MATHEMATICS HIGH SCHOOL

1. Simplify the expression.(6+6i)-(2+i)

2. Simplify the expression.
(8+i)(2+7i)

3. Find the conjugate of the complex number 8+12i
A. 96
B. 8-`1i
C. -96i
D. 20

4. Use the complex conjugate to find the absolute value of 8+12i
A. 12
B. square root of 208
C. square root of 84
D. 8

Answers

Answer 1

Answer:

The correct answers are:

(1) 4+5i

(2) 9+58i

(3) 8 - 12i (Option B; The question's options have a typo)

(4) Square root of 208 (Option B).

Explanations:

(1) Given: (6+6i)-(2+i)

We need to simplify the given expression. For that, add real parts with each other, and add imaginary parts of the complex numbers with each other. Remember that the numbers with the symbol "i" are the imaginary parts of the complex number. Therefore,

(6-2) + (6i - i) = 4 + 5i (ans)

(2) Given: (8+i)(2+7i)

Now in this case we will multiply two complex numbers with each other; here in this case, we have to remember that $i^2 = -1$ . Now let us find out the multiplication of two complex numbers:

(8+i)(2+7i)

8(2+7i) + i(2+7i)

$16+56i+2i+ 7i^2$

16 + 58i + 7(-1)

= 9 + 58i

Hence the correct answer is 9+58i.

(3) Given: 8+12i

In simple terms, in order to find the conjugate of the complex number, we take the real number of the complex number as is, but we change the sign of the imaginary part of the complex number. In the given expression, 8 is the real number; hence, we will take it as is, whereas, +12i is the imaginary part of 8+12i. So to find the conjugate, we will change +12i to -12i.

Therefore, the conjugate of the complex number will become 8 - 12i (Option B; The question's options have a typo).

(4) Given: 8+12i

First, we need to find the complex conjugate of the given complex number. Please see the explanation given in Part (3) above to find the complex conjugate. The complex conjugate of 8+12i is 8-12i

Now, to find the absolute value of the complex conjugate 8-12i, follow these steps:

|8-12i|

We will add the square of the real number (8) with the square of the imaginary number (-12) and take the square-root at the end to find the absolute value:

$√((8)^2 + (-12)^2) \n √(64 + (144)) \n √(208)$

Hence the correct answer is square root of 208 (Option B).

Answer 2

Answer: 1. 4 + 5i
2. 9 - 58i
3. tbh idek
4. /sqrt{208}

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Create and solve a linear equation that represents the model, where circles and a square are shown evenly balanced on a balance beam.A. x + 10 = 6; x = -4

B. x = 6 + 10; x = 16

C. x + 6 = 16; x = 10

D. x + 6 = 10; x = 4

Answers

Answer:

D. x + 6 = 10; x = 4

Step-by-step explanation:

to balance the beam, the weight on the left side must be equal to the right side.

x + 6 = 10 let x = box

x = 10 - 6

x = 4

therefore, the answer is D. x + 6 = 10; x = 4

x + 6 = 10; x = 4 is the linear equation and the solution that represents the model, where circles and a square are shown evenly balanced on a balance beam.

1. **Modeling the Balance**: In this problem, you are given a scenario where circles and a square are evenly balanced on a balance beam. To represent this balance mathematically, you need to ensure that the total weight (or the "value" of the shapes) on the left side of the balance is equal to the total weight on the right side.

2. **UnknownWeight**: You are asked to find the value of the square, represented by 'x.' This 'x' represents the weight or value of the square on one side of the balance.

3. **Equation Setup**: To set up the equation, you note that on the left side of the balance, you have 'x' (the square) plus 6 (the circles). On the right side, you have 10 (implying there's something with a weight or value of 10 units).

So, you set up the equation as:

x + 6 = 10

This equation says that the weight of the square plus the weight of the circles on one side equals the weight of whatever is on the other side.

4. **Solving for x**: To find the value of 'x' (the weight of the square), you isolate 'x' on one side of the equation. To do that, you subtract 6 from both sides of the equation:

x + 6 - 6 = 10 - 6

This simplifies to:

x = 4

So, 'x' represents a square with a weight or value of 4 units. This means that the square's weight on one side of the balance is balanced by 6 units of weight from the circles on the other side, resulting in a total of 10 units on both sides, ensuring the balance.

To know more about linear equation :

brainly.com/question/18073665

#SPJ3

Pls someone help me with this question i provided a picture below

Answers

Answer: (x-8)(x+9)

To rewrite the expression in the form (x+a)(x+b), you must factor the expression. First split the equation into two sides. Since 9 times 8 equals 72, we want to figure out how they add to equal 1 (which is the x).
If 9 times -8 equals -72, this works. -8 + 9 = 1. This translates to -8x + 9x = x. This is how we split it.

x^2 - 8x + 9x - 72
(x^2 - 8x) + (9x - 72)
Since x^2 and -8x both share x, factor out x from the parentheses. And since 9x and -72 are both divisible by 9, factor out 9.
x(x - 8) + 9(x - 8)

We can now factor out the common term, x-8. Then the x and 9 outside the parentheses will be combined.
(x-8)(x+9).
This is our answer

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