Use the following diagram for questions 21-24 in which G is the centroid of AABC, FC=35, AG=42, BF=57, and
DG=14.
Find AC
Find BG
Find GC
Find AE
​

1 + 2i in polar form is 5√2∠63.4°.

What is a polar form ?

In mathematics, the polar form is a way of representing complex numbers using their magnitude and angle. A complex number can be represented in the form r(cos θ + i sin θ), where r is the magnitude (or modulus) of the complex number, and θ is its argument (or phase angle). Alternatively, the polar form can be represented in terms of magnitude and angle as r ∠θ, where r is the magnitude and θ is the angle in radians. This form is also known as the exponential form of a complex number. The polar form is useful in calculations involving complex numbers, especially in multiplication and division, where it is often easier to work with the polar form rather than the rectangular form (a + bi).

D. 5√2∠63.4°

To convert a complex number from rectangular form to polar form, we use the following formulas:

r = √(a^2 + b^2)

θ = tan^-1 (b/a)

Where a and b are the real and imaginary parts of the complex number, respectively.

In this case, a = 1 and b = 2, so:

r = √(1^2 + 2^2) = √5

θ = tan^-1 (2/1) = 63.4°

Therefore, 1 + 2i in polar form is 5√2∠63.4°.

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The probability that the participant either is a teen or prefers country music is given as follows:

P(C or T) = 0.55.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The desired outcomes for this problem are given as follows:

There were 520 people in the research, hence the probability that the participant either is a teen or prefers country music is given as follows:

P(C or T) = (170 + 114)/520

P(C or T) = 0.55.

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Answer:

1. is 10

2. is 4

3. is 2

?= is 2

Answer:

45

Step-by-step explanation:

translation :

140% of x = $63

x = $63 ÷ 1.4

x = $45

FUN FACTS :

interesting: 100% means double that number or times 2

if a price is $20 & it increases 100% in price that means its $20 times 2 or $40

percent means per 100

cent means 100 in latin

that's why the decimal moves 2 spaces

for the 2 zeros in 100

chatgpt

Answer:

trust yourself cuh

Step-by-step explanation:

Ava walks 2.5 feet in one second.

Ava walks 5 feet in 2 seconds, which means that the ratio of feet to seconds is 5 to 2.

We will use proportionality  concept , to find out how many feet Ava walks in one second,

Let x be the number of feet Ava walks in one second. Then we can set up the proportion:

5 feet / 2 seconds = x feet / 1 second

solving for x, we can cross-multiply:

5 feet * 1 second = 2 seconds * x feet

Simplifying, we get:

5 feet = 2x feet

Dividing both sides by 2, we get:

x  =   2.5 feet

In conclusion, Ava walks 2.5 feet in one second.

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Complete question:

. Ava is walking at a constant speed where for every 5 feet it takes 2 seconds. So, the ratio of feet to seconds is 5 to 2.

(c) How many feet does Ava walk in one second?

Answer:

7.2

Step-by-step explanation:

The 1 looks at the number to the right of it. If the number to the right is 5 or more, the 1 moves up to a 2. Hope this  helps!

Answer:

Assuming a vertical number line:

- Plot the point at 7/10 above the origin, between 0 and 1.

- Plot the opposite of 7/10 by reflecting it across the origin to the point at -7/10 below the origin, between 0 and -1.

- Label the point at 7/10 as "7/10" and the point at -7/10 as "-7/10".

The number line would look like this:

1

|

|

|

|

| 7/10

|

|

|

|

0

|

|

|

|

|

| -7/10

|

|

|

|

-1

The true statements are:

(B) Both figures are congurent.

(C) The two figures have the same orientation but different positions.

(E) Corresponding angles and sides have the same measures.

In geometry, how an item is positioned in the space it occupies—such as a line, plane, or rigid body—is described in terms of its orientation, angular position, attitude, bearing, and direction.

It refers more particularly to the fictitious rotation required to shift an object from a reference placement to its present location.

To get to the current positioning, a rotation might not be sufficient.

It could be required to include a fictitious translation known as the object's location (or position, or linear position).

Together, the position and orientation completely explain where the object is situated in space.

Therefore, the true statements are:

(B) Both figures are congurent.

(C) The two figures have the same orientation but different positions.

(E) Corresponding angles and sides have the same measures.

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Consequently, the circle's diameter is 28π√3.

The radius of a circular or other curved geometry form refers to its length. It is the border across any two-dimensional circle surface measured linearly in one dimension.

Since the circle is divided into six equal pieces, the shaded region represents one-sixth of the total area of the circle. Therefore, the total area of the circle can be found by multiplying the shaded area by 6:

Total area of circle = 6 × 98π = 588π

The formula for the area of a circle is A = πr², where r is the radius of the circle. Solving for r, we get:

r² = A / π = 588π / π = 588

r = √588 = 2√147 = 2√3 × √49 = 14√3

C = 2r is the method for calculating a circle's diameter. Plugging in the value of r, we get:

C = 2π(14√3) = 28π√3

Therefore, the circumference of the circle is 28π√3.

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the expression describing all the angles that are coterminal with 8° is: θ = 8° + 360°k, where k is an integer.

How to solve and what is angle?

An angle of 8° has an initial side on the positive x-axis and rotates counterclockwise by 8°.

Any angle coterminal with 8° can be expressed as:

θ = 8° + 360°k

where k is an integer.

Therefore, the expression describing all the angles that are coterminal with 8° is:

θ = 8° + 360°k, where k is an integer.

An angle is a geometric figure formed by two rays, called the sides of the angle, that share a common endpoint, called the vertex of the angle. Angles are typically measured in degrees or radians and are used to measure the amount of rotation or turn between two intersecting lines or planes.

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The supplementary angle will be 60°.

What are supplementary angles?

Supplementary angles are angles (only two) whose sum is equal to 180 degrees. In other words, if we add two angles together and the result is 180 degrees, those angles are considered supplementary.

For example, if we have angle A that measures 60 degrees, its supplement angle B will measure 120 degrees (180 - 60 = 120). Angles A and B are supplementary angles.

Supplementary angles can be adjacent, meaning they share a common vertex and side, or they can be non-adjacent. In either case, their sum will always be 180 degrees.

Supplementary angles are commonly used in geometry and trigonometry to solve problems related to angles and triangles.

Now,

Let x = measure of the angle.

Then, the supplement angle is 180 - x.

According to the problem, x is twice less than the supplement angle. In other words, the supplement angle is twice greater than x. We can write this as:

180 - x = 2x

Solving for x, we get:

180 = 3x

x = 60

Therefore, the angle measures 60 degrees.

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Right Question:- The measure of an angle is twice less than that of its supplement angle. find that angle?

The interest rate paid by Scott is 4.25% for the 72 months.

We can determine the simple interest of the given problem by the simple interest formula which is given as :

I=PRT

Where,

I=Interest

P=principal

R=rate in decimal

T=time in years

Converting the given 72 months into years we get time t :

1 year = 12months

72 months / 12months = 6 years

t=6

From the given data

I=8925

P=35000

R=r

T=6

Substituting the above values in the simple interest equation we get:

8925 = 35000*r*6

8925 = 210000*r

divide both sides by 210000

R = 0.0425

Therefore, the interest rate is 4.25%

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The number of bags that had exactly 27 orange candies is given as follows:

Zero.

A stem and leaf plot is a type of data visualization that displays numerical data in a way that shows the distribution of the data while also preserving the individual data points. It is particularly useful for small to medium-sized data sets.

In a stem and leaf plot, the digits in each data point are split into two parts: the stem and the leaf. The stem is usually the leftmost digits of the number, while the leaf is the rightmost digit. The stems are listed in a column from top to bottom, and each leaf is listed next to its corresponding stem. The resulting plot looks like a table with two columns, where the first column shows the stems and the second column shows the leaves.

From the plot given at the end of the answer, the measures are given as follows:

20, 22, 22, 22, 32, 33, 37, 37, 39, ..., 59.

As the number 27 does not show up in the data-set, there were zero bags with exactly 27 candies.

