The following octagon is formed by removing four congruent right triangles from a rectangle. What is the total area of
the octagon?
44 cm 2
52 cm 2
10 cm 2
58 cm 2
Answers
10cm^
To find the total area of the octagon, we need to find the area of the rectangle and subtract the areas of the four congruent right triangles that were removed.
Let's assume the length of the rectangle is L and the width is W.
The area of the rectangle is L * W.
The two smaller sides of the right triangle are congruent to the width of the rectangle, which is W. The hypotenuse of each right triangle is congruent to the length of the rectangle, which is L.
The area of a right triangle is (base * height) / 2. In this case, the base is W and the height is L.
So, the area of one right triangle is (W * L) / 2.
Since there are four congruent right triangles, the total area of the right triangles is 4 * (W * L) / 2 = 2 * (W * L).
Therefore, the total area of the octagon is (L * W) - 2 * (W * L).
The total area of the octagon = L * W - 2 * W * L.
We don't know the actual values of L and W, so we cannot calculate the exact area. However, we can simplify the expression.
The total area of the octagon = L * W - 2 * W * L = LW - 2WL = LW - 2WL = LW - 2WL = LW.
Therefore, the total area of the octagon is equal to the area of the rectangle.
Related Questions
pls help will mark as brainliest
Answers
Answer:
1. Onesimus is the box 1
2. Gauls is box 8
3. Tarsus is box 3
4. Damascus is box 6
5. Ephesus is box 9
6. Colossae is box 12
7. Thessolonica is box 4
8. Ananias is box 2
9. Philippians is box 7
10. Tychicus is box 10
11. Phoebe is box 5
12. Epaphrase is box 11
Step-by-step explanation:
Hope this helps.
Doug is a dog, and his friend Bert is a bird. They live in Salt Lake City, where the streets are 1/16 miles apart and arranged in a
square grid (see map). They are both standing at the corner of 6th avenue and L street. Doug can run at an average speed of 30
mi/hr through the streets of Salt Lake, and Bert can fly at an average speed of 20 mi/hr. They are about to race to the corner of
10th avenue and Estreet. who would win and why?
Answers
No map given but it shouldn't matter.
E is the 5th letter, L the 12th.
Start at S(6,12). End at E(10,5)
The vector between them, E-S=(4,-7)
Each unit is 1/16 of a mile, though that probably doesn't matter that much.
Doug has to stay on the grid, so has to run |4|+|7|=11 units. At 30 mi/hr that takes (11/16)/30 = 0.022916 hours.
Bert can go diagonally, so flies √(4²+7²)=√65 ≈ 8.06 units. At 20 mi/hr that takes (8.06/16)/20 = 0.025194 hours.
Answer: Doug wins
Why? Because it's quicker to cover 4+7 at 30 mph than it is to cover √(4²+7²) at 20 mph. That is, Doug is 1.5 times faster and the 1.5 times the diagonal distance is more than the grid distance.
Answer:
Doug wins. He finishes in 1.38 minutes. Bert takes 1.51 minutes.
Step-by-step explanation:
Each city block is a square 1/16 mile by 1/16 mile.
From 6th Av and L Street to 10th Av and E Street, they need to go 4 avenues and 7 streets over. These two distances along blocks are the legs of a right triangle. The right triangle has legs of length 4 * 1/16 mile and 7 * 1/16 mile.
leg1 = 4 * 1/16 mile = 0.25 mile
leg2 = 7 * 1.16 mile = 0.4375 mile
The hypotenuse of the right triangle can be calculated by the Pythagorean theorem.
a^2 + b^2 = c^2
(0.25 mile)^2 + (0.4375 mile)^2 = c^2
c = 0.50389
The direct distance from one corner to the other is 0.50389 miles.
The bird travels this distance since the bird can fly above the streets.
The dog has to travel along the legs of right triangle by running in the streets and avenues. The dog travels 0.25 mile + 0.4375 mile = 0.6875 miles
Now we need to see what takes less time:
Bird: distance of 0.50389 miles at 20 mph, or
Dog: distance of 0.6875 miles at 30 mph
We start with the formula for speed:
speed = distance/time
s = dt
Now we solve it for time:
st = d
t = d/s
Time equals distance divided by speed.
