find the area of the pentagon in the diagram below.
15 square inches
20 square inches
25 square inches
28 square inches
Answers
The area of the pentagon is approximately 15 square inches.
To find the area of the pentagon, we can use the formula for the area of a regular pentagon:
Area = (5/4) * (s²) * (1/tan(π/5)),
where "s" is the length of the side of the pentagon.
Given that the sides of the pentagon are as follows:
Two smallest sides = 2 inches,
Two largest equal sides = 4 inches,
One other equal side = 3 inches.
Since the pentagon is not a regular pentagon, we need to find the area by dividing it into different shapes and then calculating their individual areas.
The pentagon can be divided into three shapes: a rectangle and two triangles.
Rectangle:
The two smallest sides (2 inches) form the length and width of the rectangle.
Area of the rectangle = Length * Width = 2 inches * 2 inches = 4 square inches.
Triangle 1:
The two largest equal sides (4 inches) and one of the 3-inch sides form a triangle.
To calculate the height (h) of the triangle, we can use the Pythagorean theorem, since it is a right triangle.
h² = (4 inches)² - (1.5 inches)², [1.5 inches is half of the 3-inch side]
h² = 16 inches² - 2.25 inches²,
h² = 13.75 inches²,
h ≈ 3.7 inches.
Area of Triangle 1 = (1/2) * Base * Height = (1/2) * 3 inches * 3.7 inches ≈ 5.55 square inches.
Triangle 2:
The two largest equal sides (4 inches) and the other 3-inch side form another triangle.
Using the same height (3.7 inches) from Triangle 1:
Area of Triangle 2 = (1/2) * Base * Height = (1/2) * 3 inches * 3.7 inches ≈ 5.55 square inches.
Now, to find the area of the pentagon, we add the areas of the rectangle and the two triangles:
Total Area = Area of Rectangle + Area of Triangle 1 + Area of Triangle 2
Total Area = 4 square inches + 5.55 square inches + 5.55 square inches
Total Area ≈ 15.1 square inches.
Therefore, the area of the pentagon is approximately 15.1 square inches.
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Related Questions
A car wash attendant counted the number of cars washed and the total amount of money earned. The
company charged the same price for each car washed and earned $165 for 15 cars, $231 for 21 cars, and $275
for 25 cars. Write an equation for the relationship between the number of cars washed, n, and the number of
dollars earned, m.
Answers
Answer:
total=n÷m $165÷15,$231÷21 and $275÷25
Can someone pls help me! Pretty sure my teacher hates me, and she won’t help me with these!
Answers
Answer:
5. 43.98 (if not rounding pi, if rounding pi it is 43.96)
6. 201.06 (if not rounding pi, if rounding pi it is 200.96)
7. 72.8
8. 84
9. 3.6
10. 140
11. C
12. 12.6
Step-by-step explanation:
5. C=2*pi*r
6. A=pi*r^2
7. angles in triangle must add up to 180
8. A=bh
9. radius is half of diameter
10. A=(hb)b/2
11. A=pi*r^2
12. radius is 1/2 of diameter
20 people applied for a job. Everyone either has a school certificate or diploma or even both. If 14 have school certificates and 11 diplomas how many have a school certificate only
Answers
Given:
Either has a school certificate or diploma or even both = 20 people
Having school certificates = 14
Having diplomas = 11
To find:
The number of people who have a school certificate only.
Solution:
Let A be the set of people who have school certificates and B be the set of people who have diplomas.
According to the given information, we have
[tex]n(A)=14[/tex]
[tex]n(B)=11[/tex]
[tex]n(A\cup B)=20[/tex]
We know that,
[tex]n(A\cup B)=n(A)+n(B)-n(A\cap B)[/tex]
[tex]20=14+11-n(A\cap B)[/tex]
[tex]20=25-n(A\cap B)[/tex]
Subtract both sides by 25.
[tex]20-25=-n(A\cap B)[/tex]
[tex]-5=-n(A\cap B)[/tex]
[tex]5=n(A\cap B)[/tex]
We need to find the number of people who have a school certificate only, i.e. [tex]n(A\cap B')[/tex].
