I need help determining how many roots

Convert [tex]-1+i[/tex] to polar form.

[tex]z = -1 + i \implies \begin{cases}|z| = \sqrt{(-1)^2 + 1^2} = \sqrt2 \\\\ \arg(z) = \pi + \tan^{-1}\left(\dfrac1{-1}\right) = \dfrac{3\pi}4 \end{cases}[/tex]

By de Moivre's theorem,

[tex]\left(-1+i\right)^7 = \left(\sqrt2 \, e^{i\,\frac{3\pi}4}\right)^7 \\\\ ~~~~~~~~ = \left(\sqrt2\right)^7 e^{i\,\frac{21\pi}4} \\\\ ~~~~~~~~ = 8\sqrt2 \, e^{-i\,\frac{3\pi}4} \\\\ ~~~~~~~~ = 8\sqrt2 \left(\cos\left(\dfrac{3\pi}4\right) - i \sin\left(\dfrac{3\pi}4\right)\right) \\\\ ~~~~~~~~ = 8\sqrt2 \left(-\dfrac1{\sqrt2} - \dfrac1{\sqrt2}\,i\right) \\\\ ~~~~~~~~ = -8 (1 + i)[/tex]

QED

The function has a horizontal asymptote at y = 1

The function is given as:

f(x) = -4/x + 1

Set the radicand to 0.

So, we have:

y = 0 + 1

Evaluate

y = 1

Hence, the function has a horizontal asymptote at y = 1

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Answer: sin(58) = 0.848, cos(26) = 0.898, and tan(63) = 1.962

Step-by-step explanation:

[tex] \frac{1}{4} x + 1 = 32 \\ \frac{1}{4} x = 32 - 1 \\ \frac{1}{4} x = 31 \\ x = 31 \times 4 = 124[/tex]

The answer is 124.

From the number line, the values which completes the sum in the table are:

A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numerical values that are placed at equal intervals along its length.

From the table of values (see attachment), the values on the number line are represented as follows:

a + b = a + b

R = -1 - 2

R = -3.

a + b = a + b

S = -4 + 1

S = -3.

a + b = a + b

T = -6 - 3

T = -9.

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The point of intersection of both graphs will have the coordinate (5, 9).

We are given the functions;

f(x) = x + 4

g(x) = -2x + 19

Now, the point of intersection of both graphs is when both functions are equal which is at f(x) = g(x). Thus;

x + 4 = -2x + 19

x + 2x = 19 - 4

3x = 15

x = 15/3

x = 5

Thus;

f(x) = 5 + 4 = 9

g(x) = -2(5) + 19 = 9

Thus, the point of intersection of both graphs will have the coordinate (5, 9)

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The substance's half - life is 7 days

The formula for finding the half - life is given as;

Half - life = [tex]\frac{0. 693}{k}[/tex]

The k value given is 0.1027

Half - life = [tex]\frac{0. 693}{0.1027}[/tex]

Half - life = 6. 75

Half - life = 7 days in the nearest tenth

Thus, the substance's half - life is 7 days

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The greatest common factor of the expression is 4m⁴.

GCF simply means the greatest common factor.

The greatest common factor (GCF) of a set of numbers is the largest factor that all the numbers share.

Hence,

56m⁵

68m⁴

The greatest common factor of the expression  is the largest positive expression that divides evenly into all numbers with zero .

Hence, the greatest common factor is 4m⁴

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The limit happens to be the derivative of [tex]2^x[/tex] at [tex]x=0[/tex]:

[tex]\displaystyle f'(c) = \lim_{x\to c}\frac{f(x)-f(c)}{x-c} \implies \lim_{x\to0} \frac{2^x - 1}x = (2^x)'\bigg|_{x=0} = \ln(2)\,2^x \bigg|_{x=0} = \boxed{\ln(2)}[/tex]

Answer:

A

Step-by-step explanation:

If you were to substitute 2 or -3 into equation A, the denominator would be zero and you would have to divide by zero. Thus there are asymptotes for this function at -3 and 2, matching the graph

Ray has the incorrect reasoning because he incorrectly select the sine  function when he should have utilized the tangent.

