Answers
x=18
Related Questions
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.
4x + 3 + (-3) + 7x - 6x
Answers
Answer:
5x
Step-by-step explanation:
Answer:
2x+3 is it simplified
Step-by-step explanation:
7 marbles are in a bag 2 marbles are red and the rest are black how many marbles in bag are black
Answers
Answer:
5 marbles are black.
Step-by-step explanation:
7-2=5
According to the graph what is the solution to this system of equations?
O 5.-7)
O €7.5)
O 5.7)
O 7.5)
Answers
Answer:
you showed no graph dude
This is the graph btw.
Select the graph of Y = sec X Please help!!!!
Answers
Answer:
A
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
[42
2
X Х
3
5 1 3 6
+1916 51
2,3
6
Answers
jxjxjxnxnxnnxnnxncncncxxnx
Skzkkxkxkfnzxnxnncnvnvnnv XMMMXMidjjcnfnndnmcmcmcmcmcmxmdnndjd
Write an equation if the line that passes through (0,-2) and (2,2)
Answers
Answer:
[tex]y=2x-2[/tex]
Step-by-step explanation:
Hi there!
Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)
1) Determine the slope (m)
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] where the two points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
Plug in the given points (0,-2) and (2,2)
[tex]=\frac{2-(-2)}{2-0}\\=\frac{2+2}{2}\\=\frac{4}{2}\\=2[/tex]
Therefore, the slope of the line is 2. Plug this into [tex]y=mx+b[/tex] as m:
[tex]y=2x+b[/tex]
2) Determine the y-intercept (b)
[tex]y=2x+b[/tex]
Plug in one of the given points and solve for b
[tex]2=2(2)+b\\2=4+b[/tex]
Subtract 4 from both sides to isolate b
[tex]2-4=4+b-4\\-2=b[/tex]
Therefore, the y-intercept of the line is -2. Plug this back into [tex]y=2x+b[/tex]
[tex]y=2x-2[/tex]
I hope this helps!
Simplify:
B^4 . B^3
^ = means I’m squaring it.
Answers
Step-by-step explanation:
B⁴×B³B^(4+3)B⁷stay safe healthy and happy...
The triangles have a scale of 3: 5. What is the value of a? *
Answers
Answer:
Step-by-step explanation:
multiply the ratio by 24/5 and you have
72/5 : 24
or
14.4:24
someone please helppp, i have 2 days to do 28 assignments plus a final exam
NO LINKS OR FILES OR YOU WILL BE REPORTED
Answers
9
Step-by-step explanation:
1 = x^2 - 6x
Adding 9 to both sides, we get
1 + 9 = x^2 - 6x + 9
10 = (x - 3)^2
Note that the right hand side is now a perfect square.
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
if the family chooses to give you a 20% tip and the tax rate is 8.5% how much will they pay in total??
Answers
Enter cost and tip percent to get a tip amount and total dinner amount. ... how many people? ... Calculate a tip or gratuity and get the total amount to pay. ... If you are splitting the cost at a restaurant among several people you can divide by the ... To calculate a gratuity or tip on any calculator it is a simple multiplication.
Answer:
Step-by-step explanation:
Rewrite the equation by completing the square. 4x^2-4x+1=0
Answers
Answer:
[tex][x+(-1/2)^2]=0[/tex]-------------------
[tex]4x^2-4x+1=0[/tex][tex]4(x^2-x+1)-3=0[/tex][tex]x^2-x+1-3/4=0[/tex][tex]x^2-x+1/4=0[/tex][tex]x^2-2.x.1/2+(1/2)^2=0[/tex][tex](x-1/2^2)=0[/tex][tex]x+(-1/2)^2=0[/tex]---------------------
hope it helps..
have a great day!!
Find the value of y when x=3.
y=10-3x
y=
Answers
y= 10-3x
y= 10-3(3)
y= 10-9
Therefore, y = 1
Answer:
the value of y is y= 1
Step-by-step explanation:
3×3=9
y=10-9
y= 1
how many solutions does 3 (y-2) = 3y - 6 have
Answers
Answer:
Infinitely many solutions
Step-by-step explanation:
Simplify this
3 (y-2) = 3y-6
3 (y) + 3 ( -2) = 3y-6
3y-6=3y-6
Because these two equations are equal to each other, it is infinitely many solutions.
If this helps please mark as brainliest
What is the measure of angle 2 in degrees?
Answers
Answer:
The measure of angle 2 is... 60 degrees.
Angle 1 - 93 degrees
Angle 2 - 60 degrees
Angle 3 - 27 degrees
The quadrilateral shown is rotated 90 degrees clockwise about the origin. In which quadrant is the image of the quadrilateral located? *
Captionless Image
Answers
Answer:
Option (2). 1
Step-by-step explanation:
Coordinates of point A, B, C and D are,
A(-4, 4), B(-2, 4), C(-2, 1) and D(-4, 3).
Quadrilateral ABCD when rotated 90° clockwise about the origin,
Rule for the rotation of the vertices,
(x, y) → (y, -x)
Following the rule of rotation coordinates of the image points,
A(-4, 4) → A'(4, 4)
B(-2, 4) → B'(4, 2)
C(-2, 1) → C'(1, 2)
D(-4, 3) → D'(3, 4)
Since all image points have the positive coordinates (x and y coordinates), image quadrilateral A'B'C'D' will be located in 1st quadrant.
Option (2) is the correct option.
that is the answer if it's wrong then it must of been wrong question I gave answer to or I just got it wrong
need this for final
Write the following statement as an algebraic expression: Five less than the product of 4 and a number.
Group of answer choices
5(4 - x)
5(x - 4)
4x - 5
5 - 4x
Answers
Answer:
D
Step-by-step explanation:
it means 5 minus 4x where x is the coefficient of x. Good luck.
PLS HELP ILL MARK AS BRAINLIST AND FOLLOW U
Answers
Answer:
No
Step-by-step explanation:
For the calculation for triangle area is wrong
PLSSSS HELPP MEEEEE BRAINLIEST REWARDD
Answers
Answer:
40.) the third one
42.)the last one
Step-by-step explanation:
2. The quotient of two polynomials is always a polynomials
please answer thissssssssssssssssssss
Answers
Answer:
B.) The interquartile range of the data is 2
Step-by-step explanation:
Drag tiles to fill in the blanks to complete the expression that could be used to predict the number of winners of a game. Tiles may be used once or not at all.
A)Total Number of Possible Outcomes B)Number of Winners
C)Number of Unfavorable Outcomes D)Number of Games
P(event) =
Number of Favorable Outcomes
_________________________
?????????????????????????????
=
?????????????????????????????
_________________________
11 Total Number of Contestants
(Pick two answers)
Answers
Answer:
First blank - A)Total Number of Possible Outcomes
Second blank - B)Number of Winners
Step-by-step explanation:
The exact question is as follows :
We know that,
Probability of an event is equals to Total number of Favorable outcomes divided by Total number of outcomes
So,
P(event) = Number of favorable outcomes ÷ Total Number of Possible Outcomes
As we have to predict the Number of winners of a game
So,
P(Number of winner) = Number of winners ÷ Total number of Contestants
∴ we get
P(event) = Number of favorable outcomes ÷ Total Number of Possible Outcomes
= Number of winners ÷ Total number of Contestants
five hundred dollars and eighty two cents as a decimal
Answers
Answer:
500.82
Step-by-step explanation:
Answer: 500.82 mhm mhm yup
What is the circumference of this circle
R=2km
Answers
Answer:
12.57
Step-by-step explanation:
The formula is
2 (pie) r
2(pie)2
which would equal 12.57
PLEASE I NEED HELP I DONT UNDERSTAND HOW TO DO ILL GIVW MORE IF RIGHT
Answers
Answer: 207 degrees
Step-by-step explanation:
Since a circle is 360 degrees,
103+50+35+27 = 215, 360-215=145
Add ED and BC to 145 to get - 207
what should be the price of each toaster if the company wants to make a profit of 42$ per toaster?
Answers
Answer:
$42?
Step-by-step explanation:
Is your answer I hope this helps
Yes invests $1500 that compounds interest monthly with a 4.5% rate. How much money will he have after the 12 years?
Answers
Answer:
FV= $2,571.41
Step-by-step explanation:
Giving the following information:
Initial investment (PV)= $1,500
Interest rate (i)= 0.045/12= 0.00375
Number of periods (n)= 12*12= 144 months
To calculate the future value, we need to use the following formula:
FV= PV*(1 + i)^n
FV= 1,500*(1.00375^144)
FV= $2,571.41
Tape diagram
7 a =35
Answers
Step-by-step explanation:
7a = 35
a = 35/7 = 5
do you wants to earn money on pàypal???
find the area of the shaded region
Answers
Answer:
9.82 inches²
Step-by-step explanation:
both areas are equally sized, so they are both half of the whole circle.
circle area : pi × r²
half of the circle area is therefore pi × r² / 2
the picture gives us the diameter of the circle, the radius is half of the diameter.
=> r = 5/2 = 2.5
=> shaded area = pi × r² / 2 = pi × (2.5)² / 2 = 9.82 inches²
A quadratic equation that has x-intercepts of (-2,0) and (8,0), a stretch of 3 and a vertex is a minimum. Find the equation of the parabola
Answers
Answer:
c) The standard form of the quadratic equation, y = a·x² + b·x + c
The standard form of the quadratic equation is y = 3·x² - 18·x - 48.
Step-by-step explanation: