The diagram below shows a square inside a regular octagon. The apothem of the octagon is 15.69 units. To the nearest square unit, what is the area of the shaded region? 13 U 13 U Apothem length: 15.69 O A. 1463 square units B. 816 square units C. 647 square units OD. 764 square units
Answers
perimeter of octagon
8(13)104unitsNow area
perimeter×apothem /2104(15.69)/252(15.69)815.88units²Area of square
13²169units²Area of shaded region
815.88-169646.88units²647units²Answer:
C. 647 square units
Step-by-step explanation:
To find the shaded area, subtract the area of the unshaded square from the area of the octagon.
Area of the octagon
[tex]\textsf{Area of a regular polygon}=\dfrac{n\:l\:a}{2}[/tex]
where:
n = number of sidesl = length of one sidea = apothemGiven:
n = 8l = 13a = 15.69Substitute the given values into the formula and solve for A:
[tex]\implies \textsf{Area}=\sf \dfrac{8 \cdot 13 \cdot 15.69}{2}[/tex]
[tex]\implies \textsf{Area}=\sf \dfrac{1631.76}{2}[/tex]
[tex]\implies \textsf{Area}=\sf 815.88\:\:square \:units[/tex]
Area of the square
[tex]\implies \textsf{Area}=\sf 13^2=169 \:\:square \:units[/tex]
Area of the shaded region
= area of the octagon - area of the square
= 815.88 - 169
= 646.88
= 647 square units (nearest square unit)
Related Questions
Two friends, Vani and Shaquana, took summer jobs. The equation y=28.8xy=28.8x represents Vani's earnings in dollars and cents, yy, for working xx hours. Shaquana earned $653.40 in 33 hours.
How much less per hour does Shaquana earn than Vani?
Answers
An equation is formed of two equal expressions. Shaquana earns $10 less per hour than Vani.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The equation y=28.8x represents Vani's earnings in dollars and cents, y, for working x hours.
y = 28.8x
y/x = 28.8
Hence, Vani is paid $28.8 per hour.
The amount that Shaquana earned was $653.40 in 33 hours. Therefore, per hour she was paid
Amount per hour = $653.40/33 = $19.8 per hour
The difference between the two is,
Difference = $28.8 - $19.8 = $10
Hence, Shaquana earns $10 less per hour than Vani.
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Vani - 28.8
y=28.8x
Vani earns $28.80 per hour.
Shaquana -
653.40 / 33 = $19.80 per hour
Shaquana earns $19.80 per hour.
Vani − Shaquana = $28.80
$28.80−$19.80
=$9
Shaquana earns $9 less per hour than Vani.
The cost of 5kg of rice is Rs.425. find the cost of 1kg of rice
Answers
Answer:
Rs 85
Step-by-step explanation:
Cost of 5kgs of rice = Rs 425
Cost of 1 kg of rice = 425/5
= Rs 85
So, the cost of a kg of rice is Rs 85
A green gold bracelet weighs 56g. The bracelet is made from 75% gold, 20% silver and 5% copper.
(a) What is the mass of the gold in the bracelet?
(b) What is the mass of the copper in the bracelet?
Answers
Answer:
a. 42 g
b. 2.8 g
Step-by-step explanation:
a. Since the entire thing weighs 56g and gold is 75% of the mass you simply find 75% of the mass. This is done by converting the 75% into decimal form by dividing it by 100 to get 0.75 and then multiply it by the 56 g to get (0.75 * 56 g) = 42 g
b. same thing here as the previous answer. 5%/100 = 0.05. (0.05 * 56 g) = 2.8 g
Harry used 0.75 liters of gasoline on the first day of his trip, 1.5
liters on the second, 2.25 liters on the third, and 3 liters on the
fourth. Write a function to describe the sequence, and then use
the function to predict the amount of gasoline used on the
eighth day of his trip.
Oy=0.5n; 4 L
O y = 0.75n; 6 L
Oy=n; 8L
Oy=1.5m; 12 L
Answers
The function is to describe the sequence and the amount of gasoline used on the eighth day of his trip will be y = 0.75n and 6 L respectively. Option B is correct.
What is an arithmetic sequence's sum of terms?Each consecutive term in an arithmetic sequence has a common constant difference.
The sequence of the liters of gasoline on each day is;
0.75,1.5,2.25,3
The given series is an arithmetic series with a common difference of 0.75
Common difference,d=0.75
First-term,a=0.75
The amount of gasoline used on the eighth day of his trip.