A right angle triangle is a triangle that has one of its angles as 90 degrees.

The height of the ray can be found using trigonometric ratios.

Therefore,

tan 30 = opposite / adjacent

where

opposite side = height

adjacent side = 35 inches

Therefore,

tan 30° =  height / 35

cross multiply

height = 35 tan 30°

height = 20.2072594216

height = 20.21 inches

Therefore, Ray has the incorrect reasoning because he incorrectly select the sine  function when he should have utilized the tangent.

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Answer:

1. Ray

2. Sine

3. Tangent

Step-by-step explanation:

Plato/Edmentum

Answer:

11.863 g

Step-by-step explanation:

5.623 g + 6.24 g = 11.863 g

Using proportions, the expression for the final amount is:

150(1+d).

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

For this problem, we have that:

Hence the equivalent expression is:

120 x 1.25 x (1 + d) = 150(1+d).

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Answer:

Step-by-step explanation:

According to the picture, the angles with measure of 65° and x are included between two parallel pairs of lines.

It makes them equal:

y is the exterior angle of the triangle with two remote interior angles with measure of 40° and 65°.

As per definition of the exterior angle its measure is same as the sum of remote interior angles:

The answer is x=21 the explanation is on the picture above I hope I helped

If the current in a stream moves at a rate of 7 mph. If a boat travels 98 miles downstream in the same time that it takes to travel 49 miles upstream then the speed of the boat in still water is 21 miles per hour.

Speed is the distance covered by an object in a certain time period. It is also known as velocity. The formula of speed is as follows:

Speed=Distance/ Time.

We have been given that the speed of stream is 7miles per hour.

Let v be the speed of the boat, and t the time to travel

98=t*(7+v) (1)

49=t(v-7) (2)

(1)+(2) => 2tv=147

7t+(49+7t)=98

14t+49=98

14t=49

t=49/14

t=7/2

Put the value of t in equation 1 to get the value of v:

98=t(7+v)

98=7/2(7+v)

196/7=7+v

28=7+v

v=28-7

v=21

Hence if the current in a stream moves at a rate of 7 mph. If a boat travels 98 miles downstream in the same time that it takes to travel 49 miles upstream then the speed of the boat in still water is 21 miles per hour.

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Answer:

The small piece is 6 yards and the large piece is 8 yards.

Step-by-step explanation:

Let x  = small

Let y = large

x + y = 14       3y = 4x

3y = 4x  Divide both sides of the equation by 3 to solve for y

y = [tex]\frac{4}{3}[/tex] x  Plug [tex]\frac{4}{3}[/tex] x in for y in the first equation above.

x + y = 14

x + [tex]\frac{4}{3}[/tex] x = 14  x and 1 x mean the same thing.  Another name for 1 is [tex]\frac{3}{3}[/tex]

[tex]\frac{3}{3}[/tex]x + [tex]\frac{4}{3}[/tex]x = 14

[tex]\frac{7}{3}[/tex]x = 14  Multiple both sides by [tex]\frac{3}{7}[/tex] to solve for x

([tex]\frac{3}{7}[/tex])([tex]\frac{7}{3}[/tex]x) = 14([tex]\frac{3}{7}[/tex]) you can write 14 as [tex]\frac{14}{1}[/tex]([tex]\frac{3}{7}[/tex]) = [tex]\frac{42}{7}[/tex]= 6

x = 6

If x = 6, then y must be 8 because 6 + 8 = 14

The value of x from the given expression is -2

The formula for calculating the slope of a line is expressed as:

Slope = y2-y1/x2-x1

Given the following parameters

m = 1

(x1, y1) = (0, 2)

(x2, y2) = (x, 0)

Substitute

1 = x-0/0-2

1 = x/-2

x = -2

Hence the value of x from the given expression is -2

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Answer:12

Step-by-step explanation:

Peter's age = x

John's age = y

y=2x

after 8 years = y+8=y+x+2

=(y-y)+8-2=x

=6=x

y=2(6)=12

Answer: 178 ft^3

Step-by-step explanation:

A cylinder has the formula V=pi radius ^2 height

A cone has the formula V= 1/3 pi radius ^2 height

So 1/3 of the volume of the cylinder is the volume of a cone

1/3 of 534 = 178 ft^3

The probabilities in each of the given categories are; A) 51.33%; B) 51.33% C) 30.33% D) 30.33%

The number of ways to select 2 out of 25 is; 25C2 = 25! / (23! * 2!)

