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Use the quadratic formula to solve 3x2 + 5x + 2 = 0.D. x = 2, –3

Neporo4naja [7]

Quadratic Formula:

-b +/-  √b² - 4ac
x = --------------------------
2a

In your equation 3x² + 5x + 2 = 0:

a = 3
b = 5
c = 2

Now, plug in these values into the formula.

-5 +/- √5² - 4(3)(2)    -5 +/- √25 - 4(6)
x = -------------------------------- ⇒ x = -----------------------------
2(3) 6

-5 +/- √25 -24 -5 +/- √1 -5 +/- 1
x = ------------------------ ⇒ x =  ---------------  ⇒ x = --------------
6 6 6

-5 +/- 1
Split x = ------------ into two solutions by solving it.
6

-5 + 1 -4
x = ------------ = ------
6 6

-5 - 1 -6
x = ----------- = ------ = -1
6 6

The two final solutions are x = -1 and x = -4/6

8 0

3 years ago

How many square feet of outdoor carpet will we need for this hole?

svlad2 [7]

Answer:

9.

Step-by-step explanation:

You would have to find the area of the triangle which is 1/2(bh) which would give you 9. So you would 9 feet of outdoor carpet. Which is actually already given to you as the area inside the triangle.

8 0

4 years ago

Read 2 more answers

Evaluate if x = 1 , y = 3 , and z = 5<br><br> |5z - 2y|

Aleks04 [339]

Answer:

1

Step-by-step explanation:

4 0

3 years ago

What is the quotient when the sum of 1,2 and 3 is divided by the product of 1,2 and 3

nexus9112 [7]

Answer: 1

<u>Explanation:</u>

sum = add

quotient = divide

product = multiply

$\frac{1+2+3}{1*2*3} = \frac{6}{6}$ = 1

5 0

3 years ago

Read 2 more answers

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

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

4 0

1 year ago