Match

The polygons are similar. Find the value of x and y.

harina [27]

Answer:

x = 9, y = 27

Step-by-step explanation:

Since the figures are similar then the ratios of corresponding sides are equal, that is

$\frac{x-1}{6}$ = $\frac{16}{12}$ ( cross- multiply )

12(x - 1) = 96 ( divide both sides by 12 )

x - 1 = 8 ( add 1 to both sides )

x = 9

Also

$\frac{y+1}{21}$ = $\frac{16}{12}$ ( cross- multiply )

12(y + 1) = 336 ( divide both sides by 12 )

y + 1 = 28 ( subtract 1 from both sides )

y = 27

3 0

3 years ago

A square has a perimeter of 8 cm. What is its area?

serious [3.7K]

A square has four sides which all have the same length.

So if we call the length of each side of the square 'a'

The sum of length of all the sides (the perimeter) will be ,

a + a + a + a = 4a

Now let's equal this to the perimeter to find the length of each side 'a'

$4a\quad =\quad 8\\ \\ a\quad =\quad \frac { 8 }{ 4 } \\ \\ a\quad =\quad 2$

So the length of each side of the square is 2 cm

To find area of a square we multiply the length of its two sides

So,

$a\cdot a$ is the area of the square,

$a\cdot a=\quad 2\cdot 2\quad =\quad 4\\ \\ 4\quad c{ m }^{ 2 }$

The answer :

$\boxed { 4\quad c{ m }^{ 2 } }$

6 0

4 years ago

Read 2 more answers

Find Integrating Fector: <br> ylogy dx + ( x-logy )dy=0

12345 [234]

Rewrite the ODE as

$y\log y\,\mathrm dx+(x-\log y)\,\mathrm dy=0\iff y\log y\dfrac{\mathrm dx}{\mathrm dy}+x=\log y$
$\dfrac{\mathrm dx}{\mathrm dy}=\dfrac1{y\log y}x=\dfrac1y$

so that it is now linear in $x$ . An integrating factor would

$\mu(y)=\exp\left(\displaystyle\int\frac{\mathrm dy}{y\log y}\right)=e^{\log(\log y)}=\log y$

Multiply both sides by $\mu(y)$ to get

$\log y\dfrac{\mathrm dx}{\mathrm dy}=\dfrac1yx=\dfrac{\log y}y$
$\dfrac{\mathrm d}{\mathrm dy}[x\log y]=\dfrac{\log y}y$
$x\log y=\displaystyle\int\frac{\log y}y\,\mathrm dy$
$x\log y=\dfrac12\log^2y+C$
$x=\dfrac12\log y+\dfrac C{\log y}$

4 0

4 years ago

Find the midpoint of the segment connecting (4,7) to (-2,3).

KonstantinChe [14]

If you put 2 points on a graph paper and connect them, you can find the midpoint pretty easily

8 0

3 years ago

A medical office is replacing their existing flooring with carpeting in the waiting and office areas and laminate flooring in th

Dmitrij [34]

So first, you would multiply 10 times 10 to get 100 square feet. And since there are 10 exam rooms, you multiply 100 to 10 and you would get 1000. Then to calculate the waiting area, you multiply 20 times 15 to get 300 square feet. Then the office area would be 25 times 20 which is 500. So you would add up 1000+300+500. The answer comes out as 1800 square feet. Hope this helped! Good luck!

3 0

3 years ago