Now we find the times for the bird and for the dog.
Bird:
t = d/s = (0.50389 mi)/(20 mi/h) = 0.02519 hours = 1.51 minutes
Dog:
t = d/s = (0.6875 mi)/(30 mi/h) = 0.0229 hours = 1.38 minutes
The bird takes 1.51 minutes, and the dog takes 1.38 minutes.
The dog takes less time to get there, so the dog wins.
The product of Jack's age and Florence's age is 266. Jack is 14 years
old. How old is Florence?
Answers
Answer:
19
Step-by-step explanation:
you divide 266 by 14
Answer:
19
Step-by-step explanation:
266 ÷ 14 = 19
pls help will mark as brainliest
Answers
Answer:
C
Step-by-step explanation:
Answer:
D cannot be used. first 3 are correct
Step-by-step explanation:
Chris needs at least a C+ average to pass his math class. His test grades in the class are shown below. 68, 80, 73, 72 The lowest C+ grade is 76. If there are only 5 tests, what is the minimum grade that Chris needs to get on his last test? A. 97 points B. 89 points C. 85 points D. 87 points
Answers
Answer:
C
Step-by-step explanation:
Answer:
B 89 points
Step-by-step explanation:
you calculate the mean, basically trial and error. So you add one of the answers to 68+80+73+72 and then divide by 5 because there are five tests
hope this helped<33
Find the missing angle measurements
Answers
Answer:
The angle for the top of the triangle is 79. For the right corner would be 56. Then going to the bottom of the blue triangle vertice would be 75. The missing angle next to that one would be 55/
Step-by-step explanation:
many organize a classroom party. there are 20 of cold drinks at the party, 13 of which contain diet Pepsi, what is the probability that randomly selected drink will be a diet Pepsi? answer key
Answers
Answer:
so its either 13/20
Step-by-step explanation:
if you get this wrong sorry:(
Explanation:
20 is the denominator because it is how many drinks there are in total. 13 is the numerator because that’s how many are Diet Pepsi’s and you cannot simplify this. That’s why the answer in 13/20.
P.S whenever you can simplify this you should :)
What number is the opposite of 98?
Answers
Answer:
-98
Step-by-step explanation:
hope this is right
Answer:
-98
Step-by-step explanation:
a negative number is the opposite of a positive number
Please help
Find answer Asap and I will mark as brainliest!!
Answers
Answer:
3 units.
Step-by-step explanation:
If you view the triangle face in halves, the bottom leg is units as 8/2 = 4. The hypotenuse is 5 units given in the centre of the triangular prism. You can then use the Pythagorean theorem to calculate that the height is 3.
4) The diameter of a circle is 32m. The radius is represented by 4(x + 2).
Part A: Write an equation you can use to find the value of x.
Part B: What is the value of x?
Answers
Answer:
The value of x is 2
Step-by-step explanation:
Diameter = 2r -------------------------------------------------------------------(1)
where r is the radius
The value of the diameter = 32 m and radius is given to be 4(x+2)
substitute the above into equation (1) and then solve for x
32 = 2 [ 4(x + 2)]
first open the inner bracket
32 = 2[4x + 8}
then open the outer bracket
32 = 8x + 16
subtract 16 from both-side of the equation
32 - 16 = 8x +16 - 16
16 = 8x
Divide both-side of the equation by 8
16/8 = 8x/8
2 = x
x = 2
Therefore, the value of x is 2
Can someone help me with this? ;^;
Answers
Answer:
The mode would be 10
Step-by-step explanation:
Because it is there more than the others
hope this helps! =D
Answer:
10
Step-by-step explanation:
Find the measure of the third angle of a triangle if the measures of the other two angles are given. 31.8 and 89.8
Answers
Answer:
58.4 Degrees
Step-by-step explanation:
Look at the attachment
A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The measure of the third angle of a triangle is 58.4°.
A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.
The sum of all the angle of the traingle is always 180°.
31.8° + 89.8° + x = 180°
x = 58.4°
Hence, the measure of the third angle of a triangle is 58.4°.
