Brian needs to start planning for an upcoming move. He is choosing two different size boxes to pack the majority of his stuff. The volume of the first is 1,728 in³ and the second is 13,824 in³. What is the ratio of the surface areas? Given that the boxes are cubes, what is the surface area of the larger of the two boxes?

Answer:

  a = 3x^2 +9x

Step-by-step explanation:

Put the given dimensions in the formula and simplify. The distributive property is useful.

  a = (1/2)bh

  a = (1/2)(6x)(x+3) = 3x(x +3)

  a = 3x^2 +9x

Answer: 11 stamps per page

Step-by-step explanation: 132 divided by 12

Answer:

B {6, 6, 7}

Step-by-step explanation:

Which set of numbers may represent the lengths of the sides of a triangle? (A) {2,5,9} (B) {6,6,7} (C) {6,4,2} (D) {7,8,1}

For a given triangle with 3 sides, the sun of the length of any two sides must be greater Than the third side. This can be expressed mathematically as;

Let the side be ;

x, y and z

Then:

x > (y + z) or

y > (x + z) or

z > (x + y)

For A{2,5,9}

(2 + 5) < 9 (does not meet criteria)

For B {6,6,7}

(6 +6) > 7

(7 +6) > 6

Meets all criteria

For C {6,4,2}

(4 +2) is not greater Than 6 (does not meet criteria)

For D {7,8,1}

(7 +1) is not greater Than 8 ( does not meet criteria)

Answer:

x = -34 , y = 31

Step-by-step explanation suing Gaussian elimination:

Solve the following system:

{2 x + 3 y = 25

3 x + 4 y = 22

Express the system in matrix form:

(2 | 3

3 | 4)(x

y) = (25

22)

Write the system in augmented matrix form and use Gaussian elimination:

(2 | 3 | 25

3 | 4 | 22)

Swap row 1 with row 2:

(3 | 4 | 22

2 | 3 | 25)

Subtract 2/3 × (row 1) from row 2:

(3 | 4 | 22

0 | 1/3 | 31/3)

Multiply row 2 by 3:

(3 | 4 | 22

0 | 1 | 31)

Subtract 4 × (row 2) from row 1:

(3 | 0 | -102

0 | 1 | 31)

Divide row 1 by 3:

(1 | 0 | -34

0 | 1 | 31)

Collect results:

Answer: {x = -34 , y = 31

Answer:

x = 45°, y = 53°, z = 82°

Step-by-step explanation:

x is the first angle, y is the second, and z is the third.

The sum of the second and third, which is denoted by y + z, is 3 times the measure of the first, which is just x. So, we have:

y + z = 3 * x

Additionally, the third angle, z, is 29 more than the second, y, so:

z = 29 + y

We also know that the sum of the three is 180, so:

x + y + z = 180

Let's substitute y + z in the last equation with 3 * x:

x + y + z = 180

x + 3x = 180

4x = 180

x = 45

Now, we know that y + z = 3 * 45 = 135. We also know that z = 29 + y, so substitute 29 + y in for z in y + z = 135:

y + z = 135

y + (29 + y) = 135

2y + 29 = 135

2y = 106

y = 53

Finally, use this value of y to solve for z:

z = 29 + y

z = 29 + 53 = 82

Thus, the angles are x = 45°, y = 53°, and z = 82°.

~ an aesthetics lover

Answer:

2 works

-3 is extraneous

Step-by-step explanation:

sqrt(x + 7) - 1 = x                      Add 1 to both sides

sqrt(x + 7) = x + 1                     Square both sides

(x + 7) = (x + 1 )^2

x + 7 = x^2 + 2x + 1                Subtract x from both sides

0 = x^2 + x + 1 -7                    

0 = x^2 + x - 6                        This will factor

(x + 3)(x - 2)  = 0                      Find the values for x

x + 3 = 0

x = - 3

x - 2 = 0

x = 2

Now you must check this to see if both values work

sqrt(-3 + 7)  - 1 = -3

sqrt(4) - 1 = -3

2 - 1 =? - 3

1 does not equal - 3. Therefore - 3 is extraneous. Try x = 2

sqrt(2 + 7) - 1 = 2

sqrt(9) - 1 = 2

3 - 1 = 2

2 = 2

Answer:

A. 18

Step-by-step explanation:

Order of Operations: BPEMDAS

Step 1: Write out expression

12(20 - 18) - 3(6)

Step 2: Multiply parenthesis

12(20 - 18) - 18

Step 3: Parenthesis

12(3) - 18

Step 4: Multiply

36 - 18

Step 5: Subtract

18

Answer:

t = 0.7 h

The time he rode at a slower speed is 1.2 h

Step-by-step explanation:

-The question involves algebra, to find the time the distance formula is used involving the values ​​of distance, time and speed.

- distance = speed 1 * time 1 + speed 2 * time 2

If Oscar traveled for t minutes at 9mph and it took him 15 minutes longer than when he traveled at 16mph it means that:

speed 1 * time 1 + 30 minutes.

But 30 minutes converted to hours is 0.5 hours

22 miles = 9 * (t + 0.5) + 16 * t

22 = 9t + 4.5 + 16t

17.5 = 25t

17.5 / 25 = t

The answer is: t = 0.7

Checking the value in the equation:

22 miles = 9 * (t + 0.5) + 16 * t

22 = 9 * (0.7 + 0.5) + 16 * 0.7

22 = 9 * 1.2 + 11.2

22 = 10.8 + 11.2

22 = 22

Answer:

  (A, B, C) = (8, 17, 23) inches

Step-by-step explanation:

We can let A, B, and C represent the corresponding side lengths. Then we are given ...

  A + B + C = 48 . . . . . . the perimeter is 48 inches

  B = A + 9 . . . . . . . . . . . B is 9 inches longer than A

  C = 2A +7 . . . . . . . . . . the base (remaining side) is 7 inches more than ...

Substituting for B and C in the first equation, we have ...

  A + (A+9) +(2A+7) = 48

  4A = 32 . . . . . . . . . . . . . . collect terms, subtract 16

  A = 8

  B = A+9 = 17

  C = 2A +7 = 23

Side A is 8 inches, side B is 17 inches, and side C is 23 inches.

Answer:

B

Good luck in Geometry my guy!

Answer:

15+(-37)

initial 15

fell 37 so -37

Answer:

B, or the one labeled 15 + (-37)

Step-by-step explanation:

It starts with 15 degrees F, which is positive.

Then, you'd add -37 degrees.

Adding -37 degrees to 15 is the same as subtracting 37 from 15.

Good luck mate :)

Answer:

[tex]\mathbf{S =6 \sqrt{1 + \dfrac{\pi^2}{9} }+ \dfrac{18}{\pi} In (\dfrac{\pi}{3}+ \sqrt{1+ \dfrac{\pi^2}{9}})}[/tex]

Step-by-step explanation:

Given that

curve [tex]y = \dfrac{\pi x}{3}, 0 \leq x \leq 3[/tex]

The objective is to find the area of the surface obtained by rotating the above curve about the x-axis.

Suppose f is positive and posses a continuous derivative,

the surface is gotten by the rotating the curve about the x-axis is:

[tex]S = \int ^b_a 2 \pi f (x) \sqrt {1 + (f' (x))^2 } \ dx[/tex]

The derivative of the function [tex]y' = \dfrac{\pi}{3} cos \dfrac{\pi x}{3}[/tex]

As such, the surface area is:

[tex]S = \int ^3_0 2 \pi sin \dfrac{\pi x}{3} \sqrt {1 +(\dfrac{\pi}{3}cos \dfrac{\pi x}{3})^2 } \ dx[/tex]

Suppose ;

[tex]u = \dfrac{\pi}{3}cos \dfrac{\pi x}{3}[/tex]

[tex]du = -( \dfrac{\pi}{3})^2 sin \dfrac{\pi x}{3} \ dx[/tex]

If x = 0 , then [tex]u = \dfrac{\pi}{3}cos \dfrac{\pi (0)}{3} = \dfrac{\pi}{3}[/tex]

If x = 3 , then [tex]u = \dfrac{\pi}{3}cos \dfrac{\pi (3)}{3}[/tex]

[tex]u = \dfrac{\pi}{3}(-1)[/tex]

[tex]u = -\dfrac{\pi}{3}[/tex]

The equation for S can now be rewritten as:

[tex]S = \int^3_0 2 \pi sin \dfrac{\pi x}{3} \sqrt{1+(\dfrac{\pi}{3} cos \dfrac{\pi x}{3})^2 }\ dx[/tex]

[tex]S = 2 \pi \int ^{-\frac{\pi}{3} }_{\frac{\pi}{3}}(-\dfrac{9 \ du }{\pi^2} ) \sqrt{1+u^2}[/tex]

[tex]S = 18 \pi * \dfrac{1}{\pi ^2 } \int ^{-\frac{\pi}{3}}_{\frac{\pi}{3}} \sqrt{1+u^2} \ du[/tex]

[tex]S = \dfrac{18} {\pi} \int ^{-\frac{\pi}{3}}_{\frac{\pi}{3}} \sqrt{1+u^2} \ du[/tex]

[tex]S = \dfrac{18} {\pi} (2 \int ^{-\frac{\pi}{3}}_{0} \sqrt{1+u^2} \ du)[/tex]

since [tex](\int ^a_{-a} fdx = 2\int^a_0 fdx , f= \sqrt{1+u^2} \ is \ even )[/tex]

Applying the formula:

[tex]\int {\sqrt{1+x^2}} \ d x= \dfrac{x}{2} \sqrt{1+x^2}+ \dfrac{1}{2} In ( x + \sqrt{1+x^2})[/tex]

[tex]S = \dfrac{36}{x}[ \dfrac{u}{2} \sqrt{1+u^2}+ \dfrac{1}{2} \ In (u+ \sqrt{1+u^2}) ] ^{\frac{\pi}{3}}_{0}[/tex]

[tex]S = \dfrac{36}{x}[ \dfrac{\dfrac{\pi}{3}}{2} \sqrt{1+\dfrac{\pi^2}{9}}+ \dfrac{1}{2} \ In (\dfrac{\pi}{3}+ \sqrt{1+\dfrac{\pi^2}{9}})-0 ][/tex]

[tex]S =6 \sqrt{1 + \dfrac{\pi^2}{9} }+ \dfrac{18}{\pi} In (\dfrac{\pi}{3}+ \sqrt{1+ \dfrac{\pi^2}{9}})[/tex]

Therefore, the exact area of the surface is [tex]\mathbf{S =6 \sqrt{1 + \dfrac{\pi^2}{9} }+ \dfrac{18}{\pi} In (\dfrac{\pi}{3}+ \sqrt{1+ \dfrac{\pi^2}{9}})}[/tex]

The area of the surface is,[tex]S = 6\sqrt{1+\dfrac{\pi ^2}{3}} + \dfrac{18}{3}\ ln (\dfrac{\pi }{3}+\sqrt{1+\dfrac{\pi ^2} {9}})[/tex].

Given that,

The exact area of the surface obtained by rotating the curve about the x-axis. y = sin πx\3 , 0 ≤ x ≤ 3.

We have to determine,

Area of the surface obtained by rotating the curve.

According to the question,

Suppose f is positive and posses a continuous derivative,

The surface is gotten by the rotating the curve about the x-axis is:

Area of the surface is given by,

[tex]S = \int\limits^b_a {2\pi f(x) .\sqrt{1+ (f'(x))} } \, dx[/tex]

The given curve is x-axis,

[tex]y = \dfrac{sin\pi x}{3}[/tex]

The derivative of the function is,

[tex]\dfrac{dy}{dx} =\dfrac{\pi }{3} \dfrac{ cos\pi x}{3}[/tex]

The surface area is,

[tex]S = \int\limits^b_a {2\pi f(x) .\sqrt{1+(\dfrac{\pi }{3} \dfrac{ cos\pi x}{3})^2} }}} \, dx[/tex]

Substitute the value of f(x),

[tex]S = \int\limits^3_0{2\pi\dfrac{sin\pi x}{3} .\sqrt{1+(\dfrac{\pi }{3} \dfrac{ cos\pi x}{3})^2} }}} \, dx[/tex]

Suppose;

[tex]u = \dfrac{\pi }{3}cos\dfrac{\pi x}{3}dx\\\\\du =( \dfrac{-\pi }{3})^2 sin\dfrac{\pi x}{3}dx\\\\if \ x = 0, \ then \ u = \dfrac{\pi }{3}cos\dfrac{\pi (0)}{3} = \dfrac{\pi }{3}\\\\if \ x = 3, \ then \ u = \dfrac{\pi }{3}cos\dfrac{\pi (3)}{3} = \dfrac{\pi }{3}(-1)= \dfrac{-\pi }{3}[/tex]

Then,

[tex]S = \int\limits^3_0{2\pi\dfrac{sin\pi x}{3} .\sqrt{1+(\dfrac{\pi }{3} \dfrac{ cos\pi x}{3})^2} }}} \, dx\\\\S = 2\pi \int\limits^{\frac{-\pi}{3}}_ \frac{\pi }{3} (\dfrac{-9du}{\pi ^2})\sqrt{1+u^2} \ du\\\\S = 18\pi \times \dfrac{1}{\pi ^2}\int\limits^{\frac{-\pi}{3}}_ \frac{\pi }{3} \sqrt{1+u^2} \ du\\\\S = \dfrac{18}{\pi}\int\limits^{\frac{-\pi}{3}}_ {0} 2\sqrt{1+u^2} \ du\\\\\\[/tex]

Since,

[tex](\int\limits^a_{-a}{f} \, dx = 2\int\limits^a_0 {f} \, dx , \ f = \sqrt{1+u^2}\ is \ even)[/tex]

By applying the formula to solve the given integration,

[tex]\int {\sqrt{1+x^2} } \, dx = \dfrac{x}{2}\sqrt{1+x^2} + \dfrac{1}{2} \ ln(x+\sqrt{1+x^2})\\\\S = \dfrac{36}{2} [ \dfrac{u}{2} \sqrt{1+u^2} + \dfrac{1}{2} \ ln(u+\sqrt{1+u^2})}]^{\frac{\pi }{3}}_0\\\\[/tex]

[tex]S = \dfrac{36}{2} [ \dfrac{\dfrac{\pi }{3}}{2} \sqrt{1+\dfrac{\pi^2 }{9}} + \dfrac{1}{2} \ ln(\dfrac{\pi }{3}+\sqrt{1+\dfrac{\pi ^2} {9}}-0)]\\\\S = 6\sqrt{1+\dfrac{\pi ^2}{3}} + \dfrac{18}{3}\ ln (\dfrac{\pi }{3}+\sqrt{1+\dfrac{\pi ^2} {9}})[/tex]

Hence, The area of the surface is,[tex]S = 6\sqrt{1+\dfrac{\pi ^2}{3}} + \dfrac{18}{3}\ ln (\dfrac{\pi }{3}+\sqrt{1+\dfrac{\pi ^2} {9}})[/tex]

To know more about Integration click the link given below.

https://brainly.com/question/17256859

Answer:

Options (B) and (C)

Step-by-step explanation:

We have to form a function which has following characteristics,

1). Its range is all real numbers

 Which means graph of the given function starts from negative side of the y-axis (-∞) and goes towards positive direction of the y-axis (+∞).

It's a typical characteristic of odd degree polynomial/function.

2). The graph has exactly two x-intercepts.

  Which means when we put f(x) = 0, we get exactly two values of x.

Therefore, function will be, f(x) = x³ + x²

Range of the function → (-∞, ∞) Or a set of all real numbers.

x-intercepts → f(x) = x³ + x² = 0

                             x²(x + 1) = 0

                             x = -1, 0

Therefore, Options (B) and (C) will be the answer.

Answer:

A is 1.6 and ion the other ones

Answer:

approximately 26.7 million

Step-by-step explanation:

Let x be the number of cruise passengers in 2017.

6.7% increase of x gives us 28.5 m cruise passengers in 2018.

Thus, 106.7 % of x = 28.5

[tex] \frac{106.7}{100} * x = 28.5 [/tex]

[tex] \frac{106.7x}{100} = 28.5 [/tex]

Multiply both sides by 100

[tex] \frac{106.7x}{100} * 100 = 28.5*100 [/tex]

[tex] 106.7x = 2850 [/tex]

Divide both sides by 106.7

[tex] \frac{106.7x}{106.7} = \frac{2850}{106.7} [/tex]

[tex] x = 26.7 [/tex] (approximated)

Number of passengers in 2017 must have been approximately 26.7 million

Answer:

-8 degrees

Step-by-step explanation:

4-12 = -8

It dropped 12 degrees in 7 hours.

Answer: -8°

Step-by-step explanation:

4 - 12

Answer:

Cosec θ = – 25/24

Step-by-step explanation:

From the question given, we obtained the following information:

Tan θ = – 24/7

Cosec θ =?

Tan θ is negative in the forth quadrant.

Please see attached photo.

Tan θ = Opposite /Adjacent

Opposite = – 24

Adjacent = 7

Hypothenus = x

Thus, we can obtain the value of x by using the pythagoras theory as illustrated below:

x² = (–24)² + 7²

x² = 576 + 49

x² = 625

Take the square root of both side

x = √625

x = 25

Next, we shall determine Sine θ. This can be obtained as follow:

Opposite = – 24

Hypothenus = 25

Sine θ = ?

Sine θ = Opposite /Hypothenus

Sine θ = –24/25

Finally, we shall determine the Cosec θ. This can be obtained as follow:

Cosec θ = 1 /Sine θ

Sine θ = –24/25

Cosec θ = 1 ÷ –24/25

Cosec θ = 1 × – 25/24

Cosec θ = – 25/24

Answer:

Step-by-step explanation:

5(-3)^2 - 2

5(9) - 2

45 - 2 = 43

One example is the idea of two parts of a book that open up. Each flat part is a plane and the two planes intersect along the spine of the book.

Another example would be a wall intersecting with the floor. Both are flat surfaces.

A third example would be a laptop's screen as one plane and the keyboard as the other plane. They intersect at the hinge of the laptop.

For each example, the surface has a finite amount of area and it doesn't extend forever in all four directions. Theoretically, a plane is where the flat surface extends in all four directions infinitely. Though of course, real life has limitations but the idea is still applicable in a way.

Note how for each example, the two planes intersect to form a line. Also, each plane must be flat without bending or curving in any way.

Answer:

50

Step-by-step explanation:

8 + 10a - 3 + 5a   when a=3

8+10(3)-3+5(3)=

8+30-3+15=

38+15-3=50

Answer:

D. 327.25

Step-by-step explanation:

You start out with a gross pay of $415.00. When you have a deduction from your gross pay, it means it gets subtracted. So subtract the deductions of 48, 31.25, and 8.50 from 415 and it leaves you with 327.25.

415 48-31.25-8.50 = 327.25

Answer:

[tex]0 \leq x \leq 100[/tex]

0, 40, and 80 are the values that work for this compound inequality.

Step-by-step explanation:

To create a compound inequality, we have to examine the conditions for [tex]x[/tex] to work.

Since [tex]x[/tex] can not be below 0° C, that means that [tex]x[/tex] must be greater than or equal to 0.

Which is represented as [tex]x\geq 0[/tex], or [tex]0\leq x[/tex].

Since [tex]x[/tex] can not be above 100° C, that means [tex]x[/tex] must be less than 100.

Which is represented as [tex]x \leq 100[/tex].

We can combine both inequalities into one, where [tex]x[/tex] is shared between the two. This creates [tex]0\leq x \leq 100[/tex].

Let's test each value of [tex]x[/tex] .

0 is equal to 0 and less than 100, so it works.

40 is greater  than 0 and less than 100, so it works.

80 is greater  than 0 and less than 100, so it works.

120 is greater  than 0 and greater than 100, so it doesn't work.

160 is greater  than 0 and greater than 100, so it doesn't work.

Hope this helped!

Answer:

Hey there!

There are actually multiple answers.

7 and 14 have a GCF (greatest common factor) of 7, and so do 7 and 7.

Let me know if this helps :)

Answer:

answers are:

7 and 14

The factors of 7 is:  1, 7

The factors of 14 is:  1, 2, 7, 14

28 and 7

Factors of 28:  1, 2, 4, 7, 14, 28

Facotrs of 7:  1, 7

Step-by-step explanation:

others:  

21, 3 is GCF is 3

The factors of 3 are: 1, 3

The factors of 21 are: 1, 3, 7, 21

7, 1 is GCF is 1

The factors of 1 are: 1

The factors of 7 are: 1, 7

Answer:

10

Step-by-step explanation:

Mathematical Formula: [tex]\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]

Therefore: [tex]\sqrt{\left(6-0\right)^2+\left(8-0\right)^2}[/tex]

Which = 10

Answer: 11 9/35

Step-by-step explanation: just add the whole number to the fraction.

Answer & Step-by-step explanation:

[tex]11+\frac{9}{35}[/tex]

Add the whole number to the fraction:

[tex]11 \frac{9}{35}[/tex]

:Done

Answer:

[tex]\sqrt{4}, \ \sqrt{9} \text{ are rational numbers.}[/tex]

Step-by-step explanation:

Hello,

[tex]\sqrt{n^2}=n \ for \ n\geq 0\\\\\text{For instance}\\\\\sqrt{2^2}=2=\sqrt{4}\\\\\sqrt{3^2}=3=\sqrt{9}[/tex]

Answer: Pick anyone that suits you

Step-by-step explanation:

Answer:

[tex]\large \boxed{\mathrm{Eight \ subtracted \ from \ the \ product \ of \ three \ and \ a \ number.}}[/tex]

Step-by-step explanation:

[tex]\sf 3n-8[/tex]

n is a number.

8 is subtracted from the product of 3 and a number.

The verbal expression would be :

Eight subtracted from the product of three and a number.