The largest possible volume of the box is 108000cm^3.
How can the largest possible volume of the box be found?The concept is the concept of
We can represent the length of the square box as x
we can also represent the surface of the box as S
we can represent the height of the square box as y
we can represent the volume as V= xy
Then since the top of the box is open and we can equate the material of the box is equal with surface area of box.
then S=[x^2 +2xy +2xy]
= x^2 +4xy
Then substitute the value of S we have
10800= x^2 +4xy
y= [10800-x^2/4x]
V=2700 * 1/4X^2
V=2700 * 1/4X^2
Then substitute the value of y into
V= xy
= x[10800-x^2/4x]
V= 2700x - 3/4X^2
Differentiate the volume to 0
=3x^2 = 2700
X^2 = 3600
X = 60 and Y = 30
V=2700 * 1/4X^2
V= 270(60) - 1/4* (60)^2 = 108000cm^3
Learn more about volume here: https://brainly.com/question/1972490
#SPJ1
Evaluate the following algebraic expression:
w + 8.5 when w = 6.3
O 3.2
O 14.8
O 2.2
O 4.8
Answer:
14.8 is the answer to the question
What is value of x?
Responses
12
12,
10
10,
9
9,
3
(MAKE BRAINLIEST IF I HELPED)
Answer:
x=10
Step-by-step explanation::
We can use Triangle angle bisector theorem and proportions to solve this problem. We put the small triangle side over the large triangle side
8 x+4
------ = ------------
12 2x+1
Using cross products
8(2x+1) = 12(x+4)
16x+8 =12x+48
Subtract 12x from each side
16x-12x +8 = 12x-12x+48
4x+8 = 48
Subtract 8 from each side
4x+8-8 = 48-8
4x = 40
Divide by 4
4x/4 = 40/4
x = 10
Answer:
x=10
Step-by-step explanation:
Please help an 8th grader in needdddddddddddd!!!!!!!!
Answer:
y = (24/5)x + 24
Step-by-step explanation:
Knowing that the parent equation for linear functions is "y = mx+b", where "m = slope" and "b = y-intercept", we can create an equation for the line of best fit.
We also need to know the formula for using two points to find the slope is "(y2 - y1)/(x2 - x1)", where (x2, y2) is a point on the graph and (x1, y1) is a point on the graph.
Finding the slope:
I will be using points (5, 48) and (0, 24).
(24 - 48)/(0 - 5)
(-24)/(-5)
24/5 is the slope so "m = 24/5"
We can tell from the graph (0, 24) is the y-intercept, so "b = 24"
Final equation:
y = (24/5)x + 24
Determine whether the equation below has a one solutions, no solutions, or an infinite number of solutions. Afterwards, determine two values of x that support your
conclusion.
x - 4 = 0
There is only one solution for the equation x - 4 = 0 and the solution is 4.
Equation
An equation also known as the expression consists of variables, number and the mathematical operator that are combined using the equal sign.
Given,
Here we have the equation x - 4 = 0
Now, we need to Determine whether the equation below has a one solutions, no solutions, or an infinite number of solutions. Afterwards, determine two values of x that support your conclusion.
In order to find the solution of the equation, we have to equate the equation with zero and solve it accordingly,
So, the given equation is rewritten as,
x - 4 = 0
Now, we have to move the number to the other side to get the value x, then we get,
x = 4.
Therefore, the equation has only one solution that is 4.
To know more about Equation here.
https://brainly.com/question/10413253
#SPJ1
(b) The graph of y=g(x) is shown. Draw the graph of y=g(1/2x)
The graph of the piece-wise function g(0.5x) is given by the second image at the end of the answer.
What is a piecewise-defined function?A piecewise-defined function is a function that has different definitions, depending on the input of the function.