Learn more about Triangle:
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Help ASAP please ! Explain too if you can
Answers
Answer:
B
Step-by-step explanation:
180-118=42 so angle c=42
add 42 +76 =138
in a triangle all degrees ad up to 180 so
subtract 138 from 180=42
Answer:
B) 42 degrees
Step-by-step explanation:
If we're looking for the measure of angle E, we need to know the measures of angles D and C too. (Otherwise we just have nothing to work with.)
So they already give us angle D's measurement, which is 76; we just have to find the smaller angle at C and then solve for E. If this doesn't make sense, just look at C; there's a big angle (118) and a small one that we don't know. We have to find the small one.
Well at C there's just a straight line, so we can assume that the big angle and the small angle add up to 180 degrees, because straight angles are always 180 degrees.
Now to get the small angle, we can take 118 away from 180 to get 62, which will be the measure of the smaller angle. (Comment if you don't know why I did this.)
Now that we know two out of three measures in the triangle, we can find the measure of angle E. All triangles' angles add up to 180 degrees, so we can take away 76 (measure of D) and 62 (measure of small C) from 180 to get the measure of E: 180 - 76 - 62 = 42
So the measure of angle E is 42.
what is s10 for 1 + 2 + 4 + 8+...
256
511
1023
2047
Answers
Answer:
1023
Step-by-step explanation:
[tex] S_n = \dfrac{a(1 - r^n)}{1 - r} [/tex]
a = first term
r = common ratio
n = number of terms
Here we have
a = 1
r = 2
n = 10
[tex] S_{10} = \dfrac{1(1 - 2^{10})}{1 - 2} [/tex]
[tex] S_{10} = \dfrac{1 - 1024}{-1} [/tex]
[tex] S_{10} = \dfrac{-1023}{-1} [/tex]
[tex] S_{10} = 1023 [/tex]
Of course, since 10 is not such a large number of terms, you can simply do this:
1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 512 = 1023
Two different sports teams are doing fundraising to be able to afford their uniforms. The softball team needs to raise $318.12 between the twelve girls on the team. The hockey team needs to raise $391.92 between the 24 boys on the team. If each player raises the same amount of money, does each softball player or hockey player need to raise more? How can estimation help you solve?
Answers
Answer: A softball player will need to raise more.
Step-by-step explanation:
The softball team needs to raise $318.12 among the twelve girls on the team. Each softball player needs to raise:
$318.12 ÷ 12 = $26.51
The hockey team needs to raise $391.92 among the 24 boys on the team. Each hockey player will raise:
$391.92 ÷ 24 = $16.33
A softball player will raise $26.51 while a hockey player will raise $16.33. Therefore, a softball player will need to raise more.
I will mark brainliest to first correct answer!
Answers
Answer:
C
Step-by-step explanation:
Answer:
B.
Step-by-step explanation:
2. The size of a conC. 3 times the size of a cylinder is:
A. 1/3 the size of a cylinder.
B. 2/3 the size of a cylinder.
C. 3 times the size of a cylinder.
D. the same as the size of a cylinder.
Answers
Answer:
The answer is A.
Step-by-step explanation:
The shaded numbers show a pattern in the multiplication table. Which
expression can find the number that comes next in the pattern?
Xo 1 2 3 4 5
0 0 0 0 0 0 0
10 1 2 3 4 5
2 0 2 4 6 8
3 0 3 6 9 12
4 0 4 8 12 16
5 0 5 10 15 20 25
25 X4
25 + 11
25 +
1
25 +1
25 x 6
25 x 6
Answers
Answer:
25 + 11
Step-by-step explanation:
As it is summing up by odd numbers
so 16+9 is 25
and then 25 + 11 as eleven is the next odd number after 9
Answer: 25+11
HOPE THIS HELPS
Use the Remainder Theorem to find the remainder for (2x^3- 3x^2+x)/(x-1) and state whether or not the binomial is a factor of the
polynomial.
Answers
I’m so sorry if it’s incorrect :(
As 2x³ - 3x² + x is completely divisible by x - 1 it is a factor of the polynomial.
What is a factor of a polynomial?We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.
To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.
Given a polynomial 2x³ - 3x² + x which is being divided by x - 1.
