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3 years ago

Simplify the expression 2√ 20 − 3√ 7 − 2√ 5 + 4√ 63 .

Mathematics

2 answers:

earnstyle [38]3 years ago

8 0

Answer:

The simplified form is,

$\boxed{\boxed{6\sqrt{5}+9\sqrt{7}}}$

Step-by-step explanation:

The given expression is,

$=2\sqrt{20}-3\sqrt{7}+2\sqrt{5}+4\sqrt{63}$

$=2\sqrt{4\times 5}-3\sqrt{7}+2\sqrt{5}+4\sqrt{9\times 7}$

$=2(\sqrt{4}\times \sqrt{5})-3\sqrt{7}+2\sqrt{5}+4(\sqrt{9}\times \sqrt{7})$

$=2(2\times \sqrt{5})-3\sqrt{7}+2\sqrt{5}+4(3\times \sqrt{7})$

$=4\sqrt{5}-3\sqrt{7}+2\sqrt{5}+12\sqrt{7}$

$=4\sqrt{5}+2\sqrt{5}+12\sqrt{7}-3\sqrt{7}$

$=6\sqrt{5}+9\sqrt{7}$

Tema [17]3 years ago

5 0

The simplified expression is 2sqrt(5)+9sqrt(7)

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let sin(θ) =3/5 and tan(y) =12/5 both angels comes from 2 different right trianglesa)find the third side of the two tringles b)

statuscvo [17]

In a right triangle, we haev some trigonometric relationships between the sides and angles. Given an angle, the ratio between the opposite side to the angle by the hypotenuse is the sine of this angle, therefore, the following statement

$\sin (\theta)=\frac{3}{5}$

Describes the following triangle

To find the missing length x, we could use the Pythagorean Theorem. The sum of the squares of the legs is equal to the square of the hypotenuse. From this, we have the following equation

$x^2+3^2=5^2$

Solving for x, we have

$\begin{gathered} x^2+3^2=5^2 \\ x^2+9=25 \\ x^2=25-9 \\ x^2=16 \\ x=\sqrt[]{16} \\ x=4 \end{gathered}$

The missing length of the first triangle is equal to 4.

For the other triangle, instead of a sine we have a tangent relation. Given an angle in a right triangle, its tanget is equal to the ratio between the opposite side and adjacent side.The following expression

$\tan (y)=\frac{12}{5}$

Describes the following triangle

Using the Pythagorean Theorem again, we have

$5^2+12^2=h^2$

Solving for h, we have

$\begin{gathered} 5^2+12^2=h^2 \\ 25+144=h^2 \\ 169=h^2 \\ h=\sqrt[]{169} \\ h=13 \end{gathered}$

The missing side measure is equal to 13.

Now that we have all sides of both triangles, we can construct any trigonometric relation for those angles.

The sine is the ratio between the opposite side and the hypotenuse, and the cosine is the ratio between the adjacent side and the hypotenuse, therefore, we have the following relations for our angles

$\begin{gathered} \sin (\theta)=\frac{3}{5} \\ \cos (\theta)=\frac{4}{5} \\ \sin (y)=\frac{12}{13} \\ \cos (y)=\frac{5}{13} \end{gathered}$

To calculate the sine and cosine of the sum

$\begin{gathered} \sin (\theta+y) \\ \cos (\theta+y) \end{gathered}$

We can use the following identities

$\begin{gathered} \sin (A+B)=\sin A\cos B+\cos A\sin B \\ \cos (A+B)=\cos A\cos B-\sin A\sin B \end{gathered}$

Using those identities in our problem, we're going to have

$\begin{gathered} \sin (\theta+y)=\sin \theta\cos y+\cos \theta\sin y=\frac{3}{5}\cdot\frac{5}{13}+\frac{4}{5}\cdot\frac{12}{13}=\frac{63}{65} \\ \cos (\theta+y)=\cos \theta\cos y-\sin \theta\sin y=\frac{4}{5}\cdot\frac{5}{13}-\frac{3}{5}\cdot\frac{12}{13}=-\frac{16}{65} \end{gathered}$

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1 year ago

Penelope buys bracelets in bulk at a cost of $8 each to sell at her store. She uses a markup of 125%, which is added to the brac

navik [9.2K]

The correct answer is A. $18

8 x 125% or 8 x 1.25 = 10

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3 years ago

7 watermelons cost $8.96.Which equation would help determine the cost of the 5 watermelons? Into two fractions with a expontnet

mestny [16]

Answer:

hola CTM

Step-by-step explanation:

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3 years ago

A set of equations is given below:

ipn [44]

The correct answer is 'Equation F can be written as 2d + 1 = 3d + 7'. In order to find the answer to a system of equations, the two equations must be set equal to each other. For instance, if we had the equations x = y + 1 and x = 3y - 1, we would set the two equations equal to one another to find the answer.

x = y + 1
x = 3y - 1
y + 1 = 3y - 1
1 = 2y - 1
2 = 2y
1 = y

x = y + 1
x = 1 + 1
<span>x = 2

We can use this to solve the set of equations above.

</span><span>2d + 1 = 3d + 7
</span>1 = d + 7
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c = 2d + 1
c = 2(-6) + 1
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Hope this helps!

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3 years ago

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Answer:

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2 years ago