Find the area of a trapezoid shown:

The complex number in rectangular form z = (5√3 / 4) - i 5/4 is equivalent to the complex number in polar form z = 5/2 · (cos 11π/6 + i sin 11π/6). (Correct choice: C)

Complex numbers are elements of the form z = a + i b, where [tex]a, b \in \mathbb{R}[/tex]. In other words, represents a generalization from real numbers. The polar form of a complex number is shown below:

[tex]z = r\cdot (\cos \theta + i \,\sin \theta)[/tex]     (1)

Where:

The norm is determined by Pythagorean theorem and the direction by inverse trigonometric reason. If we know that z = (5√3 / 4) - i 5/4, then its polar form is shown below:

Norm

[tex]r = \sqrt{\left(\frac{5\sqrt{3}}{4} \right)^{2}+\left(-\frac{5}{4} \right)^{2}}[/tex]

r = 5/2

Direction

[tex]\theta = \tan^{-1} \left[\frac{\left(-\frac{5}{4} \right)}{\left(\frac{5\sqrt{3}}{4} \right)} \right][/tex]

θ = 11π/6 rad

Thus, the complex number in rectangular form z = (5√3 / 4) - i 5/4 is equivalent to the complex number in polar form z = 5/2 · (cos 11π/6 + i sin 11π/6).

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Answer:

A. (-8, 0)

Step-by-step explanation:

The side of the line that is shaded contains the solutions to the inequality. (-8, 0) is in the shaded part of both graphs.

Also, 0 > -15 and 0 [tex]\geq[/tex] -9

I hope this helps :)

Answer:

42 ounces

Step-by-step explanation:

18 x 16 = 288

288 + 6 = 294

294/7 = 42

1-pound equals 16 ounces, since there are 18 pounds you will multiply 18 pounds by 16, then you will get 288, add your 6 ounces from the question, you will get 294, lastly divide by 7, which you will end up with 42

[tex]~~~~\dfrac{d}{dx} \left( \sqrt[5]{1+x} \right)\\\\\\=\dfrac{d}{dx} (1+x)^{\tfrac 15}\\\\\\=\dfrac 15 \left(1 + x\right)^{\tfrac 15 -1} \cdot \dfrac{d}{dx}(1+x)\\\\\\=\dfrac 15 (1+x)^{-\tfrac 45} \cdot(0+1)\\\\\\=\dfrac{1}{5(1+x)^{\tfrac 45}}[/tex]

Since the exponents were added based on the product rule, hence the multiplication law of exponents is TRUE

Indices are written in term of exponents. Some of the laws of indices;

[tex]a^m\times a^n=a^{m+n}[/tex] (product law of indices)

For the quotient law of indices

[tex]\dfrac{a^m}{a^n} =a^{m-n}[/tex]

According to the given expression, we are to determine if it is true or false

Check:

[tex]b^n.b^m=b^{n+m[/tex]

Since the exponents were added based on the product rule, hence the multiplication law of exponents is TRUE

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Answer:

a dash is 1/8 tsp.

Step-by-step explanation:

a dash is 1/8 tsp or called 0.13

Using translation concepts, it is found that the correct option regarding the function is:

The function h(x) is decreasing on the interval (3, ∞).

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

The parent function is given by:

[tex]f(x) = \sqrt{x}[/tex]

Which increases on (0, ∞).

The translated function is given by:

[tex]g(x) = -2\sqrt{x - 3}[/tex]

With the translation, the domain is now (-3, ∞), and the function is decreasing, hence the correct option is given by:

The function h(x) is decreasing on the interval (3, ∞).

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Answer:

x=4

Step-by-step explanation:

Based on the given conditions, formulate: 

x+8=3×x

Rearrange unknown terms to the left side of the equation:

x-3x=-8

Combine like terms:-2x=-8

Divide both sides of the equation by the coefficient of variable:x=-8/-2

Rewrite the fraction:8/2

Cross out the common factor:x=4

get the result:x=4

Answer: 4

Answer:

It would be 30.

Step-by-step explanation:

If we make a list of all the sums that we can get, we have:

1+2, 1+3, 1+4, 1+5, 1+6, 2+3, 2+4, 2+5, 2+6, 3+4, 3+5, 3+6, 4+5, 4+6, 5+6

These 15 sums can be chosen in two ways, since order matters, and we could do 2+1 instead of 1+2.

That gets us to 15x2 which is 30.

The number of ways that we can choose the marbles such that the sum of the numbers on my marbles equals the number on his would be 30.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

I have a bag with 6 marbles numbered from 1 to 6.

Mathew has a bag with 12 marbles numbered from 1 to 12.

1+2, 1+3, 1+4, 1+5, 1+6, 2+3, 2+4, 2+5, 2+6, 3+4, 3+5, 3+6, 4+5, 4+6, 5+6

These 15 sums can be chosen in two ways,

Since order matters, and we could do 2+1 instead of 1+2.

15 x 2 which is 30.

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Answer:

Step-by-step explanation:

the circle has a radius of 2.

Then

The circumference of the circle = 2πr = 2π(2) = 4π

…………………………………

Since , 45/360 = 1/8

Then, the arc is 1/8 of the entire circle.

…………………

Therefore,

the length of a 45° arc = 4π/8 = π/2 cm ≈ 1.57 cm

Using the slope concept, it is found that the ship’s horizontal distance from the lighthouse (and the shore) is of 715.09 feet.

The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.

In this problem, we have that:

Hence:

tan(11º) = 139/d

d = 139/tan(11º)

d = 715.09.

The ship’s horizontal distance from the lighthouse (and the shore) is of 715.09 feet.

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The function on the table is decreasing on the interval [-2, 0).

A function is decreasing if, as x increases, f(x) decreases.

We can see that at x = -2, f(-2) = 12.

Then at x = 0, f(0) = 0.

And for the value after that:

x = 1, f(1) = 3

So now the function increases. Then we conclude that the function is decreasing on the interval [-2, 0), and after that the function increases.

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Answer:

D. 19/50

Explanation:

Write 0.38 as

0.38/1

Multiply both numerator and denominator by 10 for every number after the decimal point

0.38 × 100

1 × 100

=

38/100

Reducing the fraction gives

19/50

Answer:

(p -3q )(p -3q  )

Step-by-step explanation:

p'2 - 6pq + 9q'2

(p -3q )(p -3q  )

find two values that add to give 6 and multiply to 9

p x p =p'2

-3q x p = -3pq   -3 x pq = -3pq    ...... -3pq - 3pq = -6pq

-3q x - 3q = 9q'2

Answer:

13/20

Step-by-step explanation:

2/5*4=8/20

1/4*5=5/20

8+5=13

13/20

Answer:

5/2a

Step-by-step explanation:

Factor out common term a: a ( 1 + 1/3 + 7/6)

= a( 1+ 1/3 + 7/6)

1+ 1/3 + 7/6 = 5/2

= a5/2

= 5/2a

The value of x is 28 millimeters in the composite figure of two right-angled triangles lying next to each other

A composite figure is a figure that is produced from the combination of two geometric shapes together.

The diagrammatic expression of a composite figure consists of two right-angled triangles lying next to each other can be seen in the image attached below.

For the left-side right-angled triangle, we have:

13² = h² + 5²

h² = 13² - 5²

h = √(169-25)

h = 12

Recall from the diagram that:

h² = pq

∴

12² = 5x

x = 144/5

x ≅ 28 millimeters

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Answer:

192

Step-by-step explanation:

so you basically make an equation like this:

4*4(5+7)

4*4(12)

4*48

=192

Transformation involves changing the form of a function. The function that represents is C; [tex]g(x) =- \sqrt[3]{x+1}[/tex]

The function is a type of relation, or rule, that maps one input to specific single output.

Function f(x) is given byy;

[tex]g(x) = \sqrt[3]{x}[/tex]

f(x) is reflected across the x-axis.

The rule of this transformation (i.e. reflection) is:

(x, y) ⇒ (x, - y)

So,

[tex]f'(x) = -f(x)[/tex]

This gives

[tex]f'(x) = - \sqrt[3]{x}[/tex]

Now, f'(x) is translated 1 unit left

The rule of this transformation (i.e. translation) is:

(x, y) ⇒ (x+ 1, y)

So,

g(x) = f'(x+ 1)

This gives

[tex]g(x) = -\sqrt[3]{x+1}[/tex]

Hence, the function that represents g(x) is (c)

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Answer:

Step-by-step explanation:

its B on Edge just did it

His monthly payment to the nearest dollar of the loan taken over 25 years = $4,391.67

The mortgage capital = $620,000

The rate of payment of interest= 4.5%

The period for the payment = 25 years.

Simple interest

= p×T×R/100

= $620,000 × 25 × 4.5/100

= 69750000/100

= $697,500

Therefore the total amount of money that will be generated = $620,000 + $697,500 = $1,317,500

Therefore the monthly payment,

= $1,317,500/12×25

= $4,391.67

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Answer:

87.5 ft^3

Step-by-step explanation:

Formula:

Volume = length x width x height.

Dimensions:

Length = 3 1/2 ft = 7/2 ft

Width = 5 ft

Height = 2 1/2 ft = 5/2 ft

Substitute and Find Volume:

Volume = (7/2 ft) x (5 ft) x (5/2) ft

Volume = 87.5 ft^3

Answer:

Point Q best represents the square root of 10.

The measure of the angle Y from the given diagram is 102.5 degrees

In order to determine the unknown angle, we will use the theorem "angle at the vertex is half the angle at its intercepted arc".

Given the following

angle at the arc= 205 degrees

required

angle at the vertex Y

According to the theorem;

<Y = 1/2arcXZ
<Y = 1/2(205)
<Y = 102.5 degrees

Hence the measure of the angle Y from the given diagram is 102.5 degrees

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The option second "A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right" is correct.

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

The options are attached in a picture please refer to the attached picture.

We have an inequality:

3(8 – 4x) < 6(x – 5)

After solving:

8 - 4x < 2(x - 5)

8 - 4x < 2x - 10

8 + 10 < 2x + 4x

18 < 6x

3 < x  or

x > 3

x ∈ (3, ∞)

Thus, the option second "A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right" is correct.

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Step-by-step explanation:

well it could be -10 < x < 10

or -9 ≤ x < 10

or -10 < x ≤ 9

or -9 ≤ x ≤ 9

Step-by-step explanation:

the picture is not representing the real angle sizes. so, don't let yourself get confused by that.

the right neighbor angle of 90° at E is also 90°.

it has to be, because it is the supplementary angle to the left 90° (that means together they are 180°).

remember, all angles around a single point on one side of a line have to sum up to 180° (because the line can be seen as the diameter of a circle, with the point being the center of the circle, and so one side of the line is representing a half-circle and therefore 180°).

for the same reason angle 1 (the lower neighbor of the 90° angle at A) is also 90°.

for the same reason the lower neighbor angle of the 60° angle at E is 180 - 60 = 120°.

for the same reason the angle ABC is 180 - 40 = 140°.

for the angle BCD we need to remember :

the sum of interior angles of a polygon with n sides is

(n − 2) × 180°.

in our case ABCDE has 5 sides, so the sum of all interior angles is

(5 - 2) × 180 = 3×180 = 540°

we know 4 of the interior angles already, so

angle BCD = 540 - 90 - 90 - 120 - 140 = 100°

x is now the supplementary angle to the angle BCD.

so,

x = 180 - 100 = 80°

Answer:

2.7m

Step-by-step explanation:

1.0m

0.5m

+1.2m

2.7m - answer