From a rectangular 5×13 piece of cardboard, four congruent squares with sides of length x are cut out, one at each corner. (See the accompanying figure.) The resulting crosslike piece is then folded to form a box. Answer the following.
a) Find the volume V of the box as a function of x.
b) Sketch the graph of y=V(x).
Answers
The Dimensions of box be:
L = 2.21406 ftD= 10.78594 ftH = 1.10703 ftVolume, V = 24.4366 ft³What is Volume of Cuboid?The volume of the cuboid is the measure of the space occupied within a cuboid. The cuboid is a three-dimensional shape that has length, breadth, and height.
a)Each side of the future box is
L = 5-2x ,D = 13-2x
and let the height of box is x
Then, volume of the box as function of x is:
V(x)= (5-2x)*(13-2x)*x
V(x)= (65-10x-26x +4[tex]x^{2}[/tex])*x
V(x)= 65x-36[tex]x^{2}[/tex]+4[tex]x^{3}[/tex]
Differentiate the above equation, we get
V'(x)= 65-72x+12[tex]x^{2}[/tex]
If V'(x) = 0, then
65-72x+12[tex]x^{2}[/tex]=0
[tex]x_{1,2} = (-b\pm \sqrt{ b^{2} - 4*a*c} ] /2a[/tex]
[tex]x_1[/tex]=4.89297
[tex]x_2[/tex]=1.10703
We will take x= 1.10703
Then the sides of the box are:
L = 5-2(1.10703) = 2.21406 ft
D = 13 - 2*x = 13 - 2x(1.10703)= 10.78594 ft
H = x = 1.10703 ft
Now, volume is
V = 2.21406*10.78594*1.10703 = 24.4366 ft³
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Related Questions
The length between the bases on a baseball field is 90 ft. A scale drawing shows the distance between the bases as 2 1/2 inches. One inch on this drawing equals how many feet?
Answers
Divide total feet by total inches
90 feet / 2 1/2 inches = 36 feet per inch
1 inch = 36 feet
Multiply the sum of -13/8 and 5/12 by their difference.
Answers
Answer:
1421/576
Step-by-step explanation:
Sum = - 13/8 + 5/12 = - 39/24 + 10/24 = - 29/24
Difference = - 13/8 - 5/12 = - 39/24 - 10/24 = - 49/24
Sum * Difference = (-29/24)*(-49/24) = 1421/576
3) Alternate exterior angles = congruent
= -1 + 14x
= 12x + 17
4) Corresponding angles = supplementary (measures add up to 180 degrees)
= 23x - 5
= 21x + 5
\\NONSENSE ANSWERS WILL BE REPORTED\\
Answers
3) x = 9, 125 degree
4) x = 5, 110 degree
Step-by-Step Explanation:
In Q3 :-
Alternate Exterior Angles are Equal.
Therefore,
=> -1 + 14x = 12x + 17
= 14x - 12x = 17 + 1
= 2x = 18
=> x = 18/2 = 9
Therefore, x = 9
Now finding each angle :-
=> -1 + 14x
= -1 + 14(9)
= -1 + 126
= 125
=> 12x + 17
= 12(9) + 17
= 108 + 17
= 125
Hence, both are Equal.
In Q4 :-
Corresponding Angles are Equal.
Therefore,
=> 23x - 5 = 21x + 5
= 23x - 21x = 10
= 2x = 10
=> x = 10/2 = 5
Therefore, x = 5
Now finding each angle :-
=> 23x - 5
= 23(5) - 5
= 115 - 5
= 110
=> 21x + 5
= 21(5) + 5
= 105 + 5
= 110
Hence, both are Equal.
Stuck on this question, not very confident with my answers. Photo is attached, please help!
Answers
Part (a)
The notation [tex]A \cap B \cap C[/tex] talks about overlapping or intersecting all three intervals. Your teacher wants to know what numbers are in all three intervals at the same time.
Refer to the diagram below. I've graphed regions A, B and C on the same number line. The vertical separation is to help tell the regions apart. Technically they should all be on the same number line. Notice how the regions overlap on the interval (0, 2] which translates over to [tex]0 < x \le 2[/tex] telling us that the answer must be choice D.
Meaning we exclude 0 but keep 2, and everything in between the endpoints.
Choice C is not possible because x = -1 is not in region C. This means choice A is ruled out also. Choice B is eliminated because x = 3 is not in region A nor region B.
Answer: Choice D=============================================================
Part (b)
As mentioned earlier, the intervals all have in common the region between x = 0 and x = 2. We exclude 0 but keep 2.
Answer: (0, 2]=============================================================
Part (c)
The graph is shown below.
We have an open circle at 0 and a closed circle at 2. There is shading in between those endpoints.
When it comes to graphing the final answer, you'll ignore the separate regions A,B,C and only graph what is shown in purple.
9. A blueprint of Miranda's living room is
shown below. Will a 9-foot by 2.5-foot
sofa fit in the room?
Explain.
| 42 cm
5 cm
Scale: 2 cm = 3 ft
Answers
Answer:
Step-by-step explanation:
1 cm = 1.5 ft
4 2/3 x 5 2/3
26 11/25 x 1 1/2
39.66 ft
9 x 2.5 =22.5
39.66ft > 22.5ft
Yes it can
The two triangles are congruent.
Answers
Answer:
B
Step-by-step explanation:
Answer:
No
Step-by-step explanation:
The tirangles are no exatly the same due to the fact that one is rotated.
This means they are similar NOT congruent
iready solve percent problems
Answers
Answer:where is the question??.?
Step-by-step explanation:
Help if u want points
Answers
Answer:
I believe the answer is C.
Step-by-step explanation:
a shopkeeper buys 25 cricket balls at a total cost of $150
a) he sells them for $ 8 each. what was his % profit?
b)he sells them for $5 each. what was his % loss?
Answers
Answer:
a) he sells them for $ 8 each. what was his % profit
Step-by-step explanation:
Can anyone help me with this? I don’t get it.
Answers
Answer:
D
Step-by-step explanation:
A triangle with sides 2, 4.5, and 6 is similar to a triangle with sides 4, 9, and 12.
[tex] \frac{4}{2} = \frac{9}{4.5} = \frac{12}{6} = 2[/tex]
Find the equivalent expression using distributive property.
Answers
[tex] \large \sf \: ⇒ \: 7(x + 6) \\ \\ \large \sf⇒ \:distributing \: 7 \: with \: bracket \\ \\ \large \sf \: ⇒7x + 42[/tex]
[tex]\boxed{\rm{Option\:A\green{✓}}}[/tex]
▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂☘
Hope it helps !
Translating Inequalities into Words
Which phrases can be used to represent the inequality? Check all that apply.
One-half + k greater-than 18
Answers
Answer:
The sum of one-half and a number is more than eighteen.
The sum of one-half and a number is greater than eighteen.
The sum of one-half and a number is above eighteen.
Step-by-step explanation:
https://brainly.com/question/12165044
Question: Which phrases can be used to represent the inequality? Check all that apply.
One-half + k greater-than 18
Answer:
a. The sum of one-half and a number is more than eighteen. b. The sum of one-half and a number is greater than eighteen.
c. The sum of one-half and a number is above eighteen.
Pete is retiring after working 27 years at a major bank. the company offers him a flat monthly retirement benefit of $50 per year for each year of service.
Answers
Answer:
1350
Explanation:
27 x 50 = 1350
(Hope this helped!)
Kansas City, mo and St. louis, mo are 248 miles apart. On a map, these two cities are 4.9 cm apart. Use this scale to determine the distance between Kansas City, mo and Louisville, KY if they at 10 cm apart on the map.
Answers
Answer:
506, 12 miles
Step-by-step explanation:
Find the measurements of a mile in centimeteres
1 mile= 160934 cm
Mulitply the miles by the amount of centimeteres in a mile.
248 x 160934= 39911632
Divide it by measurement on map to find the measurement of 1 cm on the map to real life measurement in cm
39911633 ÷ 4,9= 8145231,02 cm
Once you have the ratio multipyly it by measurement on map
10 x 81452310,2
Then divide by the amount of cm in a mile
81452310,2÷160934=506,12 miles
Sorry if this is wrong.
Kansas City and St. louis are 248 miles apart. On a map, these two cities are 4.9 cm apart. Using unitary method, the distance between Kansas City and Louisville is 506 miles (approximately) if they at 10 cm apart on the map.
What is map?Making a map or using a matching procedure wherein the points of one set are compared to the points of another provides the definition of mapping. Making a map to find your residence is an aspect of mapping.
What is unitary method?
The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
4.9 cm on a map in reality = 248 miles1 cm on a map in reality = 248/4.9 = 50.61 miles10 cm on a map in reality = 50.61 * 10 = 506.1 miles.
