Length = 19 - 2x ≈ 11.334 inches
Width = 10 - 2x ≈ 2.334 inches
Height = x ≈ 3.833 inches
V ≈ 167.386 cubic inches
Let x be the side length of each square cut from the corners of the cardboard. Then the length, width, and height of the resulting box will be:
Length = 19 - 2x
Width = 10 - 2x
Height = x
The volume of the box is given by:
V = length × width × height
V = (19 - 2x) × (10 - 2x) × x
Expanding the product and simplifying, we get:
V = 4x^3 - 58x^2 + 190x
To find the value of x that maximizes the volume, we can take the derivative of V with respect to x and set it equal to zero:
dV/dx = 12x^2 - 116x + 190 = 0
Solving for x using the quadratic formula, we get:
x = (116 ± sqrt(116^2 - 4×12×190)) / (2×12) ≈ 3.833 or 7.833
Since x must be less than 5 (half the width of the cardboard), the only valid solution is x ≈ 3.833.
Therefore, the dimensions of the box of largest volume are:
Length = 19 - 2x ≈ 11.334 inches
Width = 10 - 2x ≈ 2.334 inches
Height = x ≈ 3.833 inches
And its volume is:
V ≈ 167.386 cubic inches
To know more about quadratic formula refer here:
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Help me somebody please
Dan is stocking up on AA and AAA batteries. He bought 10 packages of batteries for a total of 72 batteries. The AA batteries are sold in packages of 6, and the AAA batteries are sold in packages of 8. Write, but do not solve, a system of equations that can be used to find how many packages of each type of battery Dan bought.
Answer:
x + y = 10
6x + 8y = 72
Step-by-step explanation:
Number of packages = 10
Total batteries = 72
For AA:
batteries per package = 6
Let number of packages = x
For AAA:
batteries per package = 8
Let number of packages = y
Number of AA packages + number of AAA packages = 10
Sum of AA + sum of AAA equals 72 batteries
x + y = 10
6x + 8y = 72
Answer:Answer:
x + y = 10
6x + 8y = 72
Step-by-step explanation:
Number of packages = 10
Total batteries = 72
For AA:
batteries per package = 6
Let number of packages = x
For AAA:
batteries per package = 8
Let number of packages = y
Number of AA packages + number of AAA packages = 10
Sum of AA + sum of AAA equals 72 batteries
x + y = 10
6x + 8y = 72
Step-by-step explanation:
Solve the following proportions 6.5/40.3=m/12.4
Answer:
m = 2
Step-by-step explanation:
cross multiply to get:
40.3m = 6.5(12.4)
40.3m = 80.6
m = 80.6/40.3
m = 2
if 20(mod 9) is equivalent to y(mod 6) find y
Answer:
First, reduce 20(mod 9) to its simplest form in mod 9; 9 x 2 + 2 = 2(mod 9)
If 2(mod 9) y(mod 6), then y = 2 by comparism
Hope it helped!!!
Need help ASAP
48 ÷ 2 (9 + 3) = ?
Answer:
I think the answer is 288
Step-by-step explanation:
I think this because 48/2=24 and 9+3=12 (parentheses means multiply) 24x12=288
Please help, and show steps :)
Which functions readily show the y-intercept of their graphs?
Answer:
to find your y intercept use y= mx + c
Evaluate 10m + n²/4 when m=5 and n=4
Answer:
16.5
Step-by-step explanation:
Break down the equation:
10*5=50
4 with an exponent of 2= 16
Then you have: 50+16 / 4
You can simplify it to 66/4
Finally, divide 66 by 4 which equals 16.5
Hope this helps!
Micah is saving money for his first car his parents gave him 250 for his birthday and each week he plans on putting $40 into his savings account
Answer:
whats the question though?
Four triangles with bases of 12 centimeters and heights of 8 centimeters were used to form a parallelogram. Calculate the area of the parallelogram.
Answer:
192
Step-by-step explanation:
12 x 8 x 4 x1/2 = 192
192
Given: A regular hexagon; M is the midpoint of angle NO and RP. Prove: Angle NRM = Angle OPM
Answer:
Step-by-step explanation:
Since it is a regular hexagon, the length of its sides are equal. And same as the distance across its flats.
So that;
NR ≅ OP (property of a regular polygon)
PM ≅ RM (half of the distance across flats of a polygon)
NM ≅ OM (half of the distance across flats of a polygon)
<NMR ≅ <PMO (vertically opposite angles)
<NRM ≅ <OPM (alternate angle property)
<RNM ≅ <POM (alternate angle property)
This therefore proves that: ΔNRM = ΔOPM
it’s sad when I help people because they can’t do the same thing for me pls just for once answer this pls :(((((((
Answer:
D
Step-by-step explanation:
It compares two values.
Hope this helps!
Answer:
D because it have asked the question
On sports day at Lakewood middle school, gold, silver, and bronze medals were awarded to the top three finishers in each event Miniature replicas of the medals were sold as souvenirs in booths around the field. For $26, attendees could purchase a package containing 5 gold, 4 silver, and 2 bronze replicas, or one containing 4 gold, 4 silver, and 4 bronze replicas, or one that had 3 gold, 4 silver, and 6 bronze replicas. Which system of equations may be used to find the price, in dollars, of each type of replica?
