Answer:
d = |145 − (−235)|
Step-by-step explanation:
Jae is constructing an open box from a piece of cardboard that is 9 in. wide and 12 in. long. He cuts squares of equal size from each comer of
the cardboard, as shown in the picture, and then folds up the sides of the box. Write and simplify a polynomial function V for the volume of the box in terms of x
Answer:
The polynomial function for the volume of the box ([tex]V[/tex]) in terms of [tex]x[/tex] is
[tex]V(x)= 108\cdot x -42\cdot x^{2}+4\cdot x^{3}[/tex].
Step-by-step explanation:
We present a representation of the specifications of the open box in a image attached below. The volume of the open box ([tex]V[/tex]), measured in cubic inches, is represented by this expression:
[tex]V = w\cdot h \cdot l[/tex]
Where:
[tex]w[/tex] - Width, measured in inches.
[tex]h[/tex] - Height, measured in inches.
[tex]l[/tex] - Length, measured in inches.
Polynomial functions in standard form are represented by the following form:
[tex]y = \Sigma_{i=0}^{n} c_{i}\cdot x^{i}[/tex]
Where:
[tex]n[/tex] - Order of the polynomial, dimensionless.
[tex]c_{i}[/tex] - i-th Coefficient, dimensionless.
[tex]x[/tex] - Indepedent variable, dimensionless.
[tex]y[/tex] - Dependent variable, dimensionless.
If we get from figure that [tex]w = 12 - 2\cdot x[/tex], [tex]h = x[/tex] and [tex]l = 9 - 2\cdot x[/tex], then:
[tex]V = (12-2\cdot x) \cdot x \cdot (9-2\cdot x)[/tex]
[tex]V = (12\cdot x -2\cdot x^{2})\cdot (9-2\cdot x)[/tex]
[tex]V = 108\cdot x-18\cdot x^{2}-24\cdot x^{2}+4\cdot x^{3}[/tex]
[tex]V = 108\cdot x -42\cdot x^{2}+4\cdot x^{3}[/tex]
The polynomial function for the volume of the box ([tex]V[/tex]) in terms of [tex]x[/tex] is
[tex]V(x)= 108\cdot x -42\cdot x^{2}+4\cdot x^{3}[/tex].
The volume of a box is the amount of space the box can occupy.
The polynomial function is: [tex]\mathbf{V(x) = 4x^3 -42x^2 + 108x }[/tex]
The dimension of the cardboard is given as:
[tex]\mathbf{Length = 12}[/tex]
[tex]\mathbf{Width = 9}[/tex]
Assume the size removed from the box is x
The dimension of the box becomes
[tex]\mathbf{Length = 12 -2x}[/tex]
[tex]\mathbf{Width = 9 -2x}[/tex]
[tex]\mathbf{Height = x}[/tex]
So, the volume (V) of the box is:
[tex]\mathbf{V = Length \times Width \times Height}[/tex]
Substitute known values
[tex]\mathbf{V = (12 -2x) \times (9 - 2x) \times x}[/tex]
Open brackets
[tex]\mathbf{V = (12 -2x) \times (9x - 2x^2)}[/tex]
Open brackets
[tex]\mathbf{V = 108x -24x^2 - 18x^2 + 4x^3}[/tex]
[tex]\mathbf{V = 108x -42x^2 + 4x^3}[/tex]
Rewrite as:
[tex]\mathbf{V = 4x^3 -42x^2 + 108x }[/tex]
Express as a function
[tex]\mathbf{V(x) = 4x^3 -42x^2 + 108x }[/tex]
Hence, the polynomial function is:
[tex]\mathbf{V(x) = 4x^3 -42x^2 + 108x }[/tex]
Read more about volumes and functions at:
https://brainly.com/question/1758167
Somebody plz answer this correct!!
Grade 4math
(Mark as brainliest if correct)
I mean, it depends how long it will take you to shovel the snow please add more context if I read this wrong below!
(Mark as Brainliest Please)
Step-by-step explanation:
Math which one is right? Giving brainlist
Answer:
Third option.
Step-by-step explanation:
[tex]5-2\left(3x-9\right)=-1[/tex]
Use the distributive law: [tex]a(b-c)=ab-ac[/tex]
[tex]5-2\times3x-\left(-2\right)\times9=-1[/tex]
Double negative = Positive
[tex]5-6x+18=-1[/tex]
m(x) = 4x + 15; m(x) = 7
Hi there! :)
[tex]\huge\boxed{x = -2}[/tex]
m(x) = 4x + 15
Find the value of "x" that would satisfy m(x) = 7:
4x + 15 = 7
Subtract 15 from both sides:
4x = -8
Divide both sides by 4:
x = -2.
Find the solution set.
r^2 = 16
Separate the two values with a comma.
The solution set is r = (+4, -4) .
Is quadrilateral DEFG a parallelogram? Why or why not? Question 16 options: A) No, because opposite sides aren't parallel. B) Yes, because opposite sides aren't congruent. C) Yes, because opposite sides are parallel. D) There isn't enough information.
Answer:
No, because opposite sides aren't parallel.
Step-by-step explanation:I took the test
HELP ME PLESA IM DESPO PAKJDCD PLS HELP
Answer:
144 cm²
Step-by-step explanation:
A prism's surface has 2 triangles & 3 rectangles.
In both the triangles , length of :
Perpendicular = 4 cm
Base = 6 cm
So , Area of both triangles = [tex]2(\frac{1}{2} * Base * Perpendicular) = 2(\frac{1}{2}* 6 * 4) = 24 cm^2[/tex]
In the 3 rectangles ,
Length = 8 cm
Width = 5 cm
So , Area of the rectangles = [tex]3( Length * Width) = 3(8 * 5) = 120 cm^2[/tex]
Hence the total surface area of the prism is = 120 + 24 =144 cm²
Solve the system of linear equations by elimination. 12x - 7y = -2 8x + 11y = 30
The solutions for the the system of equations are given as x = 1 and y = 2 respectively.
What is a system of linear equations?A system of linear equations is a group of equations having same number of variables and degree.
For the n number of variables n number of equations are required.
On the basis of number of solutions a system of equations can be classified as consistent and inconsistent.
The given system of linear equations are as follows,
12x - 7y = -2 (1)
8x + 11y = 30 (2)
In order to solve by elimination, multiply equation (1) by 2 and (2) by 3 and then subtract to obtain,
2(12x - 7y) - 3(8x + 11y) = 2 × -2 - 3 × 30
=> -14y - 33y = -94
=> -47y = -94
=> y = 2
Substitute y = 2 in equation (1) to get,
12x - 7 × 2 = -2
=> 12x = -2 + 14
=> x = 12/12 = 1
Hence, the given system of linear equations is solved by elimination to give x = 1 and y = 2 respectively.
To know more about system of equations click on,
brainly.com/question/24065247
#SPJ2
Out of 100 students of a class, 30%use smart mobile phones. How many
students use the sm art phones?
Answer:
u can calculate yourself
Answer:
30
Step-by-step explanation:
This is the answer hope it helped
Solve for x:
6x + 9 = 4x + 25
Answer:
x = 8
Step-by-step explanation:
Solve for x:
6 x + 9 = 4 x + 25
Subtract 4 x from both sides:
(6 x - 4 x) + 9 = (4 x - 4 x) + 25
6 x - 4 x = 2 x:
2 x + 9 = (4 x - 4 x) + 25
4 x - 4 x = 0:
2 x + 9 = 25
Subtract 9 from both sides:
2 x + (9 - 9) = 25 - 9
9 - 9 = 0:
2 x = 25 - 9
25 - 9 = 16:
2 x = 16
Divide both sides of 2 x = 16 by 2:
(2 x)/2 = 16/2
2/2 = 1:
x = 16/2
The gcd of 16 and 2 is 2, so 16/2 = (2×8)/(2×1) = 2/2×8 = 8:
Answer: x = 8
I need help with this one please.
Answer:
m=3
Step-by-step explanation:
slope=m=y2-y1/x2-x1
(29,97),(18,64) for given points
m=64-97/18-29 ⇒ m=-33/-11
m=3
b): 97/29 ,64/18,-14/-8, 52/14,-71/-27
No, it does not matters which points you take to calculate the slope because at each point m=3for points (18,64) and (-8,-14)m=-14-64/-8-18
m=-78/-26
m=3for points:(-8,-14) and (14,52)m=52+14/14+8
m=66/22
m=3for points (14,52) and (-27,-71)m= 3write the equation of a line at a point (-8,-14)the equation of a line: y=mx+by=-14 , x=-8 , m=3, find b-14=3(-8)+b-14=-24+bb=-14+24b=10the equation : y=3x+104 solve the equation below 5 =g/4
Answer:
g = 20
Step-by-step explanation:
multiply both sides by 4 to get g = 20
Answer:
g=20
Step-by-step explanation:
multiply both sides by 4
3x - 6 = 2(x + 4). find the value
Are same side exterior angles congruent
What is 47.2% as a fraction? (can someone show the work)
Answer: 59/125
Step-by-step explanation:
What is 47.2% as a fraction or mixed number in simplest form? 47.2% is 47.2/100 which is 472/1000 which is 59/125. 47.2% = 0.472 = 472/1000 = 59/125.
-3.09 +x= -0.7 What is the answer?
Answer:
2.39
Step-by-step explanation:
-3.09+X=-0.7
X=-0.7+3.09
X=2.39
Which sets of ordered pairs show equivalent ratios use the grid to help you check all that apply
Answer:
(2,2), (4,4), (6,6)
Step-by-step explanation:
2×1= 2
2×2 = 4
2×3 = 6
Answer:
2nd and 4th options are correct choices.
Step-by-step explanation:
From the incomplete picture given below, we have:
2nd = (2,2), (4,4), (6,6)
4th = (4,1), (8,2), (12,3)
Enjoy!
Wyatt mows lawns to earn money. He charges by the area
of the yard. A new customer has a yard in the shape of a
triangle with a base of 200 feet and a height of 70 feet.
What is the area of the yard?
4,667 ft?
540 ft?
7,000 ft
270 ft?
The area of the triangular yard is 7000 ft².
What is the area of a triangle?The entire area enclosed by three sides of a triangle is the area of it.
Given,
The base of the triangle is 200 feet and the height of the triangle is 70 feet.
Therefore, the area of the triangle
= (1/2) × base of the triangle × height of the triangle = (1/2) × 200 × 70 ft² = 7000 ft².
Learn more about the area of a triangle here: https://brainly.com/question/22625791
#Tag #SPJ2
Matthew drove 74 miles in 2 hours. On average,how fast did he drive in hours per mile?
Answer:
37 mph
Step-by-step explanation:
Step 1:
74 ÷ 2
Answer:
37
Hope This Helps :)
Which set of ordered pairs represents a function?
O {(-4,9), (-4,7), (1, -5), (7, -8)}
{(-5, -5), (-9,1), (8,-6), (-9,-4)}
{(-6, -6), (-2,-2), (7,-6),(-5,0)}
{(-7, -9), (-7, -7), (3,-7), (5,-5)}
Submit Answer
Answer: {(-6, -6), (-2,-2), (7,-6),(-5,0)}
Step-by-step explanation:
To find the ordered pairs that represent a function, we want to find one that doesn't have multiple outputs for one input.
{(-6, -6), (-2,-2), (7,-6),(-5,0)} is the correct answer because all the x are different, and have only one output.
Look at the number in the place-value table. The value of the 8 in the hundreds
place is how many times the value of the 8 in the tens place?
Hundred
Thousands
Ten
Thousands
Thousands
Hundreds
Tens
Ones
6
5
S
S
0
(3) 100
>) 10
») 80
0800
Oh
Answer:
10 times the value
Step-by-step explanation:
The value of 8 in the hundreds place (800) is 10 times the value of 8 in the tens place (80).
I figured this out by dividing 800 by 80 = 10.
Rewrite (x – 3) (x + 5) + (x – 3) (2x – 1) as the product of two binomials.
(x - 3)(x + 5) + (x - 3)(2x - 1)
We can factor out (x - 3) since both terms have that in common. Then we simply add together x + 5 and 2x - 1
(x - 3)(3x + 4) is the final answer.
Solution for: 2 [32-(4-1)³ ]
Answer:
5
Step-by-step explanation:
Answer:
10
Step-by-step explanation:
2[32-3^3]
2[32-27]
2×5
10
Jose has $178.74 in his checking account. He wrote checks for $36.52, $18.92, and $25.93. He also deposited $300.00, $100.00, and $205.16. What is the final balance in Bob's checking account?V
Answer:
$702.53
Step-by-step explanation:
Start with Jose's initial balance.
[tex]178.74[/tex]
He wrote checks, so we have to subtract the total amount the checks were worth. Let's first add the three amounts.
[tex]36.52+18.92+25.93[/tex]
Solve.
[tex]81.37[/tex]
Subtract the total amount of the checks from Jose's initial balance.
[tex]178.74-81.37[/tex]
Solve.
[tex]97.37[/tex]
The amount above is now what is in Jose's checking account.
But, he also deposited money, meaning he put money in his checking account. Now, let's add the three amounts he deposited.
[tex]300.00+100.00+205.16[/tex]
Solve.
[tex]605.16[/tex]
The amount above is what Jose adds to his checking out.
Add the total value of the deposited money and his new balance.
[tex]605.16+97.37[/tex]
Solve.
[tex]605.16+97.37=702.53[/tex]
20. SAILING On a sailing trip, each passenger needs a
life jacket, a lunch, and a bottle of water. Write an
expression in simplest form that represents the
weight carried by r passengers on the sailing trip.
Interpret the expression.
The record high temperature in Alabama is 112°F and the record low temperature is −27°F. What is the difference between the highest and lowest temperature?
The difference between the highest and lowest temperature is 85°F.
Answer: 139F
Step-by-step explanation: You take 112F, and add negative which is -27F and you get the difference.
Can someone please help me?
Answer:
no
Step-by-step explanation:
u r a n00b hahahahahahahahahahahahahaahahhaahahahahahahahahahahahahahahahahahahhahahau suk balz hhahahahahahahahahahahahahahaha
PLEASE I NEED THIS IN AN HOUR OR SO (15 point)
A line goes through the points (4, 6) and (–2, 3). What is the slope of the line perpendicular to that line?
Write the equation of the line through the points (–6, 3) and (9, 8).
What is the volume of a book when the length is 42 cm, the width is 12 cm and the height is 4 cm?
What is the mass of a rock if the volume is 54 ml and the density is 3.2 g/ml?
What is the density of a block of wood that has a mass of 38 g and a volume of 19 cm3?
What is the mass of a liquid that has a density of 2.4 g/ml and a volume of 32 ml?
What is the volume of gold with the mass of 1500 g if the density of gold is 19.32 g/ml?
What is the density of a box if the mass is 160 g and the volume is 12 ml?
What is the volume of a shark’s tooth when you start with 75 ml of water in a graduated cylinder and when the shark’s tooth is placed in the water, the water level rises to 90 ml? (use water displacement)
The mass of a pencil is 8 g and the density is 1.24 g/ cm3. What is the volume of the pencil?
Answer: What is the volume of a book when the length is 42 cm, the width is 12 cm and the height is 4 cm? 2016 (length x width x height)
What is the mass of a rock if the volume is 54 ml and the density is 3.2 g/ml? 172.8 (when finding the mass you always multiply the volume and density so 54ml x 3.2 g/ml = 172.8)
What is the density of a block of wood that has a mass of 38 g and a volume of 19 cm3? 2cm3 (38g/19cm3=2cm3
What is the density of a box if the mass is 160 g and the volume is 12 ml? 13.3 (160/12=13.3)
What is the volume of a shark’s tooth when you start with 75 ml of water in a graduated cylinder and when the shark’s tooth is placed in the water, the water level rises to 90 ml? (use water displacement) 15 (If you measure the amount the water level increases, you can find the volume of the water pushed out of the way.)
The mass of a pencil is 8 g and the density is 1.24 g/ cm3. What is the volume of the pencil? 6.45cm3 (8/1.24/cm3=6.45
Step-by-step explanation:
Name this angle in three different ways
Angle LMN
Angle NML
Angle M
These are the only ways to name this angle
Answer:
Angle NML, LMN, and the angle created by rays MN and ML intersecting at point M.
Step-by-step explanation:
The first two ways are just the points in order. The third can be written in multiple ways but I believe this one is quite explanatory.