A regular pentagonal prism has a height of 14 in. and a base edge length of 10 in. Identify its lateral area and surface area.
Can anyone help me solve this?
Answers
So the lateral area = 5 * 10 * 14 = 700 (in squared)
Consider one of the bases of the prism.
As shown in the figure, the pentagon is made up of 5 isosceles triangles.
The vertex of each of these 5 triangles is 360°/5=72°.
Draw the altitude, which forms 2 right triangles with angle measures 36°-54°-90°.
Let he hypotenuse be s and the altitude be h in, as shown in the figure.
x*cos54°=5
x=5/(cos54°)=5/(0.588)=8.5
then,
h=x*sin54°=8.5*(0.8)=6.8 (in)
Thus, the area of one of the 5 congruent isosceles triangles is
[tex] \frac{1}{2}*10*6.8= 34[/tex] (in squared)
The area of the pentagonal base is 34*5 = 170 (in squared)
Thus the surface area = lateral area + 2 base area
= 700+2*170 = 700+340 = 1040 (in squared)
Answer:
lateral area: 700 in squared
surface area: 1040 in squared
Answer:
L = 700 in2 ; S = 1044.1 in2
Step-by-step explanation:
Lucky guess :)
Related Questions
Ira purchased a new dishwasher for $361.35. The dishwasher was on sale for 17.5% off. What was the original price of the dishwasher, to the nearest dollar?
Answers
To solve this equation, you cross multiply. I first subtracted 17.5 from 100 in order to get the percentage value that $361.35 was of its original price. Since 100 - 17.5 = 82.5, the washing machine is 82.5% of its original price.
I cross multiplied by writing [tex] \frac{361.35}{1} * \frac{82.5}{100} [/tex], and multiplying [tex]361.35 * 100[/tex] and [tex]82.5 * 1[/tex]. The result was [tex] \frac{36135}{82.5}[/tex]. This becomes $438. There is no rounding needed to be done.
The original price of the dishwasher with a 17.5 percentage discount is $361.
We have,
To find the original price of the dishwasher, we need to figure out what the discount amount is and subtract it from the sale price.
The discount amount is 17.5% percentage of the original price, which can be expressed as:
Discount amount = 0.175 x Original price
We can rearrange this equation to solve for the original price:
Original price = Discount amount / 0.175
The discount amount is:
Discount amount = 0.175 x $361.35 = $63.25
So the original price of the dishwasher was:
Original price = $63.25 / 0.175 = $361.43
Rounding this to the nearest dollar gives an original price of $361.
Thus,
The original price of the dishwasher with a 17.5 percentage discount is $361.
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60,000 is ten times as much as
Answers
x=6000
Video DVDs (ignoring the hole in the middle) have an area of 36π cm^2 The formula to calculate the circumference, C, for a circle is c=2√Aπ, where A is the area of the circle. What is the circumference of the disc?
12πcrr
18πcrr
24πcrr
30πcrr
Answers
Final answer:
The circumference of a DVD with an area of 36π cm^2 is 12π cm.
Explanation:
The question asks for the circumference of a DVD with an area of 36π cm2. The circumference C of a circle is related to its area A by the formula C = 2√(Aπ). In this case, we need to substitute the given area of the disc into the formula to calculate the circumference.
First, we'll start by plugging in the area into the formula:
C = 2 √(36π π)
C = 2 √(36)√(π)√(π)
C = 2 × 6 × π
C = 12π
Therefore, the circumference of the disc is 12π cm.
A scientist finds the temperature of a sample at the beginning of an experiment is t degrees celcius. After 1 hour, the temperature is t^2 degrees celcius. If the temperature after 1 hour is 81 degrees celcius, what are two possible original temperatures? What is the difference between the possible original temperatures?
Answers
The two possible original temperatures are 9 and - 9 degrees Celcius and the difference between the temperature is 18 degrees Celcius.
What is a quadratic equation?Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
As we know, the formula for the roots of the quadratic equation is given by:
[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]
It is given that:
A scientist finds the temperature of a sample at the beginning of an experiment is t degrees Celcius.
After 1 hour, the temperature is t² degrees Celcius. If the temperature after 1 hour is 81 degrees Celcius.
From the question:
t² = 81
Taking square root on both sides:
t = ±√81
t = ±9
t = 9 degrees Celcius
Or
t = -9 degrees Celcius
The difference between the temperature = (9) - (-9) = 18 degrees Celcius
Thus, the two possible original temperatures are 9 and - 9 degrees Celcius and the difference between the temperature is 18 degrees Celcius.
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Carlos can print a document on apricot printer which the speed is 8 in 4.5 minutes how long would it take him to print the same document on a sure-fire printer which the speed is 12
Answers
The surefire printer has a speed of 12.
The surefire is faster than the apricot printer, so it wll take less time to print a document.
The apricot printer takes 4.5 minutes.
Therefore by proportion, the surefire printer takes
(8/12)*4.5 = 3 minutes.
Answer: 3 minutes
How many tenths are equal to 4/5 mile using a diagram
Answers
One tenth equals to 0.1
0.8 = 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1
We need ten lots of 0.1 to make 0.8
Please help to solve... Need steps
Answers
x =0.25y
substitute x = 0.25y into x + y = 360
x + y = 360
0.25y + y = 360
1.25y = 360
y = 288
x = 288 (0.25) = 72
Jose has 72 stamps
Maria has 288 stamps
288 - 72 = 216
answer
Maria has 216 more stamps than Jose
Cat breeders often mate cats that have special traits that they will pass on to offspring. This is an example of
Answers
blame it on me if you get it wrong:C
I need help with this.
Answers
(the green numbers on the image are the step numbers)
We can solve this using PEMDAS.
I wrote out how I solved it in the image, and here I will go more into detail:
Step 1
Write out the equation
Step 2
Put in the variables
Step 3
Solve:
Parentheses - Multiply
Step 4
Parentheses - Subtract
Step 5
Multiply
Step 6
Add
There's your answer! :)
The answer is 42
Hope this helps! :)
8(3) + 6[2(5)-7]
You have to multiply the numbers in the parenthesis with the adiacent one.
24 + 6(10-7)
24+6(3)
24+18
42
Two trucks leave from the same truck stop at the same time. One travels east on interstae 80 and the other travels west. The eastbound truck averages 40 miles per hour, and the westbound truck averages 50 miles per hour. In how many hours will the trucks be 300 miles apart?
Answers
Answer:
About 3 hours
Step-by-step explanation:
Imagine one truck going West and the other East. One is going 50 miles per hour and the other is going 40 miles per hour. Because you need to use the equation 50x+40x=300. You should get x = 3.3.
help me please. I don't know how to do this. so can you take me step by step if possible.
Answers
If f(x)= -x²+3x+5, find f(-3), f(0), f(2), f(5), and f(8).
Answers
-(-3)^2+3(-3)+5
-9-9+5
-18+5
-13 <======
f(0)
-(0)^2+3(0)+5
-0+0+5
5 <=======
f(2)
-(2)^2+3(2)+5
-4+6+5
7 <=======
f(5)
-(5)^2+3(5)+5
-25+15+5
-5 <======
f(8)
-(8)^2+3(8)+5
-64+24+5
-35 <======
Translate the sentence into an inequality.
Three subtracted from b is less than or equal to −17.
Answers
"is less than or equal to" = ≤
"-17" = -17
Putting it all together...
b-3≤-17
Which expressions are equivalent to 3(x + 3y + 2x − y)?
Answers
= 9x + 6y
See if any of these match an answer option.
3(x + 3y + 2x - y)
= 3(x) + 3(3y) + 3(2x) + 3(-y)
= 3x + 9y + 6x - 3y
= 9x + 6y
Therefore, 9x + 6y is equal to 3(x + 3y + 2x - y)
Also, 9x + 6y can be factored into 3(3x + 2y).
3(3x + 2y)
= 3(3x) + 3(2y)
= 9x + 6y
So this pair is equivalent: 3(3x + 2y) and 9x + 6y
use the numbers 2,3,5, and 8 to write an expression that has a value of -1
Answers
On a test hailey answered 64 out of 75 questions correctly. What percent of her answers
Were correct?
Answers
Answer:
[tex]\bold{85\frac13\,\%}[/tex]
Step-by-step explanation:
[tex]\dfrac{64}{75}\cdot100\,\%=\dfrac{64}{3}\cdot4\,\%=\dfrac{256}{3}\,\%=85\frac13\,\%[/tex]
Which equation represents an exponential function with an initial value of 500
Answers
So, the hint for you to find is the term 500 right before the term with an exponent. For example, the function would be: y = 500(1.8)^x.
There is a 70% chance of rain tomorrow and a 20% chance that the volleyball game will be postponed. What is the probability that it will rain tomorrow and the volleyball game will be postponed?
Answers
0.20/0.70 = 0.2857
28.6% chance
round the answer as needed.
I believe it is 14%
because 20% = 0.2 and 70% = 0.7
then 0.2 * 0.7 = 0.14
0.14 = 14%
14% is answer srry if wrong
What is the place value of 8 in 0.829
Answers
HELP??
A scatter plot is shown below
Which two ordered pairs can be joined to draw most accurately the line of best fit on this scatter plot?
(4, 9.5) and (10, 5.5)
(5, 0) and (10, 10)
(0, 6) and (5, 0)
(0, 9.5) and (10, 1.5)
Answers
Answer: The correct answer is D!
Step-by-step explanation:
What is an expression that is equal to 12m+12n
Answers
Find the area of the parallelogram shown.
35 yd 2
24 yd 2
26 yd 2
40 yd 2
Answers
area = base x height
base = 5
and height = 7
so area = 7*5 =35 square yards
PLEASE ANSWER ALL PARTS I WILL GIVE BRAINLIEST
Julian compared numbers with similar digits. Using mathematical language, explain how each set of numbers is different
SET A: 13.542 AND 35.42
SET B: 781 AND 78.1
SET C: 1.2 AND 01.20
Answers
13.542 is 10 more than 10% of 35.42
781 = 78.1 * 10
781 is equal to 10 times 78.1
1.2 has two significant figure but 01.20 has 3 significant figure
An acute angle θ is in a right triangle with sin θ = seven eighths. What is the value of cot θ?
ANSWERS
square root of fifteen divided by eight
eight divided by the square root of fifteen
seven divided by the square root of fifteen
square root of fifteen divided by seven
Answers
Let CB=7 units, AC=8 units, so by the Pythagorean theorem:
[tex]AB= \sqrt{ AC^{2} - BC^{2} }= \sqrt{ 8^{2} - 7^{2} }= \sqrt{64-49} = \sqrt{15} [/tex] (units)
so we have drawn a triangle where sin∅=7/8
in this triangle, cot∅=(adjacent side)/(opposite side)=[tex] \frac{ \sqrt{15} }{7} [/tex]
Answer: square root of fifteen divided by seven
In my block of 100 flats a painter is kept employed by painting one flat each month from January to November. The flats are painted in the same order and he takes a holiday every December. If my flat was last painted in August 2010 when will it be next painted?
Answers
January to November == 11 months.
11 flats are painted every year.
100 flats / 11 flats per year = 9 years + 1 month
the next time it will be painted is September 2019.
Answer:
The answer is September 2019.
Step-by-step explanation:
In order to determine the date of the painting flat, we have to know how the painter works.
Every year, the painter paints 11 flats, because he paints one flat each month and he doesn't work in December.
Also, if we consider that "my flat" is currently in the first position, we have to wait until the painter paints the 100 position because the painter has to paint 99 flats more.
So, "my flat was painted in August 2010", then the painter paints 3 flats more that year (September, October, November).
Now we add more painted flats every year:
3+11+11+11+11+11+11+11+11=91
At beginning of 2019, the painter has painted 91 flats. So in 9 months later, the painter will be paint the 100 position, that is in September 2019.
Finally "my flat" will be painted in September 2019.
You are studying for your final exam of the semester. up to this point, you received 3 exam scores of 67%, 68%, and 78℅. to receive a grade of C in the class, you must have an average exam score between 70% and 79% for all 4 exams including the final.
Answers
(213 + x) / 4 = 70
213 + x = 70 * 4
213 + x = 280
x = 280 - 213
x = 67
(213 + x) / 4 = 79
213 + x = 79 * 4
213 + x = 316
x = 316 - 213
x = 103
lowest u can make is 67, highest u can make is 100
Answer: its 68,100 on plato
What is the prime factorization of 162?
Answers
Start by dividing by the smallest prime number.
162/2 = 81
81/3 = 27
27/3 = 9
9/3 = 3
2 * 3 * 3 * 3 * 3 = 2 * 3^4
a person or company that allows others to borrow money is called
Answers
Answer:
ummm its called a lender since that person is "lending" you something
Step-by-step explanation:
A person or company that allows others to borrow money is called a "lender".
What is a Lender?A lender is a person, a group (public or private), or a financial organization that makes cash accessible to a person or business with the expectation of repayment. Payment of any interest or fees will be included in the repayment.
Repayment might take place in installments (such as a monthly mortgage payment) or as a flat amount. A mortgage is one of the largest loans that individuals obtain from lenders.
The loan duration varies depending on the type of debt. While some loans are for 1-2 years, the majority are for 6-12 months.
Thus, a person or company that allows others to borrow money is called a "lender".
To learn more about the Lender link is given below.
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The center of an ellipse is located at (0, 0). One focus is located at (12, 0), and one directrix is at x = 14 1/12.
what is the equation that represents the ellipse?????????
Answers
[tex] \frac{(x-h)^{2}}{a^{2}} + \frac{(y-k)^{2}}{b^{2}} =1[/tex]
where
(h,k) = coordinates of the center
a, b = semi-major and semi-minor axes
Refer to the figure shown below.
The center of the ellipse is at (0,0).
Therefore, h=0, k=0.
One focus is at (12, 0)
Therefore
c = 12
One directrix is at 14 1/12 = 169/12.
Because the directrix is located at x = a²/c, therefore
a²/12 = 169/12
a² = 169/144
a = 13
Because c² = a² - b², obtain
b² = a² - c²
= 169 - 144 = 25
b = 5
Answer:
The equation for the ellipse is
[tex] \frac{x^{2}}{169} + \frac{y^{2}}{25} =1[/tex]
The equation that represents the ellipse with the given coordinates of the center, one focus, and one directrix is x^2/144 + y^2/(25/12) = 1.
Explanation:The equation that represents the ellipse with the center at (0, 0), one focus at (12, 0), and one directrix at x = 14 1/12 can be found using the standard form of the equation for an ellipse:
(x - h)^2/a^2 + (y - k)^2/b^2 = 1
where (h, k) is the center of the ellipse, a is the distance from the center to the vertices, and b is the distance from the center to the co-vertices.
Since the center is at (0, 0), the equation becomes:
x^2/a^2 + y^2/b^2 = 1
The distance from the center to one focus is 12, so the value of a is 12. To find the value of b, we need to use the distance from the focus to the directrix. Since the directrix is x = 14 1/12, the distance from the focus to the directrix is |14 1/12 - 12|. Simplifying, we get |14 1/12 - 12| = 2 1/12. Therefore, the value of b is 2 1/12.
Substituting these values into the equation, we get:
x^2/144 + y^2/(25/12) = 1
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What's 2 ways to write 100203
Answers
one hundred thousand two hundred and three (word form)
hope this helps