What is the volume of the composite figure? Explain your work. A complete answer should include how you broke up the figure, which numbers you multiplied to find the volume. You may want to use the formula for volume to find the solution.
Answers
Answer:
[tex]15,000\:\mathrm{mm^3}[/tex]
Step-by-step explanation:
The composite figure consists of a square prism and a trapezoidal prism. By adding the volume of each, we obtain the volume of the composite figure.
The volume of the square prism is given by [tex]V=s^2\cdot h[/tex], where [tex]s[/tex] is the base length and [tex]h[/tex] is the height. Substituting given values, we have: [tex]V=14^2\cdot 30=196\cdot 30=5,880\:\mathrm{mm^3}[/tex]
The volume of a trapezoidal prism is given by [tex]V=\frac{b_1+b_2}{2}\cdot l\cdot h[/tex], where [tex]b_1[/tex] and [tex]b_2[/tex] are bases of the trapezoid, [tex]l[/tex] is the length of the height of the trapezoid and [tex]h[/tex] is the height. This may look very confusing, but to break it down, we're finding the area of the trapezoid (base) and multiplying it by the height. The area of a trapezoid is given by the average of the bases ([tex]\frac{b_1+b_2}{2}[/tex]) multiplied by the trapezoid's height ([tex]l[/tex]).
Substituting given values, we get:
[tex]V=\frac{14+24}{2}\cdot (30-14)\cdot 30,\\V=19\cdot 16\cdot 30=9,120\:\mathrm{mm^3}}[/tex]
Therefore, the total volume of the composite figure is [tex]5,880+9,120=\boxed{15,000\:\mathrm{mm^3}}[/tex] (ah, perfect)
Alternatively, we can break the figure into a larger square prism and a triangular prism to verify the same answer:
[tex]V=30^2\cdot 14+\frac{1}{2}\cdot10\cdot 16\cdot 30=\boxed{15,000\:\mathrm{mm^3}}\checkmark[/tex]
Related Questions
The average age of three people running for election is 42. A fourth person joins the race and the average drops to 40. What is the fourth
person's age?
OA. 32
OB. 34
ОО
C. 35
D. 36
E. 40
Answers
Answer:
B. 34
[tex]let \: sum \: of \: ages \: of\: 3 \: people \: be \: x \\ 42 = \frac{x}{3} \\ x = 126 \\ let \:age \: of \: fourth \: person \: be \: y \\ 40 = \frac{x + y}{4} \\ 160 = x + y \\ 160 = 126 + y \\ y = 34 \\ = 34 \: years[/tex]
if there are 420 students in a school.if 40% of them are girls find the number of girls
Answers
Answer:
168 girls
Step-by-step explanation:
420 × 0.40
= 168
Answer:
Step-by-step explanation:
no of students=420
girls percentage=40%
no of girls=40/100*420
=16800/100
=168
therefore number of girls is 168.
Which point is located at (4, -2)?
А
4
10
3
N
+
万一-3-2-14
--2-
1 2 3 4 5 X
B
D
-5
Ο Α
ОВ
OD
Answers
The 3rd one please!
I’ll mark you the brainliest!!!!
Answers
Answer:
around 150 to 170 votes
Step-by-step explanation:
exactly atleast 160
Now that you know how long it will take to buy your house from Assignment 4 and how much you need to save for retirement given different start times in your life (Assignment 5), you will now determine the time you will start saving for retirement. Add the savings time it takes to buy your house (2 years or the months you calculated, whichever is greater) to the age 22. By using the new budget from assignment 4, determine if you can afford the savings it takes from assignment 5 to retire with $1,000,000 based on your new age after buying your house. If you cannot, you have a choice, change your budget, or retire will less money.
For your answer, tell me your age, if you can afford in your budget to retire with $1,000,000. If you can, write your budget with the retirement savings added in. If you cannot, write that you cannot afford it and tell me if you are going to change your budget to afford it or simply retire with less money. Then write your budget with what savings you can afford. Remember, retiring with less money does not mean that you will have a smaller retirement income, it just means that you will pass on less than a million dollars to your children.