[tex]n(A\cap B')=n(A)-n(A\cap B)[/tex]
[tex]n(A\cap B')=14-5[/tex]
[tex]n(A\cap B')=9[/tex]
Therefore, 9 people have a school certificate only.
Use a graphing calculator to approximate the vertex of the graph of the parabola defined by the following equation.
y = negative 2 x squared + 7 x + 4
a.
( 1.75, -2.125)
c.
( 1.75, 10.125)
b.
( 1.75, 4)
d.
( -1.75, 10.125)
Answers
Given:
The equation of a parabola is:
[tex]y=-2x^2+7x+4[/tex]
To find:
The vertex of the graph of the given equation by using a graphing calculator.
Solution:
We have,
[tex]y=-2x^2+7x+4[/tex]
By using the graphing calculator, draw the graph of the given equation as shown below.
From the below graph it is clear that the function is maximum at point (1.75,10.125).
So, the vertex of the given equation is (1.75,10.125).
Therefore, the correct option is c.
The entrance hall in Black's family house has a perimeter of 71 2/3 ft.IF it is 9 2/5 ft wide, how long is it?
Answers
Answer: 26 13/30 feet
Step-by-step explanation:
The hall is in the shape of a rectangle. The perimeter of a rectangle is:
= 2(length + width)
= 2l + 2w
Since perimeter = 71 2/3 ft and Width = 9 2/5 ft wide, the length will be calculated thus:
Perimeter = 2l + 2w
71⅔ = 2l + 2(9 2/5)
71 2/3 = 2l + (2 × 47/5)
71 2/3 = 2l + 94/5
71 2/3 = 2l + 18 4/5
Collect like terms
2l = 71 2/3 - 18 4/5
2l = 71 10/15 - 18 12/15
2l = 52 13/15
l = (52 13/15 ÷ 2)
l = 793/15 × 1/2
l = 793/30
l = 26 13/30
Therefore, the length is 26 13/30ft
I need help with these two problems ASAP. Please show your work:)
Answers
The formula for the circumference of a circle is [tex]\pi d[/tex].
In a:
The radius is 8 cm.
Therefore the diameter (d) would be 16cm (8 * 2)
Hence, the circumference is [tex]16\pi[/tex]
In b:
The diameter is already given: 13 in.
Thus, the circumference is [tex]13\pi =40.84[/tex] (2dp)
During a sale, a dress is marked down from a selling price of $90 to a sale price of $72. What is the percent markdown?
Answers
Answer:
20 %
Step-by-step explanation:
If the three lengths form a triangle, then determine if the three lengths form an acute, right, or obtuse triangle. Show your work.
Answers
Answer: Acute Triangle.
Step-by-step explanation:
3 square root 15 + 16 + 11 = 38.6189500386 degrees ughhhh why does this exist.
An acute triangle is less than 90 degrees so this an acute triangle.
WILL MARK FOR BRAINIEST!!!!
Find the area of the composite shape.
Answers
a=bh/2
6x10=60
7x6=42/2=21
Add together: 60+21=81
81 is your final answer
Round to the nearest tenth
1. Find x.
Answers
Answer:
x= 25.5 not rounded x=25.51393657
Step-by-step explanation:
Decide what trig ration you need/want to use. The 27 degrees are opposite of the 13 and adjacent to the x which means your ratio should be o/a or 13/x. The trig ratio needed is Tangent. Now you can write the equation as tan(27)=13/x and start solving.
tan(27)=13/x multiply the x on both sides and you'll have x * tan(27)=13 and decide which to put into your calculator and you'll get x=25.51393657 rounded as 25.5
The lengths of a certain species of fish are approximately normally distributed with a given mean ll and standard
deviation. According to the Empirical Rule, what percentage of the fish will have lengths within 1 standard deviation
of the mean?
-34%
-47.5%
-68%
-99.7%
Answers
The percentage of fish which will have the lengths within 1 standard deviation of the mean is 68%.
What is Empirical Rule?Empirical rule is a rule for normally distributed data which defines that almost all the data observed ranges between three standard deviations from the mean.
According to empirical rule,
68% of the data lies in the standard deviation of ±1.
95% of the data lies in the standard deviation of ±2.
99.7% of the data lies in the standard deviation of ±3.
Given,
The lengths of a certain species of fish are approximately normally distributed with a given mean and standard deviation.
According to the Empirical Rule, 68% of the fish will have lengths within 1 standard deviation of the mean.
Hence the required percentage is 68%.
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Amelia can spend no more than $90 per day to rent a car. A car rents for $35 per day plus $0.22 per mile. How many miles can Amelia drive without going over her budget?
Which of the following inequalities best represents the given scenario?
A. 35+0.22m≤90
B
35m+0.22≤90
C
35+0.22m≥90
D
35m+0.22≥9
Answers
Answer:
c
Step-by-step explanation:
I need Help please!!
Answers
Help asap! No links or weird answers, please :(
The question and answer choices are in the picture below. The question is about scatter plots.
Answers
Answer: b
Step-by-step explanation:
im guessing
The volume of a cylinder is 720π cm3. The height of the cylinder is 20 cm. What is the radius of the cylinder?
Answers
Answer:
Radius = 3.38 cm
Step-by-step explanation:
Here's your solution
=> The volume of cylinder = 720π cm^3
=> The height of cylinder = 20 cm
=> Radius = ?
=> Formula of volume of cylinder = πr^2h
=> 22/7 * r^2 * 20 = 720π cm^3
=> r^2 = (720*7)/20*22
=> r^2 = 11.45
=> r = √11.45
=> r = 3.38 cm
hope it helps
BRAINLIEST BRAINLIEST BRAINLIEST PLEASE ANDSER IT IS TIMED THANK YOU SO MUCCH
Answers
Answer:
x=-b/2a
Step-by-step explanation:
hope that helps :)
mark as brainliest please :)
Answer:
The axis of symmetry is x
Give brailiest, i gave you correct answer
determine whether a triangle with given side lengths will be a right triangle?
19.5,12,13
20.8,15,17
21.2,4,7
22.7,24,25
23.3,9,10
24.12,13,25
Answers
Answer:
Step-by-step explanation:
Apply the Pythagorean Theorrem. Find the sum of the squares of the two shortest sides and determine whether this sum equals the square of the longest side:
#19: 5^2 + 12^2 = ? = 13^2
25 + 144 = ? = 169 This is true, so you do have a right triange in #19.
#21: 2^2 + 4^2 = ? = 7^2, or 4 + 16 = ? = 49 This is false. Not a right
triangle.
Apply this same approach (Pythagorean Theorem) to the remaining problems.
Abby's friend told her that he drew a quadrilateral with exactly one pair of parallel sides. Abby said it must be a trapezoid. Is she correct
Answers
Answer:
Yes, she is correct
Step-by-step explanation:
A trapezoid has exactly one pair of parallel lines and 4 sides
6/4.2 = n/7
What is the value of n
Giving a brainliest
Also dont do one of those link answers or I will report you
Answers
Step-by-step explanation:
Given
6/4.2 = n/7
Cross multiply
6* 7 = 4.2n
4.2n = 42
n = 42 / 4.2
n = 10
Hope it will help :)❤
Answer: n= 10
I use this app called Cymath
11 to the power of negative 4 / 11 to the power to 8
Answers
Answer:
11^-12 or 11 to the power or negative twelve
Step-by-step explanation:
11^-4 / 11 ^ 8
according to the laws of indices, when dealing with powers, division is subtraction. so:
-4 - 8 = -12
answer = 11^ -12
Answer:
Hello There!
Your answer is:
2.2This is rounded, since you get this: 2.2094836e-42If this helps, please give me a thanks!!
- abakugosimp
1. Which of the following natural numbers are perfect squares? Give reasons in support
of your answer.
(i) 729
(ii) 5488
(iii) 1024
(iv) 243
Answers
Answer:
729 and 1024
Step-by-step explanation:
If you take the square root of all of these numbers, only 729 and 1024 will give whole numbers.
Have a Great Day!
WHATS TYE ANSWER TO ALL OF THESE! I NEED TO KNOW ASAP! PLEASE!
Answers
Answer:
[tex]x+3>27\\ x-8>12\\ 7x\leq 14\\ x+15\geq 4[/tex]
Find the value of x and y. Triangle MNP = triangle TUS
Answers
Answer:
x = 32, y = 51
Step-by-step explanation:
Since the triangles are congruent then corresponding sides and angles are congruent, that is
∠ U = ∠ N
∠ N = 180° - (142 + 24)° = 180° - 166° = 14° , then
2x - 50 = 14 ( add 50 to both sides )
2x = 64 ( divide both sides by 2 )
x = 32
and
NP = US
2x - y = 13
2(32) - y = 13
64 - y = 13 ( subtract 64 from both sides )
- y = - 51 ( multiply both sides by - 1 )
y = 51
Using the triangle theorem, the values of x and y is 32° and 51° respectively
From △MNP
∠M + ∠N + ∠P = 180° (Sum of interior angles in a triangle)
N = 180 - (142 + 24)
N = 180 - 168
N = 14°
Equate the expression :
2x - 50 = 14
2x = 14 + 50
2x = 64
x = 64 / 2
x = 32°
From ; 2x - y = 13 _____(1)
Substitute x = 32 into the expression ;
2(32) - y = 13
64 - y = 13
64 - 13 = y
51° = y
Therefore, the values of x and y is 32° and 51° respectively.
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Which of the following has the smallest probability?
(a) Pt > 2) ift has 5 degrees of freedom.
(b) P(t > 2) ift has 2 degrees of freedom.
(C) PC: > 2) ifz is a standard Normal random variable.
(d) Pt <2) ift has 5 degrees of freedom.
(e) Plz < 2) if z is a standard Normal random variable.
Answers
The expression with the smallest probability is: (C) P(z > 2), if z is a standard Normal random variable.
What is a z-core?A z-core is also known as a standard score and it can be defined as a measure of the distance between a data point (raw score) and the mean, when standard deviation units are used.
In Statistics, z-scores can either be positive or negative and it is calculated by using this formula:
[tex]Z=\frac{x\;-\;u}{\delta}[/tex]
Where:
x is the sample mean or observed data.u is the mean.[tex]\delta[/tex] is the standard deviation.In this exercise, we would have the smallest probability for P(z > 2), when z is a standard Normal random variable.
Read more on z-scores here: https://brainly.com/question/4302527
I really need help please I’ll mark Brainlest
Answers
“28 is 40% of what number?” i got 70, is that correct?
Answers
Answer:
70
You got it correct :)
Step-by-step explanation:
[tex]\frac{28}{y} =\frac{40}{100}[/tex]
y × 40 = 100 × 28
40y = 2800
40y ÷ 40 = 2800 ÷ 40
y = 70
Dr. Seals borrows $15,000 to remodel her backyard. The interest rate is 3%. The interest is compounded twice a year for two years. How much is the total she pays? How much is the interest?
Answers
Answer:
$1688.26
interest= $188.26
Step-by-step explanation:
Nathan made cookies for Remembrance Day. He made 2 2/3 dozen chocolate cookies, 1
dozen peanut cookies, and 2 1/2 dozen oatmeal cookies. If he puts the same number of each
cookie in each bag and has no cookies left over, what is the largest number of bags he can fill?
Answers
20 m
12 m
b
What is the perimeter?
meters
Answers
Answer:
if length is 20 and width is 12 then the perimiter is 64
Step-by-step explanation:
The table shows the prices of some breakfast items at a restaurant. Sara ordered 2 eggs, a slice of bacon, and a glass of juice for breakfast. The sales tax for the order was $0.48. She paid for her breakfast with a $10 bill.
How much change should sara receive from the $10 bill?
Answers
Answer:
$3.56
Step-by-step explanation:
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Answer:
3.56
Step-by-step explanation:
First you wanna add the prices of all the food so its
Two Eggs= 3.38
Slice of Bacon= 1.49
Orange Juice= 1.09
Add All then you get 5.96 and add sales tax so you get 6.44
The Subtract 10.00 - 6.44 = A/3.56