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sveta [45]
2 years ago
10

What is the area of a rectangle with a width of x2 + x + 1 and a length of 3x2 - 2x - 1?

Mathematics
1 answer:
nata0808 [166]2 years ago
7 0

Answer:

x^{4} + 3x³ - 3x - 1

Step-by-step explanation:

The area (A) of a rectangle is calculated as

A = lw ( l is the length and w the width ) , thus

A = (3x² - 2x - 1)(x² + x + 1)

Each term in the second factor is multiplied by each term in the first factor, then

A = 3x²(x² + x + 1) - 2x(x² + x + 1) - 1(x² + x + 1) ← distribute parenthesis

   = 3x^{4} + 3x³ + 3x² - 2x^{4} - 2x² - 2x - x² - x - 1 ← collect like terms

   = x^{4} + 3x³ - 3x - 1

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part 2. Find the value of the trig function indicated, use for that Pythagorean theorem to find the third side if you need it.​
andreev551 [17]

Answer:  \bold{5)\ \cos \theta=\dfrac{\sqrt{11}}{6}\qquad 6)\ \tan \theta =\dfrac{8}{17}\qquad 7)\ \cos \theta = \dfrac{4}{3}\qquad 8)\ \cos \theta = \dfrac{\sqrt{10}}{10}}

<u>Step-by-Step Explanation:</u>

Pythagorean Theorem is: a² + b² = c²  , <em>where "c" is the hypotenuse</em>

5)\ \cos \theta=\dfrac{\text{side adjacent to}\ \theta}{\text{hypotenuse of triangle}}=\dfrac{3\sqrt{11}}{18}\quad \rightarrow \large\boxed{\dfrac{\sqrt{11}}{6}}

Note: (15)² + (3√11)² = hypotenuse²   →   hypotenuse = 18

6)\ \cos \theta=\dfrac{\text{side adjacent to}\ \theta}{\text{hypotenuse of triangle}}=\dfrac{8}{17}\quad =\large\boxed{\dfrac{8}{17}}

Note: 8² + 15² = hypotenuse²   →   hypotenuse = 17

7)\ \tan \theta=\dfrac{\text{side opposite to}\ \theta}{\text{side adjacent to}\ \theta}=\dfrac{20}{15}\quad \rightarrow \large\boxed{\dfrac{4}{3}}

Note: hypotenuse not needed for tan

8)\ \cos \theta=\dfrac{\text{side adjacent to}\ \theta}{\text{hypotenuse of triangle}}=\dfrac{2}{2\sqrt{10}}\quad =\large\boxed{\dfrac{\sqrt{10}}{10}}

Note: 2² + 6² = hypotenuse²   →   hypotenuse = 2√10

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2 years ago
Solve for all values of x by factoring.<br> x^2 + 4x – 30 = -3x
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Answer:

{x}^{2}  + 4x - 30 =  - 3x \\{x}^{2}  + 7x - 30 = 0 \\  {x}^{2}  - 3x + 10x - 30 = 0 \\ x(x - 3) + 10(x - 3) = 0 \\ (x - 3)(x + 10) = 0 \\  \boxed{x = 3} \\  \boxed{x =  - 10}

<h3><em><u>x=3 or x=-10</u></em> is the right answer.</h3>

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