In this problem, the function given by the first graph has two definitions, as follows:
To the left of x = 0.To the right of x = 0.The two functions are linear with intercept 0, hence the definitions are given as follows:
x < 0: y = 2x, as when x increases by 1, y increases by 2, hence slope of 2.x > 0: y = -0.5x, as when x increases by 2, y decreases by 1, hence slope of -0.5.After the transformation x -> 0.5x, the definitions are given as follows:
g(0.5x) = 2(0.5x) = x, x < 0.g(0.5x) = -0.5(0.5x) = -0.25x, x > 0.Missing InformationThe graph of g(x) is given by the first image at the end of the answer.
More can be learned about piece-wise functions at https://brainly.com/question/18499561
#SPJ1
The function f(x) = 16.4x + 2 is used by a construction company to estimate the amount of fuel necessary for a truck to get to a job site depending on the miles from the office, x. The mathematical domain for the function is the set of real numbers.
How does the reasonable domain differ from the mathematical domain?
The reasonable domain is the set of positive real numbers.
The reasonable domain is the set of positive whole numbers.
The reasonable domain is the set of real numbers greater than 2.
The reasonable domain is the set of whole numbers greater than 2.
The domain of the function f(x) = 16.4·x + 2, where x is the distance from the office, which is (always) a positive number is the set of all real numbers but the reasonable domain differs from the mathematical domain in that; The reasonable domain is the set of positive real numbers
What is the domain and range of a function?The domain is the set of the possible inputs while the range is the set of the possible outputs of the function.
The mathematical domain is the set of the inputs that the function accepts
The function, f(x) = 16.4·x + 2, mathematically, is continuous for all real number value of x. that is the function has an output when the input, x, is a member of the set of real numbers which includes negative number.
The number of miles from the office, which is the distance from the office is (always) a positive number, because it is the distance between two places, and therefore is not a negative number.
The values of x are therefore positive numbers and the reasonable values of the variable, x, which is the distance from the office is the set of positive real numbers.
The option that indicates how the reasonable domain differ from the mathematical domain is therefore;
The reasonable domain is the set of positive real numbersLearn more about the domain and range of a function here:
https://brainly.com/question/28757609
#SPJ1
Given is a 30-60-90 Triangle. From the answer
choices below, select all that represent possible
side lengths.
○3√3; 3; 6
O 10√3; 15; 5√3
08:8√3:24
○ 5√2; 5√6; 10√/2
The represent possible side lengths of perimeter is 8;8√3;24.
What is perimeter?
perimeter is the distance of around the edge of a shape. Learn how to find of the perimeter by adding up to the side lenghth of various shapes.
The perimeter is the distance around the object.
Sol-as per the given question the angle value of the triangle is -
7 in
(x+4)in
(4x+1)in
Here,
X+4=4x+1
X=1
Perimeter:- 5+5+7 =
17 Inches.
Thus the perimeter of the triangle is 17 Inches.
To know more about perimeter click-
https://brainly.com/question/19819849
#SPJ1
Explain if Todd’s Conclusion is logical.How did you decide? If it is not logical,what can you do to improve his reasoning?
Answer:
Todd's conclusion is logical. I know this because all people named Todd are logical beings who always come to logical conclusions. But seriously though, please comment down below more of your question so I can accurately answer it, thanks!
Step-by-step explanation:
(-3,6), (0,3), (-1,2), and (2,-1) all lie on a line. Find the Slope of the Line. Make Sure You Do Number 11 On The Paper!
to get the slope of any straight line, we simply need two points off of it, let's use those two from the picture below
[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{-1}~,~\stackrel{y_2}{2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{2}-\stackrel{y1}{6}}}{\underset{run} {\underset{x_2}{-1}-\underset{x_1}{(-3)}}} \implies \cfrac{-4}{-1 +3} \implies \cfrac{ -4 }{ 2 } \implies - 2[/tex]
6. Solve the following inequalities for the variable and graph the solution.
3+4x>-5.
Answer:
3+4x>-5
4x>-5-3
4x>-8
x>-8/4
x> -2
A house on the market was valued at $447,000. After several years, the value decreased by 17%. By how much did the house's value decrease in dollars? What is the current value of the house?
