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2 years ago

How to solve a quadratic equation that does not factor?

1 answer:

7 0

Use the formula or complete the square.
The zeroes of the quadratic can be real and rational; real and irrational; complex conjugates.
If the quadratic is ax²+bx+c, x=(-b+√b²-4ac)/2a.
If b² > 4ac the solutions are real. If b²-4ac is a perfect square, the solutions are real and rational; otherwise they’re real but irrational.
If b² < 4ac the solutions are complex.

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Use the identity tan(theta) = sin(theta) / cos(theta) to show that tan(???? + ????) = tan(????)+tan(????) / 1−tan(????) tan(????

VMariaS [17]

Answer:

See the proof below.

Step-by-step explanation:

For this case we need to proof the following indentity:

$tan(x+y) = \frac{tan (x) + tan(y)}{1- tan(x) tan(y)}$

So we need to begin with the definition of tangent, we know that $tan (x) =\frac{sin(x)}{cos(x)}$ and we can do this:

$tan (x+y) = \frac{sin (x+y)}{cos(x+y)}$ (1)

We also have the following identities:

$sin (a+b) = sin (a) cos(b) + sin (b) cos(a)$

$cos(a+b)= cos(a) cos(b) - sin(a) sin(b)$

Now we can apply those identities into equation (1) like this:

$tan (x+y) =\frac{sin (x) cos(y) + sin (y) cos(x)}{cos(x) cos(y) - sin(x) sin(y)}$ (2)

We can divide numerator and denominator from expression (2) by $\frac{1}{cos(x) cos(y)}$ we got this:

$tan (x+y) = \frac{\frac{sin (x) cos(y)}{cos (x) cos(y)} + \frac{sin(y) cos(x)}{cos(x) cos(y)}}{\frac{cos(x) cos(y)}{cos(x) cos(y)} -\frac{sin(x)sin(y)}{cos(x) cos(y)}}$

And simplifying we got:

$tan (x+y) = \frac{tan(x) + tan(y)}{1-tan(x) tan(y)}$

And that complete the proof.

8 0

3 years ago

Find each answer mentally.

trapecia [35]

Answer:

1: 1/4 dollars or .25 dollars or 25%

2: 150 cents

3: 100 cents

4: 1/100 dollars, or 0.01 dollars, or 1%

Step-by-step explanation:

8 0

2 years ago

What is the intermediate step in the form (x + a)? = b as a result of completing the

Mrac [35]

Answer:

(x + 9)² = 36

Step-by-step explanation:

Given

x² + 18x + 57 = 12 ( subtract 57 from both sides )

x² + 18x = - 45

To complete the square

add ( half the coefficient of the x- term)² to both sides

x² + 2(9)x + 81 = - 45 + 81

(x + 9)² = 36

5 0

2 years ago

Show work <br> 3=x+3-5x<br> Please help! Thanks!

alexandr1967 [171]

Answer:x=0

Step-by-step explanation:

subtract 3 from both sides

3=3=x+3-5x-3

simplify

0=x-5x

switch sides

x-5x

add similar elements ; x-5x=-4x

-4x=0

divided both side by -4

-4x/-4 . = . 0/-4

5 0

3 years ago

Read 2 more answers

Solve for x: 3 < x + 3 < 6

timurjin [86]

Answer:

x:3-3<x+3-3<6-3

0<x<3

do you get the process?

7 0

2 years ago