Answers
Answer:
a. length: 20-2x; width: 12-2x; height: x
b. V = 4x^3 -64x^2 +240x
c. cubic trinomial
d. 262.7 cubic inches maximum for a 2.4 inch square
e. 15 × 7 × 2.5 inches for 262.5 in³ volume
Step-by-step explanation:
a.If the square cut from each corner has side length x, the dimensions are ...
height: xwidth: 12 -2xlength: 20 -2x__
b.The volume is the product of length, width, and height.
V = LWH
V = (20 -2x)(12-2x)(x) = 4(x-10)(x-6)x = 4(x^2 -16x +60)x
V = 4x^3 -64x^2 +240x
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c.The volume function is a cubic trinomial.
__
d.The maximum volume will be found where the derivative of the volume function is zero.
V' = 12x^2 -128x +240 = 0
x^2 -32/3x +20 = 0 . . . . divide by 12
(x -16/3)^2 = 76/9 . . . . . complete the square
x = (16 -√76)/3 ≈ 2.4 . . . . size of the square
V = 4(2.4)(10 -2.4)(6 -2.4) ≈ 262.7 . . . cubic inches
The maximum box volume is about 262.7 cubic inches when the square is about 2.4 inches on each side.
__
e.A graphing calculator shows there to be two solutions for a volume of 262.5 cubic inches. The rational solution is x = 2.5 inches. The box dimensions would be ...
length = 20 -2(2.5) = 15 incheswidth = 12 -2(2.5) = 7 inchesheight = 2.5 inches
Related Questions
Simon used these steps to solve an equation:
Step 1: -6(x + 7) = 2(x − 11)
Step 2: -6x − 42 = 2x − 22
Step 3: -8x − 42 = -22
Step 4: -8x = 20
Answers
Find the product. Write your answer as a mixed number in simplest form 3 x 4 7/9
Answers
Answer:
14 1/3
Step-by-step explanation:
3 × 4 7/9
=3 × 43/9
= 43/3
= 14 1/3
Answer:
43/3
Simply 14⅓
Step-by-step explanation:
4 7/9 can also be expressed as (4x9+7)/9 = 43/9
3x43/9 = 43/3
After simplifying = 14⅓
find the area of a square of the side 8cm
Answers
Answer:
64cm squared
All squares side lengths are the same. 8*8=64.Answer:
64cm²
Step-by-step explanation:
8cm x 8cm = (8cm)²
8 x 8 = 64
cm x cm = cm²
=64cm²
The points (2, 5) and (6,-3) fall on a particular line. What is its equation in slope-intercept form?
y = -2
x+ ?
Answers
Answer:
y = -2x + 9
Step-by-step explanation:
slope intercept form : y = mx + b
where m = slope and b = y intercept
first let's find the slope
slope formula :
[tex]m = ( \frac{y2 - y1}{x2 - x1} )[/tex]
where the x and y values are derived from the given points
here we are given (2,5) and (6,-3)
(x1,y1) = (2,5) so x1 = 2 and y1 = 5
(x2,y2) = (6,-3) so x2 = 6 and y2 = -3
we now plug these values into the formula
recall formula
[tex]m= ( \frac{y2 - y1}{x2 - x1} )[/tex]
plug in x1 = 2, y1 = 5, x2 = 6 and y2 = -3
m = (-3 - 5) / ( 6 - 2 )
m = (-8)/(4)
m = -2
the slope is -2
now to find the y intercept we plug in the slope and the x and y value of a given point into slope intercept form and solve for b
y = mx + b
given point : (2,5) x = 2 , y = 5, m = -2
5 = -2(2) + b
5 = -4 + b
9 = b
so the equation would be y = -2x + 9
hi please figure this out me and my sister are so confused
Answers
Answer:
y = - 7
Step-by-step explanation:
Since the solution is always the same for y, y equals that solution and does not depend on x.
[tex] \rm \bold{ If \: f ( x ) = tan \: x , \: Then \: Show \: That \: f (2x) = \frac{2f(x)}{1 -[f(x)] } }[/tex]
⭐Thenku ~
Answers
[tex]\qquad \sf \: \huge \bf༆ Answer ༄[/tex]
Here's the solution ~
[tex]\qquad \sf \dashrightarrow \: f(x) = \tan(x) [/tex]
[tex]\qquad \sf \dashrightarrow \: f(2x) = \tan(2x) [/tex]
[tex]\qquad \sf \dashrightarrow \: f(2x) = \dfrac{2 \tan(x) }{1 - { \tan {}^{2} (x) }^{} } [/tex]
replace tan(x) with f(x) in the given equation ~
[tex]\qquad \sf \dashrightarrow \: f(2x) = \dfrac{2 (f(x) )}{1 - { (f {}^{} (x)) {}^{2} }^{} } [/tex]
The expression that was proved is [tex]tan2x=\frac{2[f(x)]}{1-[f(x)^2]}[/tex]
Double angle of functionGiven the trigonometry identity
f(x) = tanx
f(2x) tan2x
From double angle theorem;
[tex]tan2x=\frac{tanx+tanx}{1-tanx(tanx)} \\tan2x=\frac{2tanx}{1-tan^2x}[/tex]
Since f(x) = tan(x), substitute into the result to have:
[tex]tan2x=\frac{2[f(x)]}{1-[f(x)^2]}[/tex] (Proved)
Learn more on double angle here: https://brainly.com/question/14691
Simplify this expression
-4 - 10x
Answers
___% of $10 = $2
Please help me I can not figure it out
I need it please
Answers
Answer:
20%.Step-by-step explanation:
Sentence should be:
2 is what percent of 10.How we get the %:
To get it, we need to find the fraction of 20% (0.2) (2/10)So, we simply do this:2/10.We then get 20%.2 is 20% of 10.
20% of 10 is 2.
You are arranging 60 pictures on a poster board. the board can fit up to 4 rows of pictures and each row can have up to 20 pictures. you want each row to have the same numbers of pictures. how many different ways can you arrange the pictures?
Answers
Answer:
2 different ways
Step-by-step explanation:
You are looking at the factors of 60.
1×60 does not work, too many pictures in a row.
2×30 does not work, too many pictures in a row.
3×20 THIS WORKS!
4×15 THIS ALSO WORKS!
5×12 Nope, too many rows
6×10, no, too many rows
So there's just two ways to arrange the pictures.
What percentage of the apples are green?
Answers
Answer:
6 of the 30 apples are green
6 / 30 = .2
So 20% of the apples are green.
Percentage of the apples are green is 20%
What is a percentage?
"A Percentage is a number or ratio that represents a fraction of 100. It is often denoted by the symbol %".
According to the question
Total Apples = 30
Red Apples = 24
Green Apples = 6
Percentage of the apples are green = [tex]\frac{6}{30}[/tex]×[tex]100[/tex]
= [tex]20[/tex] % or [tex]0.2[/tex]
∴ Percentage of the apples are green is 20%.
Learn more about percentage here
https://brainly.com/question/16797504
#SPJ2
A.(-2, -1) is a solution to the linear system B.(-2, -1)is not a solution to the linear system
Answers
Answer:
A. (-2, -1) is the solution to the linear system
Step-by-step explanation:
Substitute for x and y and see if the equations are true.
-1 = 3(-2) +5 . . . . true
-2 +(-1) = -3 . . . . .true
(-2, -1) is the solution to the linear system.
en una bolsa hay menos de 30 semillas. podemos hacer grupos de 4 semillas sin que sobre ninguna. si hacemos grupos de 5 semillas tampoco sobra ninguna. ¿Cuántas semillas hay en la bolsa?
Answers
20 se puede dividir por 4 y serán 5 grupos sin sobrar ninguna.
y
20 se puede dividir por 5 y serán 4 grupos sin sobrar ninguna.
does anyone know the answer to ts ?
Answers
Answer: C is your answer
Step-by-step explanation:
help me with geometry please
Answers
Answer:
80°
Step-by-step explanation:
the triangles are symmetrical. therefore their angles will be equal.
interior angles of a triangle = 180°
180° - 30° - 70° = m<D
80° = m<D
Which value, when divided by 5/16, results in a quotient of 1?
Answers
Answer:
0.666777
Step-by-step explanation:
not sure not my grade level
what is the hypotenuse?
225cm
55°
390cm
165cm
165cm
please help meeeee i neeeed it quickkkk with the calculations
Answers
Answer:
390cm
Step-by-step explanation:
martin works in a furniture store. he earns a base salary of $1,800 per month, plus a 15% commission on the amount of furniture sales he makes during the month. if martin needs to earn at least 3,000 each month to pay his expenses, what is the minimum amount of furniture sales he must make each month?
Answers
Answer:
$8000
Step-by-step explanation:
With the provided values you get the equation
1800+.15x=3000
with x being the amount of sales he needs
1. 3000-1800=1200
gives 1200=.15x
2. 1200/.15 = 8000
so x = 8000
Maysoun drove 1116 kilometers in 12 hours. At the same rate, how long would it take her to drive 651 kilometers?