Decrease in value:
Current house value:
The rate that the house's value decrease in dollars, that is the current value of the house in terms of:
Decrease in value: $75,990Current house value: $371,010What causes a decline in market value?A stock's price rises if there is a greater demand (buyers) than supply (sellers) for it. On the other hand, if there was a bigger supply than there was a demand for a stock, the price would drop. It's simple to comprehend supply and demand.
The price decreases by:
= $447, 000 * (0.17)
=$75,990.
The current value is:
= 447, 000 - 75,990
= $371,010.
Learn more about market value decreased from
https://brainly.com/question/29206198
#SPJ1
Students from the local high school are selling tickets to the town's annual carnival. Adult admission is $4.00 and child admission is $2.00. Four hours after the carnival opened its first day, 440 tickets had been sold totaling $1380. How many adults and how many children entered the carnival after it was opened?
The number of adults is 200 and the number of children that entered the carnival after it was opened is 240.
How to find the number tickets sold?Let a represent the number of adult tickets sold
Let c represent the number of children tickets sold
4a + 2c = 1380
Hence,
a + c = 440
Solving for c
4 (440-c) +2c = 1280
1760-4c +2c = 1280
-4c+2c = -480
-2c=-480
Divide both side by -2c
c = -480/-2
c = 240 (children tickets)
Solving for a
a =440-c
a =440 -240
a=200 (Adult tickets)
Therefore 240 and 200 tickets were sold.
Learn more about number of tickets sold here:https://brainly.com/question/11986887
#SPJ1
The table shows a set of points on a line.
y
6
5
4
3
What is the slope of the line?
X
-6
-3
0
3
The slope of the line is -3 and the equation of the line formed by the points is y + 3x = 6.
From the table we can see that the line passes through the points:
(-6,6) ,(5,-3) ,(4,0) and (3,3) .
Let us consider any two points on the line (4,0) and (3,3) .
We know that the slope of the line can be found by using the intercept formula
Hence slope = (3-0) / (3-4) = 3/ -1 = -3
Now the equation of the line is :
y - 3 = -3(x-3)
or, y - 3 = -3x +9
or, y + 3x = 6
The letter m is frequently used to represent the slope of an object that resembles a line in the plane that contains the x and y axes. The slope is defined as the difference in two independent locations along the line expressed in y coordinate less by the equivalent difference in x coordinate.
Therefore slope of the line is -3.
To learn more about slope visit:
https://brainly.com/question/11559942
#SPJ1
2. A local grocery store received 240 turkeys the week prior to Thanksgiving. On Sunday,
they sold 3/8 of them. How many turkeys were sold on Sunday? Solve the problem
using the Draw a Diagram strategy.
The number of turkeys that they sold on Sunday is 90 turkeys
Total number of turkeys = 240
On Sunday, they sold 3/8 of them
The fraction of turkeys they sold on Sunday = 3/8
To find the number of turkeys that they sold on Sunday we have to find the 3/8 fraction of 240
Then,
The number of turkeys that they sold on Sunday = Total number of turkeys × The fraction of turkeys they sold on Sunday
Substitute the values in the equation
The number of turkeys that they sold on Sunday = 240 × 3/8
= 240 × 0.375
= 90 turkeys
Hence, the number of turkeys that they sold on Sunday is 90 turkeys
Learn more about fraction here
brainly.com/question/10708469
#SPJ1
Geometry Gina wilson pls help
For the given measures of angles of heptagon, the value of x is equal to 27° .
As given in the question,
Sum of all the interior angles of the heptagon is equal to 900.
Given measure of all the angles of the heptagon is given by :
135°+( 5x - 4 )° +( 7x - 64 )° + 120° +( 6x - 8 )° +( 4x + 15 )° + ( 3x + 31 )°= 900°
Arrange all the like terms of the given expression together we get,
⇒ ( 5x + 7x + 6x + 4x + 3x )° + ( 135 - 4 - 64 + 120 - 8 + 15 + 31 )° = 900°
⇒ 25x° + 225° = 900°
⇒ 25x° = 900° -225°
⇒ 25x° = 675°
⇒ x = 27°
Therefore, for the given measures of angles of heptagon, the value of x is equal to 27° .
