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3 years ago

15

Rationalise 2 divided by 2 square root 3

1 answer:

ElenaW [278]3 years ago

5 0

Answer:

$\displaystyle \frac{\sqrt{3}}{3}$

Step-by-step explanation:

$\displaystyle \frac{2}{2\sqrt{3}} = \frac{1}{\sqrt{3}} = \boxed{\frac{\sqrt{3}}{3}}$

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A piece of cardboard has the dimensions (x + 15) inches by (x) inches with the area of 60 in 2 . Write the quadratic equation th

pochemuha

Answer:

$x^2 + 15x - 60 = 0$

The actual dimension is 18.28 by 3.28

Step-by-step explanation:

Given

Dimension:

$(x + 15)\ by\ x$

$Area = 60in^2$

Required

Determine the quadratic equation and get the possible values of x

Solving (a): Quadratic Equation.

The cardboard is rectangular in shape.

Hence, Area is calculated as thus:

$Area = Length * Width$

$60= (x + 15) * x$

Open Bracket

$60= x^2 + 15x$

Subtract 60 from both sides

$x^2 + 15x - 60 = 0$

<em>Hence, the above represents the quadratic equation</em>

Solving (b): The actual dimension

First, we need to solve for x

This can be solved using quadratic formula:

$x = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}$

Where

$a = 1$

$b = 15$

$c = -60$

So:

$x = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}$

$x = \frac{-15 \± \sqrt{15^2 - 4*1*-60}}{2*1}$

$x = \frac{-15 \± \sqrt{225 + 240}}{2}$

$x = \frac{-15 \± \sqrt{465}}{2}$

$x = \frac{-15 \± \21.56}{2}$

Split:

$x = \frac{-15 + 21.56}{2}$ or $x = \frac{-15 - 21.56}{2}$

$x = \frac{6.56}{2}$ or $x = \frac{-36.36}{2}$

$x = 3.28$ or $x = -18.18$

But length can't be negative;

So:

$x = 3.28$

The actual dimensions: $(x + 15)\ by\ x$ is

$Length =3.28 +15$

$Length =18.28$

$Width = x$

$Width =3.28$

<em>The actual dimension is 18.28 by 3.28</em>

3 0

3 years ago

I keep trying to use the Pythagorean Theorem to find the missing sides length but it comes to a -31 then an Error when square ro

OverLord2011 [107]

Diagonal of the left triangle = ((8)^2+(7)^2)^0.5= (113)^0.5
x =( 12^2 -(113)^0.5)^2))^0.5=( 144- 113)^0.5= (31)^0.5= 5.57

For ur working, ur mistake lies in the line : x^2+12^2=10.6^2
It shld be 12^2= x^2+10.6^2

3 0

4 years ago

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What are the graphs?

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Janice has a box of colored pencils. She shares them equally with her friend Tracy. Her sister Nicole gives her two more colored

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Answer:

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Step-by-step explanation:

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Principal Howard ordered 116 shirts from the Brand Blast custom clothing shop for his staff members to wear during the school's

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Answer:

$13

Step-by-step explanation:

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