Mathematics High School

What is the area of the region of the complex plane defined by $|z|<5$?

Answers

Answer 1

This will be the same area as that inside a circle with a radius of 5

So....the area will be ≈ pi * 5^2 ≈ 25 pi units^2

Answer 2

Final answer:

The area of the region of the complex plane defined by |z|<5 is 78.5 square units.

Explanation:

The region of the complex plane defined by |z|<5 is the inside of the circle with radius 5 centered at the origin. To find the area of this region, we can use the formula for the area of a circle, which is A = πr². In this case, the radius is 5, so the area is A = 3.14 × 5² = 78.5 square units.

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Related Questions

Find the special product (5s-3)^(2)

A. 10s2 - 9
B. 25s2 -30s - 9
C. 25s2 - 9
D. 25s - 9 30x + 9

Answers

Use the formula: (a - b)^2 = a^2 - 2ab + b^2.

=> (5s - 3)^2 = (5s)^2 - 2(5s)(3) + (3)^2 = 25s^2 - 30s +9

The list of options is mistyped, so you must use the right list of choices and find which is 25s^2 - 30s + 9.

Answer: 25s^2 - 30s + 9

In the diagram, JG = 5 cm and GE = 10 cm. Based on this information, can G be a centroid of triangle HJK? Point G cannot be a centroid because JG does not equal GE. Point G cannot be a centroid because JG is shorter than GE. Point G can be a centroid because GE and JG are in the ratio 2:1. Point G can be a centroid because JG + GE = JE.

Answers

Point G cannot be a centroid because JG is shorter than GE. Without the diagram, this problem is rather difficult. But given what a centroid is for a triangle, let's see what statements make or do not make sense. Assumptions made for this problem. G is a point within the interior of the triangle HJK. E is a point somewhere on the perimeter of triangle HJK and that a line passing from that point to a vertex of triangle HJK will have point G somewhere on it. Point G cannot be a centroid because JG does not equal GE. * If G was a centroid, then JG would not be equal to GE because if that were the case, you could construct a circle that's both tangent to all sides of the triangle while simultaneously passing through a vertex of the triangle. That's impossible, so this can't be the correct choice. Point G cannot be a centroid because JG is shorter than GE. * This statement would be true. So this is a good possibility as the correct answer assuming the above assumptions are correct. Point G can be a centroid because GE and JG are in the ratio 2:1. * There's no fixed relationship between the lengths of the radius of a circle who's center is at the centroid and the distance from that center to a vertex of the triangle. And in fact, it's highly likely that such a ratio will not even be constant within the same triangle because it will only be constant of the triangle is an equilateral triangle. So this statement is nonsense and therefore a bad choice. Point G can be a centroid because JG + GE = JE. * Assuming that the assumption about point E above is correct, then this relationship would hold true for ANY point E on the side of the triangle that's opposite to vertex J. And only 1 of the infinite possible points is correct for the line JE to pass through the centroid. So this is also an incorrect choice. Since of the 4 available choices, all but one are complete and total nonsense when speaking about a centroid in a triangle, that one has to be the correct answer. So "Point G cannot be a centroid because JG is shorter than GE."

in short terms it's b lol

the greatest wind speed ever recorded on earth's surface is 231 miles per hour. what is the speed in kilometers per hour

Answers

if it is 231 mph it would be 372 km/h

To convert 231 miles per hour to kilometers per hour, multiply by the conversion factor of 1.60934, resulting in approximately 371.76 km/h.

The greatest wind speed ever recorded on Earth's surface is 231 miles per hour (mph). To convert this speed into kilometers per hour (km/h), we use the conversion factor that 1 mile is approximately 1.60934 kilometers. Therefore, the speed in kilometers per hour is given by multiplying the speed in miles per hour by this conversion factor.

Here is the calculation:
231 mph x 1.60934 = 371.75774 km/h.

Approximately, the wind speed would be 371.76 km/h after converting from miles per hour.

Expand the logarithm. log₅ 5x⁻⁵

PLS HELP!

Answers

Recall that logab=loga + logb

log₅5x⁻⁵=log₅5+log₅x⁻⁵=1-5log₅x.

Five more than three times a number q is written as

Answers

5+(3q)= is the answer

Answer:

Step-by-step explanation:

5+(3q) I think

Miranda wants to buy as many collectible dolls as possible, for $2.50 each. If she has $45.00 to spend, how many dolls can she buy?

Which equation BEST represents this situation?
A) 45x = 2.5
B) 2.5x = 45
C) x + 2.5 = 45
D) x + 45 = 2.5

Answers

Answer choice B is the best one

B. 2.5x = 45 because your wanting to buy as many dollars possible with 45 dollars and to do that you would multiply 2.5 by x. For the fun of it I will solve. 45 divided by 2.5 is 18 x = 18

Hope I helped

Brainliest if happy :D

Write the ratio of dogs to cats in simplest form. 12 dogs, 16 cats

Answers

12 dogs, 16 cats = 3 : 4.

Can somebody PLEASE help me on this question, I really need an answer. What are the reasons for a,b,c, and, d?

Answers

Short Answers (Explanation in next section below)

Reason A: Distributive Property

Reason B: Additive Property of Equality

Reason C: Combine like terms

Reason D: Additive Identity Property

----------------------------------------------------------

Further Explanation:

Reason A: The distributive property is the idea where we multiply a number by a block of values inside a parenthesis. In this case we have 3 outside the parenthesis multiplied by the x inside and the -4 inside as well. So 3 times x = 3x and 3 times -4 = -12 indicating that 3*(x-4) = 3*x+3*(-4) = 3x-12. Be sure to multiply the outer 3 by EVERY term inside the parenthesis. Often it is easy to forget a term inside.

Reason B: We are adding 12 to both sides. The goal is to have the -12 go away. Notice in the next line -12+12 = 0 which is effectively canceled out. Adding the same value to both sides is the Additive Property of Equality. It must be done to both sides to balance things out. The general rule is that if a = b, then a+c = b+c. We have added c to both sides.

Reason C: We just do arithmetic here. On the left side -12+12 turns into 0. On the right side 33+12 turns into 45. This is considered "combine like terms" as all of these terms have something in common: they don't have variables attached to them. Which is why they are common or like terms

Reason D: The additive identity property says that adding 0 to anything leads to the same thing as before. For example, adding zero to 5 gets us 5+0 = 5. Nothing has changed, which is what we expect. That's why 3x+0 turns into 3x. At this point, the -12 a few steps prior has been canceled out. In general, the additive identity property is x+0 = x or 0+x = x

Express the complex number -3i in trigonometric form.

Answers

Use the formula z=a+bi=|z|(cosθ+isinθ), with |z|=√(a²+b²), and tanθ=b/a

in this case, a=0, b=-3 so |z|=√0²+(-3)²)=3
tanθ=[tex] \frac{-3}{0} [/tex], notice the denominator is 0, undefined, so the value of θ=π/2
Substitute the values of θ=π/2 and |z|=3. into the formula, you'll get 3(cos([tex] \frac{ \pi }{2} [/tex])+isin([tex] \frac{ \pi }{2} [/tex]))

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2x^2+20x=-38
show work

Answers

2x^2+20x = -38

2x^2 + 20x + 38 = 0

Divide both sides by 2.

x^2 + 10x + 19 = 0

The quadratic formula works very well here.

Let a = 1, b = 10 and c = 19

x = [-b +- sqrt{b^2 - 4ac}]/(2a)

Plug those values into the formula to find two answers for x.

One is negative and the other positive.

Good luck.

Move 38 to the left side of the equation by adding it to both sides.
2x ^2 + 20x + 38 = 0
Use the quadratic formula to find the solutions.
−b±√b^2 − 4 (ac)/2a
Substitute a = 2, b = 20, and c = 38 into the quadratic formula and solve for x.
−20±√20 ^2 − 4⋅(2⋅38)/2⋅2
Simplify. x = −5±√6
The result can be shown in both exact and approximate form.
x = −5±√6
x ≈ −2.55051025, −7.44948974

Someone help with number 11 please!! Thank you

Answers

36 degrees (it's an acute angle)

The sum of the measures of the interior angles of an n-sided polygon is 180(n - 2).

A pentagon has 5 sides, so for a pentagon, the sum of the measures of the interior angles is

180(n - 2) =

= 180 (5 - 2)

= 180 * 3

= 540

Since this pentagon is regular, all interior angles are congruent.
Each one measures 540/5 = 108, or 108 degrees.

The upper 108-degree angle together with the 2 angles marked x form a straight angle.

x + x + 108 = 180

2x + 108 = 180

2x = 72

x = 36

Anna lives 2.5 miles to the east of her school, and Ben lives 2 miles to the west of the same school. Anna draws a map with a number line connecting her house to Ben’s house. On the number line, the school is at 0 and her house is at the point +2.5. On the map, Ben’s house is at the point

Answers

Answer:

Ben's house is at point -2

Step-by-step explanation:

Given that Anna lives 2.5 miles to the east of her school, and Ben lives 2 miles to the west of the same school

When Anna draws a map with a number line connecting her house to Ben’s house, with school marked as 0 then to the east would be +2.5

Since Ben lives 2 miles to the west, Ben would be marked as negative -2.

(West denotes negative in number line)

So answer is Ben's house is at point -2

Ben's house is at the point -2 on the map of number line.

What is Number line?

A number line is pictorially represented as a horizontal straight line where numbers are placed at equal distance. Usually integers are placed in the number line with negative numbers placed to the left of 0 and positive numbers placed to the right of 0.

Number lines are used in performing basic operations in mathematics such as addition, multiplication, subtraction and division.

Here, it is given that Anna lives 2.5 miles to the east of her school and Ben lives 2 miles to the west of the same school.

So school is a common point here with respect to which both of their distance to house are marked.

On the number line school is at 0.

Anna's and Ben's house lies two opposite sides from the school.

So if one of their houses is at the positive side, the house of other one's will be at the negative side.

Given that, Anna's house is at positive side at the point +2.5.

Then clearly Ben's house will be at the negative side and the point will be -2 since it is 2 miles away from the school.

Hence, Ben's house will be at the negative side of the number line at point -2.

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Two radical expressions with the same degree and the same _____ are called like terms.

Answers

Answer:

Two radical expressions with the same degree and the same radicand are called like terms.

Step-by-step explanation:

All the terms that have same power and vari ables are called like terms.

For example: 3x²y and 5x²y are like terms, 2x³ and 7x³ are like terms, etc.

The number under the root is known as radicand.

Two radical expressions are like terms if

1. They have same degree.

2. They have same radicand.

Therefore the two radical expressions with the same degree and the same radicand are called like terms.

Two radical expressions are called like terms if they have the same degree and the same:

E. radicand

Two radical expressions are called like terms if they have the same degree and the same radicand. The radicand is the number or expression inside the radical symbol. For example, in the radical expression [tex]$\sqrt{5}$[/tex], the radicand is 5. For two radical expressions to be like terms, they must not only have the same index (degree) of the radical but also the same radicand.

Consider the expressions [tex]$\sqrt{3}$ and $2\sqrt{3}$[/tex]. These are like terms because they both have the same degree (square root, which is an index of 2) and the same radicand (3). Similarly, [tex]$\sqrt[3]{7}$ and $4\sqrt[3]{7}$[/tex] are like terms because both are cube roots with a radicand of 7.

However, [tex]$\sqrt{2}$ and $\sqrt{3}$[/tex] are not like terms because their radicands differ. Likewise, [tex]$\sqrt[4]{5}$ and $\sqrt{5}$[/tex] are not like terms because their degrees (indices) differ. Therefore, for radical expressions to be like terms, matching radicands and degrees are essential.

The correct question is:

Two radical expressions are called like terms if they have the same degree and the same

A. denominator

B. radical

C. term

D. number

E. radicand

HELP PLEASE!!

Graph the system of linear equations.
-1/2y=1/2x+5 and y=2x+2

The solution to the system is ( _ , _ )

Answers

the correct answer is -4, -6

Multiply (2x2 + 3x − 6)(x − 1).

Answers

2x^3+x^2-9x+6

Distribute

In space, the intersection of a line and a plane is
A) not possible.
B) a point or a line.
C) a line or a plane.
D) a point or a plane.

Answers

i believe the answer is A) Not possible not sure

Solve by completing the square
X^2+12x-13=0

Answers

I order to do this question, you need to put the 13 on the right side. So now you have x^2+12x+0=13. Now, take half of 12, and square it. Add this to both sides to get x^2+12x+36=49. Now factor the left side by putting the half of 12 into this blank to get, (x+_)^2=49. Final Answer is,
(x+6)^2=49.

Final answer:

To solve the quadratic equation x^2 + 12x - 13 = 0 by completing the square, follow these steps. The solutions to the equation are x = 1 or x = -13.

Explanation:

To solve the quadratic equation x^2 + 12x - 13 = 0 by completing the square, follow these steps:

Move the constant term to the other side of the equation:x^2 + 12x = 13Take half of the coefficient of the x-term and square it:(12/2)^2 = 36Add this value to both sides of the equation:x^2 + 12x + 36 = 13 + 36Factor the left side of the equation, which should be a perfect square:(x + 6)^2 = 49Take the square root of both sides and solve for x:x + 6 = ±√49x + 6 = ±7x = -6 ± 7Therefore, the solutions to the equation are x = 1 or x = -13.

Evaluate the numerical expression. 4.2 − 3.5 ÷ 0.7 + 2.4 A) −3.2 B) 1.6 C) 11.6 D) 3.4

Answers

4.2 − 3.5 ÷ 0.7 + 2.4
= 4.2 − 5 + 2.4
= -1.6

answer
- 1.6

4.2 -3.5/0.7+2.4

order of operations, do division first

-3.5/0.7 = -5

now you have:

4.2-5 +2.4

now just add/subtract from left to right

4.2-5 = -0.8 + 2.4 = 1.6

Answer is B

Solve the following equation. Then place the correct number in the box provided. 2x - 1 ≤ x + 5

Answers

Answer:

The solution for the inequality is [tex]x \leq 6[/tex].

Step-by-step explanation:

Consider the provided inequality.

[tex]2x - 1 \leq x + 5[/tex]

Subtract x from both the sides.

[tex]2x -x- 1 \leq x-x + 5[/tex]

[tex]x- 1 \leq 5[/tex]

Add 1 to both the sides.

[tex]x- 1+1 \leq 5+1[/tex]

[tex]x \leq 6[/tex]

Hence the solution for the inequality is [tex]x \leq 6[/tex].

Which are the possible side lengths of a triangle?

A.3 cm, 5 cm, 9 cm
B.4 cm, 8 cm, 10 cm
C.6 cm, 9 cm, 17 cm
D.8 cm, 10 cm, 18 cm

Answers

Final answer:

The possible side lengths of a triangle, according to the Triangle Inequality Theorem, must adhere to the principle that the sum of any two sides must be greater than the third side. Option B, with side lengths of 4 cm, 8 cm, and 10 cm, fulfills this requirement and forms a valid triangle.

Explanation:

The question asks which set of side lengths can form a triangle. In order to determine the possible side lengths of a triangle, we must use the Triangle Inequality Theorem. The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Now, let's evaluate the options provided:

A. 3 cm, 5 cm, 9 cm: Here, 3 + 5 is not greater than 9, so these sides do not satisfy the theorem.

B. 4 cm, 8 cm, 10 cm: In this case, 4 + 8 is greater than 10, 8 + 10 is greater than 4, and 4 + 10 is greater than 8, satisfying the inequality.

C. 6 cm, 9 cm, 17 cm: For these measurements, 6 + 9 is less than 17, failing to meet the criteria.

D. 8 cm, 10 cm, 18 cm: Here too, 8 + 10 is less than 18, thus not compliant.

Hence, the correct answer is B. 4 cm, 8 cm, 10 cm, as these are the only side lengths that satisfy the Triangle Inequality Theorem and can form a triangle.

Tommy is twice as old as his younger sister.The sum of the siblings' ages is 21. Which equation can be used to determine the age of Tommy's younger sister? A. x-2=21 B. x+2x=21 C. 2x=21 or D. x/2=21

Answers

2x+x=21(tommy+his sister is 21)It could be B

C. 2x=21 because he Is 21 and that can solve

What is 7 feet converted to miles?

Answers

Answer:

Step-by-step explanation:

Use the factor-label method you learned in chemistry (also known as dimensional analysis), keeping in mind 2 things:

the label you want needs to be on the top of the equivalent ratio, and

that there are 5280 feet in 1 mile. Having said that:

[tex]7feet*\frac{1mile}{5280 feet}=[/tex]

The math tells us to divide 7 by 5280. That means that

7 feet = .0013257576 miles, to however many decimal places you need. That 7575 is repeating, btw.

Question 14 a certain drug is made from only two ingredients: compound a and compound
b. there are 3 milliliters of compound a used for every 4 milliliters of compound
b. if a chemist wants to make 497 milliliters of the drug, how many milliliters of compound b are needed?

Answers

A drug is made from a compound A and a compound B:
A : B = 3 : 4
A = 3 k
B = 4 k
3 k + 4 k = 7 k
7 k = 497 ml
k = 497 ml : 7 = 71 ml
B = 4 * 71 ml
B = 284 ml.
Answer: 284 ml of compound B are needed.

The number of State Parks in California is 36 more than one third the number of State Parks in Florida. There are 85 State Parks in California. Which of the following equations would you use to find the number of State Parks in Florida? Note: f represents the number of state parks in Florida. 3(f − 36) = 85 1 over 3f + 36 = 85 Quantity f minus 36 all over 3 equals 85 Quantity f plus 36 all over 3 equals 85 Question 3(Mu

Answers

c = 1/3f + 36
c = 85

1/3f + 36 = 85 <===

At day camp, hiking began at 8:30 a.m. and lasted 2 hours and 42 minutes. What time did hiking end? A. 9:02 a.m. B. 10:12 a.m. C. 11:12 a.m. D. 12:02 p.m.
Plz help ppl

Answers

The correct answer is B. 10:12

Solve the inequality
5x < 16 + x.

A.) x < 1/4
B.) x > 1/4
C.) x < 4
D.) x > 4

Answers

C: is you Answer x<4

4x>16
x>4
Correct answer is D

In which number is the digit 8 ten times larger than it is in the number 18? A) 108 B) 387 C) 801 D) 1,840 E) 8,205

Answers

B. is the correct answer as 387 contains 80 and 8 * 10 = 80. I hope this helps!!

umm D I'm pretty shure

Which angle in triangle XYZ has the largest measure?

Answers

Answer:

A. [tex]\angle x[/tex]

Step-by-step explanation:

We have been given measure of three sides of a triangle. We are asked to determine, which angle has the largest measure.

We know that the side of triangle corresponds to its opposite angle. The angle opposite to smallest side will have smallest measure and angle opposite to largest side will have largest measure.

We can see that the measure of largest side of our given triangle is 9 and it is opposite to angle x, therefore, [tex]\angle x[/tex] has the largest measure and option A is the correct choice.

What is 16% of 43 minutes

Answers

6.88 i hope this helps u

Answer:

16% of 43 minutes are 6.8 minutes.

Step-by-step explanation:

To know the percentage of a quantity first you should divide the percentage by a hundred, then you should multiply the quantities, as follows.

1. Calculate the percentage:

[tex]\frac{16}{100}=0.16[/tex]

2. Multiply the percentage by the quantity:

[tex]0.16*43=6.88[/tex]

Therefore 16% of 43 minutes are 6.8 minutes.

find the center and radius for the circle, given the equation: x2+16x+y2-6y=-24

Answers

Hello,

[tex]x^2+16x+y^2-6y=-24\\\\ x^2+2*8*x+64+y^2-2*3*y+9-64-9=-24\\\\ (x+8)^2+(y-3)^2=49\\\\ [/tex]
Center=(-8,3), radius=7

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