All categories

3 years ago

A square has a perimeter of 12x^4 + 36x^3 inches. What is the length of each side?

Mathematics

1 answer:

Ghella [55]3 years ago

5 0

Answer:

3x^4+9x^3

Step-by-step explanation:

Perimeter of a square is expressed as;

P = 4L

L is the length of each side

Given

P = 12x^4 + 36x^3

12x^4 + 36x^3 = 4L

4(3x^4+9x^3) = 4L

Divide both sides by 4

4(3x^4+9x^3)/4 = 4L/4

(3x^4+9x^3) = L

L = 3x^4+9x^3

Hence the length of each side is 3x^4+9x^3

You might be interested in

Subtract 7x+4 from 2x-10

KengaRu [80]

Answer:

-5x-6

Step-by-step explanation:

2x-10

7x+4

____

-5x-6

+ - = the greater numbers sign

4 0

2 years ago

Read 2 more answers

A roulette wheel has the numbers 1 through 36, 0, and 00. A bet on four numbers pays 8 to 1 (that is, if you bet $1 and one of t

Natasha_Volkova [10]

Answer:

Lose $0.05

Step-by-step explanation:

There are 38 possible spots on the roulette wheel (numbers 1 to 36, 0 and 00).

If the player can choose four numbers on single $1 bet, his chances of winning (W) and losing (L) are as follows:

$P(W) = \frac{4}{38} \\P(L) = 1-P(W) = 1-\frac{4}{38} \\P(L) = \frac{34}{38}$

The expected value of the bet is given by the probability of winning multiplied by the payout ($8), minus the probability of losing multiplied by the bet cost ($1)

$EV=\frac{4}{38}*\$8 -\frac{34}{38}*\$1\\EV= -\$0.05$

On each bet, the player is expected to lose 5 cents ($0.05).

4 0

3 years ago

PLEASE HURRY IM TIMED!!!

andriy [413]

Answer-

A. Brandon’s sound intensity level is 1/4th as compared to Ahmad’s.

Solution-

Given that, loudness measured in dB is

$L=10\log \frac{I}{I_0}$

Where,

I = Sound intensity,

I₀ = 10⁻¹² and is the least intense sound a human ear can hear

Given in the question,

I₁ = Intensity at Brandon's = 10⁻¹⁰

I₂ = Intensity at Ahmad's = 10⁻⁴

Then,

$L_1=10\log \frac{I_1}{I_0}=10\log \frac{10^{-10}}{10^{-12}}=10\log \frac{1}{10^{-2}}=10\log 10^{2}=2\times10\log 10=20$

$L_2=10\log \frac{I_2}{I_0}=10\log \frac{10^{-4}}{10^{-12}}=10\log \frac{1}{10^{-8}}=10\log 10^{8}=8\times10\log 10=80$

$\therefore \frac{L_1}{L_2} =\frac{20}{80} =\frac{1}{4}$

5 0

3 years ago

What is the equation for the plane illustrated below?

TiliK225 [7]

Answer:

Hence, none of the options presented are valid. The plane is represented by $3 \cdot x + 3\cdot y + 2\cdot z = 6$ .

Step-by-step explanation:

The general equation in rectangular form for a 3-dimension plane is represented by:

$a\cdot x + b\cdot y + c\cdot z = d$

Where:

$x$ , $y$ , $z$ - Orthogonal inputs.

$a$ , $b$ , $c$ , $d$ - Plane constants.

The plane presented in the figure contains the following three points: (2, 0, 0), (0, 2, 0), (0, 0, 3)

For the determination of the resultant equation, three equations of line in three distinct planes orthogonal to each other. That is, expressions for the xy, yz and xz-planes with the resource of the general equation of the line:

xy-plane (2, 0, 0) and (0, 2, 0)

$y = m\cdot x + b$

$m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Where:

$m$ - Slope, dimensionless.

$x_{1}$ , $x_{2}$ - Initial and final values for the independent variable, dimensionless.

$y_{1}$ , $y_{2}$ - Initial and final values for the dependent variable, dimensionless.

$b$ - x-Intercept, dimensionless.

If $x_{1} = 2$ , $y_{1} = 0$ , $x_{2} = 0$ and $y_{2} = 2$ , then:

Slope

$m = \frac{2-0}{0-2}$

$m = -1$

x-Intercept

$b = y_{1} - m\cdot x_{1}$

$b = 0 -(-1)\cdot (2)$

$b = 2$

The equation of the line in the xy-plane is $y = -x+2$ or $x + y = 2$ , which is equivalent to $3\cdot x + 3\cdot y = 6$ .

yz-plane (0, 2, 0) and (0, 0, 3)

$z = m\cdot y + b$

$m = \frac{z_{2}-z_{1}}{y_{2}-y_{1}}$

Where:

$m$ - Slope, dimensionless.

$y_{1}$ , $y_{2}$ - Initial and final values for the independent variable, dimensionless.

$z_{1}$ , $z_{2}$ - Initial and final values for the dependent variable, dimensionless.

$b$ - y-Intercept, dimensionless.

If $y_{1} = 2$ , $z_{1} = 0$ , $y_{2} = 0$ and $z_{2} = 3$ , then:

Slope

$m = \frac{3-0}{0-2}$

$m = -\frac{3}{2}$

y-Intercept

$b = z_{1} - m\cdot y_{1}$

$b = 0 -\left(-\frac{3}{2} \right)\cdot (2)$

$b = 3$

The equation of the line in the yz-plane is $z = -\frac{3}{2}\cdot y+3$ or $3\cdot y + 2\cdot z = 6$ .

xz-plane (2, 0, 0) and (0, 0, 3)

$z = m\cdot x + b$

$m = \frac{z_{2}-z_{1}}{x_{2}-x_{1}}$

Where:

$m$ - Slope, dimensionless.

$x_{1}$ , $x_{2}$ - Initial and final values for the independent variable, dimensionless.

$z_{1}$ , $z_{2}$ - Initial and final values for the dependent variable, dimensionless.

$b$ - z-Intercept, dimensionless.

If $x_{1} = 2$ , $z_{1} = 0$ , $x_{2} = 0$ and $z_{2} = 3$ , then:

Slope

$m = \frac{3-0}{0-2}$

$m = -\frac{3}{2}$

x-Intercept

$b = z_{1} - m\cdot x_{1}$

$b = 0 -\left(-\frac{3}{2} \right)\cdot (2)$

$b = 3$

The equation of the line in the xz-plane is $z = -\frac{3}{2}\cdot x+3$ or $3\cdot x + 2\cdot z = 6$

After comparing each equation of the line to the definition of the equation of the plane, the following coefficients are obtained:

$a = 3$ , $b = 3$ , $c = 2$ , $d = 6$

Hence, none of the options presented are valid. The plane is represented by $3 \cdot x + 3\cdot y + 2\cdot z = 6$ .

8 0

3 years ago

If a phone card is used to make a long distance phone call, you are charged $0.50 per call plus an additional $0.31 per minute.

Nikitich [7]

Part A: c for cost. c=0.31m+0.5

0.31m is the cost per minute. 0.5 is cost per call.

Part B: 0.31m+0.5=5.15 to solve we must rearrange.

subtract 0.5 from each side giving us 0.31m=4.85

divide by 0.31 giving us m=15.65

7 0

3 years ago