Find the area of the shaded region below.
All shapes in the figures are regular polygons.
PLSS HELP
Answers
Answer:
Step-by-step explanation:
We have 2 hexagons there, so we need to use the area formula for the large hexagon - the area of the small hexagon. As long as both of these are regular (and they are), we will use the formula
[tex]A=\frac{1}{2}ap[/tex]
where a is the apothem and p is the perimeter of the hexagon. We'll start with the large one first.
Note that a hexagon has 6 central angles that are all equivalent in degree. 360 / 6 = 60 degrees. Each of those 6 triangles has a vertex angle of 60. If we extract one of those triangles and then cut it in half by dropping an altitude from the vertex angle to the base of the triangle, we get a right triangle. The vertex angle is 30, one base angle is 90 and the other is 60. The height of this right triangle is the apothem, for which we want to solve. Using right triangle trig,
[tex]tan(60)=\frac{a}{7}[/tex] The 7 comes from the fact that when we split the triangle in half by dropping an altitude, we not only split the vertex angle in half, we also split the base length in half...from 14 to 7. Continuing,
7 tan(6) = a and
a = 12.124
Filling in the area now for the large hexagon:
[tex]A=\frac{1}{2}(12.124)(84)[/tex] {the perimeter is 6 sides times a length of 4 per side} and
A = 509.208
Now for the small hexagon. We'll do the same thing...extract a triangle and cut it in half by dropping an altitude and solving for a which is the height of the triangle. This half triangle has a base of 3 (half of 6).
3 tan(60) = a and
a = 5.196
Filling in the area now for the small hexagon:
[tex]A=\frac{1}{2}(5.196)(36)[/tex] and
A = 93.528
Now subtract the smaller area from the larger:
509.208 - 93.528 = 415.68
Related Questions
2 people are trying different phones to see which one has the better talk time. ChatLong has an average of 18 hours with a standard deviation of 2 hours and Talk-a-Lot has an average of 20 hours with a standard deviation of 3. The two people who tested their phones both got 20 hours of use on their phones. For the z-scores I got 1 for the ChatLong company and 0 for Talk-a-lot. What is the percentile for each z-score?
Answers
Answer:
Step-by-step explanation:
The percentile for the z scores are gotten from the normal distribution table. The z cores are already known.
1) For the ChatLong company, the z score is 0. The area corresponding to the z score from the normal distribution table is 0.5. Therefore, the percentile is
0.5 × 100 = 50%
2) For the Talk-a-lot company, the z score is 1. The area corresponding to the z score from the normal distribution table is 0.84. Therefore, the percentile is
0.84 × 100 = 84%
It costs $10 to make earphones, and the start-up costs for manufacturing are $5,000. How many earphones must be produced to get to a cost per unit of $20 a. 100 b. 30 c. 200 d. 500
Answers
With that information we can create the equation
10x + 5000 = 20x
where x is the number of earphones produced
10x is the cost to make each earphone, 5000 being the fixed costs of manufacturing, and 20x being the total revenue of selling each earphone for $20
Now to solve the equation:
subtract both sides by 10x
10x - 10x + 5000 = 20x - 10x
5000 = 10x
Now divide both sides by 10
5000/10 = 10/10 x
500 = x
Answer: D
Hope it helps :)
500 earphones must be produced to get the cost price of one ear phone of $20.
What is linear equation in one variable?The linear equations in one variable is an equation which is expressed in the form of ax + b = 0, where a and b are two integers, and x is a variable and has only one solution.
According to the given question
The start-up costs for manufacturing earphones is $5,000.
Also, the cost to make earphones is $10.
Let x number of earphones will produced to get a cost per unit of $20.
From the given conditions, we will get a linear equation in one variable
10x + 5000 = 20x
⇒ 5000 = 20x -10x
⇒ 5000 = 10x
⇒ x = 500
Hence, 500 earphones must be produced to get the cost of earphone of $20.
Learn more about linear equation in one variable here:
https://brainly.com/question/17139602
#SPJ2
Write each expression in radical form. (3b)^4/3
Answers
Answer:
Step-by-step explanation:
(3b)^(4/3) is equivalent to ∛(3b)^4.
∛[81b^4] is also equivalent.
at the farmer’s market, you can buy 3 melons for $13.50. What is the cost of one melon
Answers
Answer:
4.50 per melon
Step-by-step explanation:
Take the price and divide by the number of melons
13.50/3
4.50 per melon
Is triangle PTC congruent to triangle LAF?
Answers
Answer:
Yes; LA (D)
Step-by-step explanation:
one of the legs are congruent. LA and PT are congruent. This makes up the "L" part of "LA"
Also, angle PCT and angle LFA are congruent base on the diagram. This makes up the "A" part of "LA"
On a shopping trip, Rachel spent $3 on a bus ticket, $10 on a book, and $4 for a smoothie . She had $21 left after the trip. How much money did she start with?
