-by-step explanation:

to find the perimeter first:

13×3=39

13×3=39

5×3=15

5×3=15

39+39+15+15=108

P=108

i hope it's useful

Answer:

The bottom right

Step-by-step explanation:

A relation is just a set of ordered pairs.  A function is a special relation.  In a function every input (x) has only one output (y).  

You can use the vertical line test.  If you took your pencil and vertical passed over the graph left to right. If there is any point that more than one point would be under the pencil, the relation is not a function.

Answer:

no

Step-by-step explanation:

the percentage has nothing to do with how many of them there are, forgive me if im wrong

The exact number of books on the shelf cannot be determined based on the information given.

An expression is a grouping of one or more mathematical or logical operators, operands (values, variables, or other expressions), and brackets in mathematics and computer programming that denote a computation that can be evaluated to generate a value.

We know that between 50 and 100 books are stored on a shelf, so let's assume the number of books is some integer value between 50 and 100, inclusive. Let's call this value "n".

Exactly 20% of the books are textbooks, which means there are 0.2n textbooks on the shelf.

Exactly one-seventh of the books are novels, which means there are (1/7)n novels on the shelf.

We know that n, 0.2n, and (1/7)n are all integers because they represent whole numbers of books. We can write this as:

n = a

0.2n = b

(1/7)n = c

where a, b, and c are integers.

From the second equation, we know that 0.2n is a multiple of 1/10. From the third equation, we know that n is a multiple of 7. Therefore, we can rewrite these equations as:

n = 10b

n = 7c

Since n is equal to both 10b and 7c, we know that n must be a multiple of the least common multiple of 10 and 7, which is 70.

So, n must be a multiple of 70, and therefore must be one of the integers 50, 70, or 90. However, we cannot determine which of these three values is the correct one based on the information given, because all three satisfy the conditions in the problem:

If n=50, then 20% of the books (i.e., 10 books) are textbooks, and 1/7 of the books (i.e., 7.14 books, which we round down to 7) are novels.

If n=70, then 20% of the books (i.e., 14 books) are textbooks, and 1/7 of the books (i.e., 10 books) are novels.

If n=90, then 20% of the books (i.e., 18 books) are textbooks, and 1/7 of the books (i.e., 12.86 books, which we round down to 12) are novels.

Therefore, the exact number of books on the shelf cannot be determined based on the information given.

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For the given pair of parallel lines AG and BH , CF is the transversal then ∠ADE and ∠BEF are corresponding angles.

As given in the question,

Given :

Pair of parallel lines are AG and BH.

CF is the transversal.

Transversal CF intersect line AG at point D and

Transversal CF intersect line BH at point E

Four pair of corresponding angles

Two pair of alternate interior angles

Corresponding pair of angles in the pair of parallel lines are congruent.

∠ADE ≅ ∠BEF

∠ADE and ∠BEF are corresponding angles.

Therefore, for the given pair of parallel lines AG and BH , CF is the transversal then ∠ADE and ∠BEF are corresponding angles.

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If the p-value is 0.023 from a hypothesis test is compared to a significance level of 0.05, the conclusion which we would make is: A) accept the null hypothesis.

A p-value is also referred to as the probability value and it can be defined as a probability which arises when the null hypothesis (H₀) is true of obtaining a sample result that is at least as unlikely as what is originally observed.

In Mathematics, the following rules are applicable to both a p-value and a hypothesis test:

In this context, we can logically deduce that the null hypothesis would be accepted because the p-value (0.023) is greater than a significance level of 0.05 and not statistically significant.

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Answer:

1). True

2). x = 16.4 m^2

3). A = 24, h = 4

4). A = 18.39

5). 162

Step-by-step explanation:

I took this quiz on K12 and got everything correct! Brainliest welcome! :)

The length of the railing is 105.81 inches.

Given,

The stair has 7 steps

The rise of each step = 8.5 inches

The tread of each step = 12.5 inches

Slope of each step = x

We have to find the length of the railing.

Length of railing = 7x

Then,

Slope of step, x can be determined using Pythagorean theorem.

Let rise be the height of the right angled triangle and tread be the base of the triangle

Then,

Hypotenuse= Slope, x  = [tex]\sqrt{Rise^{2} + Tread^{2} }[/tex]

x = [tex]\sqrt{8.5^{2}+ 12.5^{2} }[/tex]

x = [tex]\sqrt{72.25 + 156.25}[/tex]

x = √228.5

x = 15.12 inches

That is,

The slope, x of one step is 15.12 inches

Now,

Length of the railing = 7x = 7 × 15.12 = 105.81 inches

Therefore,

The length of the railing is 105.81 inches.

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You owe on the loan is $64512.90

Given,

In the question:

You owe $46,212.35 on a student loan that carries an APR of 6.9%. You place the loan into forbearance for 5 years.