The plot is given by the image presented at the end of the answer.

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To find the height of the tent, we need to use trigonometry. Let's draw a diagram to help visualize the problem

           /|\

          / | \

      h /  |  \ h

        /   |   \

       /    |    \

      /     |     \

     /      |      \

    /_  _|_ __\

       b   81.5   b

We can see that the height of the tent (h) forms one leg of a right triangle, with the base (b) being half of one of the equal sides of the isosceles triangle. We can use the angle at the peak of the tent (103 degrees) to find the height using the tangent function:

tan(103) = h/b

To find b, we can use the fact that the equal sides of the isosceles triangle are 163 cm long, so b = 163/2 = 81.5 cm.

Now we can plug in b and the angle measure into the tangent equation and solve for h:

tan(103) = h/81.5

h = 81.5 * tan(103)

h ≈ 370.5 cm

Therefore, the height of the tent is approximately 370.5 cm or 371 cm to the nearest centimeter.

All corresponding side lengths have a ratio of [tex]\frac{1}{3}$[/tex] or less, we can conclude that the scale factor of the dilation is less than or equal to [tex]\frac{1}{3}$[/tex]

We can use the distance formula to find the length of the sides of both quadrilaterals, and then find the ratio of corresponding side lengths to determine the scale factor of the dilation.

Let's start with the original quadrilateral ABCD. The length of AB is:

[tex]$\sqrt{(9 - (-3))^2 + (3 - 0)^2} = \sqrt{12^2 + 3^2} = \sqrt{153}$[/tex]

Similarly, the lengths of BC, CD, and DA are:

[tex]BC: $\sqrt{(9 - 9)^2 + (9 - 3)^2} = 6$[/tex]

[tex]CD: $\sqrt{(-3 - 9)^2 + (3 - 9)^2} = \sqrt{144 + 36} = \sqrt{180} = 6\sqrt{5}$[/tex]

[tex]DA: $\sqrt{(-3 - (-3))^2 + (3 - 0)^2} = 3$[/tex]

Now, let's find the corresponding side lengths of the dilated quadrilateral A'B'C'D'. The length of A'B' is:

[tex]$\sqrt{(3 - (-1))^2 + (1 - 0)^2} = \sqrt{16 + 1} = \sqrt{17}$[/tex]

Similarly, the lengths of B'C', C'D', and D'A' are:

[tex]B'C': $\sqrt{(3 - 3)^2 + (3 - 1)^2} = 2$[/tex]

[tex]C'D': $\sqrt{(-1 - 3)^2 + (1 - 3)^2} = \sqrt{16 + 4} = \sqrt{20} = 2\sqrt{5}$[/tex]

[tex]D'A': $\sqrt{(-1 - (-3))^2 + (1 - 0)^2} = \sqrt{4 + 1} = \sqrt{5}$[/tex]

Now we can find the ratio of corresponding side lengths:

[tex]$\frac{\text{length of A'B'}}{\text{length of AB}} = \frac{\sqrt{17}}{\sqrt{153}} = \frac{\sqrt{17} \cdot \sqrt{153}}{153} \approx 0.821$[/tex]

[tex]$\frac{\text{length of B'C'}}{\text{length of BC}} = \frac{2}{6} = \frac{1}{3}$[/tex]

[tex]$\frac{\text{length of C'D'}}{\text{length of CD}} = \frac{2\sqrt{5}}{6\sqrt{5}} = \frac{1}{3}$[/tex]

[tex]$\frac{\text{length of D'A'}}{\text{length of DA}} = \frac{\sqrt{5}}{3}$[/tex]

Since all corresponding side lengths have a ratio of [tex]\frac{1}{3}$[/tex] or less, we can conclude that the scale factor of the dilation is less than or equal to [tex]\frac{1}{3}$[/tex]. To find the exact scale factor, we can choose any two corresponding side lengths and take their ratio.

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Answer:

15 miles

Step-by-step explanation:

7 miles from game store to school plus another 8 miles from school to skate park equal 15.

The total amount of money you will pay back when borrowing $1,000 for 4 years at an annual interest rate of 8% with annual compounding is $1,360.50.

