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
Awnser question and show your work if you can (i will give brainliest
Answers
Answer:
answer is -1.75
Step-by-step explanation:
[tex]y = 12 \\ y = - 4x + 5 \\ \\ \: \: \: \: 12 = - 4x + 5 \\ - 5 \: \: \: \: \: \: \: \: \: \: \: - 5 \\ \\ 7 = - 4x \\ \div - 4 \: \: \: \: on \: both \: sides \\ \\ - 1.75 = x[/tex]
A rectangle with a length of 22 feet and an unkown width,W, has a perimeter of 74 feet. Set up and slove an equation to find the vaulur of W
Answers
Answer: W=15
Step-by-step explanation: The equation you set up is 2(L) + 2(W)=74
2(22) + 2W=74
44+2W=74
Subtract 44 from both sides
2W=30
Divide both sides by 2
W=15
some math put with other math equals 15
In a cookie jar containing 6
6
chocolate
chip cookies, 8
8
wafer cookies and 10
10
double chocolate cookies, what is the
probability that a person who isn't looking
when they get a cookie will get a chocolate
chip cookie?
Answers
What is the value of b?
Help please
Answers
Answer:
4/3 is ur answer which is equal to 6.92820323028
which i B's side length
Step-by-step explanation:
Which means that the longer leg=square root of 3 times the shortest leg ( the shortest leg lies opposite of the 30 degrees angle)
=4_/3 or the second choice
Last week the team ran 21 1/2 miles total. this week the track coach had the team run 5 1/2 miles on monday and 4 3/4 miles on tuesday. the next three days the team averaged 6 miles a day
Answers
Pythagorean Theorem Level 2
Answers
Answer:
10
Step-by-step explanation:
Pyth. Theorem:
a = leg, b = leg, c = hypotenuse
[tex]c = \sqrt{ {a}^{2} + {b}^{2} }[/tex]
The length of the third side
=
[tex]\sqrt{ {5 \sqrt{3} }^{2} + {5}^{2} }[/tex]
=
[tex]\sqrt{75 + 25}[/tex]
=
[tex]\sqrt{100}[/tex]
= 10
we struggling at the moment
Answers
Answer:
hi
Step-by-step explanation:
area of square is a²
14²=196 m
haveca nice day
The rectangle ABCD is reflected across the y-axis. What are the
coordinates of the vertex A'?
Answers
Solve for h. 28 = h 9 + 23
Answers
Answer:
28 = h 9 + 23
28 = h 32
h = 32 - 23
h = 9
-23 -23
5=h9
5/9= h
what is the value of 11²
Answers
Answer: 121
11^2 = 11 x 11 = 121
Answer:
121
Step-by-step explanation:
To square a number, we have to multiply the number by itself. This means we'll multiply 11 by 11.
11 · 11 = 121
So, 11² = 121.
I hope this helps :)
What is the perimeter?
Answers
Answer:
41.13m
Step-by-step explanation:
the circumference of the circle is 25.13 and the 8 on both sides equals to 16
Zeroes of a polynomial can be determined graphically. Number of zeroes of a polynomial is equal to number of points where the graph of polynomial.
2 points
a. intersects y-axis
b. intersects x-axis
c. intersects y-axis or intersects x-axis
d. none of these
Answers
9514 1404 393
Answer:
b. intersects x-axis
Step-by-step explanation:
A zero of the polynomial is where y = 0. The equation y = 0 is the equation of the x-axis, so intersections of the graph of the function with the x-axis are places where the function value is zero.
The number of (distinct real) zeros is equal to the number of points where the graph intersects the x-axis.
_____
Additional comment
When (x -p)^n is a factor of the polynomial, the graph will intersect the x-axis at x=p. The zero is said to have "multiplicity n". For odd values of n, the graph will cross the x-axis (change sign) at x=p. For even values of n, the graph will touch the axis at x=p, but will not cross there.
So, the number of intersections with the x-axis tells the number of distinct real zeros, but does not say anything about their multiplicity. Complex zeros will not cause the graph to touch the x-axis.
Please help me with this
Thanks
Answers
As you see, 2/10 = 8/40
2/4 = x/40, multiply by 10
2/4 = 20/40
Then add because same denominator
Now you would get:
8/40 + 20/40 = 28/40
Answer:
8/40 + 20/40 = 28/40
Step-by-step explanation:
It's about finding the common denominator for the fractions.
we can easily see that 40 is a common denominator for denominators 10 and 4. 20 would work too, but 40 is "instantly seen".
