A regular octagon with side length a cm can be made by cutting off
the four corners of a square board. How long should the sides of the
board be?
Answers
Answer:
one side = [tex]\frac{a\sqrt{2}}{2}[/tex]
Step-by-step explanation:
if you draw an octagon on a piece of paper, you can draw a square around it, you should be able to see a diagram of this attached, ignore the 6.
Let's say TP = a
since it's a regular octagon, TP = HT
and using the Pythagoras Theorem, we know a² + b² = c² and thus:
√(AT² + HA²) = HT
and since AT = HA which we will call x, the equation becomes:
√(2x²) = HT = a
rearrange the equation to solve for x and you get:
2x² = a²
x² = [tex]\frac{a^{2} }{2}[/tex]
x = [tex]\frac{a}{\sqrt{2}}[/tex]
which, if you rationalise the denominator, you get:
x = [tex]\frac{a\sqrt{2}}{2}[/tex]
Related Questions
please help tysm ! Giving brainliest to best answer
Answers
Step-by-step explanation:
here is your answerrrrrrrrrrr
A small box of pens costs $6. A large box of pens costs $8. The table shows the
costs of buying certain numbers of boxes of pens. Which ordered pair represents
the cost of 5 small boxes and 5 large boxes?
Answers
Explanation: Multiple
David drew this diagram of a picture frame he is going to make. Each square represents 1 square inch. What is the area of the picture frame?
Answers
Answer:
64 in²
Step-by-step explanation:
Find the area of the larger rectangle first, and then minus the area of the smaller rectangle.
The length of the larger rectangle
= 9-3 = 6 in
The width of the larger rectangle
= 17-1 = 16 in
The area of the larger rectangle
= 6×16
= 96 in²
The length of the smaller rectangle
= 8-4 = 4 in
The width of the smaller rectangle
= 13-5 = 8 in
The area of the smaller rectangle
= 4×8
= 32 in²
The area of the picture frame
= 96-32
= 64 in²
15 POINTS!!! PLEASE HELP ASAP! WILL MARK BRAINLIST!
Find the missing side of this right
triangle.
Х
6
10
X=
= V[?]
Enter the number that belongs in the green box.
Answers
Answer:
136
Step-by-step explanation:
hyo^2=opp^2+adj^2
x^2=6^2+10^2
x^2=36+100
x^2=136
x=
[tex] \sqrt{136} [/tex]
In the figure above, ABCD is a cyclic quadrilateral. What ja the value of x in degrees?
Answers
Answer:
Step-by-step explanation:
Remark
The diagram makes the line AB look like it is tilted a bit to the right. I'm going to assume that isn't right. AB extended is a straight line. ADC is supplementary to the 80o angle.
Solution
<ADC + 80o = 180 They are on the same straight line
<ADC = 180 - 80 Subtract 80 from both sides
<ADC = 100o
Opposite angles of a cyclic quadrilatral are supplementary
<ADC + <ABC = 180 Property of cyclic quadrilaterals
100 + <ABC = 180 Subtract 100 from both sides
<ABC = 80 degrees.
<x + <ABC = 180
<x + 80 = 180
<x = 100 degrees
Discussion
I cannot be sure what the arc at B is equal to. Is the arc = 80 o or is <ABC = 80. And it is unresolvable. My suggestion is that you ask your teacher.
PLEASE ANSWER!!
Carl is filling flower pots with soil. Each flower pot is a cylinder with radius 7in and height 20in. His bag of potting soil contains 12,000 cubic inches of soil. How many flower pots will he be able to COMPLETELY FILL with his one bag of soil?
A: 1 flower pot
B: 2 flower pots
C: 3 flower pots
D: 4 flower pots
Answers
Answer:
3 pots
Step-by-step explanation:
V(cylinder)= π×r²×h=3078.8 cubic inches
12,000 / 3078.8= 3.89
so you can only fill 3 pots
help me please
:)
i really need it
Answers
Answer:
3.5 qt or 3 qt and 2c
Step-by-step explanation:
4 cups makes 1 quart
14/4 = 3.5
Can someone please help me
Answers
Answer:
1/6
Step-by-step explanation:
he has 1 chance to roll 6 different numbers
help me out, thank you !
Answers
Explanation: a ^2 +b^2 = c^2
7^2 + 10.2^2 = c^2
49 + 104.04=c^2
153.04 =c^2
c ≈ 12.37
Round: 12.4
What is the correct angle measure 42° 38° 142° 158°
Answers
Answer:
142°
Step-by-step explanation:
If it's goes from right to left, you read bottom numbers.
if it goes from left to right, you read the top numbers.
Hey guys is this correct?.
Answers
Answer:
Step-by-step explanation:
Please answer this question correctly
Answers
Answer: 44
EC is basically EF times 2
Answer: EC=44
Step-by-step explanation:
Given the triangle
find the length of side 2 using the Law of Sines.
Answers
Pleas help grade depends on it
Answers
Answer:
C. 62x+239=672
Step-by-step explanation:
X represents hours , which means 62 miles per hours equals 62x. Since Ed has already traveled 239 miles the opposite would be to add in order to subtract in the equation. 672 would be the equivalent of traveling 672 miles in x hours.
PLSS HELP IMMEDIATELY!!!! ILL MARK BRAINIEST IF U DONT LEAVE A LINK OR GUESS!!!!
Answers
Answer:19
Step-by-step explanation:
7x3=21
21-2=19
Answer:
total of 7 fabric needed but 2 are given so:total fabric minus 2 is; 7 minus 2 is 5 needed
Find the variable in the figure. The diagram is not to scale.
Volume=16π
Answers
r = 2
The volume of a cone can be found using the following equation
[tex]V = r^2\frac{h}{3} \pi[/tex]
After putting in the information that we already know we get
[tex]16\pi = r^2\frac{12}{3} \pi \\16\pi = r^2(4) \pi \\4 = r^2\\ r = 2\\[/tex]
For proof's sake, we can try the equation again with the information we know
[tex]V = r^2\frac{h}{3} \pi \\V = 2^2\frac{12}{3} \pi \\V =4(4) \pi \\V = 16\pi[/tex]
can you guys help me with this
Answers
Answer:
BD = 3.2.
CD = 2.4.
Step-by-step explanation:
By Pythagoras:
AB^2 = 3^2 + 4^2 = 25
AB = 5.
Triangles ADC and ACB are similar, so
AC / AB = AD / AC
3 / 5 = AD / 3
AD = 3*3/5
AD = 9/5 = 1.8
So BD = 5 - 1.8
= 3.2.
CD^2 = AC^2 - AD^2 (Pythagoras)
CD^2 = 3^2 - 1.8^2 = 5.76
CD = 2.4.
A line with a slope of -5 passes through the point (-3, 1). Write the
equation of the line in slope-intercept form.
Answers
Answer:
1/2
Step-by-step explanation:
Help me and show me how to do it I’m lost
Answers
Answer:
x⁴
Step-by-step explanation:
-16/-4=4
a negative divided by a negative equals a positive
answer dis or somethinggg
Answers
Answer:
ok just did now give be brainlyest
Step-by-step explanation:
Answer:
ur mom ur mom ur mom ur mom ur mom ur mom ur mom
Step-by-step explanation:
please help me!!!! pleasseeeee
Answers
Answer: I'm not to sure, but Khan Academy does a really good job at this. Anything apart of STEM they have a step by step video on.
Step-by-step explanation:
write the number in word form .0001
Answers
Answer:
0.0001 in word form is ten thousandth
The area of this shape is
Answers
Answer:
Step-by-step explanation:
Answer:
169.4ft^2
Step-by-step explanation:
Area of right triangle= base x height /2
Area of right triangle= 24.2x (7x2) /2
Area of right triangle= 24.2x (14) /2
Area of right triangle= 24.2x (14) /2
Area of right triangle= 169.4ft^2
Need help take your time and thx
Answers
Answer:
if you factor it the answer is (x−5)(x−9)
1) ABC is a right-angled triangle.
AB = 50 cm.
Angle ABC= 24°
Work out the length of BC.
Give your answer correct to 1 decimal place.
Answers
Answer:
112.3
Step-by-step explanation:
How many solutions are there to this nonlinear system?
A.Two solutions
B. One solution
C. No solutions
Answers
There’s only one spot where both lines meet to form a common point.
Dominique has a movie collection. The types of movies in Dominique's collection are shown in
the circle graph.
Dominique's Movie Collection
Mysteries
30%
comedie
Comedies
25%
Biographies + 10%
Dramas
15%
Cartoons
20%
Dominique has 260 movies in her collection. How many more cartoons, biographies, and
comedies than all other types of movies does Dominique have in her collection?
Answers
Captain Levi once said, "Give up on your dreams and die"
Anyways the answer is 10
Write this number in standard form.
sixty thousand twenty-two and five tenths
Answers
someone help me i don’t understand this !
Answers
Answer: put it in the calculator with the () and they will give it to you right like you need it
Step-by-step explanation: :)
Answer:
I help you
Step-by-step explanation:
I help you _GUTI_ discord
PLEASE HELP
Square tiles measuring 4 inch on each side will be used to tile a 1-foot by 1-foot area. How many of these tiles are needed?
Answers
Answer:9
Step-by-step explanation:
4 inches fits into 12 inches three times. Three rows multiplied by three columns equals 12.
Hope that helps!