4. (a) Determine the sum of the interior angles of a dodecagon (12-sided polygon). Show your
work.
(b) Determine the sum of the exterior angles.

Answer:

15

Step-by-step explanation:

a = 3d

Let d=5

a = 3*5

a = 15

The length L of the base of a rectangle is 5 less than twice its height H. Then the algebraic expression be, area of rectangle = 2H² - 5H.

Let, the given information be "The length L of the base of a rectangle is 5 less than twice its height H".

L be the length of the rectangle

H be the height of the rectangle

By converting the given information into an algebraic expression, we get

Length = 2H - 5

The area of a rectangle is given by the formula;

Area of rectangle = L [tex]*[/tex] H

Where L is the Length.

H is the Height.

Substituting the values into the formula, we have;

Area of rectangle = (2H - 5) [tex]*[/tex] H

Area of rectangle = 2H² - 5H

Therefore, the area of rectangle = 2H² - 5H.

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Answer:

last option is correct 3/2

Answer:

x = 3/2

Step-by-step explanation:

9^x = 729 ^ 1/2

We need to get the bases the same

729 = 9^3

9^x = 9^3 ^ 1/2

We know that a^b^c = a^(b*c)

9^x = 9^3/2

Since the bases are the same, the exponents are the same

x = 3/2

Answer:

Step-by-step explanation:

you can use the rise over run technique, where you count how many units you go down or up, left or right to get to the next point. or use the slope formula :

(y2-y1)/(x2-x1)

the pairs given :

(1,6) and (3,2)

(2-6)/(3-1) = -4/2 = -2

-2 is the slope. the line is going downwards so there is a negative slope

1. 2

2. The Y axis

3. 3 rights and 1 down (3, -1)

Answer:

y=-176/x

y=176/9

Step-by-step explanation:

[tex]y = \frac{k}{x} \\ - 11 = \frac{k}{16} \\ k = - 176 \\ y = \frac{ - 176}{x} \\ y = \frac{ -176}{ -9} = 19 \frac{5}{9} [/tex]

Answer:

A) 89 personas prefieren ver sólo deportes.

B) 122 personas prefieren ver sólo un programa de televisión

C) 33 personas prefieren ver películas o musicales.

Step-by-step explanation:

Dado que una empresa realizó una encuesta a 250 personas para saber qué programa de televisión prefieren ver en domingo, y se les dieron 3 opciones: deportes, películas o musicales, donde el resultado de la encuesta fue: 130 personas prefieren deportes; 80 prefieren ver películas; 40, musicales; 25 prefieren deportes y películas; 20, películas y musicales; 10, deportes y musicales; y sólo a 6 personas les gustan los tres tipos de programas; para determinar A) cuántas prefieren ver sólo deportes, B) cuántas prefieren ver sólo un programa de televisión; y C) cuántas prefieren ver películas o musicales, se deben realizar los siguientes cálculos:

A)

130 - 25 - 10 - 6 = 89

B)

80 - 25 - 20 - 6 = 29

40 - 20 - 10 - 6 = 4

89 + 29 + 4 = 122

C)

29 + 4 = 33

Answer:

hi hi hi hi hi

Step-by-step explanation:

plz follow me

The third and last law tells us that when we have to multiply a power in a bracket, by another power outside the bracket, we have to multiply the two powers together to get the answer.

Answer:

84%

Step-by-step explanation:

I'm not sure how I got that answer but I'm just smart like that. I'm sorry I couldn't give a better explanation. I'm in a bit of a rush but I hope this answer is helpful to you. Percentage was the only way I could think of. Sorry again.

The difference between  CDs sold between 1993 and 2001 will be 76.7 × 10⁵.

To subtract in mathematics is to take something away from a group or a number of objects.

In another meaning subtraction is a mathematical operation such that two values are going to subtract and give a resultant value.

The group's total number of items decreases or becomes lower when we subtract from it.

Given that sell of CDs in 1993 is 2.3 × 10⁶.

Sell of CDs in 2001 is 7.9 × 10⁷.

The difference between sell is = 7.9 × 10⁷ - 2.3 × 10⁶

⇒ 76.7 × 10⁵ hence it will the correct option.

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9514 1404 393

Answer:

Step-by-step explanation:

1. All of the x-values are unique, so the relation is a function. The statement is False.

__

2. It is true that integer values of x in the interval 3 ≤ x ≤ 8 are the domain of the function. However, the inequality does not limit values of x to being integers. x=3.5 satisfies the inequality, but is not in the domain. The statement is False.

__

3. The range of the function is the set of y-values. The statement is True.

Answer:

(2b - 5) + b + (b + 80) = 983

Step-by-step explanation:

Given that,

Total score of three teams = 983

Since the teams' scores are given in reference to team B's score, let 'b' be the score of team B.

So,

The scores of Team A = (2 * b) - 5

The scores of Team B = b

The scores of Team C = (b + 80)

Thus,

The equation for determining the total points of Team B would be:

(2b - 5) + b + (b + 80) = 983

On solving,

(2b - 5) + b + (b + 80) = 983

⇒ 2b + b + b = 983 + 5 - 80

⇒ 4b = 908

⇒ b = 908 ÷ 4

⇒ b = 227

Team B's score = 227

Team A's score = (2 * 227 - 5)

= 449

Team C's score = 227 + 80

= 307

Total ⇒ 449 + 227 + 307 = 983

Hence proved.

Answer:

36n = 360

Step-by-step explanation:

A dozen is 12

3 dozen is 3*12 = 36

36 * n boxes = 360

36n = 360

2+3=5cm

Step-by-step explanation:

2 and 3 would have to be added together to get the radius of the circle, resulting in the answer being 5. 2+3=5cm that's your answer

The equation of circle with center (h,k) and radius r units is

(x -  h)^2 + (y - k)^2 = r^2

The equation of the circle with center (2,3) and radius 5 cm is

= (x - 2)^2  + (y - 3)^2 = 5^2

= x^2  -  4x + 4 + y^2 - 6y + 9 = 25

= x^2 + y^2 - 4x - 6y - 12 =0

hope it helps and is right

Answer:

Y=-2x-5

Step-by-step explanation:

Y=Mx + b where m is the slope and b is the y intercept

y=-2x-5

brainliest is appreciated

Answer:

[tex]0.12x+0.2y=14,\:x+y=100\quad :\quad x=75,\:y=25[/tex]

Step-by-step explanation:

.12x + .2y = 14

x + y = 100

Answer:

Its B

Step-by-step explanation:

Answer:

30°

Step-by-step explanation:

As the chord has same length of radius, the chord and the two radius form a equilateral triangle. Each angle of triangle is 60.So the chord subtended  at the center is 60. So the angle subtended at the remaining part of the circle = 30°

The measure of angle between the tangent and chord = 30  {Alternate segment theorem}

Answer:

Step-by-step explanation:

I posted a picture at the bottom of the post that you need to look at in order to understand this problem. I labeled everything inside that circle and then created a triangle. That triangle is made up of 3 sides that are all the same length, and that length is the length of the radius. By definition, if a triangle has all 3 of its sides the same length, it is equilateral. It is also equiangular. That means that every angle inside that triangle measures 60 degrees. The central angle, the one that comes off the center, intercepts an arc. The arc measure is the same measure as this angle, so the intercepted arc measures 60 degrees. To find the measure of the angle in question, the one you need that is labeled with a pink θ, has a rule that says the angle is going to be half the measure of the intercepted arc. That means that your angle is going to measure 30 degrees.

Answer:

She used 11 charms.

Step-by-step explanation:

25-14=11

22-11=11

Answer: She used 11 charms.

