If e pieces of candy cost $2.10, how much would 4 pieces cost?

EXPLANATION

The reason is that

[tex]i^2=-1[/tex]

If we multiply [tex]a+bi[/tex] by its conjugate [tex]a-bi[/tex]

We obtain;

[tex](a+bi)(a-bi)[/tex]

This is difference of two squares so we obtain;

[tex](a+bi)(a-bi)=a^2-(bi)^2[/tex]

This further gives us,

[tex](a+bi)(a-bi)=a^2-b^2i^2[/tex]

Since the [tex]i^2=-1[/tex], we substite to get;

[tex](a+bi)(a-bi)=a^2-b^2(-1)[/tex]

The [tex]i[/tex] is now eliminated and we get,

[tex](a+bi)(a-bi)=a^2+b^2[/tex]

Multiplying a complex number by its conjugate eliminates the imaginary part because [tex]\(i^2\)[/tex] equals -1, simplifying to a real number.

Multiplying a complex number [tex]\(a + bi\)[/tex] by its conjugate[tex]\(a - bi\)[/tex] eliminates the imaginary part because of the difference of squares. Let's break it down:

Step 1:

Write the complex number and its conjugate.

[tex]\(a + bi\) and \(a - bi\).[/tex]

Step 2:

Multiply using the distributive property.

[tex]\((a + bi)(a - bi)\).[/tex]

Step 3:

Apply the FOIL method (First, Outer, Inner, Last).

[tex]\((a \times a) + (a \times -bi) + (bi \times a) + (bi \times -bi)\).[/tex]

Step 4:

Simplify the product.

[tex]\(a^2 - abi + abi - (bi)^2\).[/tex]

Step 5:

Notice that the cross terms [tex]\(abi\)[/tex] and [tex]\(-abi\)[/tex] cancel each other out.

[tex]\(a^2 - (bi)^2\).[/tex]

Step 6:

Recall that [tex]\(i^2 = -1\), so \((bi)^2 = -b^2\).[/tex]

[tex]\(a^2 - (-b^2)\).[/tex]

Step 7:

Simplify further to obtain the final expression.

[tex]\(a^2 + b^2\).[/tex]

The resulting expression, [tex]\(a^2 + b^2\),[/tex] is real and has no imaginary component, hence eliminating the [tex]\(i\).[/tex] This process is fundamental in simplifying expressions involving complex numbers.

i cant tell what is says so ill just give you the formulas

perimiter = Length x 2 + Width x 2

Area = Length x Width.

Answer:

(-1)^2 = +1

Step-by-step explanation:

(-1)(-1) is equivalent to (-1)^2, and vice versa.  Recall that when two negative numbers are mult. together, the product is positive.  Thus, (-1)^2 = +1.

Based on the definition of the square of a negative number, the result of (-1)² is: 1.

The square of a number represented as "x" can be found by multiplying "x" by itself, expressed as x², where "x" represents the number being squared.

When you square a number, you multiply it by itself. In this case, you are squaring -1.

Calculation:

(-1)² = (-1) * (-1) = 1

So, (-1)² is equal to 1. The negative sign is squared along with the number, resulting in a positive value.

Learn more about Square on:

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the answer is 340,000

When you reflect a function in the x-axis, the first coordinate of a point stays the same, and the second coordinate changes sign (what was positive is now negative and vice versa).  See the attached picture.

Question 11:  f(x) = -5x + 2.  The function changes to its opposite, so g(x) = -(-5x + 2) = 5x - 2.

When you reflect a function in the y-axis, the first coordinate of a point changes to its opposite, but the second coordinate stays the same.  Replace  x  with  -x .

Question 14:  f(x) = |2x - 1| + 3.  Replacing x with -x produces  g(x) = |2(-x) - 1| + 3  which simplifies to  g(x) = |-2x -1| + 3.

Question 15 works the same way as #14.

This is the Pythagorean theorem, that equation is a^2 + b^2 = c^2, but if you dont have b you can manipulate the equation, that equation is c^2-a^2=b^2. So you take 15^2 - 12^2 and that equals 81, then you take the square root of 81, which equals 9, so your answer would be 9 feet. Hope that helped :)

The unknown side of the right-angled triangle measures 9 feet. We found this using the Pythagorean theorem.

This problem falls under the topic of Pythagoras theorem in Mathematics. The Pythagorean theorem describes the relationship between the lengths of the sides of a right-angled triangle. It is stated as: a² + b² = c², where c represents the length of the hypotenuse, and a and b are the lengths of the other two sides of the triangle.

If one side (say, a) of the right triangle is 12 feet and the hypotenuse (c) measures 15 feet, we can calculate the length of the other side (b) using the principle of the Pythagorean Theorem. By rearranging the theorem to solve for 'b', we get the equation:

b = √(c² - a²)

Substitute the given values into the equation:

b = √((15)² - (12)²) = √(225 - 144) = √81

Hence, the unknown side 'b' measures 9 feet.

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Answer:

The correct answer is D. I hope i help you))

The correct answer is Option D. The graphed function consists of a constant value of 5 for (x < 2) and a linear equation with a positive slope for ([tex]x \geq 2)[/tex]

The graph represents a piecewise function. Let’s analyze it step by step:

Left Segment (for (x < 2)):

The graph is a horizontal line at (y = 5).

This corresponds to the piecewise component (f(x) = 5) for (x < 2).

Right Segment (for [tex](x \geq 2))[/tex]:

The graph is an oblique line passing through points (2,5) and (5,8).

The slope of this line is [tex](\frac{8 - 5}{5 - 2} = 1).[/tex]

It intersects the y-axis at (y = -2).

This corresponds to the linear equation (f(x) = x + 3) for ([tex]x \geq 2[/tex]).

Therefore, the function graphed is a piecewise function with two parts:

For (x < 2): (f(x) = 5)

For [tex](x \geq 2)[/tex]: (f(x) = x + 3)

The vertical angles are congruent (or equal) so,

32 = 2x

2x = 32

2x/2 = 32/2 ..... dividing both sides by 2

x = 16 which is the answer

X=16 because 16 x 2=32 and both sides look pretty equal so.

this is for question 3 if she purchased 2 pairs of shoes at $50 each then thats $100 for both then adding $30.00 for the dress and $20.00 for the pair of trousers your total WITHOUT sales tax is $150.00

to calculate sales tax you would multiply 4% with 150 (your total sales equaling 6

(0.04 x150=6)

lastly add 6 (your calculated sales tax) to your total sale price

getting a final answer of $156.00

We are given : Number of diagonals of a polygon = 1127 diagonals.

We know relation between number of diagonals and number of sides of the polygon.

Plugging d=1127 in above formula, we get

[tex]\frac{n(n-3)}{2}=1127[/tex]

Multiplying both sides by 2, we get

[tex]n(n-3)=2254[/tex]

[tex]n^2-3n=2254[/tex]

[tex]n^2-3n-2254=0[/tex]

Solving quadratic equation by factoring, we get factors

[tex]\left(n-49\right)\left(n+46\right)=0[/tex]

Solving for n, we get

n-49=0

n=49.

n+46=0.

n=-46.

We can't take number of sides by a negative number.

Therefore, number of sides does the polygon have 49 side.

the dimensions are 7, 9, 9 because when you do 9+9 which is both sides except the garage you get 7

-hope this helps

This is a Mathematics problem about perimeter. If Brian has 25ft of fencing and one side of the rectangle is 9ft, the equation created is 2x =16. Solving for x gives the other dimension as 8ft which means the kennel's dimensions are 9ft by 8ft.

The subject of this question is Mathematics and it involves a problem of perimeter in geometry. In this problem, Brian has 25ft of fencing and one side of the rectangular area, the one against the garage, doesn't need fencing, and that side is 9ft.

Let the other side be 'x'. In a rectangle, opposite sides are equal. Since one of the sides is already fenced, we need fencing for only three sides. So we can create the equation 9 + x + x = 25. This simplifies to 2x = 16. Therefore, 'x' equals 8. The dimensions of the rectangular kennel are 9ft by 8ft.

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a) plug in x =2700 into the given equation and solve for y

b) plug in y = 43 into the given equation and solve for x

c) plug in y = 0 into the given equation and solve for x

hope this helps.

Joseph earns $15 for every lawn he mows. Is the amount of money he earns proportional to the number of lawns he mows? Make a table to help you identify the type of relationship.

First let's start by making a table. I've attached an image of my drawing of the table and how it should look like. Feel free to comment below any questions you may have! :)

The type of relationship is definitely proportional, as for every lawn Joseph mows he gains 15 dollars. The relationship would be y = 15x, where y represents Joseph's earnings and x represents the number of lawns Joseph mows.

Hope this helped you!