The nth term of the arithmetic sequence is;
[tex]\rm a_n = a+(n-1)d \\\\ \rm a_8 = 0.75+(8-1)0.75 \\\\ a_8 = 6[/tex]
The 8th term of the arithmetic sequence is 6L.
The function is to describe the sequence and the amount of gasoline used on the eighth day of his trip will be y = 0.75n and 6 L.
Hence, option B is correct.
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Doubling the dimensions of a rectangle increases the area by a factor of 4.
If p represents doubling the dimensions of a rectangle and q represents the area increasing by a factor of 4, which are true? Select two options.
Answers
p → q represents the original conditional statement and the contrapositive of the original conditional statement. Then the correct options are A and E.
The missing options are given below.
What is dilation?Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.
There is no effect of dilation on the angle.
Doubling the dimensions of a rectangle increases the area by a factor of 4.
If p represents doubling the dimensions of a rectangle and q represents the area increasing by a factor of 4.
Then the true statement will be
Then the correct options are A and E.
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Solve the inequality and express your answer in interval notation.
Answers
The correct answer is option B which is (-4-√11) and (-4+√11).
What is inequality?
Inequality is the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.
The inequality is given as x² + 8x + 5 < 0 for we will draw a graph of the inequality and find the range of x which ranges from ( -7.31,- 0.68) So these points in the options will be equal to (-4-√11) and (-4+√11).
(-4 - √11) = -4 -3.31 =-7.31
(-4 + √11) = -4 +3.31 = -0.68
Therefore the correct answer is option B which is (-4-√11) and (-4+√11).
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Jane and David had identical chocolate bars.
David ate 78 of his chocolate bar.
Jane ate more of her chocolate bar than David.
What fraction of her chocolate bar could Jane have eaten?
Answers
Answer:
Step-by-step explanation:
I'm assuming you meant "David at 78% of his chocolate bar" which means he at 78/100 of his chocolate bar. So if Jane ate more she could've eaten n/100 of her chocolate bar where [tex]78 < n \leq 100[/tex]. Greater than 78 since David at 78/100 and less than or equal to 100 since 100/100 means Jane at the entire thing at 101/100 wouldn't make any sense.
Mr. Browner has 7 keys. He has 1 key
for his home, 2 keys for his car, and
the rest are for drawers in his office.
If Mr.
Browner picks one of his keys
without looking, what is the probability
it is for his car?
Options: 1/7, 2/7, 3/7, 5/7, 6/7
Answers
Answer:
2/7
Step-by-step explanation:
there are 7 total possibilities for the keys he picks, and out of those possibilities, 2 of them are car keys. this means the probability that it is for his car is 2/7.
[tex]\huge\mathscr\color{gold}\colorbox{black}{ANSWER:}[/tex]
[tex]{\qquad\qquad\qquad}[/tex]
You can choose Options: 2/7
[tex]__________________________________[/tex]
[tex]\large\mathcal\color{gold}\colorbox{black}{STEP-BY-STEP\: EXPLANATION:}[/tex]
[tex]{\qquad\qquad\qquad}[/tex]
Will i can choose 2/7 because 7 is probability keys he picks, and 2 keys he picks for looking a drawers in office to finding.
[tex]__________________________________[/tex]
Hope it helps Correct me if I'm wrong[tex]__________________________________[/tex]
[tex]\normalsize\color{brown}\boxed{☕TheQuestionner☕}[/tex]
When the sum of a list of integers is divided by the mean of the integers, the result is x. What does x represent?
Answers
Answer:
it is the number of intigers in the list
Based on the concept of integer and the options available, x does represent the number of 2 integers in the list.
What is Integers?An integer is a mathematical term that is known as the number zero, a positive natural number, or a negative integer with a minus sign.
Generally, Integers the negative numbers are the additive inverses of the corresponding positive numbers.
In this case, it has been mathematically proven that when the sum of a list of integers is divided by the mean of the integers the result x represents the total number of integers in the list.
Hence, in this case, it is concluded that the correct answer is option H. The numbers if integers in the list.
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find the value of x
a) 5
b) 35
c) 3
d) 7
Answers
Answer:
x=3
Step-by-step explanation:
due to its same angle of the graphic. it has to be +6 as well
23-29-35
35=11.×+2
35-2=33
33=11.×
x=3
A part of a line that starts at one endpoint and extends forever in one direction is a(n)
A. angle
B.point
C.line
D.ray
Answers
Answer:
[tex]\fbox {D. ray}[/tex]
Step-by-step explanation:
A part of a line that starts at one endpoint and extends forever in one direction is a ray.
Answer: D. Ray
Step-by-step explanation:
Let's do the process of elimination.
It's not A because there is only one line.
It is not B because a point is only a dot.
It is not C because a line extends forever from BOTH ends.
The correct answer is D because a ray starts on one endpoint and extends forever in one direction.
I hope this helps!! Pls mark brainliest!! :)
dsfghjmbhjghcvjkjjbhvgjjbkjguy8uygiyugykfgjhgghgjk
Answers
The equation y = 1/3x - 2 passes through the diagonals of ZDRN
How to determine the end result?The points are given as:
Z = (-3, -1)
D= (3, -1)
R = (3, -3)
N = (-3, -3)
The equation of the line is given as:
y = 1/3x - 2
When the points and the line equation are plotted in a graph on the same coordinate (see attachment), we can see that the equation y = 1/3x - 2 passes through the points Z = (-3, -1) and N = (-3, -3)
These points are the diagonals of the shape formed by the four points
Hence, the equation y = 1/3x - 2 passes through the diagonals of ZDRN
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what is the value of k such that 5x-2y=9 and 6x+ky=4 are perpendicular?
Answers
15
5x-2y=9......(1)
6x+ky=4......(2)
slope of eqn i= -5/-2
=5/2
slope of eqn ii = -6/k
since the line are perpendicular
5/2 * -6/k = -1
-30= -2k
k=15
12 identically sized pieces of timber are
x
cm long when put together. How long is each individual piece?
Answers
Answer:
[tex]\frac{x}{12}[/tex] (x/12)
Step-by-step explanation:
if 12 pieces combine to make x, [we know they are identical], each piece must be 1/12 of x [1/12·x = x/12]
(think of it like this: "x" length must be divided amongst 12 pieces, so, we divide x/ 12)
Answer:
Timber=x/12
Step-by-step explanation:
12 pieces long is x, if the length of each one is same, so the length of each one is x/12.
The function f(x) is shown on the graph.
On a coordinate plane, a curved line shaped like a w, labeled f of x, crosses the x-axis at (negative 2, 0), (negative 1, 0), crosses the y-axis at (0, 12), and crosses the x-axis at (2, 0) and (3, 0).
What is f(0)?
Answers
The value of f(0) is 12.
What is graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
By considering the graph we have to find f(0) which means we have to find that point where x- coordinate is zero.
Also, which shows that 12 the function f(x)
So, taking the point is (0,12) we can get f(0)= 12.
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1/5 divided by 4 equals to what
Answers
Answer:
1/5 divided by 4 equals to 0.05
Helpppp I stuck so please help
Me
Answers
Answer = #2 - 1/3^3
Step-by-step explanation:
{x + 8y = -16
{x-3y = -5
Answers
Answer: y= -1 and x=-8
x+8y=-16
x=-8y-16
so x-3y=-5
-8-16-3y=-5
-11y-16=-5
-11y=-5+16
-11y=11
y=-1
x-3y=-5
x+3=-5
x=-8
Step-by-Step Solution:
=> x + 8y = -16 (Eq. 1)
=> x - 3y = -5 (Eq. 2)
Subtracting Eq. 2 from 1, we get :-
8y + 3y = -16 + 5
11y = -11
y = -11/11
=> y = -1
Therefore, y = -1
Substitute value of ‘y’ in Eq. 2 :-
x - 3y = -5
x - 3(-1) = -5
x - -3 = -5
x + 3 = -5
x = -5 - 3
x = -5 + -3
=> x = -8
Therefore, x = -8
Hence, x = -8 and y = -1 (-8, -1)
The perimeter of a rectangle is 34 cm. The length is 1 cm longer than the width. What is the length of the longest side of the rectangle?
Answers
Answer: 9 cm
Step-by-step explanation:
The formula for the perimeter of a rectangle is [tex]2l+2w=P[/tex]
Where
l is the length
w is the width
and P is the perimeter (34)
Because the length is 1 cm longer than the width instead of representing the length is l we can use w+1
Sub in the known values and solve
Step 1: Simplify both sides of the equation with the Distributive Property
[tex]2(w+1)+2w=34\\(2)(w)+(2)(1)+2w=34\\2w+2+2w=34\\(2w+2w)+(2)=34\\4w+2=34\\[/tex]
Step 2: Subtract 2 from both sides.
[tex]4w+2-2=34-2\\4w=32[/tex]
Step 3: Divide both sides by 4.
[tex]\frac{4w}{4}=\frac{32}{4} \\w=8[/tex]
Step 4: Add 1 to w to find the length of the longer side
[tex]w+1\\8+1\\9[/tex]
please help me please
Answers
Answer:
b I think.
Step-by-step explanation:
sorry if im wrong
What is the answer?????
Answers
Answer:
36.7075 Hz is the answer
Jose began the day with eight Magikarps. After spending the day at the lake, he ended up with sixteen Magikarps.
Find the Percent of increase
thats all she wrote
Answers
A percentage is a way to describe a part of a whole. The percentage increase of Magikarps is 100%.
What are Percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
Jose began the day with eight Magikarps. After spending the day at the lake, he ended up with sixteen Magikarps. Therefore, The percentage increase of Magikarps is,
Percentage increase = (16-8)/8 × 100% = 100%
Hence, The percentage increase of Magikarps is 100%.
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COMPLETE THE FOLLOWING EQUATION USING APPROPRIATE SIGN ( +,-,x,÷) IN THE BOXES GIVEN:
REMEMBER TO USE (DMAS)
Answers
Answer:
) +, -
e) x, ÷
g) ÷
Step-by-step explanation:
what is the sum of first 6 terms
Answers
Answer:
182
Step-by-step explanation:
Sum = a(r^n -1) ÷ r - 1
1(-3^6 - 1) ÷ -3 -1
= 182
r = t2 ÷ t1 * since they stated that it is geometric
Solve using substitution method:
X= y/3 +2
7x − 5y = 10
Solve for (x,y)
Answers
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:x = 5/2 [/tex]
[tex] \qquad \tt \rightarrow \: y = 3/2[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: x = \cfrac{y}{3} + 2 \: \: \: \: \: \: \: \: - (1)[/tex]
[tex]\qquad \tt \rightarrow \: 7x -5 y = 10 \: \: - (2)[/tex]
[tex] \textsf{put value of x in equation 2} [/tex]
[tex]\qquad \tt \rightarrow \: 7 \bigg( \cfrac{y}{3} + 2 \bigg) - 5y = 10 [/tex]
[tex]\qquad \tt \rightarrow \: \cfrac{7y}{3} + 14 - 5y = 10 [/tex]
[tex]\qquad \tt \rightarrow \: \cfrac{7y}{3} - 5y = 10 - 14[/tex]
[tex]\qquad \tt \rightarrow \: \cfrac{7y - 15y}{3} = - 4[/tex]
[tex]\qquad \tt \rightarrow \: - 8y = - 4(3)[/tex]
[tex]\qquad \tt \rightarrow \: y = \cfrac{ - 12}{ - 8} [/tex]
[tex]\qquad \tt \rightarrow \: y = \cfrac{ 3}{ 2} [/tex]
[tex] \textsf{put value of y in equation 1 } [/tex]
[tex]\qquad \tt \rightarrow \: x = \cfrac{y}{3} + 2[/tex]
[tex]\qquad \tt \rightarrow \: x = \bigg (\cfrac{3}{2} \sdot\cfrac{1}{3} \bigg) + 2[/tex]
[tex]\qquad \tt \rightarrow \: x = \cfrac{1}{2} + 2[/tex]
[tex]\qquad \tt \rightarrow \: x = \cfrac{1 + 4}{2} [/tex]
[tex]\qquad \tt \rightarrow \: x = \cfrac{5}{2} [/tex]
Evaluate the expression for the given values of the variables:
2a³-7b²+ 3c - (d + e) a = 3, b = 2, c = 4, d = 11, and e = 7
Answers
Answer:
yes
Step-by-step explanation:
it's hard but you'll figure it out so don't worry
how many feet? help me please
Answers
Answer:
[tex]\fbox {400.41 feet}[/tex]
Step-by-step explanation:
Here we need to take the tan ratio of the angle.
⇒ tan 4° = 28/x = 0.0699268119
⇒ x = 28/0.0699268119
⇒ x = 400.41 feet
6 less than a number is less than the quotient of the number and 3.
Answers
Answer:
x<9
Step-by-step explanation:
x-6<x/3
3(x-6)<x
3x-18<x
3x-x<18
2x<18
X<18/2
X<9
There are 10 marbles in a bag. are red and the others are blue. 5 What is the ratio of red marbles to blue marbles? Question 11 * 1 There are 10 marbles in a bag . are red and the others are blue . 5 What is the ratio of red marbles to blue marbles ?
Answers
Answer:
%50 1÷2
if there is missing information. if there is 10 total marbels 5 would be red, 5would be blue.
We have two fractions, 1/6 3/8 and we want to rewrite them so that they have a common denominator (and whole number numerators). What numbers could we use for the denominator? Choose 2 answers:
Answers
Answer:
See below
Step-by-step explanation:
The denominator has to be divisible by 6 and 8
you could choose 24 48 72 96 etc
