Which expression represents the number −3i^4+2i^3+2i^2+\sqrt(-9) rewritten in a+bi form?
A) −1−i
B)−1+5i
C)−5+i
D)−5−5i
E)−5−i

Answer:

[tex]\frac{2\pi}{3}[/tex]

Step-by-step explanation:

So here they are asking for one angle that gives you the cosine value is equal to -1/2 while being in quadrant 2.

So you look in quadrant 2 and find x=-1/2 which is at [tex]\frac{2\pi}{3}[/tex].

[tex]\cos^{-1}(\frac{-1}{2})=\frac{2\pi}{3}[/tex] while being in quadrant 2.

Answer:

6

Step-by-step explanation:

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

We know f(1) = 10

Let n=1

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

f(2) = 10-2 =8

We now know f(2)

Let n=2

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

f(3) = 8 -2=6

f(3) =6

Answer:

The correct option is B:

Subtract 2 from both sides

Step-by-step explanation:

We have the equation x²-4x+16=2

The first step to solve this equation is:

Subtract 2 from both sides

We get;

x²-4x+16=2

x²-4x+16-2=2-2

x²-4x+14=0

Now this is the quadratic equation. You can use quadratic formula to solve this equation....

Answer:

The answer is C) 13.

Step-by-step explanation:

To find the hypotenuse (longest side) of a right triangle, you need to use the Pythagorean Theorem. The formula for the hypotenuse is a^2 + b^2 = c^2.

5^2 (five squared) equals 25, and 12^2 (twelve squared) equals 144.

25 + 144 = 169

Next, find the square root of 169. It is 13. 13 is the length of the hypotenuse.

I hope this helped! :)

In the right triangle ABC, the length of the AC is equal to [tex]13[/tex] units.

" Right triangle is defined as a triangle with one of the interior angles with measure equals to [tex]90[/tex] degrees."

Formula used

Pythagoras theorem,

(Hypotenuse)² = ( adjacent side)² + (opposite side)²

According to the question,

In the right triangle ABC,

Adjacent side 'BC' [tex]= 12[/tex] units

Opposite side 'AB' [tex]= 5[/tex] units

'AC' represents the hypotenuse of the right triangle

Substitute the value in the Pythagoras theorem we get,

[tex]AC^{2} = BC^{2} +AB^{2} \\\\\implies AC^{2} = 12^{2} + 5^{2} \\\\\implies AC^{2} = 144 + 25\\\\\implies AC = \sqrt{169} \\\\\implies AC =13units[/tex]

Hence, Option(C) is the correct answer.

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Answer:

The system is inconsistent because there is no solution.  

Step-by-step explanation:

I'm going to put both of these in slope-intercept form (y=mx+b where m is slope and b is y-intercept).

3x-6y=20

Solve for y.

3x-6y=20

Subtract 3x on both sides:

  -6y=-3x+20

Divide both sides by -6:

    y=(-3/-6)x+(20/-6)

Reduce:

  y=(1/2)x+(-10/3)

The slope is 1/2 and the y-intercept is -10/3.

2x-4y=3

Solve for y.

2x-4y=3

Subtract 2x on both sides:

   -4y=-2x+3

Divide both sides by -4:

    y=(-2/-4)x+(3/-4)

Reduce:

   y=(1/2)x+(-3/4)

The slope is 1/2 and the y-intercept is -3/4.

The lines are parallel so they have no intersection. I know they are parallel because they have the same slope and different y-intercept.

The system is inconsistent because there is no solution.  

Answer:

B) Inconsistent

Step-by-step explanation:

Step 1: Write both equations

3x - 6y = 20

2x - 4y = 3

Step 2: Find x in terms of y

3x - 6y = 20

x = 20+6y/3

Step 3: Substitute x in one of the equations to find y

2x - 4y = 3

2(20+6y/3) - 5y = 3

40 + 12y - 12y = 9

0 ≠ -31

Therefore, these system of equations have no solution.

Step 4: Choose the option

A) consistent- A consistent system of equations has at least one set of equations. Therefore, this option is incorrect.

B) inconsistent- An inconsistent system of equations has no solution. Therefore, this option is correct.

