Answer: 30 degrees
This is the minimum amount of rotation.
Why this value? Well because 360/12 = 30
Consider a triangle with 3 sides. Specifically I mean an equilateral triangle. We can rotate it 120 degrees to have it line up with itself. Now notice that 360/3 = 120.
For a square, we can rotate it 90 degrees and we can say 360/4 = 90
So the general rule is that the minimum angle of rotation is 360/n, where n is the number of sides. This rule only works for regular polygons. Regular polygons have the same side length and the same angle measure (the side and angle measure won't necessarily be equal).
So going back to this 12 sided dodecagon, we have n = 12 and 360/n = 360/12 = 30 as the minimum angle of rotation. Each 30 degree rotation will have the polygon match up perfectly with its old image. The preimage and image will be identical.
The sum of the first n terms of an arithmetic sequence is n/2(4n + 20).
a) Write down the expression for the sum of the first (n − 1) terms.
b) Find the first term and common difference of the above sequence.
Answer:
(a).
[tex]S_{n} = \frac{n}{2} (4n + 20) \\ \\S _{n - 1} = \frac{(n - 1)}{2} (4n - 4 + 20) \\ \\ S _{n - 1} = \frac{(n - 1)}{2} (4n + 16) \\ \\S _{n - 1} = \frac{(n - 1)(4n + 16)}{2} \\ \\ { \boxed{S _{n - 1} = {2 {n}^{2} + 6n - 8}}} \\ [/tex]
(b).
from general equation:
[tex]S _{n - 1} = \frac{(n - 1)}{2} (4n + 16)[/tex]
first term is 4n
common difference:
[tex]16 = \{(n - 1) - 1 \}d \\ 16 = (n - 2)d \\ d = \frac{16}{n - 2} [/tex]
Triangle JKL is similar to triangle PQR. What is the measure of angle R?
Please answer as soon as possible.
Answer:
x = 43°
Step-by-step explanation:
59 + 78 + x = 180
137 + x = 180
(137 - 137) + x = 180 - 137
x = 43°
Help please! Describe how figure 20 will look like
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Answer:
Each colored block in Figure 20 will be a 20×20 square of smaller squares of the same color. The red-green pattern will be identical.
Step-by-step explanation:
Each colored block in Figure N is an N×N array of small blocks the same color. The pattern of red and green N×N blocks is the same from one figure to the next. We expect Figure 20 to fit this description.
Find the missing lengths of the sides.
A) a = 6^3 ft, b = 6^3 ft
B) a = 12 ft, b = 12 ft
C) a = 6 ft, b = 6 ft
D) a = 6 ft, b = 6^2 ft
Answer:
The choose B) a=12, b=12
Step-by-step explanation:
sin45= a/12√2 —> a=12
cos 45= b/12√2 —> b=12
I hope I helped you^_^
A number is multiplied by 16, and that product is added to 4. The sum is equal to the product of 4 and 9. Find the number.
Answer:
The number is 2
Step-by-step explanation:
x * 16 + 4 = 9*4
x * 16 + 4 = 36
x * 16 + 4 - 4 = 36 - 4
x * 16 = 32
x * 16 / 16 = 32 / 16
x = 2
Answer:
The number is 2
Step-by-step explanation:
let the number be "a"
16a+4=4×9
16a+4=36
16a=36-4
16a=32
a=2
Which of the following is equal to square root of 3 and square root of 6.
Answer:
the answer is the second option which is 6⅓
Answer:
6^1/6
Step-by-step explanation:
Rewriting with the exponents as fractions
(6^1/3) ^1/2
We know a^b^c = a^(b*c)
6^(1/3*1/2)
6^1/6
Kelsey deposited $3,600 in a bank account with annual interest rate 4.25%. How much interest was earned in 5 years?
Answer:
765
Step-by-step explanation:
1)4.25/100=0.0425
2)0.0425*3600=153
3)153*5=765
find a formula for the arithmetic sequence consisting of the positive multiples of 4
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Answer:
4n
Step-by-step explanation:
For positive multiple number 'n', the value is 4n.
a[n] = 4n . . . . . where a[n] is the n-th term of the sequence
Answer:
an = 4n
Step-by-step explanation:
got it right on test
22. which month did the business make the most profit
23. which month did the business make the least profit
Answer:
JulyMarchis your answer. I HOPE YOUR DAY GOES GREAT.
I’ll give you 50 points if it’s answer correctly
Answer:
. The line passes through the quadrants I, II and III. ii. The line intersects the Y-axis at (0, 1).
Name prime numbers 1-30
Answer:
2,3,5,7,11,13,17,19,23 and 29
Step-by-step explanation:
hope this helps
Find the greatest common factor of these two expressions.
28xy8v7 and 14x6v3
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Answer:
14xv^3
Step-by-step explanation:
Coefficients are 28 and 14, which have a GCF of 14.
x exponents are 1 and 6, so the GCF is x^1 = x
y exponents are 8 and 0, so the GCF is y^0 = 1
v exponents are 7 and 3, so the GCF is v^3
The GCF of the two terms is the product of the factors just found:
14xv^3
Question 3
1 pts
Use the number line below to find the midpoint of segment AB
midpoint of segment AB (answer1]
Answer:
The midpoint is -4
Find the fraction that is exactly halfway between 3/7 and6/7 pls help
Answer:
[tex]\frac{9}{14}[/tex]
Step-by-step explanation:
1. Add two fractions together.
[tex]\frac{3}{7}[/tex] + [tex]\frac{6}{7}[/tex] = [tex]\frac{9}{7}[/tex]
2. Divide by 2.
[tex]\frac{9}{7}[/tex] ÷ 2 = [tex]\frac{9}{14}[/tex]
Which is the graph of f(x) = 100(0.7)?
Answer:
70; The following graph is simply a horizontal line at the value 70.
Step-by-step explanation:
Answer:
Graph A. On a coordinate plane, a curve approaches y = 0 in quadrant 1 and curves up into quadrant 2. It goes through (2, 49) and (0, 100).
Step-by-step explanation:
Edge
Help ASP!
Sarah has 80 pennies. Lou
has 10 times as many
pennies as Sarah.
Joe has 1/10 as many
pennies as Sarah. How many
pennies do Lou
and Joe have together?
the score analysis of a school show the following.
180student register for Economics, 90 student Economics and political science,10 student Economics only, 150 student Economics and Geography, 120 student political science and Geography, 210 Geography, total number of students that register for the subjects= 250. find the number of students who register for.
1. political science
2. political science and Geography but not econs
3. Economics and political science but not Geography
Answer:
Economics and political science but not Geography
is right answer i think
PLS HELP ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! LOOK IMAGE FOR OPTIONS
Which table represents a direct variation function?
if two adjacent sides of rectangle having perimeter 21 cm are in the ratio 3:4 what is the area of the rectangle is ...cm ?
Write the equation of the line in fully simplified slope- intercept form .
4/6+1/4 =
Pliss help me
Answer:
11/12.
Step-by-step explanation:
The lowest common denominator of 6 and 4 is 12, so we have
4/6 + 1/4
= 4*2 / 6*2 + 1*3 / 4*3
= 8/12 + 3/12
= 11/12.
Divide 3m 80cm of ribbon in the ratio of 1/3 : 3/4 : 1/2 what is the result?
Answer:
80 cm / 180 cm / 120 cm
Step-by-step explanation:
the smallest common multiple of 3, 4 and 2 is 12.
so, to be able to truly compare these fractions we need to bring all denominators to .../12.
1/3 = 4/12
3/4 = 9/12
1/2 = 6/12
in total we have therefore 19 (4+9+6) equally large parts of the ribbon that are then combined :
4 parts for the first segment.
9 parts for the second segment
6 parts for the third segment.
so, one part is
380 cm / 19 = 20 cm
therefore the first segment of the ribbon is
4×20 = 80 cm long
the second segment
9×20 = 180 cm long
the third segment
6×20 = 120 cm long
Jenny completed four-fifths of her summer reading assignment. Her classmate Antonio completed seven-eighths of his assignment, and classmate Jerry completed three-fourths of his assignment. Which student read the least? Which student read the most? Which student fell in the middle? (Show all work.)
Answer:
Jerry, Antonio, Jenny
Step-by-step explanation:
To solve this, we can represent the numbers as fractions, make them have one common denominator, and go from there
First, we can represent these as fractions:
Jenny:
four-fifths = 4/5
Antonio:
seven-eighths = 7/8
Jerry:
three-fourths = 3/4
Next, we can find the lowest common multiple. We can do this by listing the multiples of each number until something is in common for all 3
4:
4, 8, 12, 16, 20, 24, 28 ,32, 36, 40, 44, 48
8:
8, 16, 24, 32, 40, 48, 56, 64
5:
5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60
One number that is in common is 40.
Our next step is to find out what we need to multiply each number by to equal 40. We can do this via division.
4:
40/4 = 10
8:
40/8 = 5
5:
40/5 = 8
Next, we can multiply the numerator and denominator by the same number, essentially multiplying it by 1. For example, 4/5 * 5/5 = 20/25, which is still equal to 4/5 because 5/5 = 1 and multiplying any number by 1 keeps it the same.
3/4 * 10/10 = 30/40
7/8 * 5/5 = 35/40
4/5 * 8/8 = 32/40
We can see that 3/4 (Jerry) is the lowest, 7/8 (Antonio) is the highest, and 4/5 (Jenny) is in the middle
Fred and Gina are playing tennis. The first player to win 2 sets wins their match. Fred has a 3/5 chance to win each set while Gina has a 2/5 chance. What is the probability that the match goes three sets until someone wins?
Answer:
60/125 which can be reduced to 12/25
Step-by-step explanation:
Gina wins
2/5 * 2/5 = 4/25
3/5 * 2*5 * 2/5 = 12 /125
2/5 * 3/5 * 2/5 = 12/125
Fred Wins
3/5 * 3/5 = 9/25
2/5 * 3/5 * 3/5 = 18/125
3/5 * 2/5 * 3/5 = 18/125
P(3 sets) = (18 + 18 + 12 + 12)/125 = 60/125
P(2 sets) = (20 + 45)/125 = 65/125
I found the probability of 2 sets so I could add the results together to see if the probability totals 1. It does. This question is done correctly.
Juan Carlos grew 2.79 inches last year. Which shows a way to represent the value of the 9 in this number?
Answer:
0.09
Step-by-step explanation:
hope it helps!!!!!!
Please Help! I am so confused. I will give you the brainiest and a lot of points.
Please show work
Read each number from top to bottom. Each digit is in base 20, and as I pointed out in another question of yours, 1 bar = 5, 1 dot = 1, and disk = 0.
(47) Only 1 digit here, with 2 bars and 4 dots. So this is 14.
(49) 3 digits, in order from top to bottom: 19, 0, 6. So this number is
[19]06₂₀ = 19×20² + 0×20¹ + 6×20⁰ = 7606
(51) 3 digits: 8, 8, 8.
888₂₀ = 8×20² + 8×20¹ + 8×20⁰ = 3368
(53) 4 digits: 2, 0, 0, 11.
200[11]₂₀ = 2×20³ + 0×20² + 0×20¹ + 11×20⁰ = 16011
(55) 4 digits: 10, 10, 0, 10.
[10][10]0[10]₂₀ = 10×20³ + 10×20² + 0×20¹ + 10×20⁰ = 84010
(57) 6 digits: 5, 10, 0, 6, 2, 3.
5[10]0623₂₀ = 5×20⁵ + 10×20⁴ + 0×20³ + 6×20² + 2×20¹ + 3×20⁰ = 17602443
(59) 6 digits: 10, 5, 0, 0, 11, 4.
[10]500[11]4₂₀ = 10×20⁵ + 5×20⁴ + 0×20³ + 0×20² + 11×20¹ + 4×20⁰ = 32800224
Use the order of operations to simplify the expression below. 990 ÷ (12-9)
Hi ;-)
[tex]990:(12-9)^2=990:3^2=\\\\=990:(3\cdot3)=990:9=\boxed{110}[/tex]
Someone please help!
-it is a 4 digit number.
-the vaule of the digit in the thousands place is 10 times greater than the value of the digit in the hundreds place.
-the least digit is in the tens place.
-the sun of the digits is 19. -the digit in the ones place is 4 more than the digit in the hundreds place.
-whats the mystery number?
Answer:
5539
Step-by-step explanation:
You should conclude that the number in the thousands place and the one in the 100s place are the same.
x * 1000 + x * 100 + y + x + 4
So you could sum the digits as
3x + y + 4 = 19 Subtract 4 from both sides
3x + y = 15
x can be six That means y = 1 which is OK
x can be five That means y = 3 which is OK
Now we run into a little grief. Can x be 4? No
x cannot be 4 that would mean that y = 19 - 12 = 7 The tens digit is too big.
Come to think of it, x cannot be 6 because then the units digit will be 10 -- not possible.
So the answer is
1000*5 + 100*5 + 10*3 + 9
5539 is the answer.
Thanks for posting.
We want to find a 4-digit number that meets some given conditions. We will find two, which are:
4438 and 5509
A general 4-digit number can be written as:
a*1000 + b*100 + c*10 + d
Where a, b, c, and d are single-digit numbers.
a is the thousands digit
b is the hundreds digit
c is the tens digit
d is the units digit.
Here we know that:
"the value of the digit in the thousands place is 10 times greater than the value of the digit in the hundreds place."
So the first term is 10 times the second term, this means that:
(a*1000) = 10*(b*100)
a*1000 = b*1000
a = b
-the least (the smaller one) digit is in the tens place.
so:
c < a, b, d
- The sun of the digits is 19.
So:
a + b + c+ d = 19
-The digit in the ones place is 4 more than the digit in the hundreds place.
so:
d = b + 4
Now we can rewrite all of these conditions as:
b = ac < b, a, da + b + c + d = 19d = b + 4Using the first one, we can replace all the b's by a's in the other conditions, so we have:
c < a, d2a + c + d = 19d = a + 4Now we can use the third equation and replace it in the second one to get:
2a + c + d = 19
2a + c + (a + 4) = 19
3a + c + 4 = 19
3a + c = 19 - 4
3a + c = 15
Now we need to remember that:
c < a.
So we can try with different values of a.
For example, if a = 3, then:
3*3 + c = 15
9 + c = 15
c = 15 - 9 = 6
here we have c > a, so we can discard this.
If a = 4, then:
3*4 + c = 15
12 + c = 15
c = 15 - 12 = 3
c < a
From this we can construct our number:
a = b = 4
c = 3
d = b + 4 = 4 + 4 = 8
Then the number is:
4438
If a = 5, then:
3*5 + c = 15
15 + c = 15
c = 15 - 15 = 0
c < a
So we also can have:
a = b = 5
c = 0
d = b + 4 = 9
Such that the number is:
5509
And if a is equal to or larger than 6 we have problems, because
3*6 + c = 15
18 + c =15
c = 15 -18 = -3
And c can't be a be a negative number.
So we can conclude that we found two 4-digit numbers that meet all the conditions, and these are:
4438 and 5509
If you want to learn more, you can read:
https://brainly.com/question/19902993
What two rational expressions sum to 2x+3x2−2x−15?
Enter your answer by filling in the boxes. Enter your answer so that each rational expression is in simplified form.
The rational expressions that sum to [tex]\frac{2x+3}{(x+3)(x-5)} = \frac{2x}{(x+3)(x-5)} + \frac{3}{(x+3)(x-5)}[/tex]
The given expression is:
[tex]\frac{2x+3}{x^2-2x-15}[/tex]
Factorize the denominator
[tex]x^2-2x-15\\x^2-5x+3x-15\\x(x-5)+3(x-5)\\(x+3)(x-5)[/tex]
The given expression therefore becomes:
[tex]\frac{2x+3}{(x+3)(x-5)}[/tex]
This can be split into the sum:
[tex]\frac{2x+3}{(x+3)(x-5)} = \frac{2x}{(x+3)(x-5)} + \frac{3}{(x+3)(x-5)}[/tex]
Learn more here: https://brainly.com/question/17103002
Answer: 2x+3/x^2-2x-15 = 13/8(x-5) + 3/8(x+3)
Step-by-step explanation: I took the test and used the answer above and got the answer wrong, then the test gave me this answer:
Find the midpoint, M, of AB.
А
M
B
[?]
22
Answer:
M=11
Step-by-step explanation:
Answer:
11
Step-by-step explanation:
To find the midpoint ( or middle) we take the average of the endpoints
(A+B)/2 = (0+22)/2 = 22/2 = 11