= 25*24/2

= 300

(A) Probability of selecting 1 male and 1 female:

[(11C1) * (14C1)]/300 = [11!/(10! * 1!)] * [(14!/(12! * 2!))

= 51.33%

(B)  Probability of selecting 1 female and 1 male:

[(14C1) * (11C1)]/300 = 51.33%

(C)   Probability that 2 females are selected is;

(14C2)/300 = 30.33%

D) Probability that no males are selected is;

P(no males) = (11C0 * 14C2 )/300 = 30.33%

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The measure of the angle BAM is approximately 40.894°.

In this problem we proceed to draw the figure representing the entire figure and labeling all known lengths, both from statement and derived from Pythagorean theorem. Since the angle BAM is part of a right triangle, then we can apply the following trigonometric function:

[tex]\tan \theta = \frac{BM}{AB}[/tex]

[tex]\tan \theta = \frac{\frac{\sqrt{3}}{2}\cdot x }{x}[/tex]

[tex]\tan \theta = \frac{\sqrt{3}}{2}[/tex]

θ ≈ 40.894°

The measure of the angle BAM is approximately 40.894°.

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Using a calculator, the critical value for the t-distribution with a confidence level of 95% and 17 df is of Tc = 2.1098.

It is found using a calculator, with two inputs, which are given by:

In this problem, the inputs are given as follows:

Hence, using a calculator, the critical value for the t-distribution with a confidence level of 95% and 17 df, using the stated two-tailed test, is of Tc = 2.1098.

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Answer:

D.

Step-by-step explanation:

the suggested relation can be described as y=15x. Then the correct answer is D) Yes, the points are on the line that passes through the origin.

Answer:

m∠B > m∠C > m∠A

Step-by-step explanation:

The angle opposite the largest side in a triangle is the largest, and the angle opposite the shortest side is the smallest.

Answer: 0.18

Step-by-step explanation:

The probability of the event P(A and B) is equal to 0.18.

The correct option is (C).

A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Probability has been introduced in Arithmetic to forecast how likely occurrences are to happen.

As per the given data:

We are given the probability of two events:

P(A) = 0.60 and P(B) = 0.30

We are also given that A and B are independent events.

To find the probability of P(A and B):

The term and is equivalent to the term intersection.

P(A and B) = P(A∩B)

For any 2 independent events A and B the probability P(A∩B) is given by:

= P(A) × P(B)

By substituting the given values in the question

= 0.60 × 0.30

= 0.18

The probability of the event P(A and B) is equal to 0.18.

Hence, The probability of the event P(A and B) is equal to 0.18.

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The value of the ratio based on the angle illustrated is 1:12.

From the information given, it should be noted that the angle in a circle is 360°. Therefore, the value of theta will be:

= 360° - 330°

= 30°

The equivalent expression based on the angle will be:

= 30/360

= 1/12

= 1:12

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The speed of an object is the relationship between the distance covered by the object and the time taken. Thus, the average speed of the other car is 30 mph.

The speed of an object is the relationship between the distance covered by the object and the time taken. The expression for speed is given as;

speed = [tex]\frac{distance covered}{time taken}[/tex]

⇒ distance = speed x time taken

In the given question, the distance of the first car after 2 hours can be determined as:

distance = 80 mph x 2 h

              = 160 miles

The distance covered by the first car after 2 hours is 160 miles.

Thus, since the total distance between the two cars after 2 hours is 220 miles, then;

distance covered by the second car = 220 miles - 160 miles

                                                          = 60 miles

The distance covered by the second car is 60 miles.

So that the average speed of the other car is;

speed = [tex]\frac{60}{2}[/tex]

           = 30 mph

The average speed is 30 miles per hour (mph).

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