Answer:
The volume of the open box is [tex]V = 108\cdot x -42\cdot x^{2}+4\cdot x^{3}\,\,\,[in^{3}][/tex].
Step-by-step explanation:
Geometrically speaking, the volume of the open box ([tex]V[/tex]), measured in cubic inches, is described by the volume of a right parellelepiped. That is:
[tex]V = w\cdot l \cdot h[/tex] (1)
Where [tex]w[/tex], [tex]l[/tex] and [tex]h[/tex] are the width, length and height of the open box, respectively, measured in inches. Please notice that width of the open box is the width of the piece of cardboard ([tex]w'[/tex]), measured in inches, minus two times the side of the cut squares ([tex]x[/tex]), measured in inches, length of the open box is the length of the piece of cardboard ([tex]l'[/tex]), measured in inches, minus two times the side of the cut squares and the height of the open box is the side of the cut squares. That is:
[tex]w = w' -2\cdot x[/tex] (2)
[tex]l = l' - 2\cdot x[/tex] (3)
[tex]h = x[/tex] (4)
By applying (2), (3), (4) in (1), we expand and simplify the volume function:
[tex]V = (w'-2\cdot x)\cdot (l'-2\cdot x)\cdot x[/tex] (5)
If we know that [tex]w' = 9\,in[/tex] and [tex]l' = 12\,in[/tex], then the equation above is:
[tex]V = (9-2\cdot x)\cdot (12-2\cdot x)\cdot x\,\,\,[in^{3}][/tex]
[tex]V = (108-24\cdot x-18\cdot x+4\cdot x^{2})\cdot x\,\,\,[in^{3}][/tex]
[tex]V = (108-42\cdot x +4\cdot x^{2})\cdot x \,\,\,[in^{3}][/tex]
[tex]V = 108\cdot x -42\cdot x^{2}+4\cdot x^{3}\,\,\,[in^{3}][/tex]
The volume of the open box is [tex]V = 108\cdot x -42\cdot x^{2}+4\cdot x^{3}\,\,\,[in^{3}][/tex].
The rectangle below has an area of 12y^2+21y^512y 2 +21y 5 12, y, squared, plus, 21, y, start superscript, 5, end superscript. The width of the rectangle is equal to the greatest common monomial factor of 12y^212y 2 12, y, squared and 21y^521y 5 21, y, start superscript, 5, end superscript. What is the length and width of the rectangle? \text{Width} =Width=start text, W, i, d, t, h, end text, equals
Answer:
This means that the width = 3y²
The length = 4y+7y³
Step-by-step explanation:
Given
Area of the rectangle = 12y^2+21y^5
Width of the rectangle is the greatest common monomial of 12y^2 and 21y^5
First let us get the greatest common monomial of 12y^2 and 1^5
12y^2 = (3 * y * y) * 4
21y^5 = (3 * y*y)*y*y*y* 7
Hence the greatest common monomial is 3 * y * y = 3y²
Factor out 3y² from the area function;
12y^2+21y^5
3y² (4y+7y³) = Area of the rectangle
Length * Width = 3y² (4y+7y³)
On comparing both sides of the equation
This means that the width = 3y²
The length = 4y+7y³
Answer:
4y^2
Step-by-step explanation:
What is the binary number for 15
Answer:
111
Step-by-step explanation:
notice that 1000 in binary is 16, as 1000 in binary would be 2^4 = 16. If you subtract 1 from 1000 in binary, you get 111.
If this helped please give brainliest.
1) Dave is 9 years older than his brother.
Dave is also 9 years younger than twice
his brother's Ige. How old is each?
Answer:
Dave is 27. His brother is 18.
Step-by-step explanation:
Dave is 9 years older than his brother, so if his brother is 18, he is 27. If you doubled the brother's age (18) you would get 36. Then you subtract 36 by 9 and get 27. <3
Monica weighed 135 pounds before she started a 3 week diet for her cruise. She lost 18 pounds in the first 2 weeks then gained 5 pounds back the last week. Choose the answer below that correctly identifies how much Monica weighed when she left for her cruise.
A.
112 pounds
B.
104 pounds
C.
140 pounds
D.
122 pounds
Answer:
D.
Step-by-step explanation:
135 - 18 = 117 + 5 = 122
Answer:
D. 122 pounds
Step-by-step explanation:
135-18=117
117+5=122
Mr. Ash owns a tree, which is 42 feet tall. He estimates that this tree is 75% as tall now as it will be when fully grown. How tall will the tree be when it is fully grown?
Answer:
73.5 feet
Step-by-step explanation:
The length of a tree =42 feet
Mr. Ash estimates that this tree is 75% as tall now as it will be when fully grown.
We need to find the length of the tree when it is fully grown. It means we need to find the 75% of 42 and adding 42 to it as follows :
[tex]T=75\%\times 42+42\\\\=\dfrac{75}{100}\times 42+42\\\\=73.5\ ft[/tex]
So, the tree will be 73.5 feet tall when it is fully grown.
El precio del saco de arroz es a 2 como el precio del saco de azúcar es a 3; si el producto de ambos precios es numéricamente 3 456, calcula el precio del saco de azúcar.
Answer:
El precio del saco del azúcar es de 72.
Step-by-step explanation:
Sean [tex]x[/tex], [tex]y[/tex] los precios del saco de arroz y el saco de azúcar, respectivamente. A continuación, traducimos cada oración relevante en ecuaciones matemáticas:
(i) El precio del saco de arroz es a 2 como el precio del saco de azúcar es a 3:
Aquí se menciona una igualdad entre expresiones racionales, es decir:
[tex]\frac{x}{2} = \frac{y}{3}[/tex]
[tex]3\cdot x -2\cdot y = 0[/tex] (1)
(ii) El producto de ambos precios es numéricamente 3456:
[tex]x\cdot y = 3456[/tex] (2)
Ahora resolvemos el sistema de ecuaciones, despejamos [tex]x[/tex] en (1):
[tex]x = \frac{2}{3}\cdot y[/tex]
Y la aplicamos en (2):
[tex]\frac{2}{3}\cdot y^{2} = 3456[/tex]
[tex]y^{2} = 5184[/tex]
[tex]y = 72[/tex]
El precio del saco del azúcar es de 72.
Solve this problem 48-2(8+2)
Tell me a fun fact about horses I will give brainliest to whoever tells me one I don’t know (I have been riding for 12 years) so I know a lot about horses also don’t answer this just for the points or else you will get reported
Answer:
Horses can sleep both lying down and standing up.
Step-by-step explanation:
P(-2, -3) and Q(2, 7)
Answer:
The slope is 10/4
Step-by-step explanation:
La regla de Ruffini es un procedimiento que nos permite dividir fácilmente un polinomio cuando el divisor es un binomio de la forma (x ± a). *
Verdadero
Falso
Answer:
si como estas chico
Step-by-step explanation:
help please there is actually a question this time
Answer:
D...
Step-by-step explanation:
Thats on mine and got it right
Can anyone do it I'll give you brainiest
Answer:
64°Step-by-step explanation:
? + 86 + 90 + 84 + 36 = 360
? = 360 - 86 - 90 - 84 - 36
? = 64
therefore, the missing angle = 64°
Please help. I’ll give brainliest
Answer:
x > -5
Step-by-step explanation:
What is the solutions set for -4x - 10< 2?
PLEASE ITS ALREADY LATE AND I NEED TO TURN IT TODAY
Example 1 Fatima works as an intern at a construction company earning $10 per hour. Her office is open 8
hours per day, 5 days a week. Analyze Fatima's potential earnings for the 12 weeks she interns at the
company this summer.
A. Write a function rule to model
the situation
B. Identify the independent
variable
C. Identify the dependent
variable
f(x) =
Answer:
4800
Step-by-step explanation:
I attached a picture of the work.
