Find the following product.
(4a +6) (3a? - 3a+6)
(4a + 6) (3a2- 3a +6) =

Answers

Answer 1

Answer:

12a^3+6a^2+6a+36

Step-by-step explanation:

Sana makatulong!

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Solve 2cos^2x + cosx − 1 = 0 for x over the interval [0, 2 pi ).

Answers

$2cos^(2)(x) + cos(x)-1 = 0$

This could also be written as, where $a = cos(x)$

$2a^(2) + a - 1 = 0$

This would factorize to give:

$(2a-1)(a+1)=0$

So we can factorize our original expression:

$2cos^(2)(x) + cos(x)-1 = 0 \n \n (2cosx - 1)(cosx+1) = 0$

We can then solve for $x$ as we would with a normal quadratic:

$2cosx -1 =0 \n \n cosx = (1)/(2) \n \n x = cos^(-1)( (1)/(2) ) \n \n x = ( \pi )/(3), (5 \pi )/(3)$

And also:

$cos(x)+1 = 0 \n \n cos(x)= -1 \n \n x = cos^(-1)(1) \n \n x = 0, 2 \pi$

So our values for $x$ are:

$x =0, ( \pi )/(3), (5 \pi )/(3), 2 \pi$

As: $0 \leq x\ \textless \ 2 \pi$

Our final solutions for $x$ are:

$x = \boxed{0, ( \pi )/(3), (5 \pi )/(3)}$

The solutions to the equation 2cos²(x) + cos(x) - 1 = 0 over the interval [0, 2π) are x = π/3, 5π/3, and π.

We have,

To solve the equation 2cos²(x) + cos(x) - 1 = 0 over the interval [0, 2π), we can use a substitution technique.

Let's substitute cos(x) with a variable, say, u.

The equation becomes:

2u^2 + u - 1 = 0.

Now, we can factorize the quadratic equation:

(2u - 1)(u + 1) = 0.

Setting each factor equal to zero, we have:

2u - 1 = 0 or u + 1 = 0.

Solving these equations separately, we find:

2u = 1 or u = -1.

For 2u = 1, we get u = 1/2. Taking the inverse cosine of 1/2,

We have cos(x) = 1/2.

For u = -1, we get u = -1. Taking the inverse cosine of -1, we have cos(x) = -1.

Now, we need to determine the solutions for x within the given interval [0, 2π).

For cos(x) = 1/2, the solutions within the interval are x = π/3 and x = 5π/3.

For cos(x) = -1, the solution within the interval is x = π.

Therefore,

The solutions to the equation 2cos²(x) + cos(x) - 1 = 0 over the interval [0, 2π) are x = π/3, 5π/3, and π.

Learn more about equations here:

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What is the simplest form of 9/24, 14/24, 10/15, 10/12,18/27 and 10/15?

Answers

S.F. of 9/24 = 3/8
S.F. of 14/24 = 7/12
S.F. of 10/15 = 2/3
S.F. of 10/12 = 5/6
S.F. of 18/27 = 2/3
S.F. of 10/15 = 2/3

Hope this helps!

1. 3/8
2. 7/12
3. 2/3
4. 5/6
5. 2/3
6. 2/3

I guess the third and last one is repeated. But, I wrote the answer anyways.
Hope this helps! :)

Why is important to maintain an assessment’s validity, reliability, and equity in testing?

Answers

why is important to maintain an assessment’s validity, reliability, and equity in testing?

Answer: Reliability refers to the degree to which scores from a particular test are consistent from one use of the test to the next. ... Ultimately then, validity is of paramount importance because it refers to the degree to which a resulting score can be used to make meaningful and useful inferences about the test taker

Sin x = 0.5
What is the value of x?

Answers

To find the value of x, we need to take the inverse sin (also known as arcsin) of 0.5:

x = arcsin(0.5)

Using a calculator, we find that x is approximately 30 degrees (or π/6 radians).

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