Step-by-step explanation:

The equation to find the answer is 22-C+14=25. You would minus 14 from both sides, leaving you with 22-C=11. 22-11=11, so your answer is 11 charms. Hope this helped!

Answer:

A

Step-by-step explanation:

Given 60% of students passed , then 40% of students failed.

60% = 180 ( divide both sides by 60 )

1% = 3

Then

40% = 40 × 3 = 120

120 students failed the exam

If the number of students that passed was 180, the number of students who failed the examination is 120. So, correct option is A.

To determine the number of students who failed the examination, we need to find 40% of the total number of students.

We are given that 40% of the students failed, which means that 60% of the students passed. Since we know that the number of students who passed is 180, we can set up the following equation:

60% of total students = 180

To solve for the total number of students, we divide both sides of the equation by 60% (or 0.6):

Total students = 180 / 0.6

Calculating the right-hand side of the equation, we get:

Total students = 300

Therefore, the total number of students is 300.

To find the number of students who failed, we multiply the total number of students by the percentage who failed:

Number of students who failed = 300 * 40% = 120

Hence, option A, 120, is the correct answer.

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3/4 is equivalent to 75%.

To find the percentage of a fraction, you simply just divide the numerator by the denominator. 3/4=0.75, which is 75%.

Answer:

75%....3/4 expressed as a percentage is just multiplying 3/4 and 100

Answer:

If it's hard to add together, I think you should get a calculator

One example of a measurement that requires high precision or a low level of uncertainty is the length of a silicon microchip. In the field of electronics manufacturing, even small variations in the length of a microchip can have significant impacts on its performance.

Therefore, it is essential to measure the length of a microchip with high precision, such as down to the nanometer scale, to ensure its functionality and reliability.

On the other hand, an example of a measurement that can have lower precision or a higher level of uncertainty is the temperature of a room. While temperature control is crucial in certain environments, such as a laboratory or a data center, in most cases, a general estimate of the temperature is sufficient.

A variation of a few degrees Celsius is unlikely to cause significant problems, making it unnecessary to measure the temperature with high precision.

The level of precision required for a measurement depends on the nature of the object being measured and the context in which the measurement is taken. In the case of the microchip, the manufacturing process is highly precise, and even small variations can lead to significant problems.

Therefore, it is essential to measure the length of the microchip with high precision. On the other hand, in the case of room temperature, the impact of small variations is usually insignificant, so a lower level of precision is acceptable. Overall, the precision required for a measurement depends on the importance of the measurement's accuracy and the potential consequences of imprecision.

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Answer:

B ((2.-1), (5,3), (8, 7). (11.11 )}

Step-by-step explanation:

Linear function:

The rate of change is always the same.

Item a:

x = 2 to x = 5 -> y = 1 to y = 3. Rate of change of 2/3.

x = 5 to x = 6 -> y = 3 to y = 7. Rate of change of 4.

Different rates of change, so not linear.

Item b:

We can look that for each point, when x changes by 3, y changes by 4, so the rate of change is the same and this set of points represents a linear function, and the answer is option b.

Answer:

I think is the third one but if Im wrong ignore me

[tex]\theta=225°,315°[/tex]

Answer:

Solution given:

[tex]3 tan \theta+2 =-1[/tex]

keeping constant term on one side

[tex]3Tan\theta=-1-2[/tex]

[tex]Tan\theta=-3/3[/tex]

[tex]Tan\theta =-1[/tex]

Since tan is negative in third and fourth quadrant.

[tex]Tan\theta=Tan(180+45),Tan(360-45)[/tex]

[tex]\theta=225°,315°[/tex]

Answer:

AB = 2√137

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Trigonometry

[Right Triangles Only] Pythagorean Theorem: a² + b² = c²

Step-by-step explanation:

Step 1: Define

Identify variables

a = 22 cm

b = 8 cm

Step 2: Solve for c

Answer:

AB= 2√137 cm

Step-by-step explanation:

because we have a right triangle we apply the Pythagorean theorem

hypothenuse² = side² + side²

AB² = BC² + AC², substitute the given sides BC=8 and AC=22

AB² = 8² + 22² , square the numbers and apply the square root to both side

AB = √(64 + 484), add the numbers

AB = √548, simplify the square root

AB= 2√137 cm

Answer:

x=10

Step-by-step explanation:

Answer:

One solution

Step-by-step explanation:

Hi there!

