Answers
9514 1404 393
Answer:
384 cm²
Step-by-step explanation:
It is always a good idea to take a look at what you have and what you are being asked before you go launching into formulas. Then you can pick the formula(s) appropriate to your needs.
__
Your pyramid has a square base, so four (4) triangular faces. The area being asked for is the total of the areas of the square base and those triangular faces.
The formula for the area of a square is ...
A = s² . . . . . where s represents the side length
Here, the side of the square is 12 cm, so the area of the square base will be ...
A = (12 cm)² = 144 cm²
__
The formula for the area of a triangle is ...
A = 1/2bh . . . . . where b is the base length and h is the altitude
In this problem, you're not given the altitude of the triangular face (also called the "slant height" of the triangle). Instead, you're given the height of the pyramid. So, you have to determine the slant height.
Consider the cross section you get when you cut the pyramid with a vertical plane through the peak and the middle of opposite sides. It will be an isosceles triangle with a base equal to the side length of the pyramid, and side lengths equal to the slant height of the pyramid face. See the attachment for an idea of what this looks like.
In order to determine the length of the side of that cross-section triangle, draw its altitude. That is the 8 cm height of the pyramid. Then use the Pythagorean theorem to find the hypotenuse of the right triangle with legs 6 cm and 8 cm:
slant height = √(8² +6²) = √100 = 10 . . . . cm
Now, we can find the area of one of the four triangular faces:
A = (1/2)(12 cm)(10 cm) = 60 cm²
__
The surface area of the pyramid is then ...
surface area = base area + 4 × triangular face area
surface area = 144 cm² + 4 × 60 cm² = (144 +240) cm²
surface area = 384 cm²
Related Questions
What is the coefficient in the following expression?
5a2-7
Answers
Answer:
5
Step-by-step explanation:
coefficeint is the number before the variable
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Answer:
[tex]\frac{ \frac{7}{3}}{\frac{1}{3}}[/tex] is the slope
Step-by-step explanation:
rise over run
A game of chance involves spinning a wheel with 4 number on it. The wheel is designed so that the result of each spin Xhas the following probability distribution. 2 3 Result of a spin .x Probability : 0.50
(a) Find and interpret the mean of X.
(b) Find and interpret the standard deviation of x.
(c) It costs a player $5 for a single spin. The player will receive (in dollars) three times the number that appears. So the profit for one play of this game is Yeur 5. What is the mean and standard deviation of 7
Answers
Distribution table :
X : ___ 1 _____ 2 _____ 3 ______ 4
P(x) __0.50 __0.25 __ 0.15 ____ 0.10
Answer:
1.85 ; 1.014 ;` 0.55 ; 3.042
Step-by-step explanation:
Probability distribution :
X : ___ 1 _____ 2 _____ 3 ______ 4
P(x) __0.50 __0.25 __ 0.15 ____ 0.10
The mean: E(x) = Σ(X * p(x))
(1*0.5) + (2*0.25) + (3*0.15) + (4 *0.10)
= 1.85
Standard deviation = sqrt(Var(x))
Var(x) = Σ(x²*p(x)) - E(x)²
Var(x) = ((1^2*0.5) + (2^2*0.25) + (3^2*0.15) + (4^2 *0.10)) - 1.85^2
= 4.45 - 3.4225
= 1.0275
Standard deviation = sqrt(1.0275)
Standard deviation = 1.0136567
Standard deviation(X) = 1.014
3.)
Cost of spin = $5
Amount, y to be received = 3 times the number that appears
y = 3x - cost of playing
y = 3x - 5
E(y) = E(3x - 5)
E(y) = E(3x) - 5
Recall :E(x) = 1.85
E(y) = 3(1.85) - 5
E(y) = 0.55
Standard deviation :Sd(y) =
Sd(3x - 5)
3(1.014)
= 3.042
A 300 room hotel can rent every one of its rooms at $80 per room. For every $1 increase in rent, 3 fewer rooms are rented.
How much should the hotel charge for each room to maximize its daily revenue? What is the maximum daily revenue?
Answers
Answer:
The hotel charge for each room to maximize its daily revenue and the maximum daily revenue is explained below in details.
Step-by-step explanation:
So for every $1 hike in price, the number of rooms goes underneath by 1.
So the earnings can be displayed by R(x) = (300-x)(80+x)
From that, you require to subtract 22(300-x) since it takes $22 per occupied room.
AND there is a framed cost of $1000 per day.
So your profit function is P(x) = (300-x)(80+x) - 22(300-x) - 1000
Simplified, this is P(x) = -x2 +242x + 16400.
P'(x) = -2x + 242 Set it = to 0
x = 121 which displayed the number of unoccupied rooms.
P(121) = -14641 + 29282 + 16400 = $31041
You can verify by computing P(120) and P(122) which both even $31040.
Hope this helps.
What is the measure of the angle? Enter the answer in the box.
Answers
Answer: Acute angle
Step-by-step explanation:
because it is at a 62 I think angle
What expressions are equivalent to -4/3 p -2/5
Answers
Answer:
-3/6
Step-by-step explanation:
integer rules
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Answers
Answer:
118 degrees
Step-by-step explanation:
180-62 = 118
Standard form of y=7x+10
Answers
Answer: 7x-y=10
Step-by-step explanation:
I REALLY NEED HELP? :,)
Answers
Answer:
3/7
Step-by-step explanation:
witch equation represents a linear function
Answers
Hope this helped :)
Arya saves 30% of his montly paycheck for college. He earned $270 lst month. How much money did Arya save for college?
Answers
Answer:
she saved 900 dollars
Step-by-step explanation:
30/100=270/?
30x9=270
100x9=900
Give each a sum or difference:
a. -12+4=
b. -4+1=
c. 4 - 12=
d. 4+12=
Answers
B. -3
C. -8
D. 16
What is the value of x in the equation below?