2/10 = (2*4) / (10*4) = 8/40
2/4 = (2*10) / (4*10) = 20/40
8/40 + 20/40 = (8+20) / 40 = 28/40
Find a formula for the nth term
of the arithmetic sequence.
First term 2.5
Common difference -0.2
An = [? ]n +
Answers
In the triangle below, with right angle
Find the degree measure of each angle in the triangle.
Answers
Answer:
90°, 62.8° and 27.2°
Step-by-step explanation:
180 = 5x + 133
47 = 5x
9.4= x
2 * 9.4 + 44 = 62.8°
3 * 9.4 - 1 = 27.2°
Aretha's teacher will choose two students from a class of 10 to prepare a display. Assuming the teacher chooses these students at random,
what is the probability that Aretha will not be chosen?
Answers
Answer:
80% chance she will not be chosen
Step-by-step explanation:
the ratio of students picked would be 2:10 so there would be 8:10 students not chosen that is 80%. 20% chance she would be chosen.
I hope this is correct!
The probability that Aretha will not be chosen is 0.8.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.
Given that, Aretha's teacher will choose two students from a class of 10 to prepare a display.
We know that, probability of an event = Number of favourable outcomes/Total number of outcomes
Probability of choosing 2students =2/10
Probability of not choosing students = 1-2/10
= 8/10
= 0.8
Therefore, the probability that Aretha will not be chosen is 0.8.
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Given g(x)=3x+5g(x)=3x+5, find g(-6)g(−6).
Answers
Answer:
Step-by-step explanation:
hello :
g(x)=3x+5
g(−6).=3(-6) +5 = -18+5 = -13
Algebra 2 functions. Will mark Brainliest!
Answers
Answer:
f-1(x) is just the opposite of f(x) therefore -x(x-2) =f-1(x)
Step-by-step explanation:
17.39 divided by 4.7
Answers
Answer:
3.7 is the right answer
Step-by-step explanation:
Answer:
3.7
Step-by-step explanation:
ABC is a right triangle. calculate the length of side BC (the hypotenuse)
Answers
Answer:
we have
C=(2,-1)
B=(-2,3)
since
BC is hypotenuse
length of BC=√[(-2-2)²+(3+1)²]=√32=4√2 units is your answer
Write the equation of the circle graphed below
Answers
Answer:
there isnt any image
Step-by-step explanation:
(5y+4)+(−2y+6)= find the sum
Answers
Answer:
-32
Step-by-step explanation:
Which set of ordered pairs (x, y) could represent a linear function of x?? A ((-2,8), (0,4) , (2, 3) , (4,2)) B ((1,2), (1,3),(1,4), (1,5)) C ((-2,7) , (0,12),(2,17),(4,22)) D ((3,5), 4,7) , (3, 9) , (5,11))
Answers
Answer:
A linear function is when it goes up the same amount each time. The first one does because it increases by 2 each time, so A
Step-by-step explanation:
Triangle ABC is isosceles with AB=CB. Circle M is inscribed in Triangle ABC such that it is tangent at points D, E, and F. If the length of BF is twice the length of CF and the perimeter of Triangle ABC is 32 inches, then determine the length of side BC in inches.
Answers
Answer:
The answer is "12 inches".
Step-by-step explanation:
Please find the image file of the graph.
We know [tex]AE = CF \ and \ EB = FB[/tex] so because the triangle is isosceles.
[tex]EB = 2x, FB = 2x,\ and \ CF = x[/tex] when [tex]AE[/tex] is called by [tex]x[/tex].
We know that [tex]AE = AD = x[/tex] since E and D are tangent points to a circle.
They have [tex]CD = CF = x[/tex] since D and F are tangent points only to circle.
Thus, if the perimeter is 32, the following is the result:
[tex]\to AE + EB + BF + FC + CD + DA = 32\\\\\to x + 2x + 2x + x + x + x = 32\\\\\to 8x = 32\\\\\to x = 4[/tex]
Therefore the length of [tex]BC = BF + FC = 2x + x = 3x = 12\ inches[/tex]
Ms. Roberts studied her students' geography test scores and sleeping habits. She found that students who slept less tended to earn
lower scores on the test. What conclusion should she make?
