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].
how do you write a equation with (0,2) and (3,3) in slope-intercept form?
Answer:
m= 3-2/ 3-0= 1/3
Step-by-step explanation:
y2= 3 y1= 2
x2= 3 x1= 0
5
2
+(12−7+x) if x=6
Answer:
the answer will be 6 or 10
What if a fence painting competition allowed pairs to compete? If Ben Rogers can paint the fence in 8 min on his own and Johnny Miller can paint it in 6 min, then how long would it take them working together?
If Ben can paint a single coat of the fence in 8 min, then how much of the fence could Ben paint in 1 min?
If Johnny can paint a single coat of the fence in 6 min, then how much of the fence could Johnny paint in 1 min?
If Ben and Johnny work together to paint a single coat of the fence, then let t represent the amount of time they each spend painting. What operation should be used to set up an equation that represents how long they would take to paint a single coat of the fence?
Solve the equation for t. How long will it take Ben and Johnny to paint the fence? Round your answer to the nearest tenth of a minute.
Answer:
I'm confused on what it's asking
Step-by-step explanation:
What is the quotient of -3/8 and -1/3?
Answer:
1[tex]\frac{1}{8}[/tex]
Step-by-step explanation:
I used my calculators.
Graph the equation on the coordinate plane y=-3/2x -4
Answer:
The 3, and -4 are the places where you start, then just graph 1/2 and -3 as slope
Step-by-step explanation:
Step-by-step explanation:
you start at -4 and then you go down 3 and to the right 2
Answer the questions. All help needed.
1. Multiply all the x and y by 2
M (-6,4)
A (-4,6)
T (-2,4)
H (-4,2)
2. They stayed in the same quadrants. The x and y values shifted.
3. Scale factor of 1/2
4. .....mayhaps?
The student council made a pront of $3,000 on a car wash. If they invest the money at 5% interest
compounded yearly, how much money would they have in four years?
Answer:
$3375 money would the student council have in four years if they invest $3000 at 5% interest compounded yearly.
Step-by-step explanation:
We are given:
Principal Amount = $3000
Interest Rate r = 5% or 0.05
n=1 (compounded yearly)
Years t= 4
We need to find future value (A)
The formula used is: [tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Putting values in formula and finding future value A
[tex]A=P(1+\frac{r}{n})^{nt}\\A=3000(1+\frac{0.05}{1})^{1*4}\\A=3000(1+0.05)^4\\A=3000(1.05)^4\\A=3000(1.215)\\A=3375[/tex]
So, $3375 money would the student council have in four years if they invest $3000 at 5% interest compounded yearly.
Evaluate the expression when a=4 and b=43
You help out at the bowling alley on weekends. One of the arcade games has a bin filled
with stuffed animals. A robotic arm randomly grabs a stuffed animal as a prize for the
player. You are in charge of filling the bin.
You are told that the probability of getting a stuffed giraffe today is 0.4. If there are 28
giraffes in the bin, what is the total number of stuffed animals in the bin?
Answer:
28/0.4,= 28/(2/5)=28*5/2=14*5=70, no need to use calculator
check 70*0.4=28
Step-by-step explanation:
Find the value of z. Then find the value of the interior angles
Step-by-step explanation:
[tex] \because \angle JKM [/tex] is the exterior angle of [tex] \triangle KLM [/tex]
[tex] \therefore [/tex] by remote interior angle theorem of a triangle, we have:
[tex] m\angle L + m\angle M = m\angle JKL \\\\
(18z + 3)\degree + (5z - 3)\degree = 161\degree \\\\
(18z + 3+5z - 3)\degree = 161\degree \\\\
(23z)\degree = 161\degree \\\\
23z = 161\\\\
z = \frac{161}{23} \\\\
\huge \red {\boxed {z = 7}} \\\\
\because \measuredangle L = (18z +3)\degree \\\\
\therefore \measuredangle L = (18\times 7+3)\degree \\\\
\therefore \measuredangle L = (126+3)\degree \\\\
\huge\purple {\boxed {\therefore \measuredangle L = 129\degree}} \\\\
\because \measuredangle M = (5z - 3)\degree \\\\
\therefore \measuredangle M= (5\times 7-3)\degree \\\\
\therefore \measuredangle M = (35-3)\degree \\\\
\huge\orange {\boxed {\therefore \measuredangle M = 32\degree}} \\\\[/tex]
whats 255x67777675456745675676745
Answer: 1.728330724e+25 thats what it said when I calcuated it.
Which ordered pairs are NOT a solution of y = 2x + 1? Select all that apply. (3, 7) (3, 7) (0, 1) (0, 1) (-1, 1) (-1, 1) (-3, -5) (-3, -5) (-2, 3)
Answer:
The ordered pairs are;
(-1,1) and (-2,3)
Step-by-step explanation:
Here, we want to select which ordered pair is not a solution to the given equation
The one that will not be a solution will be a point at which if we insert the x-value into the equation, we do not get the y-value at that point
For (3,7
2(3) + 1 = 7
For 0,1
2(0) + 1 = 1
For (-1,1)
= 2(-1) + 1 = -2 + 1 = -1
This is wrong
(-3,-5)
= 2(-3) + 1 = -6 + 1 = -5
(-2,3)
= 2(-2) + 1 = -4 + 1 = -3
This is wrong also
GUYS PLEASE HELP LIKE I MEAN IT CAN SOMEONE TELL ME THE ANSWER WITH AN EXPLANATION
Answer:
I think its 183 1/3
It's what I figured out & the other answer says the same.
Step-by-step explanation:
You like TommyInnit, too? Poggers! <3
Answer:
183 1/3
Step-by-step explanation:
I'm assuming that x and y are directly proportional.
So anyways:
5.5 divided by 3/4 is 7 1/3.
Because this is directly proportianol, you'll also have to mutiply y by 7 1/3.
So: 25 times 7 1/3 equal to 183 1/3
Hope this helps!
(this is english but more people are on math i think) what are two ways to introduce textual evidence??
[tex]I\;would\;say\;one\;way\;do\;it\;is\;like\;this...\\\\"He's\;not\;very\;brave\;after\;all"\;\;(Page\;12)\\\\Another\;way\;to\;do\;it\;is\;like\;this...\\\\According\;to\;the\;authour\;the\;man\;couldn't\;face\;his\;fear\;of\;heights. \;\;(Pg\;13)[/tex]
Can you help me? Thanks!
Answer:
the answer is here
Step-by-step explanation:
180- 68
=112
What is the volume of a sphere with a diameter of 23.5 in, rounded to the nearest
tenth of a cubic inch?
Answer:
V≈6795.2in³
Step-by-step explanation:
I think
Answer:
6795.2
Step-by-step explanation:
i got it right
Can yall help me on this?
Answer:
y = 3x - 2
Step-by-step explanation:
Step 1: Look at the "y" axis and see what it is going through (-2)
Step 2: Check if the line if a positive slope or a negative slope (positive)
Step 3: Since we now know this is a positive slope, it cancels out "D" and "A".
Step 4: This would not be B because the rise is "1" and the run is "3"
Final Ansr: "C" because the rise is "3" and the run is "1" with a "-2" y-intercept.
PLEASE PLEASE HELP ME ! Jerry wants to buy his grandpa's old car for $500.00. He works 10 hours a week
at $7.50 an hour. How many weeks will he need to work before he earns enough
money to buy the car? Write and equation
Answer:
Step-by-step explanation:
Needs $500 Makes 7.50 and works 10 hours week.
7.50*10= $75.00 a week
500/75= 6.6 weeks or 6 weeks and 2/3 of a week. I'd round to 7 weeks.
75(x)=500 X= weeks needed.
75x=500 if you divide 500 by 75
x=20/3 or 6.6
A store is selling 6 for $45 if you have $75 how many can you buy?
8x+3y=14,2x+y=4. PLz solve this it’s emergency
Answer:
x=1, y=2
Step-by-step explanation:
1) 8x+3y=14 Original system of linear 2d equations
2x+y=4
2) 8x+3y=14
-4 (2x+y) =-4(4) Multiply second equation by negative four.
3) 8x+3y=14
+ -8x-4y=-16 Add equations, eliminating x terms
4) -y=-2
y=2 solve for y
5) 8x+3(2)=14 Substitute solution for y to solve for x
8x=14-6
8x=8
x=1
(3+\sqrt(2))^(2)-(3-\sqrt(2))^(2)
Step-by-step explanation:
Can you take picture I don't understand the given
A sandwich is 5 1/2 feet long and divided into 1/2 foot pieces. How many pieces of sandwich are there?
Answer:
11
Step-by-step explanation:
Answer:
11 sandwich pieces
Step-by-step explanation:
identify the slope of the line. then identify a point the line passes through:
1. y - 2 =1/4(x - 5)
2. y-7=-3(x+6)
Answer:
ummmm honey I'm confused already
Solve the system by substitution. 4x=8y 2x+5y=27
Answer:
(6, 3)
General Formulas and Concepts:
Pre-Alg
Order of Operations: BPEMDASAlg I
Solving systems of equations using substitution/eliminationStep-by-step explanation:
Step 1: Define systems
4x = 8y
2x + 5y = 27
Step 2: Rewrite systems
x = 2y
2x + 5y = 27
Step 3: Solve for y
Substitute: 2(2y) + 5y = 27Multiply: 4y + 5y = 27Combine like terms: 9y = 27Isolate y: y = 3Step 4: Solve for x
Plug in y into an original equation to find x.
Substitute: 4x = 8(3)Multiply: 4x = 24Isolate x: x = 6Answer:
[tex](6,3)[/tex]
Step-by-step explanation:
[tex]4x = 8y\\4x/4 = x\\8y/4= 2y\\x=2y[/tex]
[tex]2(2y)+5y=27\\4y+5y=27\\9y=27\\9y/9=y\\27/9=3\\y=3[/tex]
[tex]x =2y\\x= 2(3)\\x=6[/tex]
What is the equation of the graphed line written in standard form?
Answer:
C. y = -2/3x -2
Step-by-step explanation:
We know the slope is negative. You can find slope using rise/run. The y-intercept is -2 because the line meets -2 at the y-intercept.
Answer:
The first answer (top)
Step-by-step explanation:
Standard form is ax+by=c
a and b are the coefficients
Take a point from the given line
I chose (0, -2)
Then, plug in the values of x and y
2*0+3*-2=-6
-6=-6
Since it works the standard form of the line is 2x+3y=-6
9) Brenn has $60 in his savings account. His brother Chris has $135 in his. Brenn decides to save $5 of his allowance each week, while Chris decides to spend his whole allowance along with $10 of his savings each week. After how many weeks will Brenn and Chris have the same amount of money in their savings accounts?
Answer:
9) 15
Step-by-step explanation:
Mai earns $7 per hour mowing her neighbors' lawns. She also earned $14 for hauling away bags of recyclables for some neighbors.
Answer:
Step-by-step explanation:
7x + 14 = 8.4x
14 = 1.4x
x = 10 hours
Each works 10 hours. Their total is 84 dollars each.
Abby takes a ride-sharing service to ride from her home to the mall. The ride-sharing service charges $1.75 per mile plus a one-time charge of $5.00. Which equation can be used to find y, the total cost of the ride, given x represents the number of miles of the ride
Answer:
y=1.75x + 5.00
Step-by-step explanation:
After traveling 345 miles, the Johnston family stopped at a rest stop for lunch. Looking at the map, they realized they had completed 3/5 of the trip. If d represents the total distance in miles, which equation can be used to find d?
A. 3/5 divided by d = 345
B. 3/5 x d = 345
C. 345 x d = 3/5
D. 345 divided by d = 5/3
Answer:
B
Step-by-step explanation:
Answer:
B. 3/5 x d = 345
Step-by-step explanation:
White any four rational numbers having the denominator 2 or power of
2. then express them in decimals. Are the decimals always terminating?
While the remarks of your investigation.
9514 1404 393
Answer:
1/2 = 0.53/16 = 0.18755/64 = 0.0781257/2048 = 0.00341796875yesStep-by-step explanation:
A terminating decimal has an equivalent denominator that is a power of 10. That is, it is the product of a power of 2 and a power of 5.
Any fraction that has a denominator that is a power of 2 can be expressed as an equivalent fraction with a power of 10 as the denominator.
Example:
[tex]\dfrac{7}{2048}=\dfrac{7}{2^{11}}=\dfrac{7\cdot5^{11}}{2^{11}\cdot5^{11}}=\dfrac{7\cdot5^{11}}{10^{11}}=0.00341796875[/tex]
hope this helps.enjoy!!!!!!