Negative 3 minus (negative 8) minus (negative 2) = x
Answers
-3 - (-8) - (-2) = x
Switch the equation to make x on the right
x = -3 - (-8) - (-2)
x = 5 - (-2)
x = 7
• A negative minus a negative will always evaluate to a positive.
• A positive minus a negative will always evaluate to a positive.
Answer:
D
Step-by-step explanation:
Took the test ;)
Help me out with this question (geometry)
Answers
Answer:
116
Step-by-step explanation:
13x-1 = 2(6x+4)
13x-1 = 12x+8
x=9
The shadow of a 60 foot pole is a 100 feet long. What is the angle of evaluation from the end of the shadow to the top of the pole?
Answers
Answer:
The angle is approximately [tex]31^{o}[/tex].
Step-by-step explanation:
The description i the given question can be represented with the sides of a right angled triangle.
Applying the appropriate trigonometric function, we have;
Tan θ = [tex]\frac{opposite}{adjacent}[/tex]
In the question, opposite side = 60 feet, and adjacent side = 100 feet.
Tan θ = [tex]\frac{60}{100}[/tex]
= 0.6
θ = [tex]Tan^{-1}[/tex] 0.6
= [tex]30.964^{o}[/tex]
θ = [tex]31^{o}[/tex]
The angle of elevation from the end of the shadow to the top of the pole is [tex]31^{o}[/tex].
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Answers
Answer:
7 : 3
Step-by-step explanation:
Divide both numbers by 6
Answer:
Step-by-step explanation:
42:18=42/18=7/3=7:3
I hope it help you
this is so easy
benjamin believes that 1/2% is equivalent to 50%. Is he correct? Why or why not?
Answers
Answer:
yes because 1 divided by 2 is 0.5 which can be converted to 50%
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Answers
33 divided by a number Q.
Answers
Answer:
33/Q?
Step-by-step explanation:
im confused on what the problem is
HELP MEEEEE this is so harddd. the picture is above.
Answers
Answer:
A)
Step-by-step explanation:
V=1/3([tex]\pi[/tex]r²)h
3* V=1/3(πr²h)*3 to get rid of the 1/3 on that side
3V/(πr²)=(πr²)h/(πr²) to get rid of the πr² on the other side(they cancel out)
3V/(πr²)=h is the final answer so that matches A
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Answers
Answer:
7. 4
8. 7
Step-by-step explanation:
7. [tex] \frac{1}{2} = \frac{x}{8} [/tex]
Cross multiply
[tex] 1*8 = x*2 [/tex]
[tex] 8 = 2x [/tex]
[tex] \frac{8}{2} = \frac{2x}{2} [/tex] (division property of equality)
[tex] 4 = x [/tex]
[tex] x = 4 [/tex]
8. [tex] \frac{3}{x - 3} = \frac{6}{8} [/tex]
Cross multiply
[tex] 3*8 = 6(x - 3) [/tex]
[tex] 24 = 6x - 18 [/tex]
[tex] 24 + 18 = 6x [/tex] (addition property of equality)
[tex] 42 = 6x [/tex]
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[tex] 7 = x [/tex]
[tex] x = 7 [/tex]
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Answers
The answer is the picture. Hope this helped.
A ski lift makes a 35° angle of elevation with the ground and takes passengers on a 6,550-foot ride up a mountain. Charlotte needs to figure out the elevation of the lift. Which equation and diagram can be used to model this problem?
Answers
Answer:
Top right one is the answer
Step-by-step explanation:
B :)
The elevation of the lift is equivalent to 11293.1 ft.
What is the angle of elevation?The angle of elevation is an angle that is formed between the horizontal line and the line of sight.
Given is that a ski lift makes a 35° angle of elevation with the ground and takes passengers on a 6,550 foot ride up a mountain.
Assume the elevation to be [x] ft. We can find the elevation as -
sin (35°) = (6550/x)
x = {6550/sin(35°)}
x = (6550/0.58)
x = 11293.1 ft
Therefore, the elevation of the lift is equivalent to 11293.1 ft.
To solve more questions on Angle of elevation, visit the link below-
https://brainly.com/question/29008290
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Answers
Answer:
the slope is= 3/2
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help me to solve this please
Answers
Answer:
-4/9
Step-by-step explanation:
We first calculate the first bracket.
[2/3-(-4/9)]
= (2/3+4/9) (we cancel out the negatives)
= (6/9+4/9) (common denominator)
= 10/9
Then we convert -2 1/2 into an improper fraction.
-2 1/2
= -5/2
Finally we calculate the division by swapping the numerator and denominator of -5/2.
10/9 / -5/2
= 10/9 * -2/5
= -20/45
= -4/9 (simplify the terms)
What is the base in the following expression?
Answers
Answer: A. 4
Step-by-step explanation: The base number is 4 and the exponent is 5. Hope this helps ^-^.
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Answers
Answer:18
Step-by-step explanation: 6x3
the formula for area: parallelogram
please help me asap will give brainliest
Answers
Step-by-step explanation:
The longest side in a triangle is opposite the largest angle, and the shortest side is opposite the smallest angle.
So the smallest angle is <P.
Hope it may help :)..
Find the solution to each equation mentally or use your calculator. (do the opposite of the number on the left side of the equation)
A: 30+a=40
B: 500+b=200
C: −1+c=−2
D: d+3,567=0
Answers
B) b= -300
C) c= -1
D) -3567
If light travel at 3 • 10^8 meters per second. How far can light travel in one minute?
Write your answer in scientific notation.
Answers
Answer:
300,000,000 per minute
Step-by-step explanation:
3*10⁸
10⁸ = 100,000,000
3*100,000,000 = 300,000,000