Answers
Answer:
[tex]\fbox{height \: of \: prism = 19 \: mm}[/tex]
Step-by-step explanation:
Given:
Shape of object is pentagonal prism
Side of pentagon= 12mm
Apothem of pentagon= 5 mm
Volume of pentagonal prism= 2,850 cubic mm.
To find:
Hieght of pentagon prism= ?
Solution:
To find height of prism it's necessary to calculate the surface area of base,
[tex]Area \: of \: regular\: pentagon = \frac{5}{2} \times side \: of \: pentagon \: \times apothem \\ Area \: of \: regular\: pentagon = \frac{5}{2} \times 12 \times 5 \\ Area \: of \: regular\: pentagon= \frac{5}{ \not2} \times \not12^{6} \times 5 \\ Area \: of \: regular\: pentagon= 5 \times 6 \times 5 \\ Area \: of \: regular\: pentagon= 150 \: {mm}^{2} [/tex]
[tex]Volume \: of \: prism = surface \: area \: of \: base \: \times height (h) \\ 2850 = 150 \times h \\ h = \frac{2850}{150} \cdot \frac{ {mm}^{3} }{ {mm}^{2} } \\ h = \frac{\not{ {2850}^{19} }} {\not150} \cdot \frac{ {mm}^{\not {3}^{1} } }{ {mm}^{\not2} } \\ \fbox{h = 19 \: mm}[/tex]
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The required height of the pentagonal prism is 19 cm
Given that,
A figure of a pentagon prism is shown with
The volume of the prism = 2850 cubic cm
Side of pentagon base = 12 mm.
And the perpendicular distance from the center to the side = 5 mm.
Volume is defined as the ratio of the mass of an object to its density.
Or in mathematics volume can be calculated as the area of the base multiplied by the height.
In order to get the height of the prism first, we have to calculate the area of the base and then divide the volume by its base area to get its height.
The base area = 5/2 * side * perpendicular height to side from center.
= 5 / 2 * 12 * 5
= 150
The volume of the prism = base area * height
2850 = 150 * height
height = 2850/15
= 19 cm
Thus, the required height of the pentagonal prism is 19 cm
Learn more about Volume here:
https://brainly.com/question/1578538
#SPJ5
Related Questions
How do I find the lengths of JK and JM?
Answers
Answer: Jk is 5 units and JM is 6 units. Have a great day.
Answer: j k is 5 and j m is 6 I think
Step-by-step explanation:
Please help me with this problem I’m very confused and cannot figure it out
Answers
1 / a + b and 5 / 2 ( a + b)
the common denominator would be 2(a+b) therefore multiple thé first fraction by 2, and the second by 1.
2 / 2(a + b) + 5 / 2(a + b)
2 + 5 = 7
the denominator stays the same
so 7 / 2(a + b)
Ms. O'hara brought 2 bags of cookies and 1 pie from Carl. She paid with a $20 bill. What is the total amount of change, in dollars, Ms. O'hara should receive?
A bag of cookies sells for $3.
A pie sells for $8.
Answers
Answer:
$6.00 (Six dollars)
Step-by-step explanation:
Two bags of cookies = $6 (2 x $3)
One pie = $8
$6 + $8 = $14
$20-$14 = $6
Ms. O'hara should receive $6 in change.
round to the nearest whole number
Answers
Answer:
SA = 527.52 cm²
Step-by-step explanation:
Cone SA = πr(r + √(h² + r²))
π = 3.14r = 7h = ?Find h
Step 1. Create a right triangle with the radius (attached image)
Step 2. Pythagorean Theorem
a² + b² = c²
7² + b² = 17²
b² = 289 - 49
b = √240
b or h = 4√15
Solve for SA
SA = πr(r + √(h² + r²))
SA = 3.14 · 7 · (7 + √(4√15² + 7²))
SA = 21.98(7 + √(240 + 49))
SA = 21.98 (7 + 17)
SA = 527.52 cm²
Hope this helps!
Find the length of the third side. If necessary, round to the nearest tenth
Pythagorean Theorem (Rounding)
Answers
a^2 + b^2 = c^2
4^2 + b^2 = 5^2
16 + b^2 = 25
b^2 = 25 - 16
b^2 = 9
b = square root of 9
b = 3
A parking garage charges a fixed amount of money for each hour that it is used.
Answers
What is the answer this math problem. -6+ -(8x - 3)
Answers
Answer:
x = -3÷8
or x = -0.375
Explanation:
-6+ -(8x-3)= -6-8x+3
= -8x -3
-8x-3= 0
-8x = 3
8x = -3
x = -3÷8
Tyler bought a wedge. He measured the arc length of the wedge to be 12 centimeters and the radius to be 8 centimeters. Priya bought a wedge that came from a circular cheese block with radius 9 centimeters. The block was cut into 6 congruent sectors. Whose wedge is larger? Explain or show your reasoning.
Answers
The wedge is an illustration of arc lengths, and Tyler's ledge is larger than Priya's wedge
How to determine the larger wedge?From the question, the arc length of Tyler's wedge is:
L = 12 cm
For Priya's wedge, we have the following highlights:
Radius = 9 cm
Angle = 60 degrees i.e. the angle when a circle is divided into 6 sectors
Priya's arc length is then calculated as:
[tex]L = \frac{\theta}{360} * 2\pi r[/tex]
This gives
[tex]L = \frac{60}{360} * 2 * 3.14 * 9[/tex]
Evaluate
L = 9.42
By comparing the arc lengths 9.42 and 12 cm, we have 12 cm > 9.42 cm
Hence, Tyler's ledge is larger than Priya's wedge
#SPJ1
Read more about arc lengths at:
https://brainly.com/question/15589041
Yo imma need this quick.
Answers
Answer:2 11/12
Step-by-step explanation:
7/12+28/12= 35/12= 2 11/12
28/12=7/3 btw
2 4/12+7/12=2 11/12
Answer:
Ok the answer is going to be 35/12
try that I hope I helped you
Step-by-step explanation:
there are 15 boys and 10 girls in mrs.rogers class what is the ratio of boys to girls ?
Answers
Answer: The ratio of boys to girls in Mrs.Rogers class is 15 to 10.
Step-by-step explanation:
= boys : girls
= 15 : 10
=15/10
= 3/2
= 3:2
Hence the ratio of boys to girls is 3:2
The radius,R, of a sphere is8.2mm . Calculate the sphere's volume,V .
Use the value 3.14 for[tex]\pi[/tex] , and round your answer to the nearest tenth. (Do not round any intermediate computations.)
Answers
The answer is 2308.4
Find three rational numbers between - 2 and - 3
And please write in step by step explination.
Answers
Step-by-step explanation:
follow these steps with tbe no. of -2 and - 3 you will come with answer
Answer:
- 21/10, -5/2 and -11/4.
Step-by-step explanation:
Rational numbers can be written as a/b where a and b are integers ( b not zero).
So three naumbers between - 2 and -3 are
-2.1, -2.5 and -2.75 which can be written as:
- 21/10, -5/2 and -11/4.
A washer and dryer cost a total of $1184. The cost of the washer is three times the cost of the dryer. Find the cost of each of them.
Answers
The cost of a washer is $1184 while the cost of a drier is $296
Word ProblemGiven Data
Total cost of washer and dryer = $1184let the cost of a washer be = wlet the cost of a drier be = dHence,
w+d = 1184 -------------1
we know that the cost of the washer is three times the cost of the dryer.
w = 3d -------------------2
put w = 3d in equation 1
3d + d = 1184
4d = 1184
d = 1184/4
d = 296
The cost of a drier is $296
put d = $296 in equation 2
w = 3*296
w = $888
Check:
$888+$296 = $1184
Learn more about word problem here:
https://brainly.com/question/25693822
In lancaster, the library is 9 miles due south of the courthouse and 4 miles due west of the
community swimming pool. what is the distance between the courthouse and the community
swimming pool? if necessary, round the nearest tenth.
Answers
use brainly to find the answer
Find the length of the third side. If necessary, round to the nearest tenth
Pythagorean Theorem (Rounding)
Answers
Using the Pythagorean theorem:
X^2 = 10^2 + 24^2
X^2 = 100 + 576
X^2 = 676
X = sqrt(676)
X = 26
answer: 26
Answer:
26 :)
Step-by-step explanation:
Pythagorean theorem: a^2 + b^2 = c^2
Lets solve!!
10^2 + 24^2 = c^2
100 + 576 = c^2
676 = c^2
Now lets find the square root!!
[tex]\sqrt{676}[/tex] = 26
Have an amazing day!!!
Please rate and mark brainliest!!
14 White shapes and black shapes
Some of the shapes are circles.
All the other shapes are squares
are used is a game
The ratio of the number of white shapes to the number of black shapes is 3:7
The ratio of the number of white circles to the sumber of white squares is 4:5
The ratio of the number of black circles to the number of black squares is 2:5
Work out what fraction of all the shapes are circles.
Answers
Answer:
1/3
Step-by-step explanation:
Check the attachment.
C
250
4.9 cm
80°
A
3.8 cm
D
B
ABC is a triangle.
D is a point on AB.
Work out the area of triangle BCD.
Give your answer correct to 3 significant figures.
Answers
Answer:
[tex]10.4\: \sf cm^2\:(3\:sf)[/tex]
Step-by-step explanation:
[tex]\Large\boxed{\sf Formulae}[/tex]
Sine Rule
[tex]\dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}[/tex]
(where A, B and C are the angles and a, b and c are the sides opposite the angles)
Cosine rule
[tex]c^2=a^2+b^2-2ab\cos C[/tex]
Area of a triangle
[tex]\textsf{Area of a triangle}=\dfrac12ab\sin C[/tex]
where:
C is the anglec is the side opposite the anglea and b are the sides adjacent the angle[tex]\Large\boxed{\sf Calculation}[/tex]
To find the area of ΔBCD, find:
length of CDangle CDBlength of BDThen use the sine rule for area of a triangle
Calculate length CD using cosine rule:
[tex]\implies CD^2=4.9^2+3.8^2-2(4.9)(3.8)\cos 80^{\circ}[/tex]
[tex]\implies CD^2=31.98334186...[/tex]
[tex]\implies CD=5.655381673...\:\sf cm[/tex]
Calculate ∠ADC using sine rule:
[tex]\implies \dfrac{\sin 80}{CD}=\dfrac{\sin ADC}{4.9}[/tex]
[tex]\implies ADC=\sin^{-1}\left(\dfrac{4.9 \sin 80}{CD}\right)=58.568949^{\circ}[/tex]
Therefore, ∠CDB = 180° - 58.568949° = 121.431051°
Use sine rule to calculate DB:
[tex]\implies \dfrac{DB}{\sin 25}=\dfrac{CD}{\sin CBD}[/tex]
[tex]\implies DB=\dfrac{5.655381673\sin25}{\sin 33.568949}=4.322471258..\: \sf cm[/tex]
[tex]\Large\boxed{\sf Solution}[/tex]
Use the sine rule for area of a triangle to find area of ΔBCD:
[tex]\implies A=\dfrac12(CD)(DB)\sin CDB[/tex]
[tex]\implies A=\dfrac12(5.655381673)(4.322471258)\sin (121.431051)[/tex]
[tex]\implies A=10.4\: \sf cm^2\:(3\:sf)[/tex]
Hello Brainilest Brains, I was wondering what 87x72 is. Please say the answer in the answer section below. Thanks for the help!
Answers
Answer:
6,264
Step-by-step explanation:
Answer:
6264
Step-by-step explanation:
72 x 8 = 576
576 x 10 = 5760
72 x 7 = 504
5760 + 504
6264
A survey on healthy choices was given to gym members at Work It Out. The results showed that 90% of its members drank protein shakes. Of the members who drank protein shakes, 30% took weight-loss medication whereas only 10% of members who did not drink protein shakes took weight-loss medication. What is the probability that a gym member does not take weight-loss medication?
Answers
Answer:
63%
Step-by-step explanation:
First, create an easy number to start being able to grasp the concept.
Let us start with 100 members of "Work it Out"
90% drank protein shakes, which translates to 90 people.
30% of 90 people took weight loss medication, this is equal to 27 people. The 10% of the members that didn't take protein shakes (10) took weight loss medication. Add 10 to 27, then subtract from 100 to get the people that don't use weight loss medication. This gets us 63, then put over the total number of members to get 63%.
Hope this helps, and please mark me brainliest! :)
Answer:
63%
Step-by-step explanation:
Mark other person, I don't have a good explanation
The question is what is the range of the function shown on the graph above?
Answers
Answer:
0 ≤ y ≤ 7
Step-by-step explanation:
Hey there! :)
Please see an explanation for better understanding, and let me know if you have any questions!
What is Range?Range in Function means set of all y-values. We know by the graph that y-value is a vertical value while x-value is horizontal value. From the graph, we have y-axis which is vertical line and x-axis which is horizontal line.
For this question, I would like you to focus on y-value instead, at best, only. That is because we are finding the range, as said above that range is the set of all y-values.
StepsTo find the range in graph, first, you must understand that range starts from minimum point/value to maximum point/value. Therefore, we will have to find y-values for both points and combine the interval.
From the graph, we see that there are two points given which are (-6,0) and (9,7). Since (-6,0) is the minimum point because below y = 0, there exists no values. On the other hand, (9,7) is our maximum point because above y = 7, there exists no values.
Focus only y-values, for both points, we have y = 0 and y = 7. Since range is minimum < y < maximum - for opened dots of both points or minimum ≤ y ≤ maximum - for closed dots for both points.
In case if you don’t know what opened dots and closed dots are. Opened dots are white dots while closed dots are colored dots, usually dark ones.
Thus, from the y-values of both point, our range is 0 ≤ y ≤ 7
1. Find the values of a and b. The diagram is not to scale. 121 354
Answers
Answer:
3 or it could also be 1 ( also like demon slayer me tooo )
HELP PLEASE URGENT!!!!!
Answers
Answer:
Solve the trigonometric equation by isolating the function and then taking the inverse. Use the period to find the full set of all solutions.
θ=π/4+2πn, 3π/4+2πn, for any integer n
Step-by-step explanation:
please help me....asap
Answers
Answer:
a.
Step-by-step explanation:
the study is on teens, and its impossible to survey every teen since they didnt specify how many teens there were. so the answer is a, survey 100 teens.
chose the measurement that is about 12 feet.
the height of a house
the length of a 5 dollar bill
the width of a bed
Answers
Answer:
'12 feet'
Step-by-step explanation:
Of these threee measurements, '12 feet' is closest to the height of a house.
Mrs. Reyes had some apples. If she gave each student 3 apples, she would have 2 apples left have. If she gave each students 4 apples each she would be 2 short. How many apples did she have.
Answers
Answer:
14 applesStep-by-step explanation:
Let
Number of apples = aNumber of students = sAccording to question we have equations
a = 3s + 2a = 4s - 2Find the number of students by substitution
3s + 2 = 4s - 24s - 3s = 2 + 2s = 4Find the number of apples
a = 3*4 + 2 = 12 + 2 = 14Answer:
14 apples
Step-by-step explanation:
Let x = number of students
Let y = total number of apples
Create a system of equations with the given information.
Equation 1
If she gave each student 3 apples, she would have 2 apples left:
⇒ y - 3x = 2
Equation 2
If she gave each students 4 apples each she would be 2 short:
⇒ y - 4x = -2
Rewrite Equation 1 to make y the subject:
⇒ y = 2 + 3x
Substitute this into Equation 2 and solve for x:
⇒ (2 + 3x) - 4x = -2
⇒ 2 + 3x - 4x = -2
⇒ 2 - x = -2
⇒ -x = -4
⇒ x = 4
Substitute the found value of x into the rewritten Equation 1 and solve for y:
⇒ y = 2 + 3(4)
⇒ y = 2 + 12
⇒ y = 14
Therefore, Mrs Reyes had 14 apples.
f g(x) = 2x + 2, find g(a + h) - g(a).
Answers
Answer: 2h
Step-by-step explanation:
The volume of a cylinder is 256pi in3. and the height of the cylinder is 1 in. What is the radius of the cylinder?
Answers
Answer:
9.03
Step-by-step explanation:
the formula is V=pir2h
(pi, radius squared, and height)
A bag contains 10 yellow cubes, 5 red cubes, and 15 blue cubes. Determine whether the following event is impossible, unlikely, as likely as not, likely, or certain.
A red cube is randomly drawn from the bag.
Answers
Answer:
I would say likely.
Step-by-step explanation:
I hope this helps.
To read her book report book, Jodi needs to read 365 pages in 10 days. Choose the correct equation and answer for this situation.
A. 365÷10 = 365/10 = 36 5/10=36 1/2 pages
B. 365 ÷ 10= 2/73 pages
C. 10÷365 = 365/10 = 3 5/10= 3 1/2 pages
D. 10÷365 = 2/73 pages
(PLS ANSWER ONE OF THE OPTIONS)
Answers
Answer: A
Step-by-step explanation:
365/10 is the best way to figure it out
Answer:
A. 365÷10 = 365/10 = 36 5/10=36 1/2 pages
Explanation:
rate = total pages/total days
Here:
total pages = 365 pagestotal days = 10 daysRate:
365 ÷ 10 = 365/10 = 36 1/2 pages per day
How do I know if a score is good or not on a math map test
Answers
Answer:
on the math and reading test, 240 (reading) and 250 (math) are typical top scores.
Step-by-step explanation:
