PLEASE HELP 14 POINTS

Answer:

Z = 5 + 3i and Z = -8 - 2i

Step-by-step explanation:

* Lets study the drawing of the complex numbers

- The x-axis is the real axis

- The y-axis is the imaginary axis

* Look to the attached figure

- Any point in the first quadrant is above the real axis and right

 to the imaginary axis (Z4)

# Z = x + yi

- Any point in the second quadrant is above the real axis and left

 to the imaginary axis (Z2)

# Z = -x + yi

- Any point in the third quadrant is below the real axis and left

 to the imaginary axis (Z3)

# Z = -x - yi

- Any point in the fourth quadrant is below the real axis and right

 to the imaginary axis (Z1)

# Z = x - yi

* Now lets solve the problem

- The point above the real axis and right to the imaginary axis lies

 in the first quadrant

∴ The real part is positive and the imaginary part is positive

∴ Z = 5 + 3i

- The point below the real axis and left to the imaginary axis lies

 in the third quadrant

∴ The real part is negative and the imaginary part is negative

∴ Z = -8 - 2i

A complex number that lies above the real axis and to the right of the imaginary axis could be '2 + 3i', while a complex number that lies below the real axis and to the left of the imaginary axis could be '-2 - 3i'. The direction in the coordinate system (upward or rightward is positive, downward or leftward is negative) determines the signs of real and imaginary components.

In the complex plane, a complex number is considered to lie above the real axis if its imaginary part is positive, and to the right of the imaginary axis if its real part is positive. Hence, an example of a complex number that lies above the real axis and to the right of the imaginary axis is 2 + 3i, where 2 is the real part and 3i is the imaginary part.

Conversely, a complex number lies below the real axis if its imaginary part is negative, and to the left of the imaginary axis if its real part is negative. So, an example of such a number could be -2 - 3i, where -2 is the real part and -3i is the imaginary part.

Remember, in the coordinate system used to plot complex numbers, motion upward or to the right is usually considered positive, while motion downward or to the left is considered negative.

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Answer:

2x^2+3x+1

Step-by-step explanation:

FOIL

Answer:

2x^2+3x+1, I believe.  

Step-by-step explanation:

Multipy 'em

Answer:

Length of garden will be 30 metres.

Step-by-step explanation:

Let the Width of garden be x metres.

then,

Length of garden will be (x+6) metres.

Area = Length × Breadth

720 = x X (c+6)

720 = x²+6x

0 = x²+6x-720

As we can see above equation is a quadratic equation in the form of ax²+bx+C.

so,

[tex] = \frac{ - b ± \sqrt{{b}^{2} - 4ac} }{2a} \\ = \frac{ - 6 ± \sqrt{{6}^{2} - 4 \times 1 \times - 720} }{2} \\ = \frac{ - 6 ± \sqrt{36 + 2880} }{2} \\ = \frac{ - 6 ± \sqrt{2916} }{2} \\ = \frac{ - 6 ± 54}{2}\\= \frac{-6+54}{2} ... \frac{ - 6 - 54}{2} \\ = \frac{48}{2} ... \frac{ - 60}{2} \\ = 24... - 30[/tex]

One of the Roots of the Quadratic equation is 24 and other is -30.

And as we know width of any garden cannot be negative so the width of garden will be 24 metres.

As we got the width,

adding 6 to it will give us the Length,

So,

24 metres + 6 = 30 metres.

Length of the garden is 30 metres.

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Quadrilateral. If you add the angles up on any quadrilateral, it equals 360 (it should always add to 360 for a quadrilateral)

The polygon you're describing is a kite.

To verify this, let's calculate the sum of the interior angles of the polygon:

Sum of interior angles = [tex](n - 2) * 180 degrees[/tex]

For a polygon with 4 sides: [tex](4 - 2) * 180 = 360 degrees[/tex]

Now, let's add up the given angle measures: 80 + 100 + 80 + 100 = 360 degrees

Since the sum of the interior angles matches the calculated sum for a four-sided polygon, and the sides are congruent, the polygon is indeed a kite.

1. Calculate the sum of interior angles: The sum of interior angles of any polygon can be found using the formula (n - 2) * 180 degrees, where 'n' represents the number of sides. For a four-sided polygon, the sum is (4 - 2) * 180 = 360 degrees.

2. Add up the given angle measures: The given angle measures are 80, 100, 80, and 100 degrees. Adding them together gives a total of 360 degrees, which matches the sum calculated for a four-sided polygon.

3. Confirming the polygon type: Since the sum of the interior angles matches the calculated sum for a four-sided polygon, and the sides are congruent (meaning all sides have the same length), the polygon fits the definition of a kite.

Therefore, the polygon with four congruent sides and angle measures of 80, 100, 80, and 100 degrees is indeed a kite.

Complete question:

What is the name of a polygon that has four congruent sides and these angle measures 80,100,80,100

Answer:

2x^2+7x-61

Step-by-step explanation:

Answer:

1556.25

Step-by-step explanation:

5 3/16.25×300=1556.25

Answer:

A. 100

Step-by-step explanation:

50 + 50 + 100

Answer:

A. 100°

Step-by-step explanation:

Let's take a look at the image and make some conclusions.

Angle BAE is 40 degrees

All angles at the crossing of BE and AC are right angles (90 degrees) because they are perpendicular lines.

Since BE is a bisector of angle ABC, we know that angles ABD and DBC are equal.

We don't know angle ABD but it's easy to find... since we know 2 angles from triangle ABE, and the sum of the interior triangles is 180.  So,

ABD = 180 - 40 - 90 = 50

Since ABD is 50 degrees and represents half of angle ABC... we know that ABC is 100 degrees.

Answer:

6200

You're rounding to the nearest hundreds place. so every number behind that needs to be a "0"

Answer: is A

Step-by-step explanation:

Answer: 5 Times

Step-by-step explanation: P(roll 4) = 1/6

---

Expected # of 4 in 30 rolls = (1/6)*30 = 5

Answer:

19.50 divided by 3

Step-by-step explanation:

Answer:

3h = 19.50

Step-by-step explanation:

First lets define the price of each hat as the variable h.

Next we know that there are 3 hats so we can write that variable as 3h

We also know that the cost of all 3 hats was $19.50. This means that we can set each side of this equation equal to each other.

This gives us the equation 3h = 19.50

If you were to solve for h, you would get

[tex]h = \frac{19.50}{3}[/tex]

Which would simplify to

h = 6.50

This means that each hat costs $6.50

ANSWER

[tex]x \: < \: 9[/tex]

EXPLANATION

The given inequality is

[tex]5x \: < \: 45[/tex]

We divide through by 5 to get:

[tex]x \: < \: \frac{45}{5} [/tex]

This will simplify to

[tex]x \: < \: 9[/tex]

Therefore the solution to the inequality is

[tex]x \: < \: 9[/tex]

x < 9

Start with 5x < 45.

Divide both sides of the inequality by 5 to get x < 45 / 5, or x < 9.

To solve the given system of linear equations -3x = 42-16y and 14x = 76-16y, use the method of elimination to find the solution (20-6y, y).

To solve the system of linear equations -3x = 42-16y and 14x = 76-16y, we can use the method of substitution or elimination. Let's use the method of elimination:

Multiply the first equation by 2 to make the coefficients of y in both equations equal. The equations become:

-6x = 84-32y and 14x = 76-16y

Add the two equations together:

-6x + 14x = 84-32y + 76-16y

Simplify:

8x = 160-48y

Rearrange the equation to solve for x:

x = (160-48y)/8

Simplify further:

x = 20-6y

The solution to the system of equations is x = 20-6y. To separate the x- and y-values, we write it as (20-6y, y).

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the answer is negative 5

It’s negative 5, because you have to substitute the x in 3x for negative one, so the equation looks like f(x)= 3(-1) - 2. Then, you solve

Answer:

[tex]x=111[/tex]

Step-by-step explanation:

Since these angles are supplementary, they add up to 180°.

Let's make an equation.

[tex]360=(x+23)+(2x+4) \\ \\ 360=x+23+2x+4 \\ \\ 360=3x+27 \\ \\ 3x=333 \\ \\ x = 111[/tex]

Answer:

[tex]x=51[/tex]

Step-by-step explanation:

We have been given an image of two intersecting lines. We are asked to find the value of x.

We can see that both angles are supplementary, so we can set an equation as:

[tex]x+23+2x+4=180[/tex]

[tex]x+2x+4+23=180[/tex]

[tex]3x+27=180[/tex]

[tex]3x+27-27=180-27[/tex]

[tex]3x=153[/tex]

[tex]\frac{3x}{3}=\frac{153}{3}[/tex]

[tex]x=51[/tex]

Therefore, the value of x is 51.

Answer:

The answer is True.   Hope this helps. :)

Step-by-step explanation:

( 4 x 3 ) 3 + 5 - 10 = 4 x 3 + 5 - 10

This is basically an example of PEMDAS.

Perimeter

Equation

Multiplication

Division

Addition

Subtraction

(Multiplication is ahead of Addition, you multiply first)

Answer:

x ≈ 6.7

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan40° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{x}{8}[/tex]

Multiply both sides by 8

8 × tan40° = x, hence

x = 6.7 ( to 1 dec. place )

I believe the answer is 14.42

The length of AC is 14.42 in the triangle ΔABC where AB=17cm, BC=9cm and angle ∠ACB=90°. This can be obtained by using Pythagoras' theorem.

Given that, AB=17cm, BC=9cm and angle ∠ACB=90°.

By using Pythagoras' theorem,

AB² = AC²+BC²

17² = AC²+9²

AC² = 17²-9² =289-81 = 208

AC = √208 =14.42

⇒AC = 14.42cm

Hence the length of AC is 14.42 in the triangle ΔABC where AB=17cm, BC=9cm and angle ∠ACB=90°.

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u need 12 pounds of clay for 12 pounds of clay?

When the bases are the same, you can combine the exponents.

x³   [x is where the base is]

For example:

x³ · y² = x³y²   You can't simplify this anymore because they have different bases/variables

[when you multiply a variable with an exponent by a variable with an exponent, you add the exponents together] so:

x² · x³ = [tex]x^{2+3}=x^5[/tex]

[when you multiply a variable with an exponent by an exponent, you multiply the exponents together] so:

(x³)²=[tex]x^{3*2}=x^6[/tex]

[tex]-2y^2*xy^4=-2x(y^{2+4})=-2xy^6[/tex]

Answer:

[tex]\large\boxed{-2xy^6}[/tex]

Step-by-step explanation:

[tex]-2y^2\cdot xy^4=(-2)(x)(y^2y^4)\\\\\text{use}\ a^na^m=a^{n+m}\\\\=-2xy^{2+4}=-2xy^6[/tex]

Answer:

14

Step-by-step explanation:

d=c/pi

45/pi=14

Answer:

14

Step-by-step explanation:

c = pi d

45 = 22/7 d

45 * 7/22 = d

2* 7      = d (approx.)

d = 14 approxiamtely

So the closest estimate dor d is 14

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Answer:

The value of k is [tex]K=100[/tex]

Step-by-step explanation:

we know that

[tex]h(x)=\frac{20x-k}{x}+50[/tex]

we have

[tex]x=20\\ h(20)=65[/tex]

substitute in the function and solve for k

[tex]65=\frac{20(20)-k}{20}+50[/tex]

[tex]65-50=\frac{400-k}{20}[/tex]

[tex]15=\frac{400-k}{20}[/tex]

[tex]15*20=400-k[/tex]

[tex]300=400-k[/tex]

[tex]k=400-300=100[/tex]

Answer:

K=100

Step-by-step explanation:

Answer:

the sine of angle R is 5/7.

Step-by-step explanation:

Recall that the sine function is defined as sin Ф = (opposite side) / hypotenuse.

The side opposite Angle R is √65 and the hypotenuse is √91.

Thus, the sine of angle R is sin R = √65 / √91, or 5/7.

Answer:

d

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given y = 5(x + 1) = 5x + 5 ← in slope- intercept form

with slope m = 5

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{5}[/tex], thus

y = - [tex]\frac{1}{5}[/tex] x + c ← is the partial equation of the perpendicular line

To find c substitute (10, 2) into the partial equation

2 = - 2 + c ⇒ c = - 2 + 2 = 4

y = - [tex]\frac{1}{5}[/tex] x + 4 ← in slope intercept form

Multiply all terms by 5

5y = - x + 20 ( add x to both sides )

x + 5y = 20 ← in standard form → D

Answer:

1.1818...

Step-by-step explanation:

Divide 13 by 11

13 ÷ 11 = 1.1818...

Answer: 1.1818...

The decimal 1.182 is equivalent to 13/11.

A fraction can be converted to a decimal by dividing the numerator by the denominator.

The fraction is given as 13/11.

The numerator is 13 and the denominator is 11.

We are asked to find the decimal form of the given fraction.

This can be done by simplifying the fraction and dividing the numerator by the denominator.

This can be done as shown below:

The fraction = 13/11

= 1.1818

≈ 1.182

The decimal form of the fraction is found. The decimal form of the fraction is 1.182.

Therefore, we have found that the decimal 1.182 is equivalent to 13/11.

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Answer:

-1/3

Step-by-step explanation:

By substitution,

[tex]g(2)=6.1g(1)[/tex]

[tex]g(3)=6.1g(2)=6.1^2g(1)[/tex]

[tex]g(4)=6.1g(3)=6.1^3g(1)[/tex]

and so on, so that

[tex]g(n)=6.1^{n-1}g(1)=2.7\cdot6.1^{n-1}

Answer:

2.7(6.1)^(n-1)

Step-by-step explanation:

[(6.1)^(n-1)]*g(1)

=[(6.1)^(n-1)]*2.7

=2.7*(6.1)^(n-1)

Answer:

Population size:5

Mean (μ): 22.54

Mean Absolute Deviation (MAD): 5.952

Step-by-step explanation: i hope this helps!!!

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Answer:

5.592

Step-by-step explanation:

The addition problem can be solved in two ways: treating each column separately without carrying and writing down the sum of each column even if it is 10 or more. Examples demonstrate each method using single-digit addition without carrying and adjusting sums that exceed single digits.

The question at hand involves solving a unique addition problem where each letter corresponds to a digit between 0 and 9. To find 2 different ways to make the addition problem work, we need to apply traditional addition rules along with the clues provided.

First, let's analyze the given examples:

To construct two solutions, let's use the same principle:

It's important to follow the instructions closely and understand that digits in these sum calculations are handled independently based on the context provided.

22.27

You need to divide the amount of servings by the amount of ounces in total