To find the how much do you owe on the loan when it comes out of forbearance?

Now, According to the question:

Based on the given conditions,

Formulate;

You owe $46,212.35 on a student

Interest is 6.9%

46212.35 x (6.9% +1)^5

Evaluate the equation/expression:

64512.90

Hence, You owe on the loan is $64512.90

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The percentage of the tip will be equal to 24.81%.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that Mia was out at a restaurant for dinner when the bill came. Her dinner came to $28. After adding in a tip, before tax, she paid $37.24.

The percentage tip will be calculated as,

P = ( (37.24 - 28 ) / 37.24

P = 9.24 / 37.24

P = 0.2481 x 100

P = 24.81%

Therefore, the percentage of the tip will be equal to 24.81%.

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The fraction of page in the photograph is 3/32.

So, the fraction of the page in the photograph:

We know that,

Now, calculate as follows:

Therefore, the fraction of page in the photograph is 3/32.

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Answer:

=3/32

Step-by-step explanation:

(1/2÷4)*3/4

1/2*1/4*3/4

1/8*3/4

There-For The Answer Is:

=3/32

The time is 2 our 55 minutes when they will take to cultivate the piece of land when working together.

What is mean by Fraction?

A fraction is a part of whole number, and a way to split up a number into equal parts.

Or, A number which is expressed as a quotient is called fraction.

It can be written as the form of p : q, which is equivalent to p / q.

Given that;

Kepteo can cultivate a piece of land in 7 hr.

Wanjiku can do the same work in 5 hr.

Now,

Since, Kepteo can cultivate a piece of land in 7 hr.

Hence, Kepteo make work in 7 h

So, In 1 hour kepteo work = 1/7

And, Since, Wanjiku can cultivate a piece of land in 5 hr.

Hence, Wanjiku  make work in 5 h

So, In 1 hour Wanjiku work = 1/5

Thus, They make with together = 1/7 + 1/5

                                                = 12/35

Hence, When they working, they make = 12/35 work per hour

So, They need number of hour to working together = 35/12 hour

                                                                               = 2 hour 55 minutes.

Thus, The time is 2 our 55 minutes when they will take to cultivate the piece of land when working together.

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20   foot² is  the area of the wall.

What does a math area mean?

Length of concrete wall = [tex]2\frac{1}{2}[/tex] foot

Breadth of concrete wall = 8 foot

Since, area means product of dimensions so we use the formula mentioned below:

Area of the concrete wall = length× breadth

                                          = [tex]2\frac{1}{2}[/tex]  * 8

                                           = 5/2  * 8

                                            =  5 * 4 = 20 foot²

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The functions g(0) = 20, g(−2.5) = 0, g(4) = 0, g(0.75) = 21.125, g(20) = -720 as a result of the mapping with the function g(x) = −2x² + 3x + 20

A function is a mapping whose codomain is the set of real numbers. It can also be defined as a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

From the function g given as g(x) = −2x² + 3x + 20, by careful mapping we have the following;

put 0 for values of x

g(0) = -2(0)² + 3(0) + 20

g(0) = 20.

put -25 for values of x

g(-25) = -2(-25)² + 3(-25) + 20

g(-25) = -12.5 - 7.5 + 20

g(-25) = 0

put 4 for values of x

g(4) = -2(4)² + 3(4) + 20

g(4) = -32 + 12 + 20

g(4) = 0

put 0.75 for values of x

g(0.75) = -2(0.75)² + 3(0.75) + 20

g(0.75) = -1.25 + 2.25 + 20

g(0.75) = 21.125

put 20 for values of x

g(20) = -2(20)² + 3(20) + 20

g(20) = -800 + 60 + 20

g(20) = -720

Therefore, by proper mapping of the function g(x) = −2x² + 3x + 20, we derived g(0) = 20, g(−2.5) = 0, g(4) = 0, g(0.75) = 21.125, and g(20) = -720.

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Answer:

g(0) = 20

g(-2.5) = 0

g(4) = 0

g(0.75) = 21.125

g(20) = -720

Step-by-step explanation:

Hello!

We can evaluate each value by plugging the value inside the parenthesis into x in the equation [tex]-2x^2 + 3x + 20[/tex].

The values are, in order, 20, 0, 0, 21.125, and -720.

The product of 17×7 using the difference of two squares is 119.

= 17×7

=(12+5)(12-5)

=12(12-5)+5(12-5)

=12×12-12×5+5×12-5×5

=12²-5²

=144-25

=119

The difference between two squares is a theorem that tells us if a quadratic equation can be written as a product of two binomials, in which one shows the sum of the square roots and the other one is the difference of the square root.

I hope this answer helps.

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1. Her Average would be 80

2. Yes, there are more dots around points 80.