A side length of the base is 6 inches, and the apothem of the base is 4 inches. The height of the prism is 18 inches. What is the area of a cross-section of the prism? What is the volume of the prism?
A) 12 in2; 216 in3 B) 24 in2; 432 in3 C) 60 in2; 1080 in3
D) 120 in2; 2160 in3
Answers
Answer:
Area and volume of pentagonal prism is 660 inches² and 1080 inches³
Step-by-step explanation:
Given : A pentagonal prism having side length of the base is 6 inches, and the apothem of the base is 4 inches. The height of the prism is 18 inches.
We have to calculate
1) area of a cross-section of the prism
2) the volume of the prism
1) Area of cross section of pentagonal prism =5ab +5bh
Where a = apothem
b - base length
h = height.
For the given pentagon
apothem = 4 inches
base = 6 inches
Height = 18 inches
Area of cross section of pentagonal prism =5 ×4 × 6 + 5× 6 × 18
Area of cross section of pentagonal prism = 120 + 540
Area of cross section of pentagonal prism = 660 inches²
2) Volume of pentagonal prism = [tex]\frac{AP}{2} \times H[/tex]
Where, A = apothem
P is perimeter of base
H= height
Perimeter of pentagon is 5b = 30 inches
Volume of pentagonal prism = [tex]\frac{4\times 30}{2} \times 18[/tex]
Volume of pentagonal prism = 1080 inches³
Thus, Area and volume of pentagonal prism is 660 inches² and 1080 inches³.
Related Questions
Write each expression as the product of two binomials x2 - 5x + 6
Answers
x(x-3)-2(x-3)
Solution:
(x-2)(x-3)
When calculated, the two differences given below are equal.
(2x^4-3x^3+2x+4)-(-x^4-3x^3+4x^2+x+3)
5x^4-2x^3+3x^2+3x-4
-(2x^4-2x^3+7x^2+2x-5)
-------------------------
A. True
B. False ...?
Answers
let be
A1 = (2x^4-3x^3+2x+4)-(-x^4-3x^3+4x^2+x+3) =
= 2x^4-3x^3+2x+4 +x^4 +3x^3- 4x^2- x-3
A1= 6x^4 -2x² +x +1
and
A2= 5x^4-2x^3+3x^2+3x-4-(2x^4-2x^3+7x^2+2x-5)
= 5x^4-2x^3+3x^2+3x-4-2x^4+2x^3-7x^2-2x+5
A2= 3x^4-4x²+x+1
A1 is not equivalent to A2
so the answer is B. False
What is the symbol that means the following true 546322. 540997?
Answers
The expression below is a sum of cubes.
125x3 + 144
A.True
B.False ...?
Answers
An expression is a sum of cubes if it can be written in form of a³ + b³, where a and b can be any constant/variables.
So, this means the given expression 125x³ + 144 can only be sum of cubes if the both the terms i.e. 125x³ and 144 are perfect cubes.
125x³ = (5x)³ . This means 125x³ is a perfect cube. However, 144 is not a perfect cube.
Hence we can conclude that the expression 125x³ + 144 is not a sum of cubes. So the answer to this question if FALSE
What is the center of the circle that you can circumscribe about a triangle with vertices A(2, 6), B(2, 0), and C(10, 0)?
Answers
Each point is then equal distance from the center, that distance being the radius of the circle.
Using the distance formula, we can find the center of the circle (x,y):
[tex]d^2 = (x-x_0)^2 + (y-y_0)^2[/tex]
Plugging in points A and B into distance formula, then setting them equal to each other gives:
[tex](x-2)^2+(y-6)^2 = (x-2)^2 + y^2[/tex]
Right away we can cancel out the x terms leaving:
[tex](y-6)^2 = y^2[/tex]
Expand Left side and Solve for y:
[tex]y^2 -12y +36 = y^2[/tex]
[tex]y = 3[/tex]
Plug in points B and C as before:
[tex](x-2)^2 + y^2 = (x-10)^2 + y^2[/tex]
Here we can cancel the y-terms.
Expand and solve for x:
[tex]x^2 -4x+4 = x^2 -20x+100[/tex]
[tex]16x = 96[/tex]
[tex]x = 6[/tex]
Therefore the center of the circle is the point (6,3)
The center of the circle that can be circumscribed about a triangle with vertices A(2, 6), B(2, 0), and C(10, 0) is calculated by finding the intersection of the perpendicular bisectors of the sides of the triangle. In this case, the center of the circle is at (6,3).
Explanation:For the triangle with vertices A(2, 6), B(2, 0), and C(10, 0), the circle that you can circumscribe about it is known as the circumcircle. The center of this circle is the circumcenter which is obtained by the intersection of the perpendicular bisectors of the sides of the triangle.
Since points A and B lie along the same vertical line, the perpendicular bisector of line AB is a horizontal line halfway between them at y=3. The bisector of line BC is a vertical line halfway between points B and C at x=6.
The intersection of these two bisectors (x=6, y=3) is the circumcenter. So, the center of the circumcircle is at (6,3).
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To meke a batch of sugar cookies , you need 0.75 cup of sugar and 1/3 cup of butter , among other ingredients. How much more sugar do you need that butter?
a) 5/12 cup b) 3/4 cup c) 1/2 cup d) 2/3 cup
Answers
you have to convert the fractions so they have the same denominator. 0.75 is 9/12 and 1/3 is 4/12. Subtract and you get 5/12
Money is invested into an account earning 4.25% interest compounded annually. If the accumulated value after 18 years will be $25,000, approximately how much money is presently in the account?
a.
$5,875
b.
$11,820
c.
$19,125
d.
$23,960
Answers
The amount of money that is presently in my investment account is $11,820.
How much is presently in my account?The formula that can be used to determine the amount in my account presently is:
P = FV / (1 + r)^n
FV = Future value P = Present value R = interest rate N = number of years25,000 / (1.0425)^18 = $11,820
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Final answer:
To find the current amount needed to reach $25,000 in 18 years at a 4.25% interest rate, the formula P = A / (1 + r)^n is used. Plugging in the values gives P ≈ $11,820, indicating that approximately $11,820 is currently in the account. Thus, the correct answer is (b) $11,820.
Explanation:
The question asks how much money needs to be present in an account now to reach a future value of $25,000 in 18 years at an annual compound interest rate of 4.25%. To find the present value, we use the formula for compound interest: P = A / (1 + r)^n, where P is the present value, A is the amount of money accumulated after n years, inclusive of interest, r is the annual interest rate (decimal), and n is the number of years the money is invested for.
In this case, A = $25,000, r = 0.0425 (4.25%), and n = 18 years. Plugging these values into the formula gives: P = $25,000 / (1 + 0.0425)^18. Calculating this gives us P ≈ $11,820, which means the amount of money currently in the account to reach $25,000 in 18 years at a 4.25% annual interest rate compounded annually is approximately $11,820. Therefore, the correct answer is (b) $11,820.
Are skew lines equidistant? Explain.
Answers
What is the common difference d of the sequence?
9, −8, −25, −42, −59, ...
Answers
What is the measure of (7x 8)°?
Answers
Two numbers differ by 13 and the sum of their squares is 125 find the numbers
Answers
By substituting the value of one number in terms of the other from the difference equation into the sum of squares equation, we find the two numbers to be 10 and -3.
Explanation:Let's solve the problem step-by-step. Given that two numbers differ by 13 and the sum of their squares is 125, we can set up the following equations where x and y are the two numbers:
Equation 1: x - y = 13 or y = x - 13 (1)Equation 2: x^2 + y^2 = 125 (2)Substitute the value of y from equation (1) into equation (2), giving us:
x^2 + (x - 13)^2 = 125
Solving this, we find that x = 10 and hence y = -3, which means the two numbers are 10 and -3.
Suppose a triangle has sides a, b, and c, and the angle opposite the side of length b is obtuse. What must be true?
A. a^2 + c^2 < b^2
B. a^2 + c^2 > b^2
C. b^2 + c^2 < a^2
D. a^2 + b^2 < c^2
Answers
For a triangle with an obtuse angle B and the longest side opposite it (side c), the correct statement is a^2 + c^2 > b^2.
The correct answer is option B.
In a triangle with sides a, b, and c, where angle B (opposite side b) is obtuse, and side c is the longest side (opposite the largest angle), we can apply the Law of Cosines. The Law of Cosines relates the lengths of the sides of a triangle to the cosine of one of its angles:
c^2 = a^2 + b^2 - 2ab * cos(B)
Given that angle B is obtuse, cos(B) will be negative. Therefore, the term -2ab * cos(B) will subtract from the sum of a^2 + b^2. The Law of Cosines now becomes:
c^2 = a^2 + b^2 + 2ab * cos(B)
Considering the given options:
A. a^2 + c^2 < b^2 - This is not necessarily true in this context.
B. a^2 + c^2 > b^2 - This is true based on the Law of Cosines.
C. b^2 + c^2 < a^2 - This is not necessarily true in this context.
D. a^2 + b^2 < c^2 - This is not necessarily true in this context.
Therefore, from the given options the correct one is option B.
A farmer wants to build a pen for his sheep. One side of the pen will be a river. The sheep need about 2000 m2 of area to graze. About what length (x) and width (y) should the organization use to use the LEAST amount of fencing possible?
Answers
so L=W= √2000=20√5
legnth and width should be 20√5 meters
the following is calculus
xy=2000 and 2(x+y)=P
solve
ok so
xy=2000
divide both sides by x
y=2000/x
sub 2000/x for y in other equation
2(x+2000/x)=P
2x+4000/x=P
to find the minimum value of this, take the derivitive and find where it equals 0
2-4000/(x^2)=0
2=4000/(x^2)
2x^2=4000
x^2=2000
x=√2000
x=20√5
y=2000/x
y=2000/(√2000)
y=√2000=20√5
x=y=20√5 meters
Rewrite 6 as a decimal number.
Answers
What is the range of these numbers?
8,4,9,2,3
Answers
It would be: 2,3,4,8,9
Range = Highest number - Lowest number
Range = 9 - 2 = 7
So, your answer is 7
Hope this helps!
9-2= 7. Your range is 7.
Hope this helps!
Solve for x: 2|x − 3| + 1 = 7
x = 0, x = 6
x = −1, x = 6
x = 0, x = 9
No solutions
Answers
Answer:
x=6 or x=0
Find the measure of each angle indicated.
Answers
The solutions are as follows:
11) 110 - alternate exterior angles
12) 84 - alternate interior angles
13) 80 - supplementary angles
14) 111 - alternate interior angles
15) 125 - alternate interior angles
16) 47 - alternate exterior angles
17) 53- corresponding angles
18) 113-alternate interior angles
Here, we have,
from the given figure, we get,
11) the required angle is alternate exterior angle of 110,
so, the value is 110.
12) the required angle is alternate interior angle of 84
so, the value is 84
13) the required angle is supplementary angle of 100
so, the value is 80
14) the required angle is alternate interior angle of 111
so, the value is 111
15) the required angle is alternate interior angle of 125
so, the value is 125
16) the required angle is alternate exterior angle of 47,
so, the value is 47.
17) the required angle is corresponding angle of 53
so, the value is 53.
18) the required angle is alternate interior angle of 113
so, the value is 113.
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What is a theorem called before it is proven?
postulate
proposition
contradiction
tautology
Answers
Before a theorem is proven, it is known as a proposition. This term indicates that the statement is proposed to be true and is pending proof.
Explanation:A theorem called before it is proven is known as a proposition. A proposition is a statement that is proposed to be true and is awaiting proof or disproof. In contrast, a postulate is a statement that is assumed to be true without proof for the purposes of reasoning in mathematics or science, whereas a contradiction refers to a statement that is always false. A tautology is a statement that is true by necessity or by virtue of its logical form.
Final answer:
A theorem before it is proven is known as a proposition. Propositions are statements considered in mathematics and philosophy for investigation and proof. Other terms like postulate, contradiction, and tautology have different distinct meanings in logic.
Explanation:
Before a theorem is proven, it is known as a proposition. A proposition is a statement that proposes an idea, which can be either true or false, but has not yet been proven to be true. In mathematics and philosophy, this term is used to describe concepts that are considered and investigated for proof. Once a proposition is proven conclusively, it becomes a theorem. Other options like postulate, contradiction, and tautology have different meanings within mathematical logic and reasoning.
Find the solution of this system of equations.
-2x-6y=-16
4x-6y=-58
Answers
2x+6y=16
4x-6y=-58
Y's cancel out, then add the rest
6x=-42
divide both sides by six
x=-7
plug x into any previous equation
2(-7)+6y=16
-14+6y=16
6y=30
y=5
Which of the following best describes the graph shown below?
A) This is the graph of a linear function
B) This is the graph of a function, but it is not one-to-one.
C) This is not the graph of a function
D) This is the graph of a one-to-one function
Answers
Answer: The answer is (B) This is the graph of a function, but it is not one-to-one.
Step-by-step explanation: We are given a graph and four options out of which we are to select the statement that best describes the given graph.
Since the graph of a linear function is a straight line, so the first option is not correct.
The given graph is of a function because for a particular value of y, there is a fixed value of 'x'.
Also, since there are two different values of x having same value for y, so the function is not one-to-one. For example, If y = f(x) is the function, then f(1.5) = f(-1) = 3.
Therefore, the graph represents a function, but it is not one-to-one.
Thus, the correct option is (B).
Aidan is paying his taxes and realizes that he was in the first tax bracket (10%) last year. Eleven years ago, he bought a common stock for $705. The same stock was sold last year for $947. During the same year, he earned $565 in dividends and $780 in coupons on a corporate bond. What will Aidan pay in taxes for last year’s investments?
$78.00
$84.75
$162.75
$199.05
Answers
Their sum is 7, and their product is 15
Answers
The numbers, their sum is 7, and their product is 15 are,
(7 + √11 i)/2 and (7 - √11 i)/2.
Use the concept of complex numbers defined as:
A real number and an imaginary number are effectively combined to create a complex number. The complex number is written as a+ib, where a and ib are real and imaginary numbers, respectively.
Let the numbers x and y such that,
x+y = 7 .....(i)
xy = 15 ......(ii)
Since we know that,
(x - y)² = x² + y² - 2xy
Add 2xy on both sides,
(x - y)² + 2xy = (x² + y² + 2xy) - 2xy
(x - y)² + 2xy = (x + y)² -2xy
put the values from equations (i) and (ii),
(x - y)² + 30 = 49 - 30
Simplify it,
(x - y)² = -11
Take square root on both sides,
x - y = √11 i .....(iii) ( i = √-1)
Add equations (i) and (iii),
2x = 7 + √11 i
x = (7 + √11 i)/2
Substitute this value of x in equation (iii),
y = (7 - √11 i)/2
Hence,
The required numbers are (7 + √11 i)/2 and (7 - √11 i)/2.
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The complete question is:
Find the complex or real numbers such that,
Their sum is 7, and their product is 15.
The prime factorization of 36 is 2^2 • 9.
True
False
Answers
But instead of 2² ·9, it would be better to simply further and say 2² · 3².
Hope this helps!
which of PQ and QR contains P
Answers
how to solve x^4+4x-1=0 ? ...?
Answers
Using the Quadratic formula
x^4 = (x^2)^2
hence
(x^2)^2 + 4x +(-1) = 0
ax^2=1(x^2)^2
bx = 4(x)
c=(-1)
Which is the last operation performed when evaluating (8-2x)^2+4 for x=3
addition
multiplication
subtraction
applying the exponent
Answers
The last operation performed when evaluating (8-2x)^2+4 for x=3 is the addition operation.
Functions and valuesEquations are known to make up of variables and constants. Given the expression;
(8-2x)^2+4
If x = 3, substitute into the expression to have:
(8-2x)^2+4
= (8-2(3))^2+4
= (8 - 6)^2 + 4
Evaluate the expression in parenthesis
= 2^2 + 4
= 4 + 4
Add the resulting expression
(8-2x)^2+4 = 8
Hence the last operation performed when evaluating (8-2x)^2+4 for x=3 is addition operation
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A BOOKSTORE ORDERED 2 GROSS, 11 DOZEN AND 7 PENCILS. EXPRESS THIS NUMBER IN BASE TWELVE AND BASE TEN? ...?
Answers
In base 10, the bookstore ordered 11*12+12*12+7 = 283 pencilsIn base 12, the bookstore ordered 23 dozen +7 = 1B7 pencils
28310=1B77
The cost to rent a dump truck is $50 per day plus $26 per hour of use. What is the maximum number of hours the truck can be used each day if the rental cost should not exceed $193 per day?
A 2.5
B 8.04
C 5.5
D 3.34
Please explain and show work! ☺☺
Thanks!
Answers
What is the slope of a line that runs parallel to y = x + 14?
Answers
The slope of y = x + 14 is 1
The slope of the parallel line will be 1 as well
If r = 8 units and x = 5 units, then what is the volume of the cylinder shown above?