What is the length of each side of a square that has the same area as a rectangle that has a length of 12.2 in. and a width of 16.6 in.?Round to the nearest tenth.

Answers

Answer 1

Answer: Area of the rectangle= l*w
Area of the rectangle= 202. 52 square inches

Area of the square={202.52}
Length of the square= 14.23 units

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Is -5 equal to 5? I need help

Answers

Answer:

yes

Step-by-step explanation:

Yes It is I think! There’s no difference so it should be yes! It’s the same thing! If you do get this wrong I am very sorry! I just think it is!

Analyze the function f(x) = - 2 cot 3x. Include: - Domain and range
- Period
- Two Vertical Asymptotes

Answers

Answer and Explanation :

Given : Function $f(x)=-2\cot 3x$

To find :

1) Domain and range

2) Period

3) Two Vertical Asymptotes

Solution :

1) Domain is defined as the set of possible values of x where function is defined.

$f(x)=-2\cot 3x$

$f(x)=-2((\cos 3x)/(\sin 3x))$

For domain, $\sin3x\neq 0$

So, $\sin3x\neq \sin n\pi$

$3x\neq n\pi$

$x\neq (n\pi)/(3)$

The value of x is define as $x\neq n\pi+(-1)^n(\pi)/(3)$

The domain of the function is all real numbers except $x\neq n\pi+(-1)^n(\pi)/(3)$

The range is defined as all the y values for every x.

So, The range of the function is all real numbers.

2) The general form of the cot function is $y=A\cot (Bx-C)+D$

Where, Period is $P=(\pi)/(|B|)$

On comparing, B=3

So, The period of the given function is $P=(\pi)/(|3|)$

3) Vertical asymptote is defined as the line which approaches to infinity but never touches the line.

The vertical asymptote is at $x= n\pi+(-1)^n(\pi)/(3)$ where function is not defined.

The two vertical asymptote is

Put n=0,

$x= (0)\pi+(-1)^(0)(\pi)/(3)$

$x=(\pi)/(3)$

Put n=1,

$x= (1)\pi+(-1)^(1)(\pi)/(3)$

$x=\pi-(\pi)/(3)$

$x=(2\pi)/(3)$

So, The two vertical asymptote are $x=(\pi)/(3),(2\pi)/(3)$

The domain for the function is:
all real numbers except n π/3 where n is an an integer

The range for the function is:
all real numbers

The period is
π/3

Vertical asymptotes
x = n π/3 where n is an integer

Which strategie would eliminate a variable in the system of equations? −x+6y=8 7x−y=−2

Answers

Answer:

substitution (or addition)

Step-by-step explanation:

A simple strategy for this system is to use substitution. The first equation is easily solved for x, so you could substitute that into the second equation:

x = 6y -8

7(6y -8) -y = -2 . . . . . x variable eliminated

The second equation is easily solved for y, so you could substitute that into the first equation.

y = 7x +2

-x +6(7x +2) = 8 . . . . . y-variable eliminated

The "addition" method is always a good way to eliminate a variable.

When the coefficient of a variable in one equation is a divisor of the coefficient of that variable in the other equation, a simple multiplication and addition will do.

To make the coefficient of x in the first equation the opposite of the coefficient of x in the second, multiply the first equation by 7. Adding that result to the second equation will eliminate x:

7(-x +6y) +(7x -y) = 7(8) +(-2)

42y -y = 56 -2 . . . . . . x-variable eliminated

Likewise, the second equation can be multiplied by 6 and added to the first to eliminate the y-variable:

(-x +6y) +6(7x -y) = (8) +6(-2)

-x +42x = -4 . . . . . . . . y-variable eliminated

It is often the case that using either substitution or "addition" requires about the same amount of work.

Here, the solutions are (x, y) = (-4/41, 54/41).

Final answer:

To eliminate a variable in the given system of equations, you can use the elimination method. By multiplying the equations by suitable numbers and adding them, you can cancel out one of the variables, simplifying the process to solve for the other variable.

Explanation:

You can eliminate a variable in the given system of equations: −x+6y=8 and 7x-y=−2 by using either the substitution method or the elimination method. For this scenario, the elimination method will work best.

Strategy:

To eliminate x, you should first multiply the first equation by 7 and the second by 1, resulting in the equations: -7x+42y=56 and 7x-y=-2
Adding these two equations together, the x terms (-7x and 7x) cancel out, giving us: 41y=54.
Finally, you divide both sides by 41 to solve for y. This process effectively eliminates the variable x from the equation, providing a solution for y.

This variable eliminationstrategy lets you solve one equation for one variable, simplifying the process of finding solutions for a system of equations.

Learn more about Variable Elimination here:

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Identify the domain of the equation y = x2 − 6x + 1.x ≤ 3

x ≥ −8

x ≥ −2

All real numbers

Answers

Find the domain by finding where the equation is defined. The range is the set of values that correspond with the domain...(I'm including the range..)

Domain:(-∞,∞),{x║x ∈ R}

Range:(-8,∞),{y║y≥-8}

Susan wants to buy a paddle boat for $840. She'll pay 20% down and pay the rest in six monthly installments. What will be the amount of each monthly payment?