Answers
Answer:
You have to answer this yourself because i believe this quesstion is directed to you and your teacher want's to know your answer
Step-by-step explanation:
(44=6x-1+9x,-5)
I don’t know how to answer this I just know it’s ( , -5)
Answers
Answer:
Step-by-step explanation:
(44=6x-1+9x.-5)
We move all terms to the left:
(44-(6x-1+9x.-5))=0
We add all the numbers together, and all the variables
(44-(6x+9x.-6))=0
We calculate terms in parentheses: +(44-(6x+9x.-6)), so:
44-(6x+9x.-6)
determiningTheFunctionDomain
-(6x+9x.-6)+44
We get rid of parentheses
-6x-9x.+6+44
We add all the numbers together, and all the variables
-6x-9x.+50
Back to the equation:
+(-6x-9x.+50)
We get rid of parentheses
-6x-9x.+50=0
We move all terms containing x to the left, all other terms to the right
-6x-9x.=-50
is 3.39 a rational number
Answers
Answer:
yes it can be written as 'a/b'
Step-by-step explanation:
3.39 is 3 39/100 which, as an improper fraction, is 339/100
as long as a decimal terminates or repeats then it is rational
examples:
.333 repeating is rational
the symbol π does not terminate or repeat so it is considered to be irrational
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answers
Answer:
y=50 but i dont know x, sorry about that its cause im in class rn lol
Answer:
x= 127
y = 50
Step-by-step explanation:
y = 180 -130(angles on a straight line)
y= 50
x= 360-(123+60+50). angles in a quadrilateral
x = 360- 233
x= 127
GO FROM BLACK DOT TO BLACK DOT FOR CALCULATIONS TO BE ACCURATE
1 BOX = 1 FOOT
Across the room are your 2 best friends Sara & Jon
Laying at the exact midpoint between them is /y
the perfect zombie killing potion. Unfortunately,
Sara & Jon have both developed a taste for brains so they won't
be much help. What are the coordinates of the potion?
ROUND TO THE TENTHS
Answers
Answer:45
Step-by-step explanation:
i know this
Which of the following is the equation for a circle with a radius of r and center at (h, v)?
Answers
Answer:
the correct answer is option A
Answer: Choice D
Your book may use the template [tex](x-h)^2 + (y-k)^2 = r^2[/tex], but it's the same idea. The center here is (h,k) and radius is r.
Identify the conditionals and truth values implied by the following biconditional. Select all that apply.
Answers
Answer:
I believe the answer is B and C
Step-by-step explanation:
From a circular sheet of a radius 5 cm, a circle of radius 3 cm is removed. Find the area of the remaining sheet.
Answers
Answer:
2 cm
Step-by-step explanation:
find the value of x........................
Answers
Answers: x = 4 and y = 3
============================================================
Explanation:
Triangle UBD is congruent to triangle RAN
Note the order of the lettering as it's important.
BD and AN are the last two letters of UBD and RAN in that order. Therefore, these sides correspond and BD = AN. From that, we know,
BD = AN
2y+5 = 3y+2
5-2 = 3y-2y
3 = 1y
y = 3
-----------
Using similar logic, UD and RN are the first and last letters of UBD and RAN respectively. So,
UD = RN
15 = 2x+7
2x+7 = 15
2x = 15-7
2x = 8
x = 8/2
x = 4
if RT= 19 meters, find LW.
Answers
Answer:
if RT = 19 meters, Find LE
Please help I am really confused with this
Answers
The answer should be A. 4 Meters
Three candidates were running for class president. Of the 250 students eligible to vote, 75 voted for Carlos and 32% of the students voted for LaToya. Of thsoe who didn't vote for Carlos or LaToya, 60% voted for Stephanie and the rest of the students chose not to vote.
Part 1: What percent of the eligible students voted for Carlos?
Part 2: How many votes did LaToya receive?
Part 3: How many votes did Stepanie recieve?
Part 4: Who won the election?
Answers
Answer:
Part 1) 30%
Part 2) 80 students
Part 3) 57 votes
Part 4) LaToya
Step-by-step explanation:
75 divided by 250 = 0.30 = 30%
32% = 0.32 and then 0.32 times 250 = 80 students
250 - 75 - 80 = 95 students that didn't vote for Carlos or LaToya. Then 0.60 times 95 = 57
LaToya had 80 votes, the most votes.
Could someone please help me?
x =
100
120
140
Answers
Answer:
x = 140
Step-by-step explanation:
The secants exterior angle theorem states that when two secants (lines that intersect a circle at two points) intersect each other outside of the circle, then the absolute value of the difference divided by (2) equals the angle formed by the intersection of the two secants. One can apply this theorem here by stating the following, call the measure of the unknown arc (y);
[tex]\frac{30-y}{2}=10[/tex]
Solve for (y) with inverse operations:
[tex]\frac{30-y}{2}=10\\\\30-y=20\\\\y = 10[/tex]
When there is a diameter in a circle, the degree measure of the arc surrounding the diameter is (180). One can apply this here by stating the following:
[tex]30 + x + 10 = 180[/tex]
Simplify,
[tex]40 + x = 180[/tex]
Inverse operations,
[tex]40+x=180\\\\x = 140[/tex]
How do you solve (-10) - (-3)
Answers
Answer:
-7
Step-by-step explanation:
-10 - -3
- 10 + 3
-7
(a double negative becomes a positive)
Answer:
-7
Step-by-step explanation:
A gift shop at an amusement park sells key chains. The gift shop has 55 key chains. When the number of key chains is below 10, the manager will reorder. If the gift shop sells 4 key chains each day, how many days will it take before the manager has to reorder?