We are given this system of equations:

5x+6y=1

-5x-8y=2

And we want to see how many solutions the equation has.

Let's solve the system in order to see how many solutions it has

Let's solve this system by elimination, where we will clear one variable by adding or subtracting the equations, solve for the other variable which wasn't cleared, and then use the value of the un-cleared variable to find the value of the variable we cleared earlier.

In order to clear a variable, the coefficients in front of those variables need to be opposites of each other (ex. if we wanted to clear y, the coefficients in front of y need to be -2 and 2 respectively). In this case, the coefficients in front of x are 5 and -5, so we can immediately add the equations

Add both equations together

-2y=3

Divide both sides by -2

y=-3/2

Now substitute -3/2 as y in either one of the equations to solve for x

If we were to do it in 5x+6y=1 for instance:

5x+6(-3/2)=1

multiply

5x-9=1

add 9 to both sides

5x=10

divide both sides by 5

x=2

So we solved the system and got x=2, y=-3/2 (or as a point, (2, -3/2)). This is the point of intersection of the two equations (in case you didn't notice, the equations are actually linear equations written in standard form). This is the ONLY point at which the lines will intersect.

Therefore, the system has one solution.

Hope this helps!

Answer:

[tex]P(B|A)=\frac{2}{7}[/tex]

Step-by-step explanation:

The probability of [tex]P(B|A)[/tex] can be read as the probability of event B occurring given event A. In this question, event A occurs when the chosen player is a girl. There are 7 girls on the soccer team. Event B occurs when the chose player plays defense. Since [tex]P(B|A)[/tex] stipulates that event A already occurred, we want the probability of choosing a player who prefers defense from the 7 girls. There are 2 girls who prefer defense, hence [tex]P(B|A)=\boxed{\frac{2}{7}}[/tex].

Alternative:

For dependent events [tex]A[/tex] and [tex]B[/tex], the conditional probability of event B occurring given A is given by:

[tex]P(B|A)=P(B\cap A)\div P(A)[/tex]

[tex]P(B\cap A)[/tex] indicates the intersection of [tex]P(B)[/tex] and [tex]P(A)[/tex]. In this case, it is the probability that both events occur. Since there are 16 kids on the soccer team and only 2 are girls and prefer defense, [tex]P(B\cap A)=\frac{2}{16}=\frac{1}{8}[/tex]. The probability of event A occurring (chosen player is a girl) is equal to the number of girls (7) divided by the number of kids on the team (16), hence [tex]P(A)=\frac{7}{16}[/tex].

Therefore, the probability of event B occurring, given event A occurred, is equal to:

[tex]P(B|A)=\frac{1}{8}\div \frac{7}{16},\\\\P(B|A)=\frac{1}{8}\cdot \frac{16}{7}=\boxed{\frac{2}{7}}[/tex]

Answer:

The speed of the boat in still water is 18 mph.

The speed of the current is 2 mph

Step-by-step explanation:

Let x represent the speed of the boat in still water.

Let y represent the speed of the current.

When the boat goes against the current, the speed is 16 mph. Assuming it traveled against the current while going upstream, its total speed would be (x - y) mph. It means that

x - y = 16  (equation 1)

Going downstream, the boat averages 20 mph. Assuming it traveled with the current, its total speed would be (x + y) mph. It means that

x + y = 20  (equation 2)

Adding both equations, it becomes

2x = 36

x = 36/2

x = 18 mph

Substituting x = 18 into equation 1, it becomes

18 - y = 16

y = 18 - 16

y = 2 mph