Now, If 2x³ - 3x² + x is divisible by x - 1 then x = 1 is a root of the polynomial
2x³ - 3x² + x.
Therefore,
2(1)³ - 3(1)² + 1 = 0
2 - 3 + 1 = 0.
3 - 3 = 0.
0 = 0.
So, The binomial x - 1 is a factor of the polynomial.
learn more about the remainder theorem here :
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50 POINTS HELP ASAP
Answers
Answer:
its 10 points not 50
Step-by-step explanation:
need answer asap!!!!!!!!!!!
Answers
Answer:
126 degrees
Step-by-step explanation:
A straight line makes a 180 degree angle. Since we know one side is 54, just subtract 54 from 180.
help please help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
4 feet by 3 feet
Step-by-step explanation:
I hope this helped you out
Jessie lives in a farm and only has 2 animals, chickens and rabbits. One day he decided to count the total number of heads and legs of his animals. He told his friends that there were 30 heads and 76 legs in all.
How many chickens does Jessie have on his farm?
How many rabbits does Jessie have on his farm?
Answers
Let x represent number of rabbits and y represent number of chickens.
We have been given that Jessie told her friends that there were total 30 heads for both animals. This means that there are total 30 animals.
[tex]x+y=30...(1)[/tex]
[tex]y=30-x...(1)[/tex]
We have been given that Jessie only had chicken and rabbits. We know that a rabbit has 4 legs, so total number of legs for x rabbits would be [tex]4x[/tex].
We know that a chicken has 2 legs, so total legs of y chickens would be [tex]2y[/tex].
Since all animals has 76 legs in all, so we can represent this information in an equation as:
[tex]4x+2y=76...(2)[/tex]
Upon substituting equation (1) in equation(2), we will get:
[tex]4x+60-2x=76[/tex]
[tex]2x+60=76[/tex]
[tex]2x+60-60=76-60[/tex]
[tex]2x=16[/tex]
[tex]\frac{2x}{2}=\frac{16}{2}[/tex]
[tex]x=8[/tex]
Therefore, Jessie have 8 rabbits on his farm.
Number of chickens would be [tex]y=30-x\Rightarrow 30-8=22[/tex].
Therefore, Jessie have 22 chickens on his farm.
100 to anyone who can answer all of these !!!
Answers
Answer:
24yrds is (a) 24.12yrds is (b) 64yrds is (c) And that's all i can do, don't get mad at me please.
Step-by-step explanation:
Can someone helpppppppppp
Answers
Answer:
A
Step-by-step explanation:
The reason it is A is because
It goes in biggest to lowest A B C D
C and B don't follow that so we are left with A and D
In answer D C and B are too close in percentage therefore it cannot be D
Therefore your answer is A
Hope this helped!
Write the equation of the circle P graphed below.
Answers
What factors do 6 and 12 have in common?
Answers
Answer:
6x^2 im pretty sure thats whats its asking for
Step-by-step explanation:
Find the area of the pentagon.
A) 107 inches2
B) 116 inches2
C) 150 inches2
D) 182 inches2
Find the area of the pentagon.
A) 107 inches2
B) 116 inches2
C) 150 inches2
D) 182 inches2
Answers
Answer:
A
Step-by-step explanation:
Answer:
A) 107 inches2
Step-by-step explanation:
4*16= 64
64/2 = 32
9+16 = 25
25/2 = 12.50
12.50*6 = 75
32 + 75 = 107
Got it right in USA TESTING
Can someone please help me with this?
Answers
i’m doing the first one.
the filled in circle goes to the 8 and put an arrow facing the right.
inequality-
x ≥ 8
What is the value of s?
units
0
5
В
8
15
S
D
Answers
Consider the triangle ABD,
Here,
AB = 5
BD = 15
AD = s
As we know,
In a triangle, the sum of lengths of two sides is greater than the third side.
So,
[tex]5 + 15 > s[/tex]
[tex]15 + s > 5[/tex]
[tex]s + 5 > 15[/tex]
Now,
To satisfy the equation, the value of s can possibly be 11, 12, 13, 14, 15, 16, 17, 18, 19
Answer: the value of s is 17 units
Step-by-step explanation: youre welcome
