If tan m =
and tan n = -6, what is the exact value of tan(m + n)?

Answer:

See below.

Step-by-step explanation:

These work just like ordinary algebraic expresssions, except you have to remember always:  i^2 = -1    i squared is negative one!

(4 - 3i)(4 + 3i)   "FOIL" the expression to get 16 - 3i + 3i - 9i^2.  But i^2 = -1, so this is the same as 16 - 3i + 3i + 9.  Combine like terms.

Ans. 25

(4 - 3i)(i)  Distribute the i to the two terms of the binomial.

4i - 3i^2 = 4i - 3(-1)

Ans. 4i + 3

(6i)(4 + 3i) = (6i)(4) + (6i)(3i) = 24i + 18i^2 = 24i + 18(-1)

Ans. 24i -18

(6i)(i) = 6i^2 = 6(-1)

Ans. -6

(-5)(4 + 3i) = -20 - 15i   That's it; there's no i^2 to deal with.

Ans. -20 - 15i

(-5)(i)   = -5i  Again, that's all there is to it.

Ans. -5i

Answer:

[tex]-9\frac{1}{4}[/tex]

Step-by-step explanation:

[tex]-5\frac{3}{4}-3\frac{1}{2}[/tex]

Step 1: Factor out the common term [tex]-1[/tex]

[tex]=-\left(5\frac{3}{4}+3\frac{1}{2}\right)[/tex]

Step 2: Add the whole numbers

[tex]5 + 3 = 8[/tex]

Step 3: Combine the fractions:

[tex]\frac{3}{4}+\frac{1}{2} = \frac{5}{4}\\\\=-\left(8+\frac{5}{4}\right)[/tex]

Step 4: Convert the improper fractions to mixed numbers

[tex]\frac{5}{4} = 1\frac{1}{4}\\\\=-\left(8+1\frac{1}{4}\right)[/tex]

Step 5: Add the numbers

[tex]8 + 1 =9 \\\\=-9\frac{1}{4}[/tex]

Therefore, the answer to the equation is [tex]-9\frac{1}{4}[/tex] in fraction, and decimal; [tex]9.25[/tex]

Answer:

[tex] \displaystyle x = \frac{3}{4} [/tex]

Step-by-step explanation:

we are given that

[tex] \displaystyle P = \left(x, - \frac{ \sqrt{7} }{4} \right)[/tex]

we want to figure out x

remember that,

In unit circle x coordinate is considered cos and y coordinate is considered sin

so in order to figure out x we should figure out the value of cos to do we can consider Pythagoras trig indentity

given by

[tex] \displaystyle \sin ^{2} ( \theta) + { \cos}^{2} ( \theta) = 1[/tex]

we are given sin=-√7/4 thus

substitute:

[tex] \displaystyle \left( - \frac{ \sqrt{7} }{4} \right) ^{2} + { \cos}^{2} ( \theta) = 1[/tex]

simplify square:

[tex] \