C) Independent- An independent system of equations has one solution. Therefore, this option is incorrect.

D) Dependent- A dependent system of equations have infinite solutions. Therefore, this option is incorrect.

Option B is the right answer

!!

Answer:

7033/10000

Step-by-step explanation:

You get his answer by times it by 1000 so the decimal point is out of the number

Final answer:

To find four consecutive even integers with a sum of -52, we denote the smallest integer as x and use the equation x + (x+2) + (x+4) + (x+6) = -52 to find that these integers are -16, -14, -12, and -10.

Explanation:

To find four consecutive even integers with a sum of -52, let's denote the smallest of these integers as x. Consequently, the next three integers can be represented as x+2, x+4, and x+6. The sum of these four integers can be expressed as the equation x + (x+2) + (x+4) + (x+6) = -52.

Combining like terms gives us 4x + 12 = -52. Subtracting 12 from both sides gives 4x = -64, and dividing both sides by 4 yields x = -16. Therefore, the four consecutive even integers are -16, -14, -12, and -10.

The four consecutive even integers with a sum of -52 are -16, -14, -12, and -10.

Let's denote the four consecutive even integers as [tex]\( x \), \( x+2 \), \( x+4 \), and \( x+6 \)[/tex].

According to the problem, their sum is -52. So, we can set up the equation:

[tex]\[ x + (x + 2) + (x + 4) + (x + 6) = -52 \][/tex]

Now, let's solve for \( x \):

[tex]\[ 4x + 12 = -52 \][/tex]

Subtract 12 from both sides:

[tex]\[ 4x = -52 - 12 \][/tex]

[tex]\[ 4x = -64 \][/tex]

Divide both sides by 4:

[tex]\[ x = \frac{-64}{4} \][/tex]

[tex]\[ x = -16 \][/tex]

Now that we've found the value of \( x \), we can find the consecutive even integers:

- First even integer: [tex]\( x = -16 \)[/tex]

- Second even integer: [tex]\( x + 2 = -16 + 2 = -14 \)[/tex]

- Third even integer: [tex]\( x + 4 = -16 + 4 = -12 \)[/tex]

- Fourth even integer: [tex]\( x + 6 = -16 + 6 = -10 \)[/tex]

So, the four consecutive even integers with a sum of -52 are -16, -14, -12, and -10.

complete question given below:

Find four consecutive even integers with a sum of -52.Find the four integeres

Answer:

n = 16

Step-by-step explanation:

1/2 n = 8 (multiply both sides by 2)

(1/2) (2) n = 8 (2)

n = 8 (2)

n = 16

Answer:

[tex]\sqrt[3]{x} -3[/tex]: The parent graph will move 3 units down.

[tex]\sqrt[3]{x-3}[/tex]: The parent graph will move 3 units right.

Step-by-step explanation:

The parent function [tex]\sqrt[3]{x}[/tex] looks like the first image attached.

Using knowledge of transformations, numbers outside the radical move the graph up or down (vertically). A positive number moves the graph up; a negative number moves the graph down.

Numbers inside the radical move the graph left or right (horizontally). A positive number moves the graph left; a negative number moves the graph right.

In the first transformation [tex]\sqrt[3]{x} -3[/tex] the number is outside of the radical, meaning that the graph will move vertically. The 3 is negative, so the graph will move 3 units down.

The first transformation moves the parent graph 3 units down.

In the second transformation [tex]\sqrt[3]{x-3}[/tex] the number is inside the radical so the graph will move horizontally. The 3 is negative so the graph will move 3 units to the right.

The second transformation moves the parent graph 3 units right.

The attached images show:

The sum of the three angles of a triangle need to equal 180

To find the third angle subtract the two known angles from 180.

Third angle = 180 - 44 - 72 = 64 degrees.

Answer:

All angles of a triangle add up to 180. Just subtract. -72 --> 108 - 44. 64

Answer:

[tex]\boxed{\textbf{1700 yr}}[/tex]

Step-by-step explanation:

[tex]-\dfrac{\text{d}L}{\text{d}t} = kL\\\\\dfrac{dL}{L}=-kdt\\\\\ln L = -kt + C\\\text{At t = 0, L = L$_{0}$, so C = $\ln L_{0}$}\\\ln L = -kt + \ln L_{0}\\\ln L_{0} - \ln L = kt\\\\\ln \dfrac{L_{0}}{L} =kt[/tex]

Data:

L₀ = 24 g

L = 20 g

k = 0.000 11 yr⁻¹

Calculation:

[tex]\ln \dfrac{24}{20} =0.000 11t\\\\\ln 1.2 = 0.000 11t\\\\0.1823 = 0.000 11t\\\\t = \dfrac{0.1823}{0.000 11} = \textbf{1700 yr}\\\\\text{It will take } \boxed{\textbf{1700 yr}}\text{ for the polonium to decay to 20 g}[/tex]

Answer:

1. 3x + 6

2. [tex]\frac{99}{14}[/tex] or 7.071

3. [tex]-\frac{1}{2}[/tex]

Step-by-step explanation:

1. 3 consecutive even integers

If the first is x, the 2nd is x+2, and the 3rd is x+4

x + (x+2) + (x+4)

= 3x + 6

2. The equation for circumference is

[tex]C=2\pi r[/tex]

If the diameter is [tex]1\frac{4}{5} = \frac{9}{5}[/tex]

The the radius is half of that.

So the circumference is

[tex]\pi * \frac{9}{4} *\frac{1}{2} * 2\\= \pi * \frac{9}{4}\\=\frac{22}{7} * \frac{9}{4}\\= \frac{198}{28}\\ =\frac{99}{14} \\=7.071[/tex]

3. To divide we multiply by the reciprocal.  So flip the fraction that we are dividing by.

[tex]\frac{1}{7} / -\frac{2}{7}\\ = \frac{1}{7} * -\frac{7}{2} \\= -\frac{1}{2}[/tex]

Answer:

Step-by-step explanation:

The tough part of this question is figuring out what to do with √(7^2). You could do it by expanding the square. √(7^2) = √49

Now what is the square root of 49? Is it not 7?

√49 = 7

7^6 * 7^1

7 ^(6 + 1)

7 ^ 7

Answer:

49

Step-by-step explanation:

Answer:2244.23136

Step-by-step explanation:

The range is the difference between the highest term and the lowest term.

The range of the numbers is 1.1.

The numbers are 2, 7, 3.1, 4.2, 1.9, 2.4, and 2.7.

The range is the difference between the highest term and the lowest term.

[tex]\rm Range = Highest \ Term - Lowest \ Term[/tex]

Here, the highest term in the numbers = 3.1

And the lowest term = 2

Therefore,

The range is given by,

[tex]\rm Range = Highest \ Term - Lowest \ Term\\\\Range = 3.1-2\\\\Range = 1.1[/tex]

Hence, the range of the numbers is 1.1.

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Answer:

The domain but not the range of the transformed function is the same as that of the parent function ⇒ answer D

Step-by-step explanation:

* Lets talk about the transformation

- If the function f(x) reflected across the x-axis, then the new

 function g(x) = - f(x)

- If the function f(x) translated horizontally to the right  by h units,

 then the new function g(x) = f(x - h)

- The domain of a function is set of the values of x which make

  the function defined

- The range is the set values of y that corresponding with the domain

- The domain of the function f(x) = IxI is the set of all real numbers

∴ The domain of f(x) is {x : x ∈ R}

- The range of  the function f(x) = IxI is the set of all real numbers

  greater than or equal 0

∴ The range f(x) = {y : y ≥ 0}

∵ f(x) reflected across the x-axis, then it will be change to g(x) = -IxI

∴ All the y-coordinates of the point on the function will be change

  from positive values to negative values

∵ The rang of f(x) is {y : y ≥ 0}

∴ The range of g(x) is {y : y ≤ 0}

∵ After the reflection the function translated 6 units to the right

∴ The x will change to x - 6

∴ The function will be h(x) = -Ix - 6I

- There is no values of x make h(x) undefined, then its domain is

  set of all real number

∴ The domain of h(x) is {x : x ∈ R}

∵ The domain of f(x) is {x : x ∈ R}

∵ The range of h(x) is the same the range of g(x)

∴ The range of h(x) is {y : y ≤ 0}

- f(x) and h(x) have same domains and different ranges

∴ The correct statement is: The domain but not the range of the

   transformed function is the same as that of the parent function

- Look to the attached graph for more understanding

# The red graph is f(x)

# The blue graph is h(x)

Answer:

d

Step-by-step explanation:

Answer:

6x^2 + 3x - 7.

Step-by-step explanation:

(6x^2 - 2x) + (5x - 7)

= 6x^2 - 2x + 5x - 7    Adding like terms we get:

6x^2 + 3x - 7.

Final answer:

To simplify the algebraic expressions (6x²-2x)+(5x-7), you combine like terms to get the final expression 6x² + 3x - 7.

Explanation:

The student's question involves adding and simplifying algebraic expressions. To add the expressions (6x²-2x)+(5x-7), you need to combine like terms. Like terms are those terms that contain the same variable raised to the same power. Here is the process step-by-step:

The resulting simplified expression is 6x² + 3x - 7.

Answer:

The larger number is 8

Step-by-step explanation:

Let

x -----> the smaller number

y ----> the larger number

we know that

x+y=10

y=10-x -----> equation A

y=4x -----> equation B

Solve by substitution

substitute equation B in equation A and solve for x

4x=10-x

4x+x=10

5x=10

x=2

Find the value of y

y=4x-------> y=4(2)=8

therefore

The smaller number is 2 and the larger number is 8

To find the larger number where the sum of two numbers is 10 and the larger is four times the smaller, the system of equations y = -x + 10 and y = 4x is used, and through solving, the larger number is determined to be 8.

The question entails finding the larger number when two numbers sum to 10, and the larger number is four times the smaller number. The system of equations representing the scenario is y = -x + 10 and y = 4x. To find the larger number, set these two equations equal to each other since they both equal y:

4x = -x + 10

Now, solve for x by adding x to both sides:

5x = 10

Then, divide both sides by 5:

x = 2

Since x is the smaller number, and y is four times larger, compute y:

y = 4x = 4(2) = 8

The larger number (y) in this case is 8.

False.

The Rational Root theorem states that P is a factor of the constant term and q is a factor of the leading coefficient.

Answer:

The correct option is D.

Step-by-step explanation:

A paralellogram is a flat shape with 4 straight sides and opposite sides are parallel.

There are six important properties of a parallelogram.

1) Opposite sides are congruent.

2) Opposite angels are congruent.

3) Consecutive angles are supplementary.

4) If one angle is right, then all angles are right.

5) The diagonals of a parallelogram bisect each other....

Answer:

its D

Step-by-step explanation:

Answer:

a- p(x) = 2xy(2x -y)(2x + y)(4x² + y²) ⇒ 2nd answer

b- repeated differences of squares ⇒ 1st answer

Step-by-step explanation:

* Lets explain how to solve the problem

∵ p(x) = 32x^5y - 2xy^5

- The coefficients of the two terms are 32 and 2

∵ 2 is a common factor in 32 and 2

∵ 32 ÷ 2 = 16 and 2 ÷ 2 = 1

∴ p(x) = 2(16x^5y - xy^5)

* Now lets find the common factors of the variables x and y

∵ The common factor is x^5 and x is x

∵ The common factor in y and y^5 is y

∴ the common factors in 16x^5y - xy^5 are xy

∵ 16x^5y ÷ xy = 16x^4

∵ xy^5 ÷ xy = y^4

∴ p(x) = 2xy(16x^4 - y^4)

- Remember that a² - b² is called difference of two squares we

 factorize it by distributed into two polynomials have same terms

 with different middle sign (a + b)(a - b)

∵ 16x^4 - y^4 is a different of two squares because √(16x^4) = 4x²

  and √9y^4) = y²

∴ The factorization of 16x^4 - y^4 is (4x² + y²)(4x² - y²)

∴ p(x) = 2xy[(4x² + y²)(4x² - y²)]

- The bracket 4x² - y² is also different of two squares because

 √(4x²) = 2x and √(y²) = y

∴ The factorization of 4x² - y² is (2x - y)(2x + y)

∴ p(x) = 2xy(2x -y)(2x + y)(4x² + y²)

a- p(x) = 2xy(2x -y)(2x + y)(4x² + y²)

b- The methods used to factor p(x) are:

    greatest common factor and repeated differences of squares

- But you ask to chose one answer of b so chose repeated

 differences of squares

Answer:

The rate of change determines the average speed of the ball when it is dropped from the building.

Step-by-step explanation:

d(t) = 16t^2

when t = 2

d(t) = 16 (2)²

d(t) = 64

when t = 5

d(t) = 16 (5)²

d(t) = 400

Average speed/rate of change = distance/time = 64/2 = 32 feet

Average speed/rate of change = distance/time = 400/5 = 80 feet

The rate of change determines the average speed of the ball when it is dropped from the building.

!!

The average rate of change of d(t) from [tex]\( t = 2 \) to \( t = 5 \)[/tex] represents that the ball traveled at an average rate of 112 feet per second during this time interval.

The average rate of change of a function over a given interval is calculated by finding the difference in the function values at the endpoints of the interval and dividing by the difference in the independent variable values. In this case, we want to find the average rate of change of the function [tex]\( d(t) = 16t^2 \) from \( t = 2 \) to \( t = 5 \).[/tex]

First, we find the values of the function at the endpoints of the interval:

- At [tex]\( t = 2 \), \( d(2) = 16(2)^2 = 64 \)[/tex] feet.

- At [tex]\( t = 5 \), \( d(5) = 16(5)^2 = 400 \)[/tex] feet.

Then, we calculate the difference in the function values:

[tex]\[ \text{Difference in } d(t) = d(5) - d(2) = 400 - 64 = 336 \text{ feet} \][/tex]

Next, we calculate the difference in the independent variable values:

[tex]\[ \text{Difference in } t = 5 - 2 = 3 \text{ seconds} \][/tex]

Finally, we find the average rate of change by dividing the difference in d(t) by the difference in t:

[tex]\[ \text{Average rate of change} = \frac{\text{Difference in } d(t)}{\text{Difference in } t} = \frac{336}{3} = 112 \text{ feet/second} \][/tex]

Answer:

Option D is correct

Step-by-step explanation:

The original polynomial is:

–2x2 + 2 + 5x3 – 5x

Arranging in decreasing power of x:

[tex]5x^3 - 2x^2 -5x+2[/tex]

Factoring the given polynomial by grouping:

[tex]5x^3 - 2x^2 -5x+2\\=5x^3-5x- 2x^2+2\\=5x(x^2-1)-2(x^2-1)\\=(5x-2)(x^2-1)[/tex]

Now, (x^2-1) can be further solved using formula:

(a^2-b^2)=(a-b)(a+b)

Solving:

[tex]=(5x-2)(x^2-1)\\=(5x-2)(x-1)(x+1)[/tex]

So, [tex](5x-2)(x-1)(x+1)[/tex] represents the factors of [tex]-2x2 + 2 + 5x3-5x[/tex]

Hence Option D is correct.

Answer: the answer is D

Step-by-step explanation:

the screen has proof it is correct... also please STOP deleting my answers its all ways the same person and its getting really annoying when im giving you the correct answer, im just trying to help :(

Answer:

B. 3

Step-by-step explanation:

A common difference in an arithmetic sequence is the value the terms in the sequence vary from one to another.You can find one term to another by adding or subtracting the common difference.

In this case, the terms are 2,5,8,11,.....

From the first term to the second term, the difference is, 5-2=3

From the second term to the third term, the difference is, 8-5=3

From the third term to the fourth term the difference is=11-8=3

Hence the common difference in this arithmetic sequence is 3

[tex]\huge{\text{Hey there!}}[/tex]

[tex]\huge\text{We could use the word {difference} in this equation}[/tex]

[tex]\huge\text{The\ difference usually means subtract in math}}[/tex] [tex]\huge\text{terms!}[/tex]

[tex]\huge{\text{So, we subtract the terms to find your answer!}}[/tex]

[tex]\huge\text{5 - 2 = 3. So we know that 3 could be a possible}[/tex] [tex]\huge\text{answer.}[/tex]

[tex]\huge\text{11 - 8 = 3 }[/tex]

[tex]\huge\rightarrow\text{8 - 5 = 3}[/tex]

[tex]\huge\text{The ratio difference = 3!}[/tex]

[tex]\boxed{\boxed{\huge{\text{Answer: B. 3}}}}\huge\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:}[/tex]

Answer:

Step-by-step explanation:

305p=1,525

305    305

p=5

The solution of the linear equation 305p = 1525 will be 5.

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

The linear equation with one variable is given below.

305p = 1525

On simplifying, we have

305p = 1525

      p = 1525 / 305

      p = 5

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Answer:

128

Step-by-step explanation:

You find the number of subsets of a set by using the formula [tex]2^{\text{ number of elements}[/tex].

We have 7 elements so that means we have [tex]2^{7}=128[/tex] subsets.

A set with 7 elements can have 128 subsets, as calculated using the equation 2^n, where n is the number of elements in the set.

In Mathematics, a subset is a portion of a set, including the empty set and the set itself. The number of subsets a set can have is calculated using the equation 2^n, where 'n' is the number of elements in the set. In this case, the set A includes 7 elements, therefore applying the equation we get: 2^7=128 subsets, which is the answer to your question.

For example, {-3, -1, 0} would be a subset of set A, as would {0, 1, 2}, {-2, 0, 2}, and so on. The complete set ({-3,-2,-1,0,1,2,3}) is also a subset, as is the empty set ({}).

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Answer:

45°

Step-by-step explanation:

I think you meant m<ACB, and from what I see here, I took half of 90°, which is 45°.

Answer:

The first one

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan30° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{AC}{BC}[/tex] = [tex]\frac{b}{8}[/tex]

Multiply both sides by 8

8 × tan30° = b, that is

b = 8tan30°

Answer:

b = (8)tan(30o)

Step-by-step explanation:

For this case we have the following expression:

[tex]6r + 5r[/tex]

We can rewrite the expression in different ways.

Form 1:

Adding similar terms:

[tex]6r + 5r = 11r[/tex]

Form 2:

Making common factor we have:

[tex]6r + 5r = (6 + 5) r[/tex]

Answer:

Some equivalent expressions are given by:

[tex]6r + 5r = 11r\\6r + 5r = (6 + 5) r[/tex]

The expression 6r + 5r simplifies to 11r by combining like terms. In this case, the 'like term' is 'r'. When we add the coefficients of the like terms, we get 11r.

The student's question involves simplifying the expression 6r + 5r. This is an addition problem in algebra where we are adding like terms. Like terms are terms in an algebraic expression that has the exact same variable(s) to the same power(s). In the given expression '6r + 5r', the like terms are '6r' and '5r' because they both have the same variable 'r'.

To simplify, we add the coefficients of the like terms. The coefficient of 'r' in '6r' is 6 and in '5r' is 5. When we add 6 and 5, we get 11. Therefore, the equivalent expression of '6r + 5r' is '11r'.

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A term is any number, variable or combination of a number and a variable in an equation.

Examples:

In 2x + 5y + 8, 2x is one term,  5y is a second term and 8 is a 3rd term.

In the equation 2x + 3 + 5x -2

Combine the like terms 2x and 5x are like terms because they both have x as a variable, there is a plus sign in fron of the 5x, so you would have 2x +5x = 7x

Then 3 and 3 are like terms, because they are just numbers, there is a subtraction sign in front of the 2, so you have 3-2 = 1

The equation then becomes: 2x + 3 + 5x -2 : 7x + 1

Answer:

9 ft

Step-by-step explanation:

The Pythagorean theorem states

a^2+b^2 = c^2 where a and b are the legs and c is the hypotenuse

Substituting in what we know (one leg is 12 and the hypotenuse is 15)

12^2 +b^2 = 15^2

144+ b^2 = 225

Subtract 144 from each side

144-144 +b^2 = 225-144

b^2 =81

Take the square root of each side

sqrt(b^2) = sqrt(81)

b = 9