Answers
The answers of the given geometrical shapes are:
1. 226.29 cubic yard
2. 46.1 cubic inches
3. 2413.71 cubic inches
4. 234.67 cubic millimeter
5. 340.48 cubic yards
6. 113.14 cubic feet
7. 528 cubic centimeter
8. 905.14 cubic centimeter
9. 56.57 cubic feet
what is mensuration?Mensuration is the branch of geometry that deals with measurement of volumes and areas of geometrical shapes.
Analysis:
1. volume of cylinder =π [tex]r^{2}[/tex]h. where r = 6/2 = 3 yard, h = 8 yard
= [tex]\frac{22}{7}[/tex] x [tex]3^{2}[/tex] x 8 = 226.29 cubic yard
2. volume of cone = [tex]\frac{1}{3}[/tex] x π [tex]r^{2}[/tex]h. where r = 2inches, h = 11
= [tex]\frac{1}{3}[/tex] x [tex]2^{2}[/tex] x [tex]\frac{22}{7}[/tex] x 11 = 46.1 cubic inches
3. volume of cylinder = π [tex]r^{2}[/tex]h. where r = 8, h = 12
= [tex]\frac{22}{7}[/tex] x [tex]8^{2}[/tex] x 12 = 2413.71 cubic inches
4. volume of cone = [tex]\frac{1}{3}[/tex] x π [tex]r^{2}[/tex]h. where r = 4, h = 14
= [tex]\frac{1}{3}[/tex] x [tex]\frac{22}{7}[/tex] x [tex]4^{2}[/tex] x 14 = 234.67 cubic millimeter
5. volume of cone = [tex]\frac{1}{3}[/tex] x π [tex]r^{2}[/tex]h. where r = 5, h = 13
= [tex]\frac{1}{3}[/tex] x [tex]\frac{22}{7}[/tex] x [tex]5^{2}[/tex] x 13 = 340.48 cubic yards
6. volume of cylinder = π [tex]r^{2}[/tex]h. where r = 3, h = 4
= [tex]\frac{22}{7}[/tex] x [tex]3^{2}[/tex] x 4 = 113.14 cubic feet
7. volume of cone = [tex]\frac{1}{3}[/tex] x π [tex]r^{2}[/tex]h. r = 6, h = 14
= [tex]\frac{1}{3}[/tex] x [tex]\frac{22}{7}[/tex] x [tex]6^{2}[/tex] x 14 = 528 cubic centimeter
8. volume of cylinder = π [tex]r^{2}[/tex]h. where r = 6, h = 8
= [tex]\frac{22}{7}[/tex] x [tex]6^{2}[/tex] x 8 = 905.14 cubic centimeter
9. volume of cylinder = π [tex]r^{2}[/tex]h. where r = 1.5, h = 4
= [tex]\frac{22}{7}[/tex] x [tex]1.5^{2}[/tex] x 4 = 56.57 cubic feet
In conclusion, the volume of cylinders and cones for the given dimensions are:
1. 226.29 cubic yard
2. 46.1 cubic inches
3. 2413.71 cubic inches
4. 234.67 cubic millimeter
5. 340.48 cubic yards
6. 113.14 cubic feet
7. 528 cubic centimeter
8. 905.14 cubic centimeter
9. 56.57 cubic feet
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Related Questions
Rewrite the expression using the distributive property and a common factor.
27x+24x
0.5n+2.5
Answers
Answer:
x(27 +24) or 3x(9 +8)0.5(n +5) or 2.5(n/5 +1)Step-by-step explanation:
The distributive property of multiplication over addition tells us that the product of a value and a sum will be the same as the sum of products of the value and the sum's addends. This property can be used to add or remove parentheses from an arithmetic expression.
a(b +c) = ab +ac . . . . expression of the distributive property
__
When applying the distributive property to a sum, the first step is to look for a factor common to the terms of the sum. That factor need not be the greatest common factor, though it is often useful if it is.
Below, we have written each expression using two different common factors.
a)27x +24x = x(27 +24) = 3x(9 +8)
__
b)0.5n +2.5 = 0.5(n +5) = 2.5(n/5 +1)
_____
Additional comment
Finding a common factor can make use of knowledge of multiplication tables, rules of exponents, and identities involving various functions used in algebraic expressions. It is sometimes useful to list the prime factors of each of the terms as an aid to finding a common one. Where fractions are involved, it is sometimes helpful to express them all using a common denominator.
The Euclidean Algorithm can also be useful for finding common factors.
The triangles below are similar. Triangle Y X Z. Side Y X is 6 centimeters, X Z is 7 centimeters, and Z Y is 3 centimeters. Triangle A B C. Side A C is 14 centimeters, A B is 12 centimeters, and B C is 6 centimeters. Which similarity statement expresses the relationship between the two triangles? Triangle Z Y X is similar to triangle C A B Triangle Z Y X is similar to triangle A C B Triangle Z Y X is similar to triangle C B A Triangle Z Y X is similar to triangle A B C Mark this and return
Answers
Answer:
(c) Triangle Z Y X is similar to triangle C B A
Step-by-step explanation:
Triangles are similar when corresponding sides have the same ratio. Corresponding sides will have corresponding end point vertices. The similarity statement lists corresponding vertices in the same order.
__
corresponding sidesThe side lengths, smallest to largest, for the two triangles are ...
3 cm -- ZY6 cm -- YX7 cm -- XZAnd for the other triangle, ...
6 cm -- BC12 cm -- AB14 cm -- ACcorresponding verticesThe points joining the each side to the next one longer, in order for the two triangles, are ...
Y, X, Z and B, A, C
The vertices corresponding to ZYX in the same order are CBA.
triangle ZYX is similar to triangle CBA
Answer:
The answer is C
Step-by-step explanation:
The preimage undergoes the sequence of transformations to produce an image, figure 1.
1. reflection across a horizontal line
2. rotation counterclockwise about point P
3. dilation with a scale factor of 1
Answers
Based on the transformations that occurred, the preimage is most likely the topmost right image.
Where is the preimage?The transformations list shows that the first transformation was the reflection across the horizontal line drawn.
When a reflection is done, the shape looks like the inverse of itself. The only shape that looks like an inverse and is therefore a reflection is the bottom right shape which means the preimage must be the top right image.
Remaining part of question:
Which is the preimage?
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Please help on this only if u know
Answers
Answer:
Option D ---> y=5x
Step-by-step explanation:
When a line is directly proportional it means it crosses the origin so has a y- and x-intercept of 0.
So if we use the format y=mx+c, it will work but our c value will be 0 as I explained above .
To work out the gradient we simply take 2 points (0,0) and (1,5)) on the graph and use the gradient formula :
m = change in y ÷ change in x
m = 5÷1
m = 5
Therefore our direct proportion equation will be y=5x
Hope this helped and have a good day
Which fraction names the shaded part of the set?
Answers
Answer:
Hello! Your answer is 1/2
Step-by-step explanation:
there are six cubes and three of them are shaded. That is half of the parallelograms.
So 1/4 wouldn't make sense because there are three shaded out of six.
1/6 doesn't make sense because since there is six in total for it to be 1/6 there needs to be 1 shaded out of six.
And finally 1/3 doesn't make sense because 1/3 would have to be two out of six shaded.
Have a wonderful day/night/afternoon and good luck my friend!
which expression is equivalent to 56x - 28y + 42?
A) 8(7x-3y + 6)
B) 7(8x + 4y +6z)
C) 7(8x - 4y + 6)
Answers
Answer: c or a
Step-by-step explanation:
Evaluate each function.
14) g(x)= 3x² - 1; Find g(-3)
Answers
[tex]g(x) =3x^2 -1\\\\g(-3)=3(-3)^2 -1 \\ \\~~~~~~~~~=3(9) -1 \\\\~~~~~~~~~=27-1\\\\~~~~~~~~~=26[/tex]
Answer:
g(26)
Step-by-step explanation:
substitute -3 for x.
g(x)=3[tex]x^{2}[/tex]-1
[tex]g(-3)=3(-3)^{2} -1\\g(-3)= 3(9)-1\\g(-3)= 27-1\\g(-3)=26[/tex]
what is the answer to 3a^-2/a^-3
Answers
Answer:
3a
Step-by-step explanation:
Tom has 12 candies and
eats 2 each minute. sue
has 6 candies and eats 1
every minute. after how
many minutes will they have
the same number of
candies?
Answers
Answer: once tom eats 6 candys he will have the same number as sue
Step-by-step explanation:
Answer:
After 6 minutes they will both have 0 candies.
Solve for x
3x-5=-x+3
Answers
Answer:
(3x - 5 = -x + 3) x = 2
Step-by-step explanation:
3x - 5 = -x + 3
3x = -x + (3 +5)
3x=-x + 8
(3x + x ) = 8
4x = 8
4/8 =2
x = 2
The function(t)--4.87+18.75 is used to model the height of an object projected in the air, where h() is the height in
meters and t is the time in seconds. What are the domain and range of the function h(0)? Round values to the nearest
hundredth.
25
20+
(1.9, 18.05)
15-
10+
st
"
Answers
The domain and range of the given function are equal to (0, 3.85) and (0, 18.75) respectively.