To identify the type of Relationship between the amount of money Joseph earns and the number of lawns he mows, we can create a table and analyze the values. The relationship is directly proportional, meaning the amount of money Joseph earns increases proportionally as the number of lawns mowed increases.

To identify the type of relationship between the amount of money Joseph earns and the number of lawns he mows, we can create a table. Let's say the number of lawns he mows is represented by x and the amount of money he earns is represented by y.

We can start by assigning different values to x and calculating the corresponding values of y. For example, if Joseph mows 1 lawn, he would earn $15. If he mows 2 lawns, he would earn $30, and so on. After creating the table, we can analyze the relationship.

In this case, we observe that the amount of money Joseph earns is directly proportional to the number of lawns he mows. This means that as the number of lawns increases, the amount of money Joseph earns also increases proportionally.

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Let's assume

x is number of hours worked

y is amount paid

Since, this is linear relationship

We can select any two points

(2,36.50) and (4,73)

so, we can also write as

x1=2 , y1 =36.50

x2=4 , y2=73

Firstly, we can find slope

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

we can plug values

[tex]m=\frac{73-36.50}{4-2}[/tex]

[tex]m=18.25[/tex]

now, we can use point slope form of line

[tex]y-y_1=m(x-x_1)[/tex]

we can plug values

[tex]y-36.50=18.25(x-2)[/tex]

now, we can solve  for y

[tex]y=18.25x[/tex]

or

[tex]y=18.3x[/tex]..............Answer

Answer:

y=18.1x and y=18x

Step-by-step explanation:

1 cup of milk is used with  

3

4

cup of water

Explanation:

A comparison between the cups of milk and cups of water can be written as a ratio:

Note that:  

1

3

>

1

4

milk : water

1

3

:

1

4

←

×

12

to get rid of fractions

12

1

×

1

3

:

12

1

×

1

4

4

:

3

4 cups of milk are used with 3 cups of water  

←

÷

4

1 cup of milk is used with  

3

4

cup of water

Answer:

The slope is 3/4.

Step-by-step explanation:

Slope formula:

[tex]\displaystyle \frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\displaystyle \frac{(-2)-4}{(-8)-0}=\frac{-6}{-8}=\frac{-6\div2}{-8\div2}=\frac{-3}{-4}=\frac{3}{4}[/tex]

Therefore, the slope is 3/4, and the correct answer is 3/4.

the answer is imports because they are getting it from another country

if the lines are parallel the slopes are the same so m=5

the equation of a line given the slope and a point is

y-y1 = m(x-x1)

y-14= 5(x-2)

y-14 = 5x-10

y=5x+4

I believe X and Y are also 61°! Report me if I am wrong!

Final answer:

Explanation of why Method A is recommended to save the fish from pesticide contamination

Explanation:

The method I would recommend to save the fish is Method A. Here's why:

Given the urgency and the higher rate of removal, Method A is the best choice to ensure the survival of the fish after the contamination event.

The answer is 7.15 which is also equivalent to 7 15/20

Answer:

32 degrees

Step-by-step explanation:

Using the sine law:

sin 116/ 17 = sinx/ 10

10 (sin116) = 17 (sinx)

0.5287 = sinx

sin^-1 0.5287 = x

x = approximately 32 degrees

answer is 3/4 because that is 24/32 reduced

Answer:

D is -31 also i checked to make sure.

Answer:

b

Step-by-step explanation:

b makes sense

hope this helps

Answer: 8, 21, 34, 47, 60...

Difference is 13 I added 13 each time.

The answer to your question is 5.03.

I hope that this helped! :)

To find the scale factor  the ratio of one length to the other is determined.

The scale factor is a measurement for comparing figures with similar appearances but differing scales or metrics.

Consider two squares that appear to be similar yet have different length of side.

The scale factor describes how much a figure has grown or shrunk in comparison to its original size.

Scale Factor is determined by dividing the new figure dimensions with the original figure.

For scale up the formula is Dimensions of the bigger figure / Dimensions of the smaller one.

On a graph

On each figure, find two corresponding sides.

To find the scale factor  the ratio of one length to the other is determined.

To know more about Scale Factor

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The area of a rectangle is its length x width.

The perimeter of a rectangle is its length + length + width + width.

Let's have l stand for length and w for width.  A will stand for area and P for perimeter.  This gives us:

399 = l x w

80 = 2l + 2w  We can divide both sides of this equation by 2 to get 40 = l + w.

Now we need to find two numbers whose sum is 40 and product is 399.

Fitting some random numbers in gives us the numbers 19 and 21 for the length and width.