Answers
The whole is 1,000,000. 50,000 is what percent of that
Answers
Answer:
500000000
Step-by-step explanation:
50,000 percent is or 1,000,000 is 500000000. I hope this is correct. I did the answer by multiplying them together.
The easiest way I can explain it is take out as many zeros as you can equally from each number, and you are left with 100 and 5, so 5%. Sorry this isn’t a good explanation.
Parallel lines are defined as lines that have only one point in common True or false
Answers
Answer:
false
Step-by-step explanation:
parallel lines are lines that never meet or cross and go side by side.
On the coordinate plane shown, each grid unit represents 10 feet. Polygon QRST has vertices Q(20, 30), R(−10, 30), S(−10, −20), and T(20, −20), and represents the floor plan of a room. Find the perimeter and area of the room.
Answers
The coordinate plane is missing, so i have attached it.
Answer:
Perimeter of room = 140 ft
Area of room = 1200 sq.ft
Step-by-step explanation:
From the cordinate plane attached, we can see the polygon QRST which represents the floor plan of the roo.
Thus;
The length of the sides of the room are;
ST = RQ = 30
QT = RS = 40
Perimeter of a rectangle is the sum of all sides of the rectangle.
Thus, perimeter of the room = (30 × 2) + (40 × 2) = 140 ft
Now, area of a rectangle is the product of two perpendicular sides.
Thus area of room = 40 x 30 = 1200 sq.ft
The slope between (1, 6) (-5, -7)
Answers
Answer:
Step-by-step explanation:
So the right answer is 13/6
please see attached picture for full solution
hope it helps
Good luck on your assignment
Choose the correct product of (8x − 4)(8x + 4). (1 point) 64x2 − 16 64x2 + 16 64x2 − 64x + 16 64x2 + 64x + 16
Answers
Answer:
The correct answer is "[tex]64*x^2 - 16[/tex]".
Step-by-step explanation:
The product [tex](8*x - 4)*(8*x + 4)[/tex] is a notable product, which happens when we have the product of the sum of two values with the subtraction of these same two values. In cases like this the answer will always be the first term squared minus the second term squared, therefore we have:
[tex](8*x - 4)*(8*x + 4) = 64*x^2 - 16[/tex]
The correct answer is "[tex]64*x^2 - 16[/tex]".
Answer:
64x^2 -16
took the test
What is the y-value when x equals 7?
y = 310 - 25(x)
Answers
Answer:
y=135
Step-by-step explanation:
To find the solution, we must put 7 in for x and solve, as shown:
[tex]y=310-(25)(7)\\y=310-175\\y=135[/tex]
Which descriptions from the list below accurately describe the relationship
between AXYZ and AUVW? Check all that apply.
Answers
Answer:
similar and same shape
Step-by-step explanation:
3/10 is equivalent to how many hundreths
Answers
It’s thirty hundredths.
The ratio of lions to tigers at the Metropolitan Zoo is 12 to 8. Which ratio is equivalent to 12 to 8? A.6 to 3 b.8 to 12 c.15 to 10 d.24 to 18
Answers
Answer:
c.15 to 10
Step-by-step explanation:
The ration 12 to 8 means that for every 12 lions there are 8 tigers in the zoo.
Ratios have the quality of conservate their meaning when both values in the ratio are multiplied or divided by the same number.
For example:
a ratio of 2 to 4 is the same as a ratio of 3 to 6 (both values are multiplied by 1.5 (or in fraction by 3/2) ).
in the same way that the ratio 9 to 3 is the same as 3 to 1 (divide both values by 3).
In this case we are looking for an equivalent ratio to the 12 to 8 ratio, the answer is
c.15 to 10
because this results from multiplying the two original values by 1.25 or, in fraction, by 5/4. You can see this becase
12*1.25 = 15
and
8*1.25 = 10
we get that when we multiply the ratio 12 to 8 by 1.5 the equivalent ratio is option C.