Answers
Answer:
7 hours
Step-by-step explanation:
12hrs=1116kms
1hr=1116÷12
1hr=93kms
Xhrs=651kms
Xhrs=(651÷93) ×1
=7×1
=7hrs
I need help on this problem, if you can help me ill really be grateful. If you could also explain it that would be great.
You are trying to solve for the zeros.
Answers
Answer:
x=3
Step-by-step explanation:
The square root of 225 is 15
so 15=4x+3
-3 -3
12=4x
If 12=4x then x=3
A scale drawing of a rectangular park is 7 inches wide and 9 inches long. The actual park
is 392 yards long. What is the area of the actual park, in square yards?
PLEASE HELP ME
Answers
Answer:
56000 square yards
Step-by-step explanation:
I hope it helps you!!!
A rectangular prism has a length of 8 meters, a width of 6 meters, and a height of 3 meters.
Which equations could be used to determine the volume, V, of the prism?
Select each correct answer.
(A) V = 8 × 6 × 6
(B) V = 8 × 6 × 3
(C) V = 8 × 9
(D) V = 48 × 3
Answers
Answer:
(B) V = 8 x 6 x 3
Step-by-step explanation:
The formula to find the volume of a rectangular prism is, V = Length x Width x Height cubic units.
V = 8 x 6 x 3 cm 3.
V = 192 cm 3.
Brainliest?!
the sum of a number squared and five
Answers
Answer:
(x+5^3 is the answer of this question
I NEED HELP WITH THIS MATH I DONT GET IT!!!!!
Answers
Answer:
It's 5
Step-by-step explanation:
-4x+5=-15 (subtract 5)
-4x=-20 (divide by -4)
x=5
Step-by-step explanation:
Work backwards. First, create a function:
f(x) = x
First, instead of adding 5, subtract it:
f(x) = x - 5
Then, divide by -4:
f(x) = (x - 5) ÷ -4
Then plug in -15:
f(-15) = (-15 - 5) ÷ 4
= -20 ÷ -4
= 20 ÷ 4
= 5
EASY POINTS
-
What are the values of a positive attitude?
Answers
Answer:
Self-confidence: When you develop a positive attitude, you will start feeling better about yourself. You will treat yourself with more respect and love, and this in turn will boost your confidence levels and inner strength. You will take on new challenges and come out of your self-limiting beliefs
find the inverse
f(x)=(2x-3)^2 -1
Answers
Is it possible to have a polygon with an exterior angle of 14 degrees
Answers
Answer:
No, a polygon cannot have a decimal number of sides.
Explanation:
exterior angle of a polygon = 360 ÷ number of sidesusing the formula:
14 = 360 ÷ number of sides
1/number of sides = 14/360
number of sides = 360/14
number of sides = 25.71428571
Answer:
all polygons have exterior angles that totL to 360 degrees from triangles to 20-gons. so 360 divided by 14 is 25.71 sides which is not possible because what would .71 of a side look like....now this is assuming that you were referring to regular polygon with all sides the same. I suppose you could gave a polygon with a whole number of sides but the relationship between the exterior angles could be such that not all of the angles have the same degree measure. I would say that an exterior angle for any polygon would need to be greater than 0 but less than 360. so my answer is yes it could be possible le
write the equation of the line?
Answers
Answer: Yellow option
Step-by-step explanation:
The points noted are (0,-2) and (3,-1)
So the slope is (-2--1)/(0-3) = -1/-3 = 1/3
So options blue, green and red are out.
So the only option is yellow
find the slope of the line,
Please Help i am confused
Answers
Answer:
Slope = -1
Step-by-step explanation:
We will use 2 points from the graph.\
(0 , 2) and (2 , 0)
formula for slope = y2 - y1/x2 - x1
0 - 2/2 - 0
=-2/2
=-1
What is the slope of the line?
3(y - 1) = 2x + 2
Answers
Rewrite the equation in slope- intercept form.
3(y-1) = 2x + 2
Use the distributive property
3y-3 = 2x + 2
Add 3 to both sides
3y = 2x + 5
Divide both sides by 3
Y = 2/3x + 5/3
Slope = 2/3
i hope this helps :)
what is 29/8 into a improper fraction (Convert mixed number).
Answers
Answer:
3 5/8
Step-by-step explanation:
divide 29 by 8,
8 times 3 is 24
29-24, remainder is 5