The interest you receive is referred to as compound interest. Using simple math, you can see how this works: if you have $100 and it generates 5% interest annually, you will have $105 at the end of the first year.

A = P*(1 + r/n)[tex]^(^n^*^t^)[/tex]

A is the total amount

P is the principal (initial amount borrowed), which is $1,000 in this case

r is the annual interest rate expressed as a decimal, which is 0.08 (8%)

n is the number of times the interest is compounded per year, which is usually 12 (monthly compounding) or 1 (annual compounding)

t is the time in years, which is 4 in this case

Assuming that the interest is compounded annually (n=1), we can plug in the values and simplify:

A = 1000*(1 + 0.08/1)¹⁴

= 1000(1.08)⁴

= 1000*1.3605

= $1,360.50

the total amount of money you will pay back when borrowing $1,000 for 4 years at an annual interest rate of 8% with annual compounding is $1,360.50.

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The answer of the question based on probability of the representing all the possible combinations of the different cups based on size and color the list is given below,

In probability theory, event is  set of possible outcomes or results of an experiment or situation. For example, rolling a six-sided die and getting even number is  event, as it consists of set of possible outcomes {2, 4, 6}.

Events can also be mutually exclusive or independent. Two events are mutually exclusive if they cannot occur at  same time, like rolling a 1 and rolling a 2 on a die.

Events can be simple or compound. A simple event consists of single outcome, like rolling particular number on a die, while  compound event consists of more than one outcome, like rolling an even number or rolling  number greater than 4 on a die.

Here is a list of all possible combinations of the different cups based on size and color:

Small, Red (S,R)

Small, White (S,W)

Small, Blue (S,B)

Medium, Red (M,R)

Medium, White (M,W)

Medium, Blue (M,B)

Large, Red (L,R)

Large, White (L,W)

Large, Blue (L,B)

There are a total of 9 possible combinations of cup size and color.

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The probability that Angela gets to go to the meeting is 2/5 or 0.4.

What is probability?

There are a total of 5 people in the club, and they need to pick 2 people to go to the meeting. The number of ways to pick 2 people out of 5 is given by the binomial coefficient:

C(5,2) = 5! / (2! (5-2)!) = 10

This means there are 10 equally likely outcomes, which can be represented by the following probability model:

Outcome            Angela goes to meeting?                 Probability

A,B                                    Yes                                              1/10

A,C                                    Yes                                              1/10

A,D                                    Yes                                              1/10

A,E                                     Yes                                              1/10

B,C                                      No                                              1/10

B,D                                      No                                              1/10

B,E                                       No                                              1/10

C,D                                      No                                               1/10

C,E                                       No                                               1/10

D,E                                       No                                               1/10

The probability that Angela gets to go to the meeting is the sum of the probabilities of the outcomes where Angela goes to the meeting:

P(Angela goes to meeting) = P(A,B) + P(A,C) + P(A,D) + P(A,E)

= 1/10 + 1/10 + 1/10 + 1/10

= 4/10

= 2/5

Therefore, the probability that Angela gets to go to the meeting is 2/5 or 0.4.

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Step-by-step explanation:

FV = PV ( 1 + i)^n     FV = future value ....what you are looking for

                                  PV = present value = $ 6000

                                    i = decimal periodic interest = .07/12

                                        n = periods = 5 yr * 12 monts/yr = 60 periods

FV = $ 6000 ( 1 + .07/12)^60 = $  8505.75

Answer:

The area of a sector can be calculated using the formula:

A = (θ/360)πr^2

where θ is the central angle measure in degrees, r is the radius, and π is the mathematical constant pi.

Substituting the given values, we get:

A = (15/360)π(11)^2

≈ 16.2 ft^2

Rounding this to the nearest tenth gives:

A ≈ 15.8 ft^2

Therefore, the area of the sector rounded to the nearest tenth is 15.8 ft^2.

Step-by-step explanation:

hope its help <:

Answer: 14x(x−3)

Step-by-step explanation:

Answer:

7/36

Step-by-step explanation:

It is given that we have two dice numbered from 1 to 6 . The maximum sum that can be obtained by rolling two dice is 6+6 = 12 and the minimum sum that can be obtained by rolling is 1+1 = 2 .

Now between 2 and 12 , the numbers which are perfect square are 4 and 9 .

Getting a sum of 4 :-

We can get a sum of four from two dice as ,

Getting a sum of 9 :-

So there are a total of 7 possibilities by which we can can get a perfect square number by rolling two dices .

Now total number of possible outcomes = 6*6 = 36 .

Henceforth the required probability would be ,

[tex]\rm\implies P( getting \ a \ square\ number) =\dfrac{Total \ number\ of \ favourable\ outcomes}{Total \ number \ of \ possible \ outcomes} [/tex]

[tex]\rm\implies \underline{\underline{\red{ P( getting \ a \ square\ number)=\dfrac{7}{36}}}}[/tex]

Hence the required probability is 7/36 .

The probability of getting a square number as the sum is therefore 7/36.

WHAT IS PROBABILITY ?

Probability is a branch of mathematics that deals with the study of random events or phenomena. It involves analyzing the likelihood of an event occurring, given the conditions or circumstances that surround it. Probability is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. The probability of an event is determined by dividing the number of favorable outcomes by the total number of possible outcomes. Probability is widely used in many fields, including statistics, physics, finance, engineering, and social sciences, to name a few.

There are 36 possible outcomes when two dice are thrown since each die has 6 possible outcomes.

Let's find the possible outcomes where the sum of the numbers on the dice is a square number. The only possible sums that are squares are 4, 9 and 16.

To get a sum of 4, the dice must land on 1 and 3 or 3 and 1. There are two possible ways of doing this, so there are 2 outcomes.

To get a sum of 9, the dice must land on 3 and 6, 4 and 5, 5 and 4, or 6 and 3. There are four possible ways of doing this, so there are 4 outcomes.

To get a sum of 16, the dice must both land on 6. There is only one possible way of doing this, so there is 1 outcome.

Therefore, there are 2 + 4 + 1 = 7 outcomes where the sum of the numbers on the dice is a square number.

The probability of getting a square number as the sum is therefore 7/36.

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Answer:

variable measurement

Step-by-step explanation:

The type of measurement you are referring to is called "variable measurement". In variable measurement, the quantity being measured can vary from one observation to another. This means that the measurement is not consistent or fixed, and can change each time it is taken. An example of variable measurement is measuring the weight of a person over time, as their weight can change from one day to another. Another example is measuring the temperature in a room throughout the day, as the temperature can fluctuate based on factors such as sunlight, air conditioning, and human activity.

Answer:

Step-by-step explanation:

To find the total distance traveled in the first second, we need to find the distance traveled during the first half-second and then double it.

The particle starts 2 cm to the right of 0, so its position function is given by:

s(t) = t - t^2 + 2

The distance traveled by the particle during the first half-second (from t = 0 to t = 0.5) is given by:

distance = |s(0.5) - s(0)|

We have:

s(0.5) = 0.5 - (0.5)^2 + 2 = 2.25 cm

s(0) = 0 - 0^2 + 2 = 2 cm

So, the distance traveled during the first half-second is:

|2.25 - 2| = 0.25 cm

To find the total distance traveled in the first second, we double this distance:

total distance = 2 * 0.25 = 0.5 cm

Therefore, the total distance traveled in the first second is 0.5 cm.

Step-by-step explanation:

For x;

[tex]{ \tt{ \tan( \theta) = \frac{opposite}{adjacent} }} \\ \\ { \tt{ \tan( 60 \degree) = \frac{x}{5} }} \\ \\ { \tt{x = 5 \tan(60 \degree) }} \\ \\ { \tt{x = 5 \sqrt{3} }}[/tex]

For y;

[tex] { \tt{\cos( \theta) = \frac{adjacent}{hypotenuse} }} \\ \\ { \tt{cos(60 \degree) = \frac{5}{y} }} \\ \\ { \tt{y = 5 \cos(60 \degree) }} \\ \\ { \tt{y = 2.5}}[/tex]