The surface area of a box is 160. the length of the box is twice its width as well as 4 less than its height. how many units are in the height of the box? (the surface area of a box is the sum of the areas of all 6 of its rectangular faces.) aops

Answers

Answer 1

Width = n
Length = 2n
Height = 2n + 4
2 (n x 2n) = 4n^2
2 (n x (2n + 4)) = 4n^2 + 8n
2 (2n x (2n + 4)) = 8n^2 + 16n

4n^2 + 4n^2 + 8n + 8n^2 + 16n = 160
16n^2 + 24n = 160
(Divide everything by 8)
2n^2 + 3n = 20
2n^2 + 3n - 20 = 0
(2n - 5)(n + 4) = 0

n = 2.5 Or n = -4

However n can not be less than 0

So n = 2.5
Height =2n +4
=2(2.5) +4
=5+4
=9

Answer 2

Final Answer:

The height of the box is 9 units.

Explanation:

Let's denote the width of the box as w, the length as l, and the height as h. According to the problem, we have the following relationships:
l = 2w (the length is twice the width) and
l = h - 4 (the length is also 4 less than the height).

The surface area SA of a rectangular box is calculated by the formula:
SA = 2lw + 2lh + 2wh.

Given that the surface area is 160, we set up our equation:
160 = 2lw + 2lh + 2wh.

Now let's substitute the relations l = 2w and l = h - 4 into the surface area equation:
Since l = 2w, 160 = 2(2w)w + 2(2w)h + 2wh.

Simplifying the equation, we have:
160 = 4w² + 4wh + 2wh
160 = 4w² + 6wh

Now we use the fact that l = h - 4 to substitute for h:
h = l + 4
h = 2w + 4

Now substitute h back into the surface area equation:
160 = 4w² + 6w(2w + 4) ,

Expand the terms:
160 = 4w² + 12w^2 + 24w,

Combine like terms:
160 = 16w² + 24w

Now, we must solve for w. Let's move all terms to one side to solve the quadratic equation:
16w² + 24w - 160 = 0

Divide all terms by 8 to simplify:
2w² + 3w - 20 = 0

We can now attempt to factor the quadratic equation:
(2w - 5)(w + 4) = 0

This gives us two solutions:
2w - 5 = 0 or w + 4 = 0

Solving the first equation for w:
2w = 5,[tex]$ w = \frac{5}{2} $[/tex]

w = 5/2
We can disregard the second solution w + 4 = 0 for w, as it gives us a negative width, which isn't possible for a box.

Now that we have w, we can find h.
Using our earlier substitute for h:
h = 2w + 4 ,
[tex]h = 2 \cdot \frac{5}{2} + 4[/tex] ,
h = 5 + 4 ,
h = 9 .
Thus, the height of the box is 9 units.

Related Questions

What is the smallest integer greater than -1/2 .

Answers

0 is greater than - 1/2 and zero is an integer.

The correct answer to your question is... 0

look at the pictures below

Answers

the answer might be negative one over 4 because it is the same but the red line is on negative

what is the approximate distance between the points (-5 1) and (-2 3) on a coordinate grid

Answers

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\\\ \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ -5 &,& 1~) % (c,d) &&(~ -2 &,& 3~) \end{array}~~ d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[-2-(-5)]^2+[3-1]^2}\implies d=\sqrt{(-2+5)^2+(3-1)^2} \\\\\\ d=\sqrt{3^2+2^2}\implies d=\sqrt{13}[/tex]

The volume, V, of a soap bubble is related to its surface area, A. In cubic centimeters, this relationship is shown by the formula V = 0.094A 3/2. What is the surface area of a bubble with a volume of 5 cm3 ?

Answers

First let's rewrite the volume expression correctly:
V = 0.094 * (A) ^ (3/2)
Now we clear the area:
(A) ^ (3/2) = V / 0.094
A = (V / 0.094) ^ (2/3)
We now replace the volume:
A = (5 / 0.094) ^ (2/3)
A = 14.14364782 cm ^ 2
Answer:
The surface area of a bubble with a volume of 5 cm3 is:
A = 14.14364782 cm ^ 2

The surface area of a soap bubble with a volume of 5 cm³, given the relationship V = 0.094 [tex]A^{3/2[/tex], can be calculated by rearranging and solving the formula, resulting in an approximate surface area of 36.3 cm².

To find the surface area of a soap bubble with a volume of 5 cm³, using the given relationship V = 0.094 [tex]A^{3/2[/tex], we need to rearrange the formula to solve for A (the surface area). We will take the following steps to find A:

First, divide both sides of the equation by 0.094 to isolate [tex]A^{3/2[/tex] on one side:

[tex]A^{3/2[/tex] = V / 0.094

Next, substitute V = 5 cm³ into the equation:

[tex]A^{3/2[/tex] = 5 / 0.094

Calculate the right-hand side:

[tex]A^{3/2[/tex] ≈ 53.19

Finally, raise both sides of the equation to the power of 2/3 to solve for A:

A = [tex](53.19)^{2/3[/tex]

Calculating the right-hand side gives us the surface area A. After performing these calculations, we find that the surface area of a bubble with a volume of 5 cm³ is approximately 36.3 cm².

A customer buys 3 bottles of water for ninety-nine cents each seven percent tax on each bottle what is the total bill

Answers

$3.18 when the tax is applied to each bottle separately or at the end of the bill.

The bill before tax is
.. 3*$0.99 = $2.97

The tax is
.. 0.07*$2.97 = $0.2079 ≈ $0.21

The total bill, including tax is
.. $2.97 +0.21 = $3.18

______
This is how every bill is computed wherever you may shop. It is a good idea to figure this out.

Algebraically prove that X^3+10/x^3+9=1+ 1/x^3+9 where x is not equal to -3

Answers

Algebraically prove that X^3+10/x^3+9=1+ 1/x^3+9 where x is not equal to -3
[tex] \dfrac{x^3+10}{x^3+9}=1+\dfrac{1}{x^3+9} \\ \\ \\ \dfrac{x^3+10}{x^3+9}=\dfrac{(x^3+9)+1}{x^3+9}\\ \\ \\ \dfrac{x^3+10}{x^3+9}=\dfrac{x^3+10}{x^3+9} \\ \\ \\x\in R \qquad x\in (-\infty, +\infty) [/tex]

An angle measures 72° less than the measure of a complementary angle. What is the measure of each angle?

Answers

Complementary angles: Two angles that add to 90 degrees

Angle a: 90 degrees - 72 degrees = 18 degrees
Angle b: 72 degrees

Answer: [tex]81^{\circ}\ \text{ and }\ 9^{\circ}[/tex]

Step-by-step explanation:

We know that the sum of two complementary angles is [tex]90^{\circ}[/tex].

Given : An angle measures 72° less than the measure of a complementary angle.

Let x be the angle , then the measure of other angle will be x-72.

Since they area complementary , then we have

[tex]x+x-72=90\\\\\Rightarrow\ 2x=90+72\\\\\Rightarrow\ 2x=162\\\\\Rightarrow\ x=\dfrac{162}{2}=81[/tex]

Therefore, the measure of angles are :

[tex]81^{\circ}\ \text{ and }\ (81-72)^{\circ}=9^{\circ}[/tex]

The measure of dispersion which is not measured in the same units as the original data is the
a. variance
b. standard deviation
c. median
d. coefficient determination

Answers

Variance is not expressed in the same units as the original data.

Variance is measured by:

Finding the difference between the mean of a data set and the variables in the data set Squaring this difference Summing up the squares

Because variance is squared, it is no longer the same units as the rest of the data set. For instance, if the data set is in centimeters, the variance will be in centimeters².

In conclusion, the variance of a data set is not measured in the same unit as the data set.

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Final answer:

The measure of dispersion which is not measured in the same units as the original data is the variance.

Explanation:

The measure of dispersion which is not measured in the same units as the original data is the variance. The variance is a squared measure and does not have the same units as the data. On the other hand, the standard deviation is derived from the variance and it measures the spread in the same units as the data.

Then again, the standard deviation, which is the square foundation of the fluctuation, is estimated in similar units as the first information. It gives a proportion of the spread of the information that is all the more effectively interpretable. The middle is a proportion of focal inclination and doesn't give data about the scattering or spread of the information.

The coefficient of assurance, otherwise called R-squared, is a proportion of how well the relapse line fits the information and isn't straightforwardly connected with scattering.

Add the reciprocal of 1 1/5 to the sum of the numbers (+1.25) and (−1 3/4 ).

Answers

To find the reciprocal of a mixed number, we first convert it to an improper fraction. 1 1/5 = 5/5 + 1/5 (remember that 1 whole would have the same numerator and denominator) = 6/5.
The reciprocal is this number flipped, so 5/6.
To find the sum of 1.25 and -1 3/4, we will convert the decimal to a fraction. 0.25 is read as "twenty-five hundredths," so the fraction would be 25/100. This will simplify to 1/4, so 1.25 = 1 1/4.
1 1/4 + -1 3/4 = -2/4 = -1/2.
Now we add 5/6 + -1/2:
Find the least common denominator (LCD). 6 is the first number that both 6 and 2 will divide into evenly. This gives us 5/6 + -3/6 (we multiply 2 by 3 to get 6, so we multiply the numerator, -1, by 3 as well). This equals 2/6 which simplifies to 1/3.

The answer would be 1/3 after adding the reciprocal of 1 1/5 to the sum of the numbers (+1.25) and (−1 3/4 ).

What is a fraction?

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

It is given that:

The fraction is 1 1/5 = 6/5

The reciprocal of the above fraction = 5/6

= 1.25 - 1 3/4 + 5/6

= 1.25 - 7/4 + 5/6

= 1.25 - 11/12

= 4/12

= 1/3

Thus, the answer would be 1/3 after adding the reciprocal of 1 1/5 to the sum of the numbers (+1.25) and (−1 3/4 ).

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describe the vertical asymptotes) and holes) for the graph of y=(x+2)(x+4)/(x+4)(x+1)
A. asymtotes: x=-1 and hole: x=4
B. asymtotes: x=2 and hole: x=-1
C. asymtotes: x= -1 and hole: x=-4
D. asymtotes: x=1 and hole: x=4
Can someone plzzzz help me!??

Answers

For this case what you should do is check the points where the function is NOT defined.
The function is not defined for those values where the denominator is equal to zero.
We have then:
y = (x + 2) (x + 4) / (x + 4) (x + 1)
Studying the denominator:
(x + 4) (x + 1) = 0
x = -4
x = -1
Answer:
C. asymtotes: x = -1 and hole: x = -4

How would paying off the lowest outstanding balance credit card first be beneficial over paying off the one with the highest interest rate?

Answers

Final answer:

Paying off the lowest outstanding balance credit card first can be beneficial for motivation and momentum, even if it's not the most mathematically efficient approach.

Explanation:

When paying off credit card debt, it can be beneficial to start by paying off the credit card with the lowest outstanding balance. This approach is called the Snowball Method and is popularized by financial expert Dave Ramsey. The Snowball Method focuses on tackling the smallest debt first, regardless of the interest rate, as it provides a psychological boost and motivates individuals to continue paying off their debts.

By paying off the smallest debt first, you can quickly eliminate one of your credit card balances. This can give you a sense of accomplishment and momentum to continue paying off your other debts. It's important to note that while the Snowball Method may not be the most mathematically efficient approach in terms of saving on interest payments, it can be effective in helping individuals stay motivated and committed to paying off their debts.

What are the approximate solutions of 4x2 + 3 = −12x to the nearest hundredth?

x ≈ −3.23 and x ≈ 0.23
x ≈ −2.72 and x ≈ −0.28
x ≈ 0.28 and x ≈ 2.72
x ≈ −0.23 and x ≈ 3.23

Answers

First
[tex] 4x^{2} + 12x + 3 = 0 [/tex]
determine if this equation were factorable, it's not for this one
so I use quadratic formula, try to search the formula online

[tex]x1 = \frac{-12 + \sqrt{(12)^{2} - 4*4*3} } {2*4} = \frac{-12 + 4\sqrt{6} }{8} = \frac{4(-3 + \sqrt{6}) }{8} = \frac{-3 + \sqrt{6}}{2} = - 0.28[/tex]
[tex]x2 = \frac{-12 - \sqrt{(12)^{2} - 4*4*3} } {2*4} = \frac{-12 - 4\sqrt{6} }{8} = \frac{4(-3 - \sqrt{6}) }{8} = \frac{-3 - \sqrt{6}}{2} = - 2.72[/tex]

x ≈ −2.72 and x ≈ −0.28 is the solution

Calculus HELP PLEASE? A highway runs due north. A car traveling at 50 mph exits the highway at a 30° angle. After driving another 1.5 hours at the same speed and direction, how far away is the car from the highway?

Answers

check the picture below.

notice that the car exits the northbound highway, and whilst going at 50mph for 1.5 hours, that simply means going for 75 miles.

make sure your calculator is in Degree mode.

Answer:

37.5 miles is the answer.

Step-by-step explanation:

Since car is travelling with a speed = 50 mph

Angle between the highway and the track on which the car is travelling = 30°

Now we know sin∅ = distance between highway and the car/Distance traveled by the car on the new track

Distance traveled by the car in 1.5 hours = speed × time

= 50 × 1.5 = 75 mi.

Therefore sin 30° = x/75

x = 75×sin30° = 75 × 1/2 = 37.5 mi.

Therefore the answer is 37.5 mi away.

Complete the statement If x/7 = 5/3, then x+7/7 =?

Answers

Lets get started :)

[tex] \frac{x}{7} = \frac{5}{3} [/tex]
We can cross multiply, to find the value of x
3x = 7 x 5
3x = 35
We have to divide by 3 on either sides to isolate x
[tex] \frac{3x}{3} = \frac{35}{3} [/tex]
3 and 3 cancels out

x = [tex] \frac{35}{3} [/tex]

Then, x + [tex] \frac{7}{7} [/tex] ( 7 divided by 7 is 1)
[tex] \frac{35}{3} [/tex] + 1 = [tex] \frac{38}{3} [/tex]

A rectangular prism has a volume of 360 in3. If the height measures 4 in., which base measurements could the prism have? 4 in. by 20 in. 45 in. by 45 in. 6 in. by 15 in. 5 in. by 19 in.

Answers

V = 360 in³
Let Ab = area of the base
h = 4 in

V = Ab × h

360 = Ab × 4

Ab = 360 ÷ 4

Ab = 90 in²

Ab = l × w
The product of the base measurements must be 90.
90 = l × w

⇒ 6 in × 15 in = 90 in² ⇒ The base measurements could be: 6 in by 15 in

A circle has an arc of length 24pi that is intercepted by a central angle of 80 degrees. what is the radius of the circle?

Answers

circumference = 2pi r

80/360 x 2pi x r = 24pi
r = 54

Which values are solutions to the inequality below?
Check all that apply.
√x ≤ 11

a) 121
b) 120
c) 111
d) -10
e) 122
f) no solutions

Answers

Final answer:

The values that are solutions to the inequality √x ≤ 11 are 121, 120, and 111.

Explanation:

To find the values that are solutions to the inequality √x ≤ 11, we first need to square both sides of the inequality. This gives us x ≤ 121. So any value of x that is less than or equal to 121 will be a solution.

Now let's check each option:

a) 121: 121 is equal to 121, so it is a solution.b) 120: 120 is less than 121, so it is a solution.c) 111: 111 is less than 121, so it is a solution.d) -10: Negative numbers do not have real square roots, so -10 is not a solution.e) 122: 122 is greater than 121, so it is not a solution.f) no solutions: This option is not a valid solution.

In summary, the values that are solutions to the inequality √x ≤ 11 are: 121, 120, and 111.

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Group of kids rode horses to canyon. 20 eyes 30 legs between them. How many horses

Answers

If all were kids, there would be 20 legs. A horse has 2 more legs than a kid. The extra 10 legs can be attributed to there being 5 horses.

Final answer:

To solve this problem, we set up equations based on the total number of eyes and legs. By solving the system, we find that the group consists of 5 horses.

Explanation:

The question asks us to solve a problem involving a group of kids and horses by using the given information about the total number of eyes and legs. Since humans have two eyes and two legs, and horses have two eyes and four legs, we can set up a system of equations to find the solution.

Let's denote the number of kids as 'k' and the number of horses as 'h'. Since each human and horse has two eyes, the total number of eyes is given by the equation: 2k + 2h = 20. Similarly, the total number of legs is given by the equation: 2k + 4h = 30. Solving these equations will give us the number of kids and horses in the group.

Solving for 'k' from the first equation gives us k = 10 - h. Substituting this into the second equation gives us 2(10 - h) + 4h = 30. Simplifying this equation results in 20 - 2h + 4h = 30, which further simplifies to 2h = 10, and thus h = 5. Therefore, there are 5 horses in the group.

Given cos A = 0.25 find angle A in degrees. Round your answer to the nearest hundredth.

34.12°

123.98°

56.78°

75.52°

Answers

we have that
cos A=0.25
so
A=arc cos (0.25)-------> using a calculator----> A=75.5225°
Round to the nearest hundredth-----> A=75.52²

the answer is
the option 75.52°

Johnny is five years older than his brother. the sum of their ages is 37. how old is Johnny

Answers

Johnny is 21 years old.
If you take 21 and add 16, you get 37.

21+16= 37
21-16= 5

johnny is 21 years old

This figure shows circle Z with chords AB and RS . mAR=55° mRB=66° AB=8 m RS=8 m What is mRS?

Answers

m AR = 55°
m RB = 66°
Like AB=8 m =RS →m RS = m AB

m AB = m AR + m RB
m AB = 55° + 66°
m AB = 121°

m RS = m AB
M RS = 121°

Answer: m RS is 121°

Answer:

The correct answer is, mRs = 121°

Step-by-step explanation:

From figure we get ,

mAR=55° mRB=66° AB=8 m RS=8 m

To find mRS

Using given information we can write,

mAB = mAR + mRB = 55 + 66 = 121°

Since AB=8 m RS=8 m,

AB = RS

⇒ mAB = mRS

mAB = 121°

Therefore mRS = 121°

The correct answer is given by,

mRS = 121°

Answers anybody?????

Answers

The area is the same no matter how you calculate it.
.. (1/2)*20*12 = (1/2)*30*h
.. h = (2/3)*12 = 8 . . . . . feet

Use the quadratic formula to determine the exact solutions to the equation.

x^2−2x−4=0

Enter your answers in the boxes.

x=__ or x=___

Answers

Answer: " x = 1 + √5 " or " x = 1 − √5" .
______________________________________________________
Given:
______________________________________________________

" x² − 2x − 4 = 0 " ;
______________________________________________

Solve for "x" by using the "quadratic formula" :

Note: This equation is already written in "quadratic format" ; that is:

" ax² + bx + c = 0 " ; { "a [tex] \neq [/tex] 0" } ;

in which: "a = 1" {the implied coefficient of "1" ;
since "1", multiplied by any value, equals that same value};

"b = -2 " ;

"c = -4 " ;
_______________________________________________________
The quadratic equation formula:

x = { - b ± √(b² − 4 ac) } / 2a ; {"a[tex] \neq [/tex]0"} ;
______________________________________________________
Substitute our known values:
______________________________________________________

→ x = { - (-2) ± √[(-2)² − 4(1)(-4)] } / 2(1) ;

→ x = { 2 ± √(4 − 4(-4) } / 2 ;

→ x = { 2 ± √(4 − (-16) } / 2 ;

→ x = { 2 ± √(4 + 16) } / 2 ;

→ x = { 2 ± √(20) } / 2 ;

→ x = { 2 ± √4 √5} / 2 ;

→ x = { 2 ± 2√5} / 2 ;

→ x = 1 ± √5 ;

_______________________________________________________
→ "x = 1 + √5" or "x = 1 − √5" .
_______________________________________________________

The formula represents the surface area S of a cube with side lengths x.

S=6x^2

Solve for x.

Answers

The solution of x is √(S/6).

The formula to find the surface area of a cube with side lengths x is:

S = 6x2

To solve for x:

Divide both sides by 6: S/6 = x2

Take the square root of both sides to isolate x: x = √(S/6)

Compute the requested average. Tim Worker receives the following income monthly from a second job. Jan. Feb. Mar. Apr. May June $200 $150 $250 $260 $285 $380 What is his average pay? (To the nearest hundredth.)
254.17255.37257.83259.85

Answers

To find the average, simply add up the values of the money that Tim earned and divide it by the six months that he worked. In this case, it would be (200 + 150 + 250 + 260 + 285 + 380) = (1525 / 6 = 254.166). This gives a closest value of choice (A), which is $254.17 per month. or Ok, all you have to do is add all the money together then divide it by how many numbers there are which is 12.
200 + 150 + 250 + 260 + 285 + 380 + 200 + 225 + 200 + 250 + 220 + 150 = 2770

2770 divided by 12 =230.83 is the average

In finding the average of the monthly income, simply sum up all the values and divided by the total number of months. Hence, 200+150+250+260+285+380=1525. Divide 1525 dollars by 6 months. The answer is 254.17 dollars which is his average monthly pay.

All side lengths of ΔJKL equal 2 units. A transformation maps ΔJKL to ΔJ'K'L'. The length of side J'K' is 5 units. Is this a rigid transformation?

No, there is no one-to-one mapping of all the points of the pre-image to the image.
No, at least one segment length is not preserved, making this a nonrigid transformation.
Yes, the vertices of the pre-image map to the vertices of the image.
Yes, all of the side lengths of the pre-image are proportionate to the image.

Answers

no because at least one segment length is not preserved.
rigid means everything stays the same, but orientation sometimes changes.

No, at least one segment length is not preserved, making this a nonrigid transformation. Option B is correct.

What is geometric transformation?

It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.

It is given that, all side lengths of ΔJKL equal 2 units. A transformation maps ΔJKL to ΔJ'K'L'. The length of side J'K' is 5 units.

A transformation that leaves a geometric figure's size or shapes unchanged is known as a rigid transformation. It is a unique type of metamorphosis in which a figure's size or shape is left unchanged.

From the definition, it is obtained that there is no rigid transformation because at least one segment length is not preserved.

Thus, no at least one segment length is not preserved, making this a nonrigid transformation. Option B is correct.

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Explain why the function f(x)=x^2 is not invertible

Answers

It doesn't pass the horizontal line test. (A function will be invertible if a horizontal line only crosses its graph in one place, for any location of that line.)

When you reflect the curve across the line y=x, it becomes multiple-valued, hence its inverse is not a function.

Use the chart above to determine the premium for 10-year term insurance. $10,000 policy for a 35-year-old male. Premium = _____?

6.11

61.10

611.00

6,110.00

Answers

Answer:

Option B 61.10

Step-by-step explanation:

Given is a chart giving the premium to be paid for 10 year term insurance for different age groups for an amount of 1000 policy.

We have to calculate the premium for a 35 year old man for 10 year term insurance for 10000 policy.

From the chart we find that for a 35 year old man premium = 6.11

This premium is for 1000 dollars.

Since here sum assured is 10000 dollars, we get the premium

=6.11(10) = 61.10 dollars

Option B is correct

Premium = 61.10 dollars

The price of 6 pretzels is $5.10. Simon and Sofia bought 8 pretzels an shared the cost equally. How much did each person pay?

Answers

Answer:

$3.40

Step-by-step explanation:

To find out the amount each person paid, let's find the total cost of the pretzels first.

6 pretzels ----- $5.10

1 pretzel ----- $5.10 ÷6= $0.85

8 pretzels ----- 8($0.85)= $6.80

The total cost of 8 pretzels is thus $6.80.

Since the total cost was shared equally amongst two people, each person paid half of the total cost.

Amount each person paid

= $6.80 ÷2

= $3.40

By taking a quotient between the total cost and the number of people, we can see that each one pays $3.40

How much did each person pay?

We know that the price of 6 pretzels is $5.10, then the price for each pretzel is given by the quotient:

$5.10/6 = $0.85

We know that Simon and Sofia bought 8 pretzels, so they pay:

P = 8*$0.85 = $6.80

And they divide that evenly between the two, so we can take the quotient:

p = $6.80/2 = $3.40

That is the amount that each person pays.

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the inverse of an exponential function is the quadratic function? true or false?

Answers

False.

The inverse of an exponential function is a logarithmic function.

Hope this helps!

Other Questions

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