Therefore, Kansas City and St. louis are 248 miles apart. On a map, these two cities are 4.9 cm apart. Using unitary method, the distance between Kansas City and Louisville is 506 miles (approximately) if they at 10 cm apart on the map.
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PLS HURRY WILLL GIVE BRAINLIEST!!!
Which is the simplified form of ( 9c^-9 )^-3 ?
Answers
Answer:
Your answer is B: 1/729c^27
Answer:
b
Step-by-step explanation:
pls give brainliest
One painter can paint a room in 2 hours; another painter requires 4 hours to paint
the same room. How long will it take them to paint the room together
Answers
Answer:
[tex]1\frac{1}{3}[/tex] hours
Step-by-step explanation:
The first painter does [tex]\frac{1}{2}[/tex] (aka [tex]\frac{2}{4}[/tex]) the job in 1 hour.
The second painter does [tex]\frac{1}{4}[/tex] the job in 1 hour.
This means together they can do [tex]\frac{3}{4}[/tex] the job in 1 hour.
This means to do [tex]\frac{1}{4}[/tex] of the job they will need [tex]\frac{1}{3}[/tex] hours. (third of the work they do in an hour means they need a third of the time)
This means they need [tex]1\frac{1}{3}[/tex] hours to paint the room together.
HELPPPPPPPP!!!!!
9) Write an equation in point-slope form for the given point and slope:
Point: (-7, 5)
Slope: 3
Answers
PLEASE HELPPP SOLVE FOR X, these are two separate question’s
Answers
[tex]\textbf{3)}\\\\~~~~~3x^2\cdot 5 = 80\\\\\implies 15x^2 = 80\\\\\implies x^2 = \dfrac{80}{15}\\\\\implies x^2 = \dfrac{16}3\\\\\implies x = \pm\sqrt{\dfrac{16}3}\\\\\implies x = \pm \dfrac 4{\sqrt 3}\\\\\textbf{4)}\\\\~~~~~~(x-5)^2 = 81\\\\\implies x -5 =\pm\sqrt{81}\\\\\implies x -5 = \pm9\\\\\implies x = 5\pm9\\\\\implies x = -4,~ x = 14[/tex]
X^2+25-10x=81
X^2-10x = 81-25
X(x-10). =. 56
X= 56. , X-10=. 56
X= 66
56, 66
100 POINTS IF YOU CAN GUESS CORRECTLY PLEASE HELP!
Answers
Rami works at a carnival dart game where groups of people try to pop balloons taped to a wall by throwing darts. He records the number of people in each group and the total number of balloons they pop. This graph represents Rami’s data.
How many balloons did the group of 5 people pop?
Enter your answer in the box.
( ) balloons
Answers
The coordinate will be (5, 12). Then the number of balloons that a group of 5 people pops will be 12.
What is coordinate geometry?Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.
Rami works at a carnival dart game where groups of people try to pop balloons taped to a wall by throwing darts.
He records the number of people in each group and the total number of balloons they pop.
This graph represents Rami’s data.
Then the number of the balloons that a group of 5 people pops will be
The coordinate will be given as
⇒ (5, 12)
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HELP ME PLEASE INNEED HELP
Answers
Answer:
65/56
Step-by-step explanation:
secant is equal to hypotenuse over adjacent
Answer:
65/33
Step-by-step explanation:
26 divided by 100,60 pls help
Answers
Answer: 0.25844930417
Step-by-step explanation:
26/100.60 = 0.25844930417
If you add Natalie's age and Fred's age, the result is 43. If you add Fred's age to 4 times Natalie's age, the result is 88. Write and solve a system of equations to find how old Fred and Natalie are.
Answers
Natalie's age = n
Fred's age = f
n + f = 43
4n + f = 88
f = 43 - n
4n + (43 - n) = 88
3n + 43 = 88
3n = 45
n = 15
f = 43 - n
f = 43 - 15
f = 28
Natalie is 15
Fred is 28
Hope this helps!
The following two-way table shows the distribution of pets in a large apartment building. A 4-column table with 3 rows titled Pets. Column 1 has entries cat, no cat, total. Column 2 is labeled dog with entries 27, 3, 30. Column 3 is labeled no dog with entries 25, 45, 70. Column 4 is labeled Total with entries 52, 48, 100. Suppose we select a resident of the apartment building at random. Let event A = Cat and event B = Dog. Calculate and interpret P(A|B). The probability that a randomly selected resident owns a , given that the person also owns a , is equal to approximately .
Answers
Answer:
The probability that a randomly selected resident owns a
✔ cat
, given that the person also owns a
✔ dog
, is equal to approximately
✔ 0.90
.
Step-by-step explanation:
Just did it on edge.
Next slide answer is:
The probability that a randomly selected resident owns a
✔ dog
, given that the person also owns a
✔ cat
, is equal to approximately
✔ 0.519
.
So I am looking at the method of elimination but I get a little bit lost why there is a positive +1 underneath the -1 , where does the +1 come from?
Answers
Answer:
it is because its being carried to the other side
Step-by-step explanation:
When you add 1 to negative 1 it becomes 0, so we are trying to make the right hand side equal to the left hand side. If that makes any sense.
When doing this you need to do the inverse operation on BOTH sides of the equation, in this case the equation is
-1 + y = -3
( the inverse operation of subtraction is addition)
So you add 1 to both sides to find out what y equals, -1 + 1 cancels out, -3 + -1 is equal to -2
Therefore the y = -2
I hope this helps, sorry if it didn’t! I’m open for questions :)
Find the inverse of y=7x+3
Answers
Answer:
7 x 3 .
Step-by-step explanation:
Divide x x by 1 1 . Since g(f(x))=x g ( f ( x ) ) = x , f−1(x)=3√49x7 f - 1 ( x ) = 49 x 3 7 is the inverse of f(x)=7x3 f ( x )
The inverse function is y= (x-3)/7
What is a function?An expression which defines the relationship between two variables (one independent and one dependent variable).
What is dependent and independent variable?The independent variable is the variable being controlled in the problem, and the dependent variable is the variable that changes with the change of independent variable.
What is inverse of a function?A function that undoes the original function is called the inverse function.
How to find the inverse of y=7x+3 ?To find the inverse function of a given function,
first we will have to interchange the variablesIn the problem,
y is the independent variable x is the dependent variabley=7x+3
To find the inverse
x = 7y + 3 ( interchanging the variables )
Now finding the value of y,
⇒ x - 3 = 7y
⇒ y = (x-3)/7
This is the inverse function.
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Based on the row relative frequencies in the table above, which statement is true? A There is an association between type of pet and food preference because the row relative frequencies are similar for the dog and cat rows B There is an association between type of pet and food preference because the row relative frequencies are not similar for the dog and cat rows There is not an association between type of pet and food preference because the row relative frequencies are similar for the dog and cat rows There is/not an association between type of pet and food preference because the row relative frequencies are not similar for the dog and cat rows
Answers
The conclusion that can be drawn from the table is (c) There is not an association between type of pet and food preference because the row relative frequencies are similar for the dog and cat rows
What is conditional relative frequency?A conditional relative frequency is simply a two-way table that shows the relationship between table entries
How to determine the association?The table is given as:
Food preference
Dog 0.47 0.52 0.495
Cats 0.53 0.48 0.505
Total 1 1 1
The entries at rows 1 and 2 i.e. 0.47 and 0.52 & 0.53 and 0.48 are close.
This means that there is no association between them because of the closeness
Hence, the conclusion about the association is (c)
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Bill buys a large can of paint. The size of the can is measured in which unit?
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[tex]\huge{\green}\fcolorbox{blue}{cyan}{\bf{\underline{\red{\color{red}Answer}}}} [/tex]
[tex] \mathbb\purple{GALLONS} [/tex]
How is the graph of the parent quadratic function transformed to produce the graph of y = negative (2 x + 6) squared + 3? The graph is compressed horizontally by a factor of 2, shifted left 3 units, reflected over the x-axis, and translated up 3 units. The graph is reflected over the x-axis, compressed horizontally by a factor of 2, shifted left 6 units, and translated up 3 units. The graph is stretched horizontally by a factor of 2, reflected over the x-axis, shifted left 3 units, and translated up 3 units. The graph is reflected over the x axis, stretched horizontally by a factor of 2, shifted left 6 units, and translated up 3 units.
Answers
Answer:
The graph is reflected over the x-axis, compressed horizontally by a factor of 2, shifted left 6 units, and translated up 3 units.
Step-by-step explanation:
Answer:
The graph is reflected over the x-axis, compressed horizontally by a factor of 2, shifted left 6 units, and translated up 3 units.
can you please help me I give you extra points
Answers
Answer:
(-7 , 3 ) , ( -6 , 5 ) , ( -4 , 5 ) , (-2 , 3 )