We need to made a function that will help us solve this
f(x)=dx; d = $ per hour, x = # of hours
step 1) identify d (in this case, the money made per hour) which = 10
f(x)=10x
step 2) identify x (# of hours total) which = 480
f(x)=10(480)
step 3) solve the equation
f(x)=4800
independent variable:
the number of hours
dependant variable:
the amount of money made after 12 weeks
What is the scale factor from triangle A to triangle B??
Answer:
3
Step-by-step explanation:
i believe this should be the answer, simply because 15÷5 is 3. if you were to find x, you would multiply the scale factor value by the first triangle
who good with graphs
- 9j + -11 = 61
What is this?
Answer:
j= - 8Step-by-step explanation:
- 9j + -11 = 61
-9j = 61 + 11
-9j = 72
j = - 8
how would you solve p-11=-14
Answer:
Step-by-step explanation:
all you would need to do is add 11 to both sides, and then you would get your answer.
David uses 1/2 cups of apple juice for every 1/8 cup of carrot juice to make a fruit drink. Write the number of cups of apple juice David uses for 1 cup of carrot juice.
Answer:
4 cups of apple juice for 1 cup of carrot juice
Step-by-step explanation:
Write an
equation for the line in the given form.
slope is -3 and (6,8) is on the line; standard form
Yo
Answer:
Step-by-step explanation:
Negative3 is6,8
Answer:
Negative3 is6,8
Step-by-step explanation:
i know it
Which of the following relations has a domain of {-4, -2, 1}?
Group of answer choices
{(1, 2), (-2, 3), (4, 6)}
{(1, 2), (-2, 2), (-2, 4), (-4, 4)}
None of the other answers are correct
{(-1, 2), (4, 3), (-2, 6), (-2, 3)}
{(1, 2), (-2, 2), (-2, 4), (4, -4)}
Answer:
{(1, 2), (-2, 2), (-2, 4), (-4, 4)}
Step-by-step explanation:
Plz mark as Brainliest!
Help plz:))) I’ll mark u brainliest
If x + 12 = 40,
what is the value of x + 7
please help
Please help i need submit it in 10 mins! show work! i will mark brainliest!
Answer:
C and D is the answer.
Step-by-step explanation:
If m∠5 = x°, according to the Corresponding Angle Theorem, m∠9 will equal the same, and because 9 and 12 are vertical angles, both of these will be the same measure.
the product of two consecutive integers is 72. find the integers
Answer:
the integers are 8 and 9
Step-by-step explanation:
consecutive means one right after the other. 9 is right after 8. and its product is 72, well 8x9 is 72.
Can somebody please help me solve problem 16 .
Answer:
i think it`s $35
Step-by-step explanation:
Because 80 divided by 2 = 40 and the problem says to subtract 5 so I believe the answer is $35.
help me please i will give out brainliest!
Answer:
A
Step-by-step explanation:
travels only on Saturdays and Sundays and has miles this month. Travels every weekday and has miles this month. If they each travel about the same number of miles each day, who travels more miles per day for this month?
Complete question :
William travels only on Saturdays and Sundays and has flown 400 miles this month. Jason travels every weekday and has flown 500 miles this month. Who travels more miles per day for this month
Answer:
WILLIAMS ; 50 miles per day
Step-by-step explanation:
Given that :
Williams travel times = Saturdays and Sundays
Total distance traveled = 400 miles
Jason travel times = Every weekday
Total distance traveled = 500 miles
Number of weeks in a month = 4
Hence, saturdays and Sundays = 4 * 2 = 8 days
Weekdays = 5 * 4 = 20 days
Miles traveled per day:
Williams :
Total distance / number of days
= 400 miles / 8 days
= 50 miles per day
Jason :
Total distance / number of days
= 500 miles / 20 days
= 25 miles per day
50 > 25
Hence, Williams travel more miles per day than Jason
Find the slope of the line passing through the two points.
(12, 1), (36, 42)
Answer:
m=41/24
Step-by-step explanation:
The slope of the line passing through the points (12, 1), (36, 42) is m=41/24.
To find slope, we need to use the slope formula*.
42 - 1/36 -12 = 41/24
m = 41/24