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3 years ago

Rationalize the denominator, then simplify 10/sqrt2

Mathematics

1 answer:

kupik [55]3 years ago

6 0

Answer:

$5\sqrt{2}$

Step-by-step explanation:

To rationalize the denominator, you need to multiply the numerator and denominator by the radical in the denominator (aka. a factor of 1):

$\frac{10}{\sqrt{2}}$

$\frac{10}{\sqrt{2}}*\frac{\sqrt{2}}{\sqrt{2}}$

$\frac{10\sqrt{2}}{2}$

$5\sqrt{2}$

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Step2247 [10]

Answer:

Area = 20 square centimeters

Step-by-step explanation:

V = lwh

V = lw3

V = 4x5x3

V = 60

A = lw

A = 4x5

A = 20

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3 years ago

There are 180 cars in a parking lot.30% are red .How many red cars are there ?

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4 years ago

Let $x_1,$ $x_2,$ $x_3,$ $x_4,$ $x_5$ be distinct positive integers such that $x_1 + x_2 + x_3 + x_4 + x_5 = 100.$ Compute the m

nikdorinn [45]

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Step-by-step explanation:

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3 years ago

Can someone walk me through these? I need a better understanding. Or maybe just one of them so I can understand and do the rest

Olin [163]

Step-by-step explanation:

I'll do the first one as an example.

"What are the coordinates of the point on the directed line segment from K(-5,-4) to L(5,1) that partitions the segment into a ratio of 3 to 2?"

Let's call the point we're trying to find P. Ratio of 3 to 2 means that the distance from K to P divided by the distance from P to L is 3/2.

KP / PL = 3 / 2

Which also means the horizontal distances and vertical distances between the points have a ratio of 3:2.

KxPx / PxLx = 3 / 2

KyPy / PyLy = 3 / 2

First, let's use the x coordinates:

(x − (-5)) / (5 − x) = 3 / 2

(x + 5) / (5 − x) = 3 / 2

2 (x + 5) = 3 (5 − x)

2x + 10 = 15 − 3x

5x = 5

x = 1

And now with the y coordinates:

(y − (-4)) / (1 − y) = 3 / 2

(y + 4) / (1 − y) = 3 / 2

2 (y + 4) = 3 (1 − y)

2y + 8 = 3 − 3y

5y = -5

y = -1

So the point P is at (1,-1).

4 0

4 years ago

Length of a rectangle is 5 cm longer than the width. Four squares are constructed outside the rectangle such that each of the sq

azamat

Answer:

The perimeter of rectangle is $18\ cm$

Step-by-step explanation:

Let

x-----> the length of the rectangle

y----> the width of the rectangle

we know that

$x=y+5$ ----> equation A

$120=xy+2x^{2}+2y^{2}$ ---> equation B (area of the constructed figure)

substitute the equation A in equation B

$120=(y+5)y+2(y+5)^{2}+2y^{2}$

$120=(y+5)y+2(y+5)^{2}+2y^{2}\\ 120=y^{2}+5y+2(y^{2}+10y+25)+2y^{2}\\ 120=y^{2}+5y+2y^{2}+20y+50+2y^{2}\\120=5y^{2}+25y+50\\5y^{2}+25y-70=0$

using a graphing calculator -----> solve the quadratic equation

The solution is

$y=2\ cm$

Find the value of x

$x=y+5 ----> x=2+5=7\ cm$

Find the perimeter of rectangle

$P=2(x+y)=2(7+2)=18\ cm$

8 0

3 years ago