Answers
Answer:
12
Step-by-step explanation:
this equation can be derived from the question
55 - 4x < 10
< = less than
x = number of days
solve for x
55 - 10 < 4x
45 < 4x
x < 11.25
at the 11th day, there would be 11 keys left
on the 12th day, there would be 7 keys left
the correct answer is 12 days
Consider the sequence 1, 4, 16, 64, 128, … Which statement describes the sequence? The sequence diverges. The sequence converges to 0. The sequence converges to [infinity]. The sequence converges to –[infinity].
Answers
Answer:
The sequence diverges
Step-by-step explanation:
The given sequence is 1, 4, 15, 64, 128, ...
By observation the sequence can be expressed as a sequence of 4 raised to increasing powers of 'x' as follows;
The sequence is 4ˣ, where; x = 0, 1, 2, 3, 4, ..., ∞
Therefore, the values of each subsequent term of the sequent is higher than the term it succeeds, the sequence does not converge to a given limit value and therefore, the sequence diverges.
Missing measure help
Answers
2-77
3-48
4-77
5-62
6-28
PLEASE HELP ME ASAP Given the following polynomial function, find f(-1): 2x^3 - 3x^2+7x-10
F(-1)=?
Answers
Answer:-22
Step-by-step explanation:Just put the value -1 wherever there is x.
Answer:
f(-1) = -22
Step-by-step explanation:
f(x): 2x^3 - 3x^2 + 7x - 10
Repace x = -1
f(-1) = 2(-1)^3 - 3(-1)^2 + 7(-1) - 10
f(-1) = -2 - 3 - 7 - 10
f(-1) = -22
What value of x would make Bl parallel to RA?
Answers
Given:
Bl parallel to RA.
To find:
The value of x.
Solution:
In triangle ATR and ITB,
[tex]\angle ATR\cong \angle ITB[/tex] [Common angles]
[tex]\angle ART\cong \angle IBT[/tex] [Corresponding angle]
[tex]\triangle ATR\sim \triangle ITB[/tex] [AA property of similarity]
We know that the corresponding sides of a similar triangle are proportional. So,
[tex]\dfrac{AT}{IT}=\dfrac{AR}{IB}[/tex]
[tex]\dfrac{x}{x+8}=\dfrac{12}{18}[/tex]
[tex]\dfrac{x}{x+8}=\dfrac{2}{3}[/tex]
On cross multiplication, we get
[tex]3(x)=2(x+8)[/tex]
[tex]3x=2x+16[/tex]
[tex]3x-2x=16[/tex]
[tex]x=16[/tex]
Therefore, the correct option is C.
Solve for xxx. Enter the solutions from least to greatest. (x -7)(-4x -2)=0(x−7)(−4x−2)=0left parenthesis, x, minus, 7, right parenthesis, left parenthesis, minus, 4, x, minus, 2, right parenthesis, equals, 0
Answers
Answer:
-1/2, 7
Step-by-step explanation:
Given the expression
(x -7)(-4x -2)=0
This means that;
x - 7 = 0 and -4x - 2 = 0
x = 0+7 snd -4x = 2
x = 7 and x = -2/4
x = 7 and -1/2
Hence the solution from least to greatest is -1/2, 7
Solve the system of equations by using substitution.
Answers
Answer:
(x, y) = (-1, 1)
Step-by-step explanation:
[tex]y = 2x +3 ----(1) \\\\y = x + 2 ----(2)\\\\substitute \ (2) \ in \ (1) : x + 2 = 2x + 3[/tex]
[tex]x - 2x = 3 - 2\\\\-x = 1\\\\x = -1\\\\Substitute \ x = -1 \ in \ (2) : y = -1 + 2 => y = 1[/tex]
Find the surface area of the cylinder.
Answers
Answer:
exact: 48pi cm^2
approximate: 150.8 cm^2
Step-by-step explanation:
SA = 2 * (pi)r^2 + 2(pi)rh
SA = 2 * pi * (3 cm)^2 + 2(pi) * 3 cm * 5 cm
SA = pi(18 cm^2 + 30 cm^2)
SA = 48pi cm^2
SA = 150.8 cm^2
Which expression is equal to
Answers
Answer:
4^5/ 4^-9
Step-by-step explanation:
the third one
Solve by using substitution
y=2x
3x-y=3
Answers
answer:
x = 3
y = 6
step-by-step explanation:
we have two equations —y = 2x
3x - y = 3
we have to use substitution so we will replace y with 2x since y = 2x3x - 2x = 3
now that we have like terms, we can solve this to find x3x - 2x = 3
x = 3
now, we will use this to find yy = 2x
y = 2(3)
y = 6
HELP HELP?/)-(:$//))/ s
Answers
Answer:
it's the last choice
Step-by-step explanation:
x int: (1/2,0) and y int (0,2)
Consider this expression.
7110 = 90
What is the value of this expression?
Enter your answer in the box.
Answers
Answer:
79 is the value
Step-by-step explanation: