Please help me solve 1/3x>-4

If sin ⁡x=725, and 0 ∠ x ∠ pi/2, what is the tan (x - pi/4)

krok68 [10]

$Tan(x-\frac{\pi }{4}) = \frac{-17}{31}$

<u>Step-by-step explanation:</u>

Here we have , sin ⁡x=7/25( given sin x = 725 which is not possible ) , $0$ . Let's find tan (x - pi/4):

⇒ $Tanx = \frac{sinx}{cosx}$

⇒ $Tanx = \frac{sinx}{\sqrt{1-(sinx)^{2}}}$

⇒ $Tanx = \frac{\frac{7}{25}}{\sqrt{1-(\frac{7}{25})^{2}}}$

⇒ $Tanx = {\frac{7}{25}}{\sqrt{(\frac{625}{625-49})^{}}}$

⇒ $Tanx = {\frac{7}{25}}(\frac{25}{24} )$

⇒ $Tanx = {\frac{7}{24}}$

Now , $Tan(x-\frac{\pi }{4}) = \frac{Tanx - Tan(\frac{\pi }{4} )}{1+ Tanx(Tan(\frac{\pi }{4} )}$

⇒ $Tan(x-\frac{\pi }{4}) = \frac{Tanx -1}{1+ Tanx(1)}$

⇒ $Tan(x-\frac{\pi }{4}) = \frac{\frac{7}{24} -1}{1+\frac{7}{24} }$

⇒ $Tan(x-\frac{\pi }{4}) = \frac{\frac{7-24}{24} }{\frac{7+24}{24} }$

⇒ $Tan(x-\frac{\pi }{4}) = \frac{-17}{24} (\frac{24}{31} )$

⇒ $Tan(x-\frac{\pi }{4}) = \frac{-17}{31}$

7 0

3 years ago

A polynomial has zeros x=0, x= -3, X = 4. What are some possible factored equations for this fourth degree polynomial.

kati45 [8]

Answer:

$x^{2} (x + 3)(x - 4)$

Step-by-step explanation:

You can multiply this out to get the full equations.

It's to the 4th degree so the x on the outside has to be squared to add the fourth degree.

To get other zeros:

x + 3 = 0

x = -3

x - 4 = 0

x = 4

Hope this helped. :0)

5 0

2 years ago

For which value of b can the expression x2 + bx + 18 be factored?

Dmitry_Shevchenko [17]

Answers:

b = -19
b = -11
b = -9
b = 19
b = 11
b = 9

====================================================

Explanation:

Here are all the ways to multiply to 18 when using integers only:

-1*(-18) = 18
-2*(-9) = 18
-3*(-6) = 18
1*18 = 18
2*9 = 18
3*6 = 18

Sum each pair of factors to find out a possible value of b.

-1 + (-18) = -19
-2 + (-9) = -11
-3 + (-6) = -9
1 + 18 = 19
2 + 9 = 11
3 + 6 = 9

Therefore, the possible values of b are

b = -19
b = -11
b = -9
b = 19
b = 11
b = 9

which are the final answers.

----------------------

An example:

Let's say b = 11. This would mean $x^2+bx+18$ becomes $x^2+11x+18$

It would factor to $(x+2)(x+9)$ since it was stated earlier that:

2+9 = 11

2 * 9 = 18

You can use the FOIL rule, distributive property, or the box method to confirm that $x^2+11x+18 = (x+2)(x+9)$ is a true equation for all real numbers x.

This same idea applies for the other values of b.

----------------------

If you're curious why this works, consider multiplying the two factors (x+p) and (x+q)

Use the FOIL rule to get $(x+p)(x+q) = x^2+qx+px+pq = x^2+(p+q)x + pq$

The middle term $(p+q)x$ has the components add to the coefficient, while those same two components multiply to get the last term. This is why when factoring we're looking for two numbers that multiply to 18, and also add to the value of b (which in the case of the last example was 11).

7 0

2 years ago

John read the first 114 pages of a novel, which was 3 pages less than start fraction, 1/3 1, divided by, 3, end fraction of the

anyanavicka [17]

HERE IS YOUR ANSWER

<span>114 = (1/3)p - 3
HOPED I HELPED AND SMASH THAT THANKS BUTTON AND ADD ME AS A FRIEND</span>

3 0

2 years ago

Can someone help me understand how to add and subtract negatives and positives?

IgorC [24]

Okay, as you know, adding a positive and a positive gives you a bigger positive number. e.g 21 + 19 = 40.

Subtracting a positive from a positive might give you a negative number or a smaller positive number. e.g 21 - 19 = 2 or 20 - 24 = -4. That's simple, we all learned this! :)

Adding two negatives (e.g -4 + -5) will always give you a negative number. To make it easier, just think of the numbers only (4, 5), add them together, and then just put a negative sign by the answer (e.g 4 + 5 = 9 so put - to make -9).

Subtracting two negatives can be a bit tricky! When we say, for example, -5 - -4, we must turn the negative number that was to the right of the minus ( -4) into a positive number! So now it becomes -5 +4 ! And then you get your answer. (which is -1).

Adding a positive to a negative can give you a positive or a negative answer. It just depends which number is "bigger". E.g -20 + 31. << 31 is the "bigger" number, and it is a positive, so we know that our answer will be positive. E.g -20 + 9. << 20 is the "bigger" number (even though it's a negative but forget about that) and it is negative, so we know that our answer will be negative.

Adding a negative to a positive can give you a negative or a positive answer. Like I said, it depends on which number is "bigger". e.g 20 + -9 . We can just remove the + sign and it now becomes 20 -9, which is easier to understand. 20 is the bigger number, and it is positive, so we get a positive answer. e.g 20 + -30 becomes 20 -30 and -30 is the "bigger" number and it is negative, so we'll get a negative answer.

Subtracting a negative from a positive does the thing I mentioned earlier: e.g 20 - -9. The -9 is right of the minus sign and becomes positive: 20 +9! :)

Subtracting a positive from a negative, like I said, depends on which number is "bigger". e.g -30 - 9 (we know 9 is positive even though we don't show the + sign). Now, to make it simple, just block out the - sign by the 30 so it becomes 30 - 9. You know what that answer is: 21. But because -30 is "bigger", and it is a negative number, the answer will be negative so it's -21. E.g -30 - 42 << Block out the - sign by the 30, and 42 is the "bigger" number, so the answer will be a positive. Just look at the difference between "bigger" number and the smaller number (without signs) . That'll give your answer. 42 - 30 = 12. 42 was the "bigger" number and a positive, and we looked at the difference. :)

3 0

3 years ago