Answer:
[tex]5G + 4S + 2B = 26[/tex]
[tex]2G + 2S + 2B = 13[/tex]
[tex]3G + 4S + 6B = 26[/tex]
Step-by-step explanation:
Given
Represent Gold with G, Silver with S and Bronze with B
Required
Determine the system of equations
The packages are represented as:
The first: 5G + 4S + 2B
The second: 4G + 4S + 4B
The third: 3G + 4S + 6B
Each of the package costs $26.
So, we have:
[tex]5G + 4S + 2B = 26[/tex] -- (1)
[tex]4G + 4S + 4B = 26[/tex] -- (2)
[tex]3G + 4S + 6B = 26[/tex] -- (3)
Divide both sides of (2) by 2
[tex]4G + 4S + 4B = 26[/tex]
[tex]2G + 2S + 2B = 13[/tex]
So, the system of equations are:
[tex]5G + 4S + 2B = 26[/tex]
[tex]2G + 2S + 2B = 13[/tex]
[tex]3G + 4S + 6B = 26[/tex]
Find the product (x + 4)
Answer:
4x
Step-by-step explanation:
It would be 4x because you have no value given of the variable "X"
therefore, your answer would just be adding the x to the 4 making it 4x
hope this helped!
Write 80.75 correct to the nearest whole number.
Answer:
81
Step-by-step explanation:
help please!!!!!!!!! Which image is a reflection of the black polygon in quadrant I?
On a coordinate plane, the black polygon is reflected across the y-axis to form the red polygon.
the black polygon in quadrant I
the red polygon in quadrant II
the blue polygon in quadrant III
the green polygon in quadrant IV
Answer:
The red polygon
Step-by-step explanation:
Think of the quadrants:
The "top right" one is quadrant I
The "top left" one is quadrant II
The "bottom left" one is quadrant III
The "bottom right" one is quadrant IV
When it says "reflected across y-axis", think of the y-axis as a "mirror"
Since the black polygon is in quadrant I, think of it looking into the mirror, or y axis. It is reflecting into quadrant II.
The red polygon is in quadrant II.
Sorry! I know this is a really weird explanation, but hope it helps!
Answer: The answer is the red polygon in quadrant ll (B)!
- just like the person above
Step-by-step explanation:
HELP PLEASE! ( number 7 btw ) please help this if half of my grade
Answer:
A,B,&E are definitely 7 or more
Portland, OR is 180 miles away from Seattle, WA. If it takes a driver 3 hours to drive from Portland to Seattle, what is the driver's average rate of speed? ill mark brainliest please help this is my final grade
Answer:
60km/h
Step-by-step explanation:
Which property is demonstrated in the equation 0 x 35=0?
Answer:
Step-by-step explanation:
the multiplication property of zero,
if you multiply anything by zero the product will be zero
Answer:
I'm pretty sure its identity
Step-by-step explanation:
If its correct can I get brainliest?
At which root does the graph of f(x) = (x – 5)2(x + 2)2 touch the x-axis?
-5
0-2
2
05
Answer:
Option B & D
Step-by-step explanation:
Function is;
f(x) = (x - 5)³(x + 2)²
We want to find the point in thich the graph of this function touches the x-axis.
Usually, the point at which the graph touches the x-axis means that y is 0 at that point.
Thus;
(x - 5)³(x + 2)² = 0
This means that;
x - 5 = 0 and x + 2 = 0
Thus,x = -5 and x = -2
What does linear mean and what does a linear graph look like?
Can you help me with this pls?
Write as a fraction and fractional model model: there is one container of fruit juice and 2 people want juice
Question seems incomplete but we would make assumptions in order to answer and explain
Answer and explanation:
If we wish to model this situation in the form of a fraction: there is one container containing 30 cans of fruit juice and 2 people want fruit juice, we would be finding how many fruit juice each person would get from the container.
Given one container= 30 cans of fruit juice
Number of persons that require fruit juice = 2
Therefore fraction of fruit juice in relation to required fruit juice= 30/2
Kim got to the grocery store at 11:19 in the morning. She spent 24 minutes in the store. Find the points on the number line that show the number of minutes after 11:00 when she got to and left the store.
Answer:
43 minutes
Step-by-step explanation:
Arrival time at grocery store = 11:19 a.m
Time spent in store = 24 minutes
Number of minutes after 11:00 a.m when she arrived and left the store :
Time she left the store :
11:19 a.m + 24 minutes = 11:43 a.m
Minutes after 11:00 when she left :
11:43 - 11:00
= 43 minutes
In Will’s garden, 71 out of 200 plants have developed seeds. Which is closest to the percent of his plants that have developed seeds?
A. 20%
B. 35%
C. 70%
D.25%
14% of math students got an A on the test. 29% got a B. What percentage of students got a C, D, or an F?
Answer:
57% of students
Step-by-step explanation:
14 + 29 = 43%
100% - 43% = 57%
Please help me...????
Answer:
el área es el número el 19
Use the equation below to find the y, M=11, x=2 and B=5
Answer:
The length and breadth of a rectangular
field are equal to 600 m and 400 m
respectively. Find the cost of the grass to be
planted in it at the rate of ₹ 2.50 per m2
4 times the sum of 3 and x can the answer be 4x plus 3 ?
Answer:
4x + 3
Step-by-step explanation:
Since you can't add variables and numbers, just switch up the operations for each number.
Basically,
4(3+x)
4 times x = 4x
4x + 3
Answer:
The answer would be 4(3x).
Step-by-step explanation:
4 times: 4(_)
The sum of 3 and x: 3x
4(_)+3x = 4(3x).
52.7 × 12= ?
help again huhuhu
Answer:
632.4
Step-by-step explanation: