A small bank vault is being designed in the shape of a rectangular prism. The vault’s sides and top should all be 3 feet thick. The outer length of the vault should be twice the outer width. The outer height should be the same as the outer width. What should the outer dimensions of the vault be if is to have 972 cubic feet of space?
(^ incase the words got cut off in the pic)
Answers
This represents the exterior length, width and height in that order.
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Work Shown:
The steps you have written so far are 100% correct.
From there, you multiply the interior width, length and height to get the interior volume 972. Solve for x
So,
(length)*(width)*(height) = volume
(2x-6)(x-6)(x-3) = 972
(2x-6)(x^2-9x+18) = 972
2x(x^2-9x+18)-6(x^2-9x+18) = 972
2x^3-18x^2+36x-6x^2+54x-108 = 972
2x^3-24x^2+90x-108 = 972
2x^3-24x^2+90x-108-972 = 0
2x^3-24x^2+90x-1080 = 0
2(x^3-12x^2+45x-540) = 0
x^3-12x^2+45x-540 = 0
From here, we can use the factor by grouping method
x^3-12x^2+45x-540 = 0
(x^3-12x^2)+(45x-540) = 0
x^2(x-12)+45(x-12) = 0
(x^2+45)(x-12) = 0
Setting each factor equal to 0 leads to....
x^2+45 = 0 doesn't have any real valued solutions for x, since sqrt(-45) is a complex number. We'll ignore this case and move on.x-12 = 0 solves to x = 12So x = 12 is the only solution here.
If x = 12, then we have these exterior dimensions:
length = 2x = 2*12 = 24 ftwidth = x = 12 ftheight = x = 12 ftThe outer dimensions are 24 ft by 12 ft by 12 ft
From that, the inner dimensions would be:
L = 24-6 = 18 ft
W = 12-6 = 6 ft
H = 12-3 = 9 ft.
Then note how L*W*H = 18*6*9 = 972 ft^3 to help confirm the answer.
Related Questions
In a test, +3 marks are given for every correct answer and -1 mark are given for every incorrect answer. Sona attempted all the questions and scored +20 marks, though she got 10 correct answers. How many incorrect answers has she attempted? (ii) How many questions were given in the test?
Answers
x = number of questions
3y = points for a correct answer
-1x or -x = points for an incorrect answer
Adding up the correct and incorrect points/answers gives us the final score. We can solve to see how many questions were incorrect. (We are told 10 were correct)
3y + (-1x) = 20
3(10) + (-1x) = 20
30 - x = 20
10 = x
x = 10
So she got 10 correct and 10 incorrect, and there were 20 questions in all.
Decide if 7x+3=4x+3 has no solution, one solution, or infinitely many solutions
Answers
Answer:
0, one solution
Step-by-step explanation:
Answer:
One solution
Step-by-step explanation:
7x+3=4x+3 only has one solution which is x = 0.
Hope this helps! :)
Try using symbolab if you're confused
There are 9 students in a class: 2 boys and 7 girls. If the teacher picks a group of 4 at random, what is the probability that everyone in the group is a girl?
Answers
What is the distance between (7,2) and (-3,2)?
A.8
B.12
C.4
D.10
Answers
Answer:
The answer is D
......(don't mind this it's because it says that it needs to be 20 characters long) but the answer is D
Explanation:
Let (7, 2) be (x1, y1) and (-3, 2) be (x2, y2)
Using the Distance Formula,
d = sqrt[(x2 - x1)^2 + (y2 - y1)^2]
= sqrt[(- 3 - 7)^2 + (2 - 2)^2]
= sqrt[(-10)^2 + 0]
= sqrt[100]
= 10 units
A hot air balloon is 45 meters above the tall seat building in a city write a equation to show the height b of the balloon if the building is t meters tall
Answers
Answer:
b = t + 45
Step-by-step explanation:
Position of hot air Ballon = 45 meters above tall seat building ;
Height of tall seat building = t
Height of Ballon, b = height of tall seat building + 45 m
Hence,
b = t + 45
Which value(s) of x are solution(s) of the equation below
Answers
Hi there!
[tex]\large\boxed{x = -1}[/tex]
We can solve by multiplying each term to get a common denominator:
[tex]\frac{1}{x - 4} + \frac{x}{x - 2} = \frac{2}{x^2-6x+8}[/tex]
[tex]\frac{x -2}{(x - 4)(x - 2)} + \frac{x(x - 4)}{(x - 2)(x - 4)} = \frac{2}{x^2-6x+8}[/tex]
Since the denominators are all the same (x² - 6x + 8 factors to (x - 2)(x - 4)), we can ignore them temporarily and solve the numerator:
x - 2 + x(x - 4) = 2
Simplify:
x - 2 + x² - 4x = 2
x² - 3x - 4 = 0
Factor:
(x - 4)(x + 1) = 0
x = -1, 4
For the values of x to be a solution, they cannot cause the denominator to be equal to 0, so:
(x - 2)(x - 4) = 0
x = 2, 4. These values result in a denominator of 0, which is undefined.
Thus, the only solution is x = -1.
need help on this plz
Answers
Answer:
Step-by-step explanation:10
Bc you times
Answer:
5.4 feet
Step-by-step explanation:
Pythagorean theorem
a^2+b^2=c^2
5^2 + 2^2=
25+4=29
√29 = 5.385....
About 5.4 feet
what is 200x400x600x800
please help i'm beggin
Answers
Answer:38400000000
Step-by-step explanation: I just do it like 2 numbers i just write it down like a line it is kind of hard you could do it an easier way but i like doing it like that :)
Help Find kif (2, k) lies on the line with equation 2x + 7y = 41
Answers
Answer:
i think 11y
Step-by-step explanation:
The topic is about secant tangles angles
Answers
Answer:
x = 42
Step-by-step explanation:
The tangent- tangent angle is half the difference of the intercepted arcs.
LN (major) = 360 - 138 = 222 , then
x = [tex]\frac{1}{2}[/tex] (222 - 138) = 0.5 × 84 = 42
How many liters of 10% silver iodide mixed with 9 liter of a 4%silver iodide solution to get 6% solution
Answers
Answer:
The correct answer is "4.5 liters". A further explanation is provided below.
Step-by-step explanation:
Let the solution needed be "x".
then, according to the question,
⇒ [tex]4 \ percent(9)+10 \ percent(x)=6 \ percent(9+x)[/tex]
By solving the above expression, we get
⇒ [tex]0.04\times 9+0.1x=0.06\times 9+0,06\times x[/tex]
⇒ [tex]0.04 x=0.54-0.36[/tex]
⇒ [tex]0.04x=0.18[/tex]
⇒ [tex]x=\frac{0.18}{0.04}[/tex]
⇒ [tex]=4.5 \ liters[/tex]
Solve
2x + 4 ( 2x + 7 ) + 3 (2x + 4)
Answers
2x+8x+28+6x+12
16x+40
16x+40 would be the answer you can’t solve it any further
Answer:
merhabalar !
HAVE A NİCE DAY
4 1/2 = 1 1/2n = plsss answer
Answers
Answer:
Step-by-step explanation:
n = 3
Answer: n= 3
Step-by-step explanation:
i hope this helped :))
anyone know this ♀️ ??
Answers
Answer:
B. 4 cups
Step-by-step explanation:
trust me
HELPP PLZZ
ASAP TYYY
Answers
Yes, this parabola is a function because it passes the vertical line test!
The vertical line test is a test where you move left to right over a graph, and look to see if there are any instances where the vertical line touches two points at the same time. If not, then the graph is a function!
Hope this helps!! :)
please help me with these two problems I need help
Answers
Answer:
24 area
18.80983669 perimeter
Step-by-step explanation:
1 (6*3/2)*2(1*3/2)+(4*3)
2 trust me
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:
People were surveyed about the types of pets they own and their housing situation. Each person has only one pet. For people who live in a condo, what is the relative frequency with which a person owns a cat?
Answers
Answer:
The answer is 6.3
Step-by-step explanation:
which Venn diagram is shaded to represent the event L AN N
Answers
Answer:
I'm not 100% sure but I think its A
As head of the Parks Department, Jada has been tracking the park’s use of different supplies over the last several years. Her research shows that, up through last year, the park’s total water usage per year was 13,505 gallons for all regular days, plus another 18.5 gallons for each special event hosted by the park. How many special events did the park host last year? Show your work.
Answers
Answer:6 events
Step-by-step explanation:
13505+ 18.5x =13616
What is the area of a rectangle whose side lengths are o and g?
Answers
Answer:
Area=Base length x Height
Area= O x g.
Isis works at a restaurant. Today, it takes him 16 minutes to fold 40 napkins. He plans to fold napkins for 30 minutes tomorrow. If he works at the same rate, how many napkins will he fold tomorrow?
Answers
O salário mensal de um vendedor é de R$ 750,00 fixos mais 2,5% sobre o valor total em reais, das vendas que ele efetuar durante o mês. Em um mês em que suas vendas totalizaram x reais, o salário do vendedor será dado pela expressão: *
Answers
Responder:
750 + 0,025X
Explicação passo a passo:
Dado que :
Rendimento Fixo = R $ 750
Ganho variável = 2,5% das vendas totais
Se vendas totais em um mês = x
O valor total ganho = custo fixo + variável
Custo variável = 2,5% * x = 0,025X
Custo total: 750 + 0,025X
PLEASE HELP! Choose one answer
Answers
Answer:
c
Step-by-step explanation:
Interquartile range or IQR is the range of the "box" in the graph. So we have 54 and 36 so we subtract 54-36.
So we get 18.
I need help... how to simplify this ?
Answers
Answer:
[tex]b^{2} \sqrt{30b}[/tex]
Step-by-step explanation:
Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.
Answer:
the answer should be 5.47 if im seeing right the 30 only the b's only the the product or something
Step-by-step explanation:
hope this helps if so mark it brainliest and if you want join meeting
Tiffany took her friends out to dinner. If the dinner was $29.53 and she gave a 20% tip, how much money did she spend total (dinner + tip)?
Answers
Answer:
$35.44
Step-by-step explanation:
We can use a proportion to solve this problem
20 : 100 : x : 29.53
x = (29.53*20)/100 = $5.906 (value of the tip)
total cost = 29.53 + 5.906 = $35.436 = $35.44
simplify
√(8+2√15)
Please hurry
Answers
Decimal form is 3.96811878
a. y-4=1/4(x-4)
b. y-12=1/4(x-6)
c. y-12=4(x-6)
d. y-6=4(x-12)
e. y-4=4(x-4)
f. y-6=1/4(x-12)
Answers
Answer:
f. y-6 = 1/4(x-12)
Step-by-step explanation:
the slope eliminates some options right away :
slope = y/x = 1/4, because x has to increase by 8 units for y to increase by 2 unit (or then simplified 4 units for 1).
so, we only need to look at equations with 1/4 as factor of x.
a. covers (12,6) but not (4,4) - wrong
b. covers none of the 2 points - wrong
c., d., e. have the wrong slope
f. is right. for x=12 y is then 6. for x=4 y is then also 4. correct !
pls help! its due today i would mark u brainliest! but pls it's an emergency do both problems!
Answers
Answer:
Step-by-step explanation:
The coordinate is (x,-y)
-20 integer whole number irrational or rational etc
Answers
Answer:
The number -20 is rational
Answer:
the answer is irrational!
Step-by-step explanation: