Who knows how to answer this. It's Dividing complex numbers.​

Answer:  see proof below

Step-by-step explanation:

Given: A + B = C                → A = C - B

                                          → B = C - A

Use the Double Angle Identity:     cos 2A = 2 cos² A - 1

                                             → (cos 2A + 1)/2 = cos² A

Use Sum to Product Identity: cos A + cos B = 2 cos [(A + B)/2] · 2 cos [(A - B)/2]

Use Even/Odd Identity: cos (-A) = cos (A)

Proof LHS → RHS:

LHS:                     cos² A + cos² B + cos² C

[tex]\text{Double Angle:}\qquad \dfrac{\cos 2A+1}{2}+\dfrac{\cos 2B+1}{2}+\cos^2 C\\\\\\.\qquad \qquad \qquad =\dfrac{1}{2}\bigg(2+\cos 2A+\cos 2B\bigg)+\cos^2 C\\\\\\.\qquad \qquad \qquad =1+\dfrac{1}{2}\bigg(\cos 2A+\cos 2B\bigg)+\cos^2 C[/tex]

[tex]\text{Sum to Product:}\quad 1+\dfrac{1}{2}\bigg[2\cos \bigg(\dfrac{2A+2B}{2}\bigg)\cdot \cos \bigg(\dfrac{2A-2B}{2}\bigg)\bigg]+\cos^2 C\\\\\\.\qquad \qquad \qquad =1+\cos (A+B)\cdot \cos (A-B)+\cos^2 C[/tex]

[tex]\text{Given:}\qquad \qquad 1+\cos C\cdot \cos (A-B)+\cos^2C[/tex]

[tex]\text{Factor:}\qquad \qquad 1+\cos C[\cos (A-B)+\cos C][/tex]

[tex]\text{Sum to Product:}\quad 1+\cos C\bigg[2\cos \bigg(\dfrac{A-B+C}{2}\bigg)\cdot \cos \bigg(\dfrac{A-B-C}{2}\bigg)\bigg]\\\\\\.\qquad \qquad \qquad =1+2\cos C\cdot \cos \bigg(\dfrac{A+(C-B)}{2}\bigg)\cdot \cos \bigg(\dfrac{-B-(C-A)}{2}\bigg)[/tex]

[tex]\text{Given:}\qquad \qquad =1+2\cos C\cdot \cos \bigg(\dfrac{A+A}{2}\bigg)\cdot \cos \bigg(\dfrac{-B-B}{2}\bigg)\\\\\\.\qquad \qquad \qquad =1+2\cos C \cdot \cos A\cdot \cos (-B)[/tex]

[tex]\text{Even/Odd:}\qquad \qquad 1+2\cos C \cdot \cos A\cdot \cos B\\\\\\.\qquad \qquad \qquad \quad =1+2\cos A \cdot \cos B\cdot \cos C[/tex]

LHS = RHS: 1 + 2 cos A · cos B · cos C = 1 + 2 cos A · cos B · cos C   [tex]\checkmark[/tex]

-5 < -3 and the second inequality is -3 > -5

Answer:

x=4

Step-by-step explanation:

Answer:

x=4

Step-by-step explanation:

Answer:

[tex]x > \frac{16}{3} [/tex]

Step-by-step explanation:

[tex]4x - 8 > 24 - 2x \\ 4x + 2x > 24 + 8 \\ 6x > 32 \\ x > \frac{16}{3} [/tex]

Answer:

[tex]x=5[/tex]

Step-by-step explanation:

To solve for x, we can use the Exterior Angle Theorem.

The Exterior Angle Theorem states that the exterior angle is equivalent to the sum of the two opposite, interior angles.

So, we can write the following equation:

[tex](6+25x)=(44)+(18x-3)[/tex]

Now, we just have to solve for x.

On the right, let's subtract. So:

[tex]6+25x=18x+41[/tex]

Now, let's subtract 18x from both sides. This gives:

[tex]6+7x=41[/tex]

Now, let's subtract 6 from both sides. This will yield:

[tex]7x=35[/tex]

And, finally, let's divide both sides by 7, giving us:

[tex]x=5[/tex]

And we're done!

We can use the Exterior Angle Theorem.

6 + 25x = 44 + 18x - 3

6 + 25x = 18x + 41

25x = 18x + 35

7x = 35

x = 5

Best of Luck!

Answer:

210 divided 2 1/2= 84....

The 210 divided by 2 1/2 is 84.

To calculate 210 divided by 2 1/2, first, we need to convert the mixed number 2 1/2 to an improper fraction. The improper fraction for 2 1/2 is (2 * 2 + 1) / 2 = 5/2.

Now, we can perform the division:

210 ÷ 5/2

To divide by a fraction, we multiply by its reciprocal:

210 * 2/5

Now, perform the multiplication:

(210 * 2) / 5 = 420 / 5

Next, simplify the fraction by dividing the numerator and denominator by their greatest common divisor (GCD), which is 5:

420 ÷ 5 = 84

The result of 210 divided by 2 1/2 is 84. So, 210 ÷ 2 1/2 = 84.

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Answer:

Please check explanation

Step-by-step explanation:

Here, in this question, we are interested in identifying the error made by Jillian in his solution of the equation.

This error is traceable to the second step of his solution. Adding 4.3 to 7.05 and subtracting again is the same thing as not adding anything or just adding zero only.

What he should have done is to subtract the value of 4.3 from both sides of the equation. In that manner, he would have been able to isolate v on the left hand side of the equation

Answer:

11 hours and 22 minutes

Answer:

b

Step-by-step explanation:

The sum of the first ten terms of the sequence is -59,048. The correct option is C.-59,048

Here is the correct question:

What is the sum of the first ten terms of the sequence 4, -12, 36, -108...

From the question,

The given sequence is 4,-12, 36, -108...

This is a geometric progression since it has a common ratio.

The common ratio, r = -3

Recall that,

Given a geometric progression, the common ratio, r is given as

[tex]r = \frac{T_{2} }{T_{1}} = \frac{T_{3} }{T_{2}} =\frac{T_{4} }{T_{3}} = ...[/tex]

From the given sequence,

[tex]T_{1} = 4[/tex]

[tex]T_{2} = -12[/tex]

[tex]T_{3} = 36[/tex]

[tex]T_{4} = -108[/tex]

∴ [tex]r = \frac{-12 }{4} = \frac{36}{-12} =\frac{-108} {36} = -3[/tex]

Therefore, the sequence is a geometric progression with a common ratio of 3

Now, to determine the sum of the first ten terms of the sequence,

From the formula

[tex]S_{n} = \frac{a(1-r^{n}) }{1-r}[/tex]

Where [tex]S_{n}[/tex] is the sum of n terms

[tex]a[/tex] is the first term

[tex]r[/tex] is the common ratio

and [tex]n[/tex] is the number of terms in the series

From the question

[tex]a = 4[/tex]

[tex]r = -3[/tex]

and [tex]n = 10[/tex] (Since, we are to determine the sum of the first 10 terms)

Now, put the parameters into the formula

[tex]S_{n} = \frac{a(1-r^{n}) }{1-r}[/tex]

We get

[tex]S_{10} = \frac{4(1-(-3)^{10}) }{1-(-3)}[/tex]

[tex]S_{10} = \frac{4(1-59049) }{1+3}[/tex]

[tex]S_{10} = \frac{4(-59048) }{4}[/tex]

[tex]S_{10} = \frac{-236192 }{4}[/tex]

[tex]S_{10} = -59048[/tex]

Hence, the sum of the first ten terms of the sequence is -59,048. The correct option is C.-59,048

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Answer:

x + y

Step-by-step explanation:

In these examples, a and b are positive numbers.

- a + ( - b) = - (a+ b)

- a - ( - b) = - a + b

- a * - b = a * b

- a / -b = a/b

Hope this helps understanding.

Refer to the attachment for solution.

Answer:6:2

Step-by-step explanation:

Answer:

how many batches you need to know? If 2 batches the answer is 6:2 and if 4 batches it is 12:4

Answer:

Sample response: The absolute value symbol in the equation indicates two solutions because absolute value is the distance from a number to zero on a number line. Two different directions, to the right and to the left, will determine the

Step-by-step explanation:

Answer:

the first component of ordered pair is domain and second component is range

Answer:

In its simplest form the domain is all the values that go into a function, and the range is all the values that come out

Answer:

The value of x is 29°...

When an angle is bisected, it is cut in half. We can assume that m<BAR = m<CAB and we know that m<CAR = m<CAB + m<BAR

88 = 2x - 14 + 2x - 14

Combine like terms

88 = 4x - 28

Add 28 to both sides

116 = 4x

Divide both sides by 4

29 = x

Answer:

+ or - $9

Step-by-step explanation:

Answer:

[tex]\boxed {\tt f(5)=101}[/tex]

Step-by-step explanation:

We are given the function:

[tex]f(x)=18x+11[/tex]

and asked to find f(5). Therefore, we must substitute 5 in for each [tex]x[/tex].

[tex]f(5)=18(5)+11[/tex]

Solve according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.

Multiply 18 and 5.

[tex]f(5)=90+11[/tex]

Add 90 and 11.

[tex]f(5)=101[/tex]

f(5) is equal to 101.

Answer:

V2 = 670.129

Step-by-step explanation:

V1T2 = V2T1

Let V2 = y

600 x 86.0 = y x 77.0

51600 = 77y

77y/77 = 51600/77

y = 670.129

since y= V2

V2 = 670.129

Points play a crucial role in defining distances, angles, and relationships between different geometric objects, providing a foundation for the study of geometry.

In geometry, a point is a fundamental concept that represents a precise location in space. It is a basic building block from which geometric figures and shapes are constructed. A point has no size, shape, or dimensions. It is often denoted by a dot or a small letter, such as point A (A). Points are used to describe the positions of other geometric elements, such as lines, curves, and polygons. They serve as reference markers and can be connected to form line segments and rays.

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Answer:4

Step-by-step explanation:

Answer:

a. i. x ≤ 25 ii. 16 < x < 35 iii. 25 < x ≤ 95  

b. The second and third car seats are appropriate for a 35 lb child.

Step-by-step explanation:

a. Model those ranges with compound inequalities

Let x represent the car seat.

i. A car seat designed for a child weighing up to  and including 25 lb is described by the inequality.

x ≤ 25

ii. A car seat designed for a child weighing between 16 lb  and 35 lb is described by the inequality.

16 < x < 35

iii. A car seat designed for a child weighing between 25 lb  and 95 lb inclusive is described by the inequality.

25 < x ≤ 95

b. Which car seats are appropriate for a  33-lb child?

Since 35 lb is included in the range of the inequalities for the second and third card seats, the second and third car seats are appropriate for a 35 lb child.

Answer:

[tex]MP= (-5,7.5 )[/tex]

Step-by-step explanation:

[tex]MP= (\frac{x_1+x_2}{2} )(\frac{y_1+y_2}{2} )[/tex]

[tex]MP= (\frac{-7+-3}{2} )(\frac{6+9}{2} )[/tex] -7+-3= -10   6+9=15

[tex]MP= (\frac{-10}{2} )(\frac{15}{2} )[/tex] -10/2=-5 15/2=7.5

[tex]MP= (-5,7.5)[/tex]

Answer:

in 3/4 year tree had grown 2/3

in 1 year tree had grown (2/3)/0.75 =8/9 feet

Step-by-step explanation:

Answer:

An integer number is one that can be written without using fractions or decimals, and it is an expression of ( 1.2.3..... ) and 0, and negative numbers (- 1-2-3...... )

Answer:

$12.5

Step-by-step explanation:

Since prize is split equally.

So, money received by each person

= 75/6

= $12.5

Hey there!☺

[tex]Answer:\boxed{3y+2}[/tex]

[tex]Explanation:[/tex]

[tex]3y+2[/tex]

Since there are no like terms and it can't be factored the answer is:

[tex]3y+2[/tex]

Hope this helps!

Answer:

Do you have a picture of the problem, please?

Step-by-step explanation:

Only then, can I edit this and provide an accurate answer! ;D

Answer:

x=7

Step-by-step explanation:

x=7

Step-by-step explanation:

35•32 or 1120 there you go