Learn more about heptagon here
brainly.com/question/12630702
#SPJ1
A line passes through the point (2, 7) and has a slope of 5. Write an equation in slope-intercept form for this line.
Answer: y = 5x - 3
Step-by-step explanation:
It is a line, so its formula is y = mx + b.
Slope(m) = 5Y-intercept(b) =[tex]y=5x+b\\7=5(2)+b\\7=10+b\\b=7-10=-3[/tex]
Therefore, the formula is y = 5x - 3.
Answer:
y=5x-3
Step-by-step explanation:
100 points for this There was a blizzard. Snow was falling at the rate of 3
inches per hour. If the snow keeps acclimating how long will 5 feet of snow to accumulate ?
Since there are 60 inches in 5 feet (5*12), we know that it will take 20 hours for 5 feet of snow to accumulate (60/3).
Hope this helps!
Brooklyn scored 27 points in the basketball game. That was 12 points more than her friend, Cienna, scored. How many points did they score altogether? * 2 points
Answer:
42 points
Step-by-step explanation:
If Brooke scored 27 points, 12 less than that would be what Cienna scored. To find this, you would do 27 - 12. This is equal to 15, so Cienna scored 15 points.
To find how much they scored together, you would add both their scores. Brooke scored 27 and Cienna scored 15, so 27 + 15 = 42. Therefore, they scored 42 points together.
Consider the following equation:
3|x+3|−12=0
Step 2 of 4: Using the definition of absolute values, convert the standard form of the given equation into two equations without absolute value signs.
The value of x in the following equation: 3|x+3|−12=0 is -7 and 1
The equation is 3|x+3|−12=0
The modulus function can be positive and negative
Considering it to be negative,
the equation is
3((-1)(x + 3) - 12
3(-x - 3) - 12
-3x - 9 - 12 = 0
3x + 21 = 0
3x = -21
x = -7
3(x + 3) - 12
3x + 9 - 12
3x - 3 = 0
3x = 3
x = 1
Therefore, the value of x in the following equation: 3|x+3|−12=0 is -7 and 1
To learn more about the algebra refer here
https://brainly.com/question/4344214
#SPJ1
At the store where you work, the prices on a clearance rack of merchandise are 0.62 of the original price. The sign on the clearance rack states that an additional 23% of the original price will be taken off at checkout. In total, what portion of the original price has been deducted to get the clearance price?
0.29
0.49
0.65
0.85
0.95
The portion of the original price that has been deducted to get the clearance price is D. 0.85
How to calculate the value?Given that the the prices on a clearance rack of merchandise are 0.62 of the original price and that the sign on the clearance rack states that an additional 23% of the original price will be taken off at checkout.
Therefore, the prices deducted will be:
= 0.62 + 23%
= 0.62 + 0.23
= 0.85
In conclusion, the correct option is D.
Learn more about percentages on:
brainly.com/question/24304697
#SPJ1
Finding a percentage of a total amount
Which number line represents the graph of x = 2?
Answer:
The 3rd one
x = 2 means how far is the line from 0
PLEASE GIVE BRAINLIEST THANK YOU!!!
I need some help please
Check the picture below.
If a = 2 and b = 3, what is the value of 2a³b2?
Answer:384
Step-by-step explanation:
first you multiply 2 times 2= 4 then 4 times 4 times 4= 64 then you multiply 3 times 2= 6 lastly you multiply 6 and 64. your welcome:)
Solve the equation: u^6 − 49 u^4 = 0 .
The given equation solved for u is u = 7 or u = -7
Solving an equationFrom the question, we are to solve the given equation.
The given equation is
u^6 − 49 u^4 = 0
First, we will write the equation properly
The given equation written properly is
u⁶ - 49u⁴ = 0
Now,
To solve the equation, we will determine the value(s) of the variable. The variable in the given equation is u.
Thus,
We will solve for u
u⁶ - 49u⁴ = 0
Add 49u⁴ to both sides of the equation
u⁶ = 49u⁴
Divide both sides by u⁴
u⁶/u⁴ = 49u⁴/u⁴
u² = 49
Then,
u²- 49 = 0
u² - 7² = 0
Factorize by applying the rule for difference of two squares
(u + 7)(u - 7) = 0
Then,
u + 7 = 0 OR u - 7 = 0
u = -7 OR u = 7
Hence, the value of u is -7 OR 7
Learn more on Solving an equation here: https://brainly.com/question/11483004
#SPJ1
h(t)= t+ 1/t^2+2t+2.
Find derivative.
The derivative of given function is H’(t) = 3 – 2/t3
A derivative is a two-party contract whose value/price is derived from an underlying asset. Futures, options, forwards, and swaps are the most prevalent types
Given that H(t)= t+ 1/t^2+2t+2
We must calculate the derivative
H(t)= t+ 1/t^2+2t+2
H(t) = 3t + 1/t^2 + 2
H’(t) = d/dt(3t + 1/t^2 + 2)
H’(t) = d/dt(3t) + d/dt (1/t^2) + d/dt ( 2)
H’(t) = 3xd/dt(t) + d/dt (1/t^2) + d/dt ( 2)
H’(t) = 3xd/dt(t) + d/dt (t-2) + d/dt ( 2)
H’(t) = 3 – 2t-3
H’(t) = 3 – 2/t3
Therefore the derivative of the given function is H’(t) = 3 – 2/t3
To learn more about derivatives visit
https://brainly.com/question/25324584
#SPJ1
What is the solution to the following system?
[3x+10y-12z = 40
X-5y = 0
X-4z = 0
(8, 40, 32)
(10, 2, 3)
(20, 4, 5)
(40, 8, 10)
The solution of the system of equations is (2, 4, 5)
The given equations are :
3x+10y-12z = 40 equation(1)
x-5y = 0 equation (2)
x-4z = 0 equation(3)
From 2nd equation, x -5y = 0, 5y = x, y = x/5
From 3rd equation, x -4z = 0, 4z = x, z = x/4
Putting the values of y and z in equation (1), we get :
[tex]3x +10y -12z = 40\\\\3x +10*\frac{x}{5} -12*\frac{x}{4} = 40\\\\3x +2x -3x =40\\\\2x = 40\\\\x = \frac{40}{2} = 20[/tex]
Now, putting the value of x = 20 to evaluate y and z, we have,
y = 20/5 = 4
and z = 20/4 = 5
Hence, the solution of the system of equations is (2, 4, 5)
To read more about the system of equations, visit https://brainly.com/question/24065247
#SPJ1
Find the quotient and remainder
using synthetic division for
x³ + 4x² + 5x +9
x + 2
Answer:
quotient: x^2+2x+1
remainder: 7
Step-by-step explanation:
Step-by-step explanation:
x³+4x²+5x+9= (x+2)(x²+2x+1)+7
Quotient= (x²+2x+1)
Remainder=7
Michelle purchases a tablet that costs
$85. The sales-tax rate in her city is 7%.
What is the total cost of the tablet?
Answer:
$90.95
Step-by-step explanation:
85 + .07(85)
85 + 5.95
90.95
9,70,499,2488,7469 complete the series
To complete the given series 9, 70 , 499, 2488, 7469 the next number is given by 7466.
As given in the question,
Given series is equal to :
9, 70 , 499, 2488, 7469
Simplify the given series to get the next sequence number we have:
Pattern of the given series is given by:
9
70 = 9 × 9 -11
= 70
499 = 70 × ( 9 -2 ) + ( 11 - 2 )
= 70 × 7 + 9
= 499
2488 = 499 × ( 7 - 2 ) - ( 9 - 2 )
= 499 × 5 - 7
= 2488
7469 = 2488 × ( 5 - 2 ) + ( 7 -2 )
= 2488 × 3 + 5
= 7469
Next number is :
7469 × ( 3 - 2 ) - ( 5- 2 )
= 7469 × 1 -3
= 7466
Therefore, to complete the given series 9, 70 , 499, 2488, 7469 the next number is given by 7466.
Learn more about series here
brainly.com/question/15415793
#SPJ1