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3 years ago

How do find length and width if you have the area?

Mathematics

1 answer:

chubhunter [2.5K]3 years ago

5 0

Answer:

Step-by-step explanation:

The area of a rectangle(A) related to the length (L) and WITDH (W) of its sides by the following Relationship:A=L W if you know the width is easy to find the length rearranging this equation to get L=A÷w if you know the length and want width rearranged to get W=A÷L this is the formula not the answer.

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A circle has the order pairs (-1, 2) (0, 1) (-2, -1) what is the equation . Show your work.

olga55 [171]

We know that:

$(x-a)^2+(y-b)^2=r^2$

is an equation of a circle.

When we substitute x and y (from the pairs we have), we'll get a system of equations:

$\begin{cases}(-1-a)^2+(2-b)^2=r^2\\(0-a)^2+(1-b)^2=r^2\\(-2-a)^2+(-1-b)^2=r^2\end{cases}$

and all we have to do is solve it for a, b and r.

There will be:

$\begin{cases}(-1-a)^2+(2-b)^2=r^2\\(0-a)^2+(1-b)^2=r^2\\(-2-a)^2+(-1-b)^2=r^2\end{cases}\\\\\\
\begin{cases}1+2a+a^2+4-4b+b^2=r^2\\a^2+1-2b+b^2=r^2\\4+4a+a^2+1+2b+b^2=r^2\end{cases}\\\\\\
\begin{cases}a^2+b^2+2a-4b+5=r^2\\a^2+b^2-2b+1=r^2\\a^2+b^2+4a+2b+5=r^2\end{cases}\\\\\\
$

From equations (II) and (III) we have:

$\begin{cases}a^2+b^2-2b+1=r^2\\a^2+b^2+4a+2b+5=r^2\end{cases}\\--------------(-)\\\\a^2+b^2-2b+1-a^2-b^2-4a-2b-5=r^2-r^2\\\\-4a-4b-4=0\qquad|:(-4)\\\\\boxed{-a-b-1=0}$

and from (I) and (II):

$\begin{cases}a^2+b^2+2a-4b+5=r^2\\a^2+b^2-2b+1=r^2\end{cases}\\--------------(-)\\\\a^2+b^2+2a-4b+5-a^2-b^2+2b-1=r^2-r^2\\\\2a-2b+4=0\qquad|:2\\\\\boxed{a-b+2=0}$

Now we can easly calculate a and b:

$\begin{cases}-a-b-1=0\\a-b+2=0\end{cases}\\--------(+)\\\\-a-b-1+a-b+2=0+0\\\\-2b+1=0\\\\-2b=-1\qquad|:(-2)\\\\\boxed{b=\frac{1}{2}}\\\\\\\\a-b+2=0\\\\\\a-\dfrac{1}{2}+2=0\\\\\\a+\dfrac{3}{2}=0\\\\\\\boxed{a=-\frac{3}{2}}$

Finally we calculate $r^2$ :

$a^2+b^2-2b+1=r^2\\\\\\\left(-\dfrac{3}{2}\right)^2+\left(\dfrac{1}{2}\right)^2-2\cdot\dfrac{1}{2}+1=r^2\\\\\\\dfrac{9}{4}+\dfrac{1}{4}-1+1=r^2\\\\\\\dfrac{10}{4}=r^2\\\\\\\boxed{r^2=\frac{5}{2}}$

And the equation of the circle is:

$(x-a)^2+(y-b)^2=r^2\\\\\\\left(x-\left(-\dfrac{3}{2}\right)\right)^2+\left(y-\dfrac{1}{2}\right)^2=\dfrac{5}{2}\\\\\\\boxed{\left(x+\dfrac{3}{2}\right)^2+\left(y-\dfrac{1}{2}\right)^2=\dfrac{5}{2}}$

7 0

3 years ago

The ratio of red poms to yellow poms on a float is 5 to 7. if there are 392 yellow poms on the float, how many red poms are ther

Marysya12 [62]

Ratio is written in x:y. therefore for this case, red:yellow
5 : 7

since the question states that there are 392 yellow poms, the 7 units represents 392 yellow poms. now you have to gind what is one unit and then multiply by 5 to find the number of red poms.

392 represents 7 units
1 unit: 392/7=56
5 units: 5×56=280 red poms

therefore the answer is 280 red poms which is C.

4 0

3 years ago

2x3 + x2 + 7x - 6)-(- 2x + 10x + 10x+9)

AVprozaik [17]

Answer:

2x³ + x² - 11x - 15

Step-by-step explanation:

Step 1: Write out expression

2x³ + x² + 7x - 6 - (-2x + 10x + 10x + 9)

Step 2: Distribute negative

2x³ + x² + 7x - 6 + 2x - 10x - 10x - 9

Step 3: Combine like terms (x)

2x³ + x² + 9x - 10x - 10x - 9 - 6

2x³ + x² - x - 10x - 9 - 6

2x³ + x² - 11x - 9 - 6

Step 4: Combine like terms (constants)

2x³ + x² - 11x - 15

5 0

3 years ago

Help me with this question please im confuesd thank you

Leto [7]

Answer:

32inches

Step-by-step explanation:

i don't know if that's correct but since the diameter is 8 inches and the wheel would turn four times it will be 32

5 0

3 years ago

Marcus earns $13.00 per hour by walking the neighbor's dogs. He walked the dogs for

Lisa [10]

Answer:

$52.00

Step-by-step explanation:

if he makes 13.00 per hour, for four hours, you just times 13 by 4 to get 52.

4 0

3 years ago

Read 2 more answers