Which of the binomials below is a factor of this
trinomial?
x2 - 13x + 30
O A. X-3
O B. X+5
O c. x-5
O D. X+ 3
Answers
Answer:
A
Step-by-step explanation:
Given
x² - 13x + 30
Consider the factors of the constant term (+ 30) which sum to give the coefficient of the x- term (- 13)
The factors are - 3 and - 10, since
- 3 × - 10 = + 30 and - 3 - 10 = - 13 , thus
x² - 13x + 30 = (x - 3)(x - 10) ← in factored form
Thus (x - 3) is a factor of the polynomial → A
Answer:
[tex](x - 3)[/tex]
Answer A is correct
Step-by-step explanation:
[tex]{x}^{2} - 13x + 30 \\ {x}^{2} - 10x - 3x + 30 \\ x(x - 10) - 3(x - 10) \\ = (x - 3)(x - 10)
\\ [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Luca decides to play Wheel of Letters. To play the game, contestants spin a wheel with 26 equal sections, lettered A through Z. If the pointer lands on any letter in the phrase "County Fair," the contestant wins a prize. What is the probability that Luca will win Wheel of Letters? Your answer must be simplified
Answers
Answer:
10/26, simpified to 5/18
Step-by-step explanation:
10 letters in "County Fair" None repeat.
26 letters in the alphabet
10/26
5/18
HELP! ASAP: The graph relates the number of gallons of white paint to the number of gallons of red paint Jess used to make the perfect pink. Write an equation that describes the relationship.
Answers
Answer:
y = (2/3)*a
Step-by-step explanation:
We can write the equation using the linear equation model:
y = ax + b
Then, to find the values of 'a' (slope) and 'b' (y-intercept), we can use two points of the graph.
Using the point (0,0), we have:
0 = a*0 + b
b = 0
Using the point (3,2), we have:
2 = a*3 + b
a = 2/3
So our equation is:
y = (2/3)*a
Answer:
The correct answer is Y= 3/4x
Step-by-step explanation:
I did savvas realize, the is the the correct answer↑
Please help me with this quick!!!!
Solve the following:
A) 4x-1/2=x+7
B) 3x+2=2x+13/3
C) 2x-7/4=x+3/3
Answers
Answer:
A) 2.5
B) 7/3
C) 11/4
Step-by-step explanation:
A)
4x-1/2=x+7
3x-1/2=7
3x=7.5
x=2.5
B)
3x+2=2x+13/3
x+2=13/3
x=7/3
C)
2x-7/4=x+3/3
x=11/4
Hope this helps!
identify the graph of the equation and find (h k). x^2-2x-y^2-2y-36=0
Answers
Answer:
c. hyperbola, (1,-1)
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
Solve this inequality; 4.2x+5.6<7.2 - 8.3x isolate the constant term on the left side odf the inequality by.................... Both sides of the inequaity
Answers
Answer:
x < 0.128
Step-by-step explanation:
The inequality given is:
4.2x + 5.6 < 7.2 - 8.3x
Let us collect like terms:
4.2x + 8.3x < 7.2 - 5.6
12.5x < 1.6
=> x < 1.6/12.5
x < 0.128
which points are separated by distance of 6 units?
A. (5,6) (4,6)
B. (1,3) (6,3)
C. (8,1) (1,1)
D. (7,2) (1,2)
Answers
Option (D) points (7,2) (1,2) are separated by distance of 6 units.
What is distance between two points?It is the length of the straight line connecting these points in the coordinate plane. This distance can never be negative, therefore we take the absolute value while finding the distance between two given points. The distance formula is an application of the Pythagorean theorem.
For the given situation,
The distance between the two points must be 6 units.
Let the points be (x1,y1) and (x2,y2)
The distance formula is
[tex]d=\sqrt{(x_2-x_1)^{2} +(y_2-y_1)^{2} }[/tex]
We need to check all the options.
Option A: (x1,y1) = (5,6), (x2,y2) = (4,6)
⇒ [tex]d=\sqrt{(4-5)^{2} +(6-6)^{2} }[/tex]
⇒ [tex]d=\sqrt{(-1)^{2} +(0)^{2} }[/tex]
⇒ [tex]d=\sqrt{1}[/tex]
⇒ [tex]d=1[/tex]
Distance ≠ 6. So option A is incorrect.
Option B: (x1,y1) = (1,3), (x2,y2) = (6,3)
⇒ [tex]d=\sqrt{(6-1)^{2} +(3-3)^{2} }[/tex]
⇒ [tex]d=\sqrt{(5)^{2} +(0)^{2} }[/tex]
⇒ [tex]d=\sqrt{25}[/tex]
⇒ [tex]d=5[/tex]
Distance ≠ 6. So option B is incorrect.
Option C: (x1,y1) = (8,1) , (x2,y2) = (1,1)
⇒ [tex]d=\sqrt{(1-8)^{2} +(1-1)^{2} }[/tex]
⇒ [tex]d=\sqrt{(-7)^{2} +(0)^{2} }[/tex]
⇒ [tex]d=\sqrt{49}[/tex]
⇒ [tex]d=7[/tex]
Distance ≠ 6. So option C is incorrect.
Option D: (x1,y1) = (7,2) , (x2,y2) = (1,2)
⇒ [tex]d=\sqrt{(1-7)^{2} +(2-2)^{2} }[/tex]
⇒ [tex]d=\sqrt{(-6)^{2} +(0)^{2} }[/tex]
⇒ [tex]d=\sqrt{36}[/tex]
⇒ [tex]d=6[/tex]
Distance = 6. So option D is correct.
Hence we can conclude that option (D) points (7,2) (1,2) are separated by distance of 6 units.
Learn more about distance between points here
https://brainly.com/question/14645718
#SPJ3
A woman is 27 years older than her daughter, if the daughter is Y years old, what is the sum of their age
Answers
Three times a number is three more than twice the number. Which equation can be used to find the value of x, the unknown
number?
O 3x = 3 + 2x
O x = 3 + 2x
O 3x + 3 = 2x
O 3x = 3 + 2 + x
Answers
Answer:
The first option: 3x = 3 + 2x
Step-by-step explanation:
The question answers itself. In short:
x is our unknown number.
If three times a number (3x) is (=) three more (3) than (+) twice the number (2x).
What is the solution to the system of equations 2x + 3y = 40 and y = x +
10?
oy - y - 12
Answers
Answer:
hope this is correct
if 2^n+2-2^n+1+2^n= C*2^n, find the value of C
Answers
Answer:
c= 1
Step-by-step explanation:
To get rid of (c) on the right side, simply divide 2^n both side. But first collect like terms on the left side so you will get 2^n + 1 which you will then simplify the like term(2^n) and you will left with c= 1.
Is the purple triangle a right triangle? Explain.
15.5
20.8 m
14.0 m
Answers
Answer:
15.5^2 + 14.0^ = 20.8^2
436.25 = 432.64
it is not a triangle because a+b is not = c
Answer: These given lengths do not make up a right triangle.
Step-by-step explanation:
In order to figure out if this is a right triangle or not, we would need to use the Pythagorean Theorem in order to verify if these lengths satisfy the properties of a right triangle. We would need to use the formula a^2 + b^2 = c^2.
14^2 + 15.5^2 = 20.8^2
196 + 240.25 = 432.64
436.25 ≠ 432.64
Therefore, this is not a right triangle.
In the distribution, the first quartile,median and mean are 30.8,48.5 and 42.0 respectively. If the co efficient skewness is -0.38, find the third quartile?
Answers
Answer:
The third quartile is 56.45
Step-by-step explanation:
The given parameters are;
The first quartile, Q₁ = 30.8
The median or second quartile, Q₂ = 48.5
The mean, [tex]\bar x[/tex] = 42.0
Coefficient of skewness = -0.38
The Bowley's coefficient of skewness (SK) is given as follows;
[tex]SK = \dfrac{Q_3 + Q_1 - 2 \times Q_2}{Q_3 - Q_1}[/tex]
Plugging in the values, we have;
[tex]-0.38 = \dfrac{Q_3 + 30.8 - 2 \times 48.5}{Q_3 - 30.8}[/tex]
Which gives;
-0.38×(Q₃ - 30.8) = Q₃ + 30.8 - 2 × 48.5
11.704 - 0.38·Q₃ = Q₃ - 66.2
1.38·Q₃ = 11.704 + 66.2 = 77.904
Q₃ = 56.45
The third quartile = 56.45.
A cake has circumference of 25 1/7inches. what is the area of the cake? use 227 to approximate π. round to the nearest hundredth. enter your answer in the box.
Answers
Answer:
Step-by-step explanation:
Hello,
The circumference of the cake is 25(1/7), but we don't know the area of the cake.
Assuming the cake has a shape of a circle,
Circumference of a circle = 2πr
Where r = radius of the circle.
Area of a circle = πr²
But π = 22 / 7
We have to first find the value of r.
2πr = 25(1/7)
2×(22/7)×r = 25(1/7)
(44/7)r = 176 / 7
(44 × 7)r = 176 × 7
44r = 176
r = 176 / 44
r = 4 inches
Area of the circle = πr²
A = (22 / 7) × 4²
A = 22 / 7 × 16
A = 352 / 16
A = 22 (inches)²
The area of the cake is 22in²
Solve for y.
–1(y–10)–11≤–19
Answers
Answer:
y≥18
Step-by-step explanation:
Answer:
y≥18
Step-by-step explanation:
Step 1 : Equation at the end of step 1 : ((0 - (y - 10)) - 11) - -19 ≤ 0
Step 2 : Equation at the end of step 2 : 18 - y ≤ 0
Step 3 : 3.1 Multiply both sides by (-1) Flip the inequality sign since you are multiplying by a negative number
Solve Basic Inequality
Inequality Plot
Answer: y ≥ 18
Hope this helps.