what is the image of n for a 144° counterclockwise rotation about the center of the regular pentagon
A. A
B. E
C. P
D. T
Answers
144 is two fifths of 360 so for a pentagon, it would cause the point to shift two places
Answer:
The correct option is C. The image of N for a 144° counterclockwise rotation about the center is P.
Step-by-step explanation:
The number of vertices of a regular pentagon is 5.
The central angle between two consecutive vertices is
[tex]\frac{360}{5}=72[/tex]
It means the central angle between two consecutive vertices is 72 degrees.
We have to find the image of N for a 144° counterclockwise rotation about the center.
If pentagon rotates 72 degree counterclockwise rotation about the center, then the image of N is E.
If pentagon rotates (72+72) degree counterclockwise rotation about the center, then the image of N is P.
The image of N for a 144° counterclockwise rotation about the center is P.
Therefore the correct option is C.
Related Questions
which is the directrix of parabola with equation x^2=4y
Answers
Answer:
[tex]y=-1[/tex]
Step-by-step explanation:
We have been given an equation of parabola [tex]x^2=4y[/tex]. We are asked to find the directrix of our given parabola.
First of all, we will divide both sides of our given equation by 4.
[tex]\frac{x^2}{4}=\frac{4y}{4}[/tex]
[tex]\frac{x^2}{4}=y[/tex]
[tex]y=\frac{x^2}{4}[/tex]
Now, we will compare our equation with vertex form of parabola:
[tex]y=a(x-h)^2+k[/tex], where, (h,k) represents vertex of parabola.
We can see that the value of a is [tex]\frac{1}{4}[/tex], [tex]h=0[/tex] and [tex]k=0[/tex].
Now, we will find distance of focus from vertex of parabola using formula [tex]p=\frac{1}{4a}[/tex].
Substituting the value of a in above formula, we will get:
[tex]p=\frac{1}{4*\frac{1}{4}}[/tex]
[tex]p=\frac{1}{1}=1[/tex]
We know that directrix of parabola is [tex]y=k-p[/tex].
Substituting the value of k and p in above formula, we will get:
[tex]y=0-1[/tex]
[tex]y=-1[/tex]
Therefore, the directrix of our given parabola is [tex]y=-1[/tex].
) the length of a rectangle is 5 cm less than twice the width. if the area of the rectangle is 88 , find the dimensions of the rectangle.
Answers
Ashur solves the following system of linear equations.
Which statement about the solution to this system can he say is true?
The values of a and b are both equal to –4.
The values of a and b are both equal to 4.
The value of a is equal to 4, and b is equal to –4.
The value of a is equal to –4, and b is equal to 4.
Answers
The values of a and b are both equal to –4.
The given equations that make up the systems are:
-3a+7b=-16...................(Equation 1)
-9a+5b=16...................(Equation 2)
To find the values of a and b we will have to solve the two equations. To solve the equations let us employ the method of elimination.
Let us multiply (Equation 1) by -3. This will give us:
[tex] -3\times (-3a+7b=-16)=9a-21b=48 [/tex]...........(Equation 3)
Let us now add (Equation 2) to (Equation 3) to eliminate a. This will give us:
-16b=64
[tex] \therefore b=-4 [/tex]
Plugging this value of b in any of the equations we will get the value of a. Let us plug it in (Equation 1). This gives:
[tex] -3(-4)+7b=-16 [/tex]
[tex] 12+7b=-16 [/tex]
[tex] \therefore b=\frac{-28}{7}=-4 [/tex]
Thus, out of the given options, the first option is the correct one. The values of a and b are both equal to –4.
Angle A is a right angle in △ABC.
Which side is opposite to angle A?
side BC
side AB
side AC
Answers
Option 1 is correct. The side opposite to angle A is side BC, which is the hypotenuse.
In a triangle, the side opposite the right angle is known as the hypotenuse. Since angle A is given as a right angle in △ABC, the side opposite this right angle will be the hypotenuse.
In △ABC:
Side AB is adjacent to angle A, forming one leg of the right triangle.
Side AC is also adjacent to angle A, forming the other leg of the right triangle.
Side BC is opposite angle A and is the longest side of the triangle, making it the hypotenuse.
Therefore, side BC is opposite to angle A in △ABC.
Complete question:
Angle A is a right angle in △ABC.
Which side is opposite to angle A?
1. side BC
2. side AB
3. side AC
How long would it take to travel 630 miles at the rate of 35 miles per hour? 18 h 35 h 220 h 350 h
Answers
Answer:
18h
Step-by-step explanation:
Use the data to create a scatter plot.
Size (lb)
8
12
9.5
5
7
7.5
Time (h)
5
6.5
4
3.5
2
5
Answers
The ordered pairs are:
(5, 8)
(6.5, 12)
(4, 9.5)
(3.5, 5)
(2, 7)
(5, 7.5)
Answer:
See attached image.
There seems to be an increase in weight as time passes.
which of the following are polynomial functions?check all that apply
(answers in picture)
Answers
Polynomial functions must have terms that have non-negative integer exponents. We can rewrite function B, [tex]F(x)=-x^3+5x^2+7\sqrt{x}-1[/tex] as:
[tex]F(x)=-x^3+5x^2+7x^1^/^2-1[/tex]
The exponent 1/2 is not an integer exponent.
We can also rewrite the function D, [tex]F(x)=\frac{3}{5}x^4-18x^2+5-\frac{10}{x^2}[/tex], as:
[tex]F(x)=\frac{3}{5}x^4-18x^2+5-10x^-^2[/tex]
We have a negative exponent, so this is not a polynomial.
Answer:
Step-by-step explanation: It is only c and e i just did the test.
If mAD=85 degrees and mBC=31 degrees find the value
Answers
To start, we know that a whole circle equals 360 degrees. If we subtract the 2 arcs we know, 85 and 31, we have 244 degrees left for the 2 congruent arcs. Dividing that by 2 gives us 122 for each arc.
Now, write the equation: 122 = 13x - 21
Solve this, to find the x = 11.
By the properties of angles on a circle, the degree measure of x in the circle is 11 degrees
Calculating the degree measure of xFrom the question, we have the following parameters that can be used in our computation:
The circle
The angle in a circle is 360 degrees.
So, we have
Unused arcs = 360 - 85 - 31
Unused arcs = 244
This means that
2(13x - 21) = 244
So, we have
13x - 21 = 122
This gives
13x = 143
Evaluate
x = 11
Hence, the degree measure of x is 11 degrees
Read more about angles at
https://brainly.com/question/11164565
#SPJ3
two positive integers have a sum of 17 and a product of 66
Answers
Sum | Product
33 and 2 35 66 X
22 and 3 25 66 X
11 and 6 17 66 ←
11 and 6 have a sum of 17 and a product of 66
The first term of a sequence is -12. The recursive formula for the sequence is an = an-1 + 9. What are the next 3 terms in the sequence?
Answers
To get each new term, we simply add 9 to the last term. So we add 9 to -12 to get -3. Then we add 9 to -3 to get 6. Finally we add 9 to 6 to get 15
In other words,
first term = -12
second term = first term+9 = -12+9 = -3
third term = second term + 9 = -3+9 = 6
fourth term = third term + 9 = 6+9 = 15
This process repeats forever though we only need three terms in this case.
So that's why the answer is the three values -3, 6 and 15
How do you determine whether to draw the boundary line of the graph of a linear inequality dashed or solid?
Answers
The amount of grass seed needed to cover a lawn is proportional to its area. The lawn is rectangular and has an area of 2c^2 + 2c square meters. Factor this polynomial to find possible expressions for the length and width of the lawn. (Assume the factors are polynomials.) HELP ASAP!!
Answers
.. area = 2c(c+1)
Possible expressions for length and width are
1, 2, c, 2c, c+1, 2(c+1), c(c+1), 2c(c+1).
Factor completely. x^2−3x−40
Answers
8x5 = 40 and -8 + 5 = -3.
Plug it into the binomial example I provided above and....
(x - 8)(x+5)=40
Voila! You have your factored quadratic expression, hope this helps!
To factor the quadratic expression x² -3x -40, we find that the expression factors into (x - 8)(x + 5).
The question involves factoring the quadratic expression x² -3x -40 completely. To factor this expression, we look for two numbers that multiply to -40 and add to -3. The numbers that meet these conditions are -8 and 5, since
(-8) * 5 = -40 and
(-8) + 5 = -3.
Therefore, the expression can be factored into (x - 8)(x + 5).
Zhi bought 18 tickets for games at a fair. Each game requires 3 tickets. Zhi wrote the expression 18 – 3g to find the number of tickets she has left after playing g games. Diego correctly wrote another expression, 3(6 – g), that will also find the number of tickets Zhi has left after playing g games. Use the drop-down menus to explain what each part of Zhi's and Diego's expressions mean.
Answers
18 - The number of tickets bought.
g - The number of games played.
The "3g" represents the number of games we can determine Zhi and Diego went to. Both equations have values and variables that mean the same thing, however Diego chose to use the distributive property in setting up his equation.
Yes, Zhi's expression multiplies the tickets per game by the number of games to get the number of tickets used and then subtracts this amount from the total tickets.
If there are 15 girls and 9 boys in an art class, the ____________ of girls to boys in the class is 5:3.
Answers
if she can read 22 pages in 1 hour how many hours did she read in 114.5 hours
Answers
Hope this helps,
♥A.W.E.S.W.A.N.♥
1. Suppose that the amount of algae in a pond doubles every 4 hours. If the pond initially contains 90 pounds of algae, how much algae will be in the pond after 12 hours? (1 point)
would it be 720lbs
Answers
50 points! Dustin and Melanie are playing a game, where two standard, six-sided number cubes are rolled, and the sum of their outcomes is found. Each player gets a chance to guess the correct sum, and the player that guesses the correct sum wins the game.
Dustin decides to guess a sum of six. Melanie decides to guess a sum of seven.
Which player made the better decision? ________
Answers
Answer:
Melanie is the right answer
Step-by-step explanation:
Melanie made the better decision if Dustin and Melanie are playing a game, where two standard, six-sided number cubes are rolled.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
We have:
Dustin and Melanie are playing a game, where two standards, six-sided number cubes are rolled.
If the sum is 6:
The possible outcomes are = {(3,3), (2,4), (4,2), (1,5), and (5,1)}
Total outcomes = 5
If the sum is 7:
The possible outcomes are = {(1,6), (6,1), (5,2),( 2,5), (3, 4), (4,3)}
Total outcomes = 7
Thus, Melanie made the better decision if Dustin and Melanie are playing a game, where two standards, six-sided number cubes are rolled.
Learn more about the probability here:
brainly.com/question/11234923
#SPJ2
Jade is painting a rectangular wall. The wall is 414 yards long and 223 yards high.The formula for the area of a rectangle is A=bh. What is the area of the wall?
Answers
The formula for the area of the rectangle is actually A = LW. The length of the rectangular wall is 414 yards while its width is 223 yards. To compute for its area, you just have to follow the formula:
A = 414 (223)
A = 92,322 yards^2
Therefore, the area of the wall is 92,322 square yards.
Answer:
hey the answer is 11 1/3
Step-by-step explanation:
ive taken the quiz and this is the answer 100%
A line includes the points (2, 10) and (1, 4). what is its equation in slope-intercept form?
Answers
This problem has two parts. First you need to find the slope, so let's do that. The equation for the slope is m = y2-y1/x2-x1
We can now plug the two given points into the equation.
m = 10-4/2-1
m = 6/1
m = 6
Now that we know the slope, and one point we can put this in slope intercept form. Slope intercept form is y=mx + b
So now we can plug in one point and the slope to find b
10 = 6(2) + b
10 = 12 + b
-2 = b
Now that we know both m and b, we can plug only those two into the equation y=mx + b, and we have the equation.
The equation is y = 6x - 2
What is the solution of the equation 5x – 1 = 45? Round your answer to the nearest ten-thousandth
Answers
Final answer:
The solution to the equation 5x – 1 = 45 is x = 9.2, rounded to the nearest ten-thousandth.
Explanation:
The solution of the equation 5x – 1 = 45 is x = 9.2.
To solve this equation, we can start by isolating the variable x. Add 1 to both sides of the equation to get 5x = 46. Then, divide both sides by 5 to solve for x, giving us x = 9.2.
Therefore, the solution to the equation 5x – 1 = 45 is x = 9.2, rounded to the nearest ten-thousandth.
plz help "geometry"
the intersection of roads M and N creat a 71.4 degrees what are the complumentry and suplumentry angels of this intersection
A 161.4' ; 18.6'
B 18.6'; 161.4'
C 108.6' ; 18.6'
D 18.6' ; 108.6',
Answers
If the measurement of a central angle is 77 degrees find the length of its intercepted arc in a circle with a radius of 15 inches.
Answers
Answer:
20.2 inches ;)
Step-by-step explanation:
a/an ______ angle measures less than 90degrees°, a/an ______ angle measures 90degrees°, a/an ______ angle measures more than 90degrees° and less than 180degrees°, and a/an ______ angle measures 180degrees°.
Answers
Right
Obtuse
Straight
A function that can be written in the form f(x)=ax2+bx+c, where a, b & c are real numbers and a is not equal to zero.
Answers
I'm not exactly sure of what answer you are looking for, however,
f(x)=ax^2+bx+c represents a quadratic function.
Quadratic functions always have their highest exponent at 2, nothing more and nothing less.
Examples of quadratic functions are...
•x^2
•3x^2
•3x^2+2
•3x^2+2x
•3x^2+2x+1
I really hope this helps!
Best wishes:)
A quadratic function seems to be a second-order polynomial function. Another quadratic function has the following general form:
[tex]f (x) = ax^2 + bx + c[/tex]here,
a, b, and c = real numbersand,
a ≠ 0The quadratic formula is obtained by completing the square on some kind of quadratic equation instead in the standard format. Because the largest power equals two, it is indeed a 2nd-degree polynomial equation.
As a result, the aforementioned response is correct.
Learn more about quadratic equation here:
https://brainly.com/question/19942005
at 4:00 am,there were 800,000 gallons of water remaining at a reservoir.after 4 hours of irrigation,there were 100,000 gallons of water remaining.write an equation that describes the number of gallons of water as a function of the time the field has been irrigated
Answers
To relate those two points we are going to use the point slope formula:
[tex]m= \frac{y_{2}-y_{1} }{x_{2}-x_{1} } [/tex]
where
[tex]x_{2}[/tex] is 8
[tex]x_{1}[/tex] is 4
[tex]y_{1}[/tex] is 800000
[tex]y_{2}[/tex] is 100000
So, [tex]m= \frac{100000-800000}{8-4} [/tex]
[tex]m= \frac{-700000}{4} [/tex]
[tex]m=-175000[/tex]
Now that we have our slope, we are going to use the point-slope formula to find our equation:
[tex]y-y_{1} =m(x-x_{1} )[/tex]
[tex]y-800000=-175000(x-4)[/tex]
[tex]y-800000=-175000x+700000[/tex]
[tex]y=-175000x+1500000[/tex]
The equation that describes the number of gallons of water as a function of the time the field has been irrigated is [tex]y=-175000x+1500000[/tex]
where
[tex]y[/tex] are the remaining gallons of water in the reservoir after [tex]x[/tex] hours
[tex]x[/tex] is the time the field has been irrigated in hours
what is the answer to f(2)=2-5(2)
Answers
Rewrite the radical exponent as a radical
Answers
when does a rhombus have 4 congruent angles?
Answers
The DIAMETER of a sphere is doubled. What is the new volume of the sphere?
A)
8/3πr3
B)
16/3πr3
C)
32/3πr3
D)
64/3πr3
Answers
[volume of a sphere]=(4/3)*pi*r³
if the diameter is doubled
then
the radius also is doubled
the new volume=(4/3)*pi*(2r)³------> 8*[(4/3)*pi*r³]-------> (32/3)*pi*r³
the answer is C)
32/3πr3