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3 years ago

Simplify (6x2 - 3 + 5x3) - (4x3 - 2x2 - 16

Mathematics

1 answer:

Masteriza [31]3 years ago

8 0

Answer:

x^3 +8x^2 +13

Step-by-step explanation:

(6x^2 - 3 + 5x^3) - (4x^3 - 2x^2 - 16)

Distribute the minus sign

6x^2 - 3 + 5x^3 -4x^3 + 2x^2 + 16

Combine like terms

x^3 +8x^2 +13

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Five less than three times a number is 10

maw [93]

Answer:

x=5

Explanation:

3x-5=10

+5 +5

3x=15

3x/3=15/3

x=5

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3 years ago

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Find area and perimeter

PSYCHO15rus [73]

Answer: The simplest (and most commonly used) area calculations are for squares and rectangles. To find the area of a rectangle, multiply its height by its width. For a square you only need to find the length of one of the sides (as each side is the same length) and then multiply this by itself to find the area.

Step-by-step explanation:

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3 years ago

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

Which of the following is a complex number?

anyanavicka [17]

:C

: I took the quiz and got the answer correct.

Hope this helps❤️

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3 years ago

The solution generated by the calculator is 5.779E–8. Describe how to interpret the solution.

Lostsunrise [7]

Answer:

5.779 x 10^-8 =0.00000005779

Step-by-step explanation:

The E-8 at the end means the number is multiplied by 10^-8.

So 5.779E-8=5.779 x 10^-8

A negative power means move the decimal place that many places to the left

So 5.779 x 10^-8 =0.00000005779

5 0

3 years ago

Read 2 more answers

Simplify (6x2 - 3 + 5x3) - (4x3 - 2x2 - 16​

Simplify (6x2 - 3 + 5x3) - (4x3 - 2x2 - 16