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2 years ago

The perimeter of a standard-sized rectangular rug is 36 is 36 ft. the length is 2 ft longer than the width. find the dimensions

1 answer:

4 0

The formula for the perimeter of a rectangle is P = 2L + 2W, where L is the length and W is the width. Because we don't know either the length or the width we can't solve the problem...too many unknowns. BUT we do have some information that will help with this problem. We are told that the length is 2 feet longer than the width, so we can use that: L = W+2. Now we can make the substitution into the formula along with the value for the perimeter that was given to us: 36=2(W+2) + 2W, and 36 = 2W + 4 + 2W; 36 = 4W + 4; 32 = 4W and W = 8. Now go back to where you said that the length is 2 feet longer than the width. If the width is 8, then 8+2 = 10 for the length.

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Whats going on in this attachment help thanks xD

rodikova [14]

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1 year ago

Q1.Simplify:

solniwko [45]

$\textbf{(i)}\\\\\{1^3 +2^3 \} \times \left(\dfrac 13 \right)^2\\\\=(1+8) \left(\dfrac 19 \right)\\\\=9\left(\dfrac 19 \right)\\\\=1\\\\$

$\textbf{(ii)}\\\\\{5^{-1}\times 4^{-1}\}^2\\\\=\left(5^{-1} \right)^2 \times \left(4^{-1} \right)^2~~~~~~~~~~~;[(ab)^m = a^mb^m]\\\\=5^{-2}\times 4^{-2}~~~~~~~~~~~~~~~~~~~~;[(a^m)^n = a^{mn}]\\\\=\dfrac 1{5^2} \times \dfrac 1{4^2}~~~~~~~~~~~~~~~~~~~~~~;\left[a^{-m} = \dfrac 1{a^m},~ a\neq 0 \right]\\\\=\dfrac{1}{400}\\\\=0.0025\\\\$

$\textbf{(iii)}\\\\\left\{ \left(\dfrac 13 \right)^{-2} \times \left( \dfrac 12 \right)^{-2}\right\}\div \left(\dfrac 14 \right)^{-3}\\\\\\=\left( \dfrac 13 \times \dfrac 12 \right)^{-2} \div\left(4^{-1}\right)^{-3}\\\\\\=\left(\dfrac 16 \right)^{-2} \div 4^3\\\\\\=\left(6^{-1} \right)^{-2}\div 4^3\\\\\\=6^2 \div 4^3\\\\\\=36\div 64\\\\\\=\dfrac{9}{16}\\\\\\=0.5625$

6 0

1 year ago

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What is the absolute value of 5 and 6

Sauron [17]

$|a|=a\ if\ a >0\\\\|0|=0\\\\|a|=-a\ if\ \ a \ \textless \ 0\\-------------------\\|5|=5\ because\ 5 \ \textgreater \ 0\\\\|6|=6\ because\ 6 \ \textgreater \ 0\\---------------\\Other\ examples:\\\\|-2|=-(-2)=2\ because\ -2 \ \textless \ 0\\|10|=10\ because\ 10 > 0\\|-5|=5\ because\ -5 \ \textless \ 0\\\vdots$

6 0

2 years ago

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Graph the linear equation:<br> 2x-y=4

juin [17]

Answer:

$Slope=2$

$x-intercept=\frac{4}{2} =2$

$y-intercept=\frac{4}{-1} =-4.00000$

Step-by-step explanation:

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

2*x-y-(4)=0

Step 1:

Equation of a Straight Line

Solve 2x-y-4 = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line 2x-y-4 = 0 and calculate its properties

Graph of a Straight Line :

( see attatchment)

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 4/-1 so this line "cuts" the y axis at y=-4.00000

y-intercept = 4/-1 = -4.00000

Calculate the X-Intercept :

When y = 0 the value of x is 2/1 Our line therefore "cuts" the x axis at x= 2.00000

x-intercept = 4/2 = 2

Calculate the Slope :

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is -4.000 and for x=2.000, the value of y is 0.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 0.000 - (-4.000) = 4.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

Slope = 2

Geometric figure: Straight Line

1. Slope = 2

2. x-intercept = 4/2 = 2

3. y-intercept = 4/-1 = -4.00000

- clarification for graph - green means rise red means run , bottom black is x intercept which is 2.000 under rise is y-intercept and under the y axis is 0.000 and -4.000.

8 0

2 years ago

Greatest common factor of 4ax^2+4ax+4a

Rina8888 [55]

Simplifying

4AX2 + 4AX + 4A = 0

Reorder the terms:

4A + 4AX + 4AX2 = 0

Solving

4A + 4AX + 4AX2 = 0

Solving for variable 'A'.

Move all terms containing A to the left, all other terms to the right.

Factor out the Greatest Common Factor (GCF), '4A'.

4A(1 + X + X2) = 0

Ignore the factor 4.

Subproblem 1

Set the factor 'A' equal to zero and attempt to solve:

Simplifying

A = 0

Solving

A = 0

Move all terms containing A to the left, all other terms to the right.

Simplifying

A = 0

Subproblem 2

Set the factor '(1 + X + X2)' equal to zero and attempt to solve:

Simplifying

1 + X + X2 = 0

Solving

1 + X + X2 = 0

Move all terms containing A to the left, all other terms to the right.

Add '-1' to each side of the equation.

1 + X + -1 + X2 = 0 + -1

Reorder the terms:

1 + -1 + X + X2 = 0 + -1

Combine like terms: 1 + -1 = 0

0 + X + X2 = 0 + -1

X + X2 = 0 + -1

Combine like terms: 0 + -1 = -1

X + X2 = -1

Add '-1X' to each side of the equation.

X + -1X + X2 = -1 + -1X

Combine like terms: X + -1X = 0

0 + X2 = -1 + -1X

X2 = -1 + -1X

Add '-1X2' to each side of the equation.

X2 + -1X2 = -1 + -1X + -1X2

Combine like terms: X2 + -1X2 = 0

0 = -1 + -1X + -1X2

Simplifying

0 = -1 + -1X + -1X2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Solution

A = {0}

3 0

2 years ago

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