How to calculate the domain of the function?In this exercise, you're given the following function h(t) = -4.87t² + 18.75t. Next, we would equate the function to zero (0) to determine its domain as follows:
0= -4.87t² + 18.75t.
4.87t(-t + 3.85) = 0
t = 0 or t = 3.85.
Therefore, the domain is 0 ≤ t ≤ 3.85 or (0, 3.85).
How to calculate the range of the function?h(t) = -4.87t² + 18.75t
h(t) = -4.87(t² - 3.85t + 3.85 - 3.85)
h(t) = -4.87(t - 1.925)² + 18.05
Therefore, the range is 0 ≤ h ≤ 18.05 or (0, 18.75).
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Answer:
A on EDGE 2022
Step-by-step explanation:
What is the solution -2x+3-(5-6x).
Answers
Answer: 2(2x-1)
Range terms
Distribute
Subtract the numbers
Which expression is equal to p + (q + r)?
(p + q) ⋅ r
(p + q) + r
p + qr
q + pr
Answers
Answer:
(p + q) + r
is the correct answer
Determine x to two decimal places.
*PICTURE ATTACHED*
*TRIGONOMETRY*
Answers
This rule is applied to triangles to determine the unknown sides and angles. The value of x from the diagram is 11.78m
Trigonometry ruleThis rule is applied to triangles to determine the unknown sides and angles.
Given the following parameter
Opposite = 5m
Adjacent = x
angle = 23 degrees
According to the theorem of tangents
tan23 = opposite/adjacent
tan23 = 5/x
x = 5/tan23
x = 11.78m
Hence the value of x from the diagram is 11.78m
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Please help!!!!!!!!!!!!!!! i need this answer really fast!!!
Answers
Answer:
What's the question you f... you amazing human being
If the quadratic equation has two rational roots,then the discriminant is_____and a perfect square
Answers
Answer:
Real and unequal
Answer:
The quadratic has two equal roots like d if it is perfect square and we may write: (x − d) 2 = x 2 − 2 d x + d 2 Then: Δ = 4 d 2 − 4 d 2 = 0 That is the discriminant is zero when the quadratic is perfect square.
Step-by-step explanation:
A high speed train travels a distance of 503 km in 3 hours.
The distance is measured correct to the nearest kilometre.
The time is measured correct to the nearest minute.
By considering bounds, work out the average speed, in km/minute, of the train to a suitable degree of accuracy.
You must show your working.
To gain full marks you need to give a one-sentence reason for your final answer the words 'both' and 'round' should be in your sentence.
Answers
The average speed, in km/minute, of the train is 2.79 km/minute
Calculating average speedFrom the question, we are to calculate the average speed in km/minute
From the given information,
Distance travelled = 503 km
Time taken = 3 hours = 3 × 60 minutes = 180 minutes
Using the average speed formula,
Average speed = Distance / Time
∴ Average speed of the train = 503 / 180
Average speed of the train = 2.79 km/minute
Hence, the average speed, in km/minute, of the train is 2.79 km/minute
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(6x10^7) divided by (2x10^3) give your answer in standard form
Answers
Answer:
In the end, the answer is: 30,000
Step-by-step explanation:
[tex]\frac{60,000,000}{2,000} = 30,000[/tex]Find the value of x. Show each step.
0.15x+(0.15-5-x)*0.2=0.1
Answers
Answer:
-21.4
Step-by-step explanation:
0.15x + 0.2(0.15-5-x) = 0.1
0.15x + 0.03 - 1 - 0.2x = 0.1
0.15x - 0.2x = 0.1 -0.03 + 1
-0.05x = 1.07
0.05x = -1.07
x = -21.4
What expression is equivalent to the given expression?
Answers
The expression which is equivalent to the given expression is [tex]\frac{27 m^{5}}{n}[/tex]
Evaluating indicesFrom the question, we are to determine the expression which is equivalent to the given expression
The given expression is
[tex]\frac{(3m^{2}n)^{3} }{mn^{4} }[/tex]
Clearing the brackets, we get
[tex]\frac{3^{3} m^{2(3)}n^{3} }{mn^{4} }[/tex]
Simplifying, we get
[tex]\frac{27 m^{6}n^{3} }{mn^{4} }[/tex]
Then,
[tex]27 m^{6-1}n^{3-4}[/tex]
[tex]27 m^{5}n^{-1}[/tex]
= [tex]\frac{27 m^{5}}{n}[/tex]
Hence, the expression which is equivalent to the given expression is [tex]\frac{27 m^{5}}{n}[/tex]
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O
O
O
-54-3 -2 -1 0 1 2 3 4 5 6 7
8
-5-4
-3 -2 -1 0 1 2 3 4 5 6 7 8
++
-5 -4
-3 -2 -1
0 1
2
3 4 5 6 7
8
+
-5 -4
-3 -2 -1 0 1
2
3
5
6
7
C
C
4
8
9 10 11 12 13
9 10 11 12 13
9 10 11 12 13
9 10 11 12 13
Answers
Step-by-step explanation:
separate the question into two inequalities then solve individually to derive at an answer then merge the two answers as one.
remember that < or > are open sets while <= or >= are closed set.
What is the product of the fractions below?
1/8 * 4/5
Answers
Answer: 1/10
Step-by-step explanation:
(1 x 4)/(8x5)
4/40
1/10
Select the correct answer.
Richard reads 28.9 inches of mercury on a barometer, which is 1 inch lower than normal atmospheric pressure. The temperature is 40°F. What type of weather is most likely to occur where Richard is?
A.
fair and dry
B.
drought
C.
rain shower
D.
snowfall
Answers
The weather that is most likely to occur where Richard is is rain shower.
What type of weather is most likely to occur?
Weather is the state of the atmosphere of a particular place over a short period of time. There is low atmospheric pressure, so it is likely that it would rain. This is because when the atmospheric pressure is low, it is likely that it would rain.
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Answer:
Rain shower is most likely to occur where Richard is. (Option c)
• The air pressure is lower than the normal and that's why it suggests that the rainfall will happen in that place because rainfall generally occurs in the place where the low pressure is formed.
• And,the temperature is above than the freezing point of the water so there are no chances of the snowfall in that place.
• That's why rainfall is the most probable thing that will happen in that place.
Step-by-step explanation:
What is X of 75 degrees 13 rounded to the nearest tenth
Answers
Step-by-step explanation:
Since you know that C is a right angle, you can use the Law of Sines to find a. The first step is to find the size of the angle A, which is 180-74-90=16. Now, you set up a ratio that involves 3 knowns and one unknown to get , which after cross multiplying yields . PM me if you have any questions?
Triangle ABC is an isosceles triangle.
AB = BC
mB = 34°
What is mA?
A. 34°
B. 56°
C. 73°
D. 112°
Answers
Answer:
C. 73
Step-by-step explanation:
angles A and C will be the same because their sides are the same length!
so to solve this, let's set up an equation
34 + 2x = 180 let x represent the missing anglenow let's solve!
2x = 146x = 73angle A = 73
let me know if you have any questions :)
Answer:
C!
Step-by-step explanation:
GIVING BRAINLIEST PLEASE ANSWER QUICKLY I APPRECIATE IT SO MUCH PLS HELP im like begging
Answers
Answer:
x=28
Step-by-step explanation:
cos60°=14/x
0.5=14/x
x=14/0.5
x=28
Answer:
A. 28
Step-by-step explanation:
The value of x is equal to 18
Hope this helps and please feel free to comment, ask questions, give feedback, and correct me if I am wrong!
Have a great day!
:)
(-14,-13), (-7,-7)
Can anyone help me solve this - algebra
Answers
Answer: y=6/7x-1
Step-by-step explanation:
I am assuming you want a line formula in y=mx+b
slope (y2-y1)/(x2-x1) = -7+13/-7+14 = 6/7
y+7=6/7(x+7)
y+7 = 6/7x+6
y=6/7x-1
Daniel runs 40/5 miles in 124/₁ minutes. What is the unit rate in terms of miles per minute? What the answer:
Answers
Using the given information, the unit rate is 0.0645 miles/minute
Calculating rateFrom the question, we are to determine the unit rate
From the given information,
Daniel runs 40/5 miles in 124 minutes
That is,
Distance = 40/5 miles = 8 miles
Time = 124 minutes
Using the formula,
Rate = Distance / Time
Rate = 8 miles / 124 minutes
Rate = 0.0645 miles/minute
Hence, the unit rate is 0.0645 miles/minute
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The unit rate is 0.0645 miles/minute
We have calculated the rate
From the question, we are to determine the unit rate
From the given information,
Daniel runs 40/5 miles in 124 minutes
Distance = 40/5 miles
Distance = 8 miles
Time = 124 minutes
What is the formula of rate?Rate = Distance / Time
Rate = 8 miles / 124 minutes
Rate = 0.0645 miles/minute
Hence, the unit rate is 0.0645 miles/minute
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What is the value of x in the equation shown Below?2(x+4)-4x=10x-4
Answers
Answer: 1
Step-by-step explanation:
find the missing angle.
Answers
Answer:90 degree
Step-by-step explanation:
Answer:
x = 90°
Step-by-step explanation:
According to the Angle Sum Property of Triangles, the sum of the internal angles is 180°.
55° + x° + 35° = 180°x° + 90° = 180°x = 90°