Answers
Step-by-step explanation:
she should tell the students that sleep less to get to their beds early, as the brain needs rest to function properly
Answer:
There is a correlation between test score and amount of sleep. There may or may not be causation. Further studies would have to be done to determine this.
Step-by-step explanation:
There is a correlation between test score and amount of sleep. There may or may not be causation. Further studies would have to be done to determine this.
At a point on the ground 50 feet from the foot of
a tree, the angle of elevation to the top of the tree is 53º. Find
the height of the tree.
Answers
Answer:
[tex] \tan(53) = \frac{x}{50} \\ x = \tan(53) \times 50 \\ x = 66.35 \: feet[/tex]
Step-by-step explanation:
I hope that is useful for you :)
The height of the tree with angle of elevation of 53⁰ is 66 ft.
What is Angle of Elevation?The angle of elevation is the angle between the horizontal line of sight and the object.
Here, Let the height of the tree be x ft.
The angle of elevation = 53⁰
Distance from ground = 50 ft.
According to question,
tan 53⁰ = x/50
x = 50 × tan 53⁰
x = 50 X 1.32
x = 66 ft.
Thus, the height of the tree with angle of elevation of 53⁰ is 66 ft.
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At 6 a.m. the temperatures was at 4.05 degrees Fahrenheit by noon the temperature had risen 16.3 degrees Fahrenheit what was the temperature at noon?
Answers
Answer:
15°F at 3:00 a.m.
Step-by-step explanation:
In order for the data in the table to represent a linear function with a rate of change of +5, what must be the value of a?
a = 3
a = 8
a = 18
a = 33
Answers
Answer: C: A=18
Step-by-step explanation: If your are adding 5 every time the x value goes up by one, then you would add 5 to13, henceforth getting 18.
The value of a that completes the table is 18
Rate of change of a functionThe rate of change of a function is expressed in term of the slope.
In order to determine the value of a, we will use the expression below;
Slope = a - 13/4-3 = 23-13/5-3
a-13 = 10/2
a - 13 = 5
Add 13 to both sides
a =5 + 13
a = 18
Hence the value of a that completes the table is 18
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URGENT - PLEASE HELP 25 POINTS AND BRAINIEST
A right triangle has legs that measure 5 and x - 1
Its hypotenuse measures x.
Solve for x
Answers
Calcula y comprueba las ecuaciones: plisss lo necesito alguien me puede ayudar a) 2X = 6 b) 10 + Z = 20 c) P + 9 = 11 d) 3X + 8 = + 29 e) 2U + 8 = 10
Answers
Answer:
a) x=3
b) z=10
c) P= 2
d) X=7
e) U=1
Step-by-step explanation:
Resolver una ecuación consiste en hallar los valores de la variable que hacen cierta la igualdad.
a) 2x= 6
El coeficiente es el número junto a la variable. En este caso, el coeficiente es 2. Para eliminar este número en la expresión 2x, debido a que la variable x esta multiplicada por 2, deberás dividir ambos lados de la ecuación entre 2, debido a que la operación opuesta de la multiplicación es la división.
(2x)÷2=6÷2
x= 3
Comprobar la solución de una ecuación se hace al remplazar la variable en una ecuación con el valor de la solución. La solución debería satisfacer la ecuación cuando se ingresa en esta.
En este caso:
2*3= 6
6=6
b) 10 + z= 20
En este caso se debe sumar o restar la constante que se encuentra acompañando a la variable en ambos lados de la ecuación de manera de aislar el término de la variable. En este caso:
10 - 10 + z= 20 -10
z= 10
Comprobación:
10 + z=20
10 + 10=20
20=20
c) P + 9= 11
P +9 - 9= 11 -9
P=2
Comprobación:
2 + 9= 11
11=11
d) 3X + 8 = 29
En este caso, se suma o resta la constante en ambos lados de la ecuación y luego se elimina el coeficiente de la variable mediante la división o multiplicación. Esto es:
3X + 8 - 8= 29 - 8
3X= 21
3X ÷3= 21÷3
X=7
Comprobación:
3*7 + 8=29
21+8=29
29=29
e) 2U + 8= 10
2U + 8 - 8= 10 -8
2U= 2
2U ÷2= 2÷2
U=1
Comprobación:
2*1 + 8= 10
2 + 8= 10
10=10
