Slope what is the slope

Answer:

a. \(z_{1} = \frac{3\sqrt{2}}{2}+j\cdot 3\frac{\sqrt{2}}{2}\), b. \(z_{3} = -j\cdot 2\), c. \(z_{4} = -j\), d. \(z_{5} = 1\)

Step-by-step explanation:

All given complex numbers are in polar form, which are characterized by:

\(z = r\cdot e^{j\cdot \theta}\)

Where:

\(r\) - Magnitude, dimensionless.

\(\theta\) - Direction, measured in radians.

The rectangular form of complex numbers is represented by:

\(z = r\cdot (\cos \theta + j\cdot \sin \theta)\)

Now, each complex number is evaluated:

a. \(z_{1} = 3\cdot e^{j\cdot \frac{ \pi}{4} }\)

\(r = 3\) and \(\theta = \frac{\pi}{4}\)

\(z_{1} = 3\cdot \left(\cos \frac{\pi}{4}+j\cdot \sin \frac{\pi}{4} \right)\)

\(z_{1} = \frac{3\sqrt{2}}{2}+j\cdot 3\frac{\sqrt{2}}{2}\)

b. \(z_{3} = 2\cdot e^{-j\cdot \frac{\pi}{2} }\)

\(r = 2\) and \(\theta = -\frac{\pi}{2}\)

\(z_{3} = 2\cdot \left[\cos \left(-\frac{\pi}{2}\right) + j\cdot \sin \left(-\frac{\pi}{2} \right) \right]\)

\(z_{3} = -j\cdot 2\)

c. \(z_{4} = j^{3}\)

By definition of complex number, \(j = \sqrt{-1}\), which means that \(j^{2} = -1\). Hence:

\(z_{4} = j^{2+1}\)

\(z_{4} = j^{2}\cdot j\)

\(z_{4} = j\cdot j^{2}\)

\(z_{4} = -j\)

d. \(z_{5} = j^{-4}\)

By definition of complex number, \(j = \sqrt{-1}\), which means that \(j^{2} = -1\).

Hence:

\(z_{5} = \frac{1}{j^{4}}\)

\(z_{5} = \frac{1}{j^{2+2}}\)

\(z_{5} = \frac{1}{j^{2}\cdot j^{2}}\)

\(z_{5} = \frac{1}{(-1)\cdot (-1)}\)

\(z_{5} = 1\)

Answer:

1..........................

Answer:

Andre scored 14 points.

Step-by-step explanation:

set up expressions with the info given:

Diego's points: a –9

Andre's points: 2d. and

n = 2d

Noah's points = 10

Use the expressions to set up equations to solve.

To find a, Andre's points, we can work backwards.

Substitute the 10 from the last expression for n in the equation n=2d, and solve for d:

10 = 2d. Divide both sides by 2

5 = d

Substitute the value of d, Diego's points, to make an equation using the first expression:

5 = a –9 Add 9 to both sides.

5 + 9 = a a = 14

Andre scored 14 points

Answer:

37

Step-by-step explanation:

x=-4

=2(5-(-4)2+1

=2(5+4)2+1

=2(9)2+1

=18(2)+1

=36+1

=37

The only solution for the equation 8 tan^2 θ = 3 cos^2 θ in the given Range is θ ≈ 19.47 degrees.

a) We are given the equation 8 tan θ = 3 cos θ.

Dividing both sides of the equation by cos θ, we have:

8 tan θ / cos θ = 3

Using the identity tan θ = sin θ / cos θ, we can substitute it into the equation:

8 (sin θ / cos θ) / cos θ = 3

Simplifying further, we get:

8 sin θ / cos^2 θ = 3

Now, multiplying both sides of the equation by cos^2 θ, we have:

8 sin θ = 3 cos^2 θ

Using the identity cos^2 θ = 1 - sin^2 θ, we can substitute it into the equation:

8 sin θ = 3(1 - sin^2 θ)

Expanding the equation, we get:

8 sin θ = 3 - 3 sin^2 θ

Rearranging the terms, we have:

3 sin^2 θ + 8 sin θ - 3 = 0

Therefore, we have successfully shown that the equation can be rewritten in the form 3 sin^2 θ + 8 sin θ - 3 = 0.

b) Now, let's solve the equation 3 sin^2 θ + 8 sin θ - 3 = 0.

To solve the quadratic equation, we can use factoring, quadratic formula, or other appropriate methods.

In this case, the equation factors as:

(3 sin θ - 1)(sin θ + 3) = 0

Setting each factor equal to zero, we have two equations:

3 sin θ - 1 = 0    or    sin θ + 3 = 0

For the first equation, solving for sin θ, we get:

3 sin θ = 1

sin θ = 1/3

Taking the inverse sine (sin^-1) of both sides, we find:

θ = sin^-1(1/3) ≈ 19.47 degrees (to 2 decimal places)

For the second equation, solving for sin θ, we have:

sin θ = -3

Since the range of sine is between -1 and 1, there are no solutions for this equation in the given range (0 ≤ θ ≤ 90 degrees).

Therefore, the only solution for the equation 8 tan^2 θ = 3 cos^2 θ in the given range is θ ≈ 19.47 degrees.

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Answer:

the 3 represent a one thousand

so that means 4.oo9* 1000 = =49

Answer:

a)  $497.70

b)  392.4 square feet

c)  $1,200

Step-by-step explanation:

A regular octagon has 8 sides of equal length.

Given each side of the octagon measures 9 feet in length, and one side does not have a railing, the total length of the railing is 7 times the length of one side:

\(\textsf{Total length of railing}=\sf 7 \times 9\; ft=63\;ft\)

If the railing sells for $7.90 per foot, the total cost of the railing can be calculated by multiplying the total length by the cost per foot:

\(\textsf{Total cost of railing}=\sf 63\;ft \times \dfrac{\$7.90}{ft}=\$497.70\)

Therefore, the cost of the railing is $497.70.

\(\hrulefill\)

To find the area of the regular octagonal gazebo, given the side length and apothem, we can use the area of a regular polygon formula:

\(\boxed{\begin{minipage}{6cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{n\;s\;a}{2}$\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the length of one side.\\ \phantom{ww}$\bullet$ $a$ is the apothem.\\\end{minipage}}\)

Substitute n = 8, s = 9, and a = 10.9 into the formula and solve for A:

\(\begin{aligned}\textsf{Area of the gazebo}&=\sf \dfrac{8 \times 9\:ft \times10.9\:ft}{2}\\\\&=\sf \dfrac{784.8\;ft^2}{2}\\\\&=\sf 392.4\; \sf ft^2\end{aligned}\)

Therefore, the area of the gazebo is 392.4 square feet.

\(\hrulefill\)

To calculate the cost of the gazebo's flooring if it costs $3 square foot, multiply the area of the gazebo found in part (b) by the cost per square foot:

\(\begin{aligned}\textsf{Total cost of flooring}&=\sf 392.4\; ft^2 \times \dfrac{\$3}{ft^2}\\&=\sf \$1177.2\\&=\sf \$1200\; (nearest\;hundred\;dollars)\end{aligned}\)

Therefore, the cost of the gazebo's flooring to the nearest hundred dollars is $1,200.

a. To find the perimeter of the gazebo, we can use the formula P = 8s, where s is the length of one side. Substituting s = 9, we get:

P = 8s = 8(9) = 72 feet

Since one side is open, we only need to find the cost of railing for 7 sides. Multiplying the perimeter by 7, we get:

Cost = 7P($7.90/foot) = 7(72 feet)($7.90/foot) = $4,939.20

Therefore, the cost of the railing is $4,939.20.

b. To find the area of the gazebo, we can use the formula A = (1/2)ap, where a is the apothem and p is the perimeter. Substituting a = 10.9 and p = 72, we get:

A = (1/2)(10.9)(72) = 394.56 square feet

Therefore, the area of the gazebo is 394.56 square feet.

c. To find the cost of the flooring, we need to multiply the area by the cost per square foot. Substituting A = 394.56 and the cost per square foot as $3, we get:

Cost = A($3/square foot) = 394.56($3/square foot) = $1,183.68

Rounding to the nearest hundred dollars, the cost of the flooring is $1,184. Therefore, the cost of the gazebo's flooring is $1,184.

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Answer:

501

Step-by-step explanation:

Answer: 51

Step-by-step explanation:

Answer:

Diagonal, I'm 90% sure it is at least!!

Answer:

3 (7 a - 5) (a - 2)

Step-by-step explanation:

Factor the following:

21 a^2 - 57 a + 30

Factor 3 out of 21 a^2 - 57 a + 30:

3 (7 a^2 - 19 a + 10)

Factor the quadratic 7 a^2 - 19 a + 10. The coefficient of a^2 is 7 and the constant term is 10. The product of 7 and 10 is 70. The factors of 70 which sum to -19 are -5 and -14. So 7 a^2 - 19 a + 10 = 7 a^2 - 14 a - 5 a + 10 = a (7 a - 5) - 2 (7 a - 5):

3 a (7 a - 5) - 2 (7 a - 5)

Factor 7 a - 5 from a (7 a - 5) - 2 (7 a - 5):

Answer: 3 (7 a - 5) (a - 2)

Answer:

A. The variation of the equation is

B. H is 10 when L is 20

Explanation:

Given that H varies directly as L, this can be written as:

and defined as:

where k is constant.

To find the value of k, we use the given values H = 15 when L = 30

Divide both sides by 30

A.

Therefore, the formula is:

B.

We want to determine H when L is 20

H is 10 when L is 20

Answer:

A

Step-by-step explanation:

The baseball teams total is 24, divided by the number of answers, 25, is 1.6.

The French Club’s total is 33, divided by the number of answers, 15, is 2.2.

2.2-1.6 is 0.6.

Approximately 34.87% of the readers surveyed don't use e-readers.

To find the approximate sample proportion of readers who use e-readers, we divide the number of readers who said they read books on e-readers (1954) by the total number of readers surveyed (3000):

Approximate sample proportion = Number of readers who use e-readers / Total number of readers surveyed

Approximate sample proportion = 1954 / 3000 ≈ 0.6513

To express this as a percentage, we multiply the sample proportion by 100:

Approximate sample proportion as a percentage = 0.6513 × 100

= 65.13%

Therefore, the approximate sample proportion of readers who use e-readers is approximately 65.13%.

This means that approximately 65.13% of the readers surveyed use e-readers.

To determine the percentage of readers who don't use e-readers, we subtract the sample proportion from 100%:

Percentage of readers who don't use e-readers = 100% - 65.13%

= 34.87%

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Answer:

d

Step-by-step explanation:

there isnt an arrow saying it keeps going past 10

The solution is, the value of the variables are x = 40 and, y = 160.

Notice that "x" and "3x+20" are supplementary angles so their sum is 180°

(x) + (3x + 20) = 180

4x + 20 = 180

4x = 160

x = 40

To solve for "y", you have 2 options: either notice that "x" and "y-20" are supplementary angles so their sum is 180° or notice that "3x + 20" and "y - 20" are vertical angles so are equal to each other. I am going to solve using the first option because it is less work.

(x) + (y - 20) = 180°

40 + y - 20 = 180

y + 20 = 180

y = 160

Answer: x=40, y=160

The solution is, the value of the variables are x = 40 and, y = 160.

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complete question:

Find the value of each variable

The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

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Answer:

No,No,No,Yes,No,Yes

Step-by-step explanation:

The larger number is obtained as 1.3.

A decimal number is the representation of a number in whole and a part. The whole is represented by an integer while the part is equivalent to a number divided by the order of 10.

The given decimal numbers are 1.05 and 1.3.

The decimal 1.3 can be written as 1.30.

Now, the two decimals can be compared as below,

1.05 and 1.30

Both the decimals have equal integer part.

Digit at tenths of 1.05 is 0 and for 1.30 is 3.

Since, 3 > 0.

⇒  1.30 > 1.05

Hence, 1.3 is greater than 1.05.

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Answer:

7/9, 18/14,

Step-by-step explanation:

its mean i have answer for that

Answer:

4 for the first box and 2*2*19 for the second.

Step-by-step explanation:

I did this lesson in 4th grade

Answer:

_4_ is not a prime number.

The correct prime factorization of 76 is  2, 2 ,19  .

Step-by-step explanation:

The value of the angle x is 30 degrees

To determine the value of the variable x, we need to know the triangle sum theorem.

The triangle sum theorem is a theorem in mathematics stating that the sum total of the interior angles in a triangle is equivalent to 180 degrees.

We should also note that angle at right angle is 90 degrees

Then, we have the angles written as;

90 degrees

2x degrees

x degrees

Equate the angles , we have;

2x + x + 90 = 180

collect the like terms, we have;

2x + x = 180 - 90

add or subtract the like terms, we have;

3x = 90

divide by the coefficient

x = 30

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Answer:

x10 gallons

Step-by-step explanation:

you said it

Answer:

You are correct it is A. cos B

Step-by-step explanation:

First find the area of the square, then the triangle.

15 times 17 = 255 sq. yd

Triangle:

(5 times 5)/2 = 12.5 sq. yd

Your answer is 267.5 sq. yd

Hope this helps.

Answer:

EF

This is just extra words

A,C,B,D,F,H are the rotations of the shape X given in the picture.

Rotations of shapes refer to the transformation of a shape around a fixed point called the center of rotation. This transformation involves rotating the shape by a certain angle while keeping the shape's size and shape consistent.

The angle of rotation determines how much the shape is rotated. It is measured in degrees or radians.

Properties of Rotations:

Rotations preserve the size and shape of the original shape.

Before and after the rotation, the distance between any two points on the shape and its centre of rotation remains constant.

The orientation of the shape may change, but its overall appearance remains unchanged.

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Answer:

0, -7

Step-by-step explanation:

Answer:

The y intercept is -7

Step-by-step explanation:

-3x-7 is the equation that passes through (-2,-1)