A rectangular sheet of metal has identical squares cut from each corner. The sheet is then bent along the dotted lines to form an open box. The volume of the box is 420 in.3.

The equation 4x3 – 72x2 + 320x = 420 can be used to find x, the side length of the square cut from each corner.

What is the side length of the square that is cut from each corner, to the nearest inch?

Answers

Answer 1

Hello,

[tex]4x^3-72x^2+320x=420\\ 4(x^3-18x^2+80x-105)=0\\ 4(x^3-3x^2-15x^2+15x+35x-105)=0\\ 4(x^2(x-3)-15x(x-3)+35(x-3))=0\\ 4(x-3)(x^2-15x+35)=0\\ \Delta=15^2-4*1*35=85\\\\ x=3\ or\ x= \dfrac{15+ \sqrt{85}}{2} \ or\ x= \dfrac{15- \sqrt{85}}{2}[/tex]

Answer 2

Answer:

3 in

Step-by-step explanation:

Related Questions

GIVING AWAY 50 POINTS TO WHOEVER SHOWS LEGIT WORK!
The lengths of the sides of three squares are s, s + 1, and s + 2. If their total area is 365 cm squared (^2), find their total perimeter.

Answers

S= one length of square 1
S+1 = one length square 2
S+2= one length square 3

Our equation would be
S^2+(S+1)^2+(S+2)^2=365

Idk if it would be called distribute but.. distribute
S^2+S^2+2S+1+S^2+4S+4=365

Add like terms
3S^2+6S-360=0

Divide everything. By 3
S^2+2S-120=0

Factor
(S-10)(S+12)=0

The two solutions are:

S-10=0
S=10

S+12=0
S=-12

Since a length can’t be a negative the only possible solution would be 10

Since a perimeter is all lengths added together we can multiply the length by four to get the perimeter

Square 1
10*4=40
Perimeter is 40cm

Square 2
S+1 =11
11*4=44
Perimeter is 44cm

Square 3
S+2=12
12*4=48
Perimeter is 48cm

Add all the perimeters together to get the total perimeter:

Total perimeter:
40+44+48=132

The total perimeter is 132cm

I hope this helps. Sorry if I messed up anything on here it was kinda hard to keep track of everything. Feel free to ask if you need anything cleared up :)

Solve the problem. 13) from the edge of a 1000-foot cliff, the angles of depression to two cars in the valley below are 21° and 28°. how far apart are the cars? round your answers to the nearest 0.1 ft.

Answers

the cars would be 724.4 feet apart!!

Final answer:

The problem is about finding the distance between the cars using the angles of depression and the height of the cliff. Calculate individual horizontal distances first and then find their difference which gives us the distance between the cars.

Explanation:

This problem can be solved using trigonometry. We've a 1000-foot cliff and a valley below where the two cars are located. From the edge of the cliff, if we draw two lines of sight to the cars, we can get two right triangles. The angles of depression to the cars are 21° and 28°, which are the angles between these lines of sight and a horizontal line.

We can use the tangent of these angles, which is the ratio of the opposite side (the vertical distance from the cliff to the cars) and the adjacent side (the horizontal distance from the cliff baseline to the cars). We know the vertical distance - it's 1000 ft (height of the cliff). So, we can calculate the horizontal distances (D1 and D2) to the cars as D1 = 1000/tan(21°) and D2 = 1000/tan(28°) respectively.

The difference between D1 and D2 will give the distance between the cars.

The calculations might give the distance in decimals, and the problem asks to round the answer to the nearest 0.1 ft.

Learn more about Triangle Trigonometry here:

https://brainly.com/question/15101552

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1. In an auditorium, there are 21 seats in the first row and 26 seats in the second row. The number of seats in a row continues to increase by 5 with each additional row.

(a) Write an iterative (explicit) rule to model the sequence formed by the number of seats in each row. Show your work.

(b) Use the rule to determine how many seats are in row 15. Show your work.

2. Rhonda started a business. Her business made $40,000 in profits the first year. Her annual profits have increased by an average of 6% each year since then.

(a) Write an iterative rule to model the sequence formed by the profits of Rhonda’s business each year.

(b) Use the rule to determine what the annual profits of Rhonda’s business can be predicted to be 20 years from the start of her business. Round your answer to the nearest dollar. Do not round until the end. Show your work.

3. The sequence 3, 12, 48, 192, … shows the number of pushups Kendall did each week, starting with her first week of exercising.

(a) What is the recursive rule for the sequence?

(b) What is the iterative rule for the sequence?

Answers

1. Let [tex]s_n[/tex] be the number of seats in the [tex]n[/tex]-th row. The number seats in the [tex]n[/tex]-th row relative to the number of seats in the [tex](n-1)[/tex]-th row is given by the recursive rule

[tex]s_n=s_{n-1}+5[/tex]

Since [tex]s_1=21[/tex], we have

[tex]s_2=s_1+5[/tex]
[tex]s_3=s_2+5=s_1+2\cdot5[/tex]
[tex]s_4=s_3+5=s_1+3\cdot5[/tex]
[tex]\cdots[/tex]
[tex]s_n=s_{n-1}+5=\cdots=s_1+(n-1)\cdot5[/tex]

So the explicit rule for the sequence [tex]s_n[/tex] is

[tex]s_n=21+5(n-1)\implies s_n=5n+16[/tex]

In the 15th row, the number of seats is

[tex]s_{15}=5(15)+16=91[/tex]

2. Let [tex]p_n[/tex] be the amount of profit in the [tex]n[/tex]-th year. If the profits increase by 6% each year, we would have

[tex]p_2=p_1+0.06p_1=1.06p_1[/tex]
[tex]p_3=1.06p_2=1.06^2p_1[/tex]
[tex]p_4=1.06p_3=1.06^3p_1[/tex]
[tex]\cdots[/tex]
[tex]p_n=1.06p_{n-1}=\cdots=1.06^{n-1}p_1[/tex]

with [tex]p_1=40,000[/tex].

The second part of the question is somewhat vague - are we supposed to find the profits in the 20th year alone? the total profits in the first 20 years? I'll assume the first case, in which we would have a profit of

[tex]p_{20}=1.06^{19}\cdot40,000\approx121,024[/tex]

3. Now let [tex]p_n[/tex] denote the number of pushups done in the [tex]n[/tex]-th week. Since [tex]3\cdot4=12[/tex], [tex]12\cdot4=48[/tex], and [tex]48\cdot4=192[/tex], it looks like we can expect the number of pushups to quadruple per week. So,

[tex]p_n=4p_{n-1}[/tex]

starting with [tex]p_1=3[/tex].

We can apply the same reason as in (2) to find the explicit rule for the sequence, which you'd find to be

[tex]p_n=4^{n-1}p_1\implies p_n=4^{n-1}\cdot3[/tex]

Answer:

i will look but i think she was right

Step-by-step explanation:

) a pair of fair dice is rolled. what is the probability that the sum of the top faces is a number 10 or greater?

Answers

possible number combinations are 1,1 2,1 3,1 4,1 5,1 6,1 1,2 2,2 3,2 4,2 5,2 6,2 1,3 2,3 3,3 4,3 5,3 6,3 1,4 2,4 3,4 4,4 5,4 6,4 1,5 2,5 3,5 4,5 5,5 6,5 1,6 2,6 3,6 4,6 5,6 and 6,6. of those 36 number combinations the ones that add up to more than 10 include: 4,6 5,5 5,6 6,4 6,5 6,6. thats 6 number combinations. 6/36 of the possible sums of the top faces equal out to 10 or more. 6/36=1/6=0.166666666666666666666666(repeating) and to put that in a percentage, 16.7%
the probability is 16.7%
Hope this helps.

please verify my probability answer!!!

Answers

The probability that the first student likes to play soccer:[tex]P(A)=\dfrac{10}{25}=\dfrac{2}{5}[/tex]
The probability that the second student likes to play baseball:[tex]P(B)=\dfrac{15}{24}=\dfrac{5}{8}[/tex]
Together:
[tex]P(A)\cdot P(B)=\dfrac{2}{5}\cdot\dfrac{5}{8}=\dfrac{1}{4}[/tex]

Answer:

1/4

Step-by-step explanation:

Hope this helped :)

The sum of the squares of two consecutive positive even integers is 100. find the two integers

Answers

The integers are 6 and 8
6^2= 36
8^2=64
36+64=100

Let's denote the two consecutive positive even integers as x and x+2.

We know their squares sum up to 100, represented mathematically as:

x^2 + (x + 2)^2 = 100.

Expanding this equation, we get:

x^2 + x^2 + 4x + 4 = 100.

Combining like terms gives us:

2x^2 + 4x - 96 = 0.

This is a quadratic equation in the form of ax^2 + bx + c = 0, where a = 2, b = 4, and c = -96.

We can solve this quadratic equation for x using the quadratic formula:

x = [-b ± sqrt(b^2 - 4ac)] / 2a.

Substituting a, b, and c into this formula, we find that:

x = [-4 ± sqrt((4)^2 - 4*2*-96)] / 2*2,
x = [-4 ± sqrt(16 + 768)] / 4,
x = [-4 ± sqrt(784)] / 4,
x = [-4 ± 28] / 4.

So the solutions are x = (28 - 4) / 4 = 6 and x = (-28 - 4) / 4 = -8.

Since we are looking for positive even integers, we discard the negative solution.

Therefore, the two consecutive positive even integers are 6 and 6 + 2 = 8.

What is the maximum volume of a square pyramid that can fit inside a cube with a side length of 18 cm?

a. 5,832 cm
b. 2,916 cm
c. 1,944 cm
d. 972 cm

Find the volume of the cylinder in terms of Pie. The diagrams are not drawn to scale.

a. 52.8 m
b. 58.08 m
c.127.78 m
d. 29.04 m

Answers

Part 1) What is the maximum volume of a square pyramid that can fit inside a cube with a side length of 18 cm?

we know that
[volume of a square pyramid]=(1/3)*b²*h
where
b is the length side of the square base-----> 18 cm (is equal to the length side of cube)
h is the height---------> 18 cm (is equal to the length side of cube)
[volume of a square pyramid]=(1/3)*18²*18----> 1944 cm³

the answer Part 1) is
c. 1,944 cm³

Part 2) Find the volume of the cylinder in terms of Pie. The diagrams are not drawn to scale.

volume of a cylinder=pi*r²*h
for r=2.2 m
h=12 m
volume of a cylinder=pi*2.2²*12-----> volume=58.08*pi m³

the answer Part 2) is
58.08*pi m³

In 2010, a city's population was 1,405,233 and it was decreasing at a rate of 1.1%. At this rate when will the city's population fall below 1,200,000?
a. 2024
b. 2027
c. 2036
d. 2049

Answers

Population in 2010, P(o) = 1,405,233
Rate of decrease, R = 1.1% = 0.011

Applicable formula

P(n) = P(o) *(1-R)^n

Where P(n) = population after n years, n = Number of years
From information given,
1,200,000 = 1,405,233 (1-0.011)^6
1,200,000/1,405,233 = (0.989)^n
0.85395 = (0.989)^n
ln (0.85395) = n ln (0.898)
n = [ln (0.85395)]/[ln (0.989)] = 14.27 years ≈ 14 years
Year in which population will fall below 1,200,000 = 2010+14 = 2024

Then, the correct answer is a.

Answer:

2024

Step-by-step explanation:

took the test

Use a coordinate grid to create a map of a town with at least five different locations, such as a house, a post office, a school, a library, and a mall. Each location must be plotted where two grid lines cross. In addition, no two locations can lie on the same vertical grid line or the same horizontal grid line.

A. Post your diagram.
B. Use the Pythagorean theorem to find the distance between two of your locations.

Answers

see attached picture:

WILL GIVE BRAINLIEST IF YOU HAVE THE REST OF THE ANSWERS

Answers

Hey, I remember this. Connexus, right?

I completed this a few months ago but don't remember the rest of the answers. Message me and I'll be able to find them for you, but anyway, I'm positive the answer is A.

Proof:
A=(123-55)/2=34

Anyone help please!!!!

Answers

We are to verify the identity:

cos(α-B)-cos(α+B) = 2 sinα sinβ

Left hand side = cos(α - B)-cos(α + B)

= cosα cosβ + sinα sinB - (cosα cosB - sinα sinβ)

= cosα cosβ + sinα sinB - cosα cosB + sinα sinβ)

= sinα sinβ + sinα sinβ

= 2 sinα sinβ

= Right Hand side

cos(a-B)-cos(a+B)
cosucosv - sinusinv = cos(u+v)
cosucosv + sinusinv = cos(u-v)

cos(a-B)-cos(a+ B) = cosa cosB + sina sinB - (cosa cosB - sina sinB)= cosa cosB + sina sinB - cosacosB + sinb sinB= 2 sina sinB

If f is a function such that f(b)-f(a)/b-a=2, then which of the following statements must be true?

Answers

Based on the type of equation, f(b) relates to y2, f(a) relates to y1, b relates to x2, and a relates to x1. If we change those around we now get:
(y2 - y1)/(x2 - x1) which is the slope formula, or the average rate of change. thus your answer would be C

At a particular music store, CDs are on sale at $14.00 for the first one purchased and $12.00 for each additional disc purchased. Maria spends $86.00 on CDs. How many CDs has Maria purchased?

Answers

To calculate the answer, we subtract $ 14 from the first CD to the total amount spent, which is $ 86.
So:
$ 86- $ 14 = 72
The rest of the CDs cost $ 12.
Then we divide $ 72 between $ 12
$ 72 / $ 12 = 6.
That means that 6 CDs were bought at $ 12 plus the first one bought at $ 14.
So the number of CDs that María bought was 7

Answer: 7

Step-by-step explanation:

Solve for x: 12(x-7)+3(2x+2)=50x-62

Answers

X= -1/2

Hope this helps

x = -1/2

This is because
12 (-1/2 - 7) + 3 (2 x -1/2 + 2) = 50x - 62
12 x -7.5 + 3 x 1 = -25 - 62
-87 = -87

A regular pentagonal prism has 9-cm base edges. A larger, similar prism of the same material has 36-cm case edges. How does each indicated measurement for the larger prism compare to the same measurement for the smaller prism? A)volume B) weight

Answers

To compare the volumes of the prism we used the scale factor:
volume scale factor=(linear scale factor)³
the linear scale factor of the prism is:
(length of larger prism)/(length of smaller prism)
=36/9
=4
thus the volume scale factor will be:
4³=64
hence the volume of the larger prism is 4 times that of the smaller prism.

Do you have the answers to this quiz?

Which of the following is not needed when making a box plot?
A - Mean
B - Minimum
C - Median
D - Third Quartile

Answers

The mean is not needed to make a box plot.

I hoped this helped!

Answer: A) Mean

You use the median as the center of the boxplot. The first and third quartiles (Q1 and Q3) make up the left and right edges of the box. The min and max are the furthest points on the left and right side of each whisker. The mean is not used at all. With outliers, the mean is skewed. If you have any outliers then its best to use the median instead.

What is the area of a square

Answers

The area of a square is found by multiplying length and width, (which just so happen to be the same number) and the unit of measurement and put the power of 2 at the end (^2).
For example, if a square's length is 4cm, then you can assume the width is going to be 4cm. Finding area, you multiply 4 and 4 to get 16, and the unit of measurement (cm) and square it (^2). Thus meaning this answer would be 16cm^2.

I hope this helps!

two angles are drawn below. the measure of angle x is 90

a. 20
b. 60
c. 100
d. 120

Answers

Since x = 90, y is smaller, so any thing smaller is correct , if there were more than one smaller angle , just estimate.

So the answer is B) 60

Your answer is a and b
Beacuse that that is an acute angle and acute is less then 90

Is 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 a number?

Answers

No I don’t think so::::::::::.:::::::::::::::

Explain how the difference of a fraction or a rational number and its additive inverse is equal to zero.

Answers

The additive inverse property states that when you add a number and its opposite (rational numbers), the result is zero. The reason is that the inverse of a number is the opposite, so if you have a number and when do the opposite with it (add the opposite), the result will be zero. This applies to adding!!!

Hope This Helped =3

Bricklayers use the formula N = 7LH to estimate the number of bricks N needed to build a wall of height H and length L. What is the height of a wall that is 30 feet long and that requires 2,310 bricks to build? a. 12 ft c. 11 ft b. 10 ft d. 20 ft

Answers

plug in 30ft for L and 2310 for n so you will get 2310=7(30)(h)... h would equal 11ft

If x varies directly with y and x=3.5 when y=14 find x when y=18

Answers

[tex]\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{x} varies directly with \underline{y}}\qquad \qquad x=ky\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ -------------------------------\\\\ \textit{we also know that } \begin{cases} x=3.5\\ y=14 \end{cases}\implies 3.5=k14\implies \cfrac{3.5}{14}=k \\\\\\ \cfrac{1}{4}=k\qquad therefore\qquad \boxed{x=\cfrac{1}{4}y} \\\\\\ \textit{when y = 18, what is \underline{x}?}\qquad x=\cfrac{1}{4}(18)[/tex]

A bag contains 3 red, 4 black and 2 white balls. what is the probability of drawing a red ball and then a white ball, if each ball is returned to the bag immediately after it is drawn? 2/27 1/9 1/3 4/27 2/9

Answers

Total number of balls = 3 + 4 + 2 = 9
red ball = 3
white ball = 2

P(red, then white) = (3/9)(2/9) = 6/81 = 2/27

Answer: 2/27

WILL GIVE BRAINLIEST... HELP ASAP!!!!!!

1. Circle A with center at (3, 4) and radius 2 is similar to circle B with center at (−4, −5) and radius 3. Below is an incorrect informal argument for proving two circles are similar:

Step 1 Translate circle B to the right 9 units and up 7 units to form concentric circles.
Step 2 Dilate circle B to be congruent to circle A using scale factor of k = r sub two over r sub one equals two over three
Step 3 When an object is dilated, the dilated object is similar to the pre-image, thus the two circles are similar.

What is the first incorrect step, and how can it be fixed?

A. All steps are correct
B. Step 1, translate circle B to the right 7 units and up 9 units
C. Step 2, use scale factor of K= r^2/r^1=3/2
D. Step 3, replace dilated with translated.

An image of two concentric circles is shown with r2 = 8 and r1 = 3:

2. Image shows a pair of concentric circles. The radius of the smaller circle is r sub 1 and the radius of the second is r sub 2.

In order to prove the two circles are similar, the radius r1 was increased to make the circles congruent. What is the scale factor used in the above image?

A. k=8/3
B. K=3/8
C. K=1/5
D. K=5

Answers

The anwser is B, k= 3/8

First one is B. Because if you're moving from -4 to 3 you don't move 9 units right instead you move 7.

In which type of quadrilateral are consecutive sides congruent?
Select the best answer from the choices provided.
trapezoid
parallelogram
square
rectangle

Answers

Final answer:

A square is the quadrilateral with congruent consecutive sides. It is an equilateral rectangle and a special type of parallelogram with equal-length sides and right angles.

Explanation:

The type of quadrilateral in which consecutive sides are congruent is a square. A square is a special type of parallelogram where all sides are equal in length and all angles are right angles. When considering a square as a rectangle (which technically it is), its diagonals (which are equal in length) bisect one another at right angles, suggesting the property of being an equilateral rectangle. Furthermore, in a larger context, if we treat the sides of any parallelogram symmetrically, such as in a notation [PQRS], the order can change to [QRSP], [QPSR], and [PRQS] without affecting its properties, which aligns with the symmetric nature of a square's sides.

A lucky integer is a positive integer which is divisible by the sum of its digits. what is the least positive multiple of 9 that is not a lucky integer?

Answers

99.

It is not divisible by 18. Before that they are all added up to 9.

The equation of the line through ab *write your answer in slope-intercept form

Answers

Sounds as tho' you have a line going thru two points, A and B, but you have not shared those points. Please do so.

But we can assume that A:(a,b) and B:(c,d), find the slope and then write the equation of the line thru points A and B:

d - b
m = -----------
c - a
d - b
then the equation of the line is y-d = ----------- (x-c)
c - a

Please ensure that you are sharing all of the info given (e. g., the coordinates of the points A and B).

A card is drawn from a standard deck of cards. Determine whether the events are mutually exclusive or inclusive. Then, find the probability.

P(a red card or a queen)

a.
inclusive, 15/26
c.
inclusive, 7/13
b.
mutually exclusive, 15/26
d.
mutually exclusive, 7/13

Answers

The correct answer is C) inclusive, 7/13.

The two events are inclusive because they can both happen at the same time.

This means we find the probability using
P(A or B) = P(A) + P(B) - P(A and B)

P(r or Q) = P(r) + P(Q) - P(r and Q)

There are 26 red cards out of 52 cards.
There are 4 queens out of 52 cards.
There are 2 red queens out of 52.

26/52+4/52-2/52 = 28/52 = 7/13

The events are mutually inclusive and the required probability is p(getting a red or a queen) is 28/52 = 7/13

What is probability?

Probability is a measure of the likelihood of an event occurring. The probability formula is defined as the possibility of an event happening is equal to the ratio of the number of favorable outcomes and the total number of outcomes. Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes.

Given here A card is drawn from a standard deck of cards. Now There are some events that can impact each other or that are overlapping. They have one or more outcomes in common. When events have outcomes in common, they are said to be overlapping events, also known as mutually inclusive events. Thus this event is defenitely inclusive.

Now the probability that a red card or a queen is =( 26 red cards + 2 black queens ) /52

= 28/52

=7/13

Hence, The events are mutually inclusive and the required probability is p(getting a red or a queen) is 28/52 = 7/13

Learn more about probability here:

https://brainly.com/question/30034780

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Which box plot represents the data?
30, 35, 25, 5, 5, 25, 40, 45, 50, 10, 15, 40

Answers

your answer would be A after you found the 5 number sequence.

The answer would be A.

The domain of {(x, y): y = 2x² + 1 is

Answers

Answer:
Domain: (- ∞, ∞)

Explanation:
The equation y = 2x² + 1 is a somewhat narrow parabola translate up 1 unit on the y-axis from the origin (0, 0). The domain of a graph indicates which x-values the diagram can potentially reach, or how far it can travels on the x-axis.

Because it is a parabola, it goes infinitely in both directions of the x-axis. Therefore, its domain is (-∞ ,∞)

Final answer:

The domain of the function y = 2x² + 1 is all real numbers, which is expressed as [tex]$ (-\infty, +\infty) $[/tex]

Explanation:

The domain of a function refers to the set of all possible input values for which the function is defined. In the case of the function [tex]$ y = 2x^2 + 1 $[/tex], it is a quadratic function, meaning it is defined for all real numbers [tex]$ x $.[/tex]

The function[tex]$ y = 2x^2 + 1 $[/tex] involves squaring [tex]$ x $[/tex], which can result in any real number. Since there are no restrictions on the values that[tex]$ x $[/tex] can take, the domain of this function is all real numbers. Mathematically, we denote this domain as[tex]$ (-\infty, +\infty) $[/tex].

This implies that for any real number you substitute in for [tex]$ x $[/tex], the function [tex]$ y = 2x^2 + 1 $[/tex] will produce a corresponding real number for [tex]$ y $.[/tex] There are no values of [tex]$ x $[/tex] for which the function becomes undefined or non-existent.

Graphically, this function represents a parabola that opens upwards, covering all real values of [tex]$ x $[/tex] along the x-axis. Therefore, the domain encompasses the entire real number line without any gaps or exclusions.

Other Questions

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