-4x+6+30 for some value of x, what is the value of -2x+5, for the same value of x?

(sin x)(tan x cos x - cot x cos x) = 1 - 2 cos2x

Aliun [14]

As

$\tan x=\dfrac{\sin x}{\cos x}$
$\cot x=\dfrac{\cos x}{\sin x}$

we have

$\sin x(\tan x\cos x-\cot x\cos x)=\sin x\left(\sin x-\dfrac{\cos^2x}{\sin x}\right)=\sin^2x-\cos^2x$

Recalling that $\cos2x=\cos^2x-\sin^2x$ , we end up with

$-\cos2x=1-2\cos2x$
$1=\cos2x$
$\implies2x=2n\pi$

(where $n$ is any integer)

$\implies x=n\pi$

5 0

3 years ago

Which of the following points is a solution of y > Ixl + 5?

Step2247 [10]

Answer:

B. (1,7)

Step-by-step explanation:

We can substitute the x and y values of each coordinate into the inequality and test if they work.

Let's start with A, 5 being y and 0 being x .

$5 > |0|+5\\5> 0+5\\5 > 5$

5 IS NOT greater than 5, they are the exact same, so A is out.

Let's try B, 1 being x and 7 being y.

$7 > |1| + 5\\7 > 1 + 5\\7 > 6$

7 IS greater than 6, so B. (1,7) does work for this inequality!

Let's do C for fun, when 7 is x and 1 is y.

$1 > |7| + 5\\1>7+5\\1>12$

1 IS NOT greater than 12, it is quite less than 12, so C doesn't work.

Therefore B. (1,7) works for the inequality of $y > |x|+5$ .

Hope this helped!

7 0

2 years ago

Given a polynomial f(x), if (x + 7) is a factor, what else must be true? f(0)=7 f(0)=-7 f(7)=0 f(-7)=0

Nataly [62]

F(-7)=0

Because that makes the (x+7) factor equal zero and any other factor multiplied by zero also results in zero.

7 0

3 years ago

Read 2 more answers

Which of the following could NOT be the lengths of the sides of a triangle?

Furkat [3]

Given:

Sides of triangles in the options.

To find:

Which could NOT be the lengths of the sides of a triangle.

Solution:

Condition for triangle:

Sum of two smaller sides of a triangle must be greater than the longest side.

In option A,

$5+5=10>5$

Sides 5 in, 5 in, 5 in are the lengths of the sides of a triangle.

In option B,

$10+15=25>20$

Sides 10 cm, 15 cm, 20 cm are the lengths of the sides of a triangle.

In option C,

$3+4=7>5$

Sides 3 in, 4 in, 5 in are the lengths of the sides of a triangle.

In option D,

$8+5=13$

Since, the sum of two smaller sides is less than the longest side, therefore the sides 8 ft, 15 ft, 5 ft are not the lengths of the sides of a triangle.

Therefore, the correct option is D.

8 0

2 years ago

The mean per capita income is 15,451 dollars per annum with a variance of 298,116. What is the probability that the sample mean

docker41 [41]

Answer: 0.5467

Step-by-step explanation:

Let X be the random variable that represents the income (in dollars) of a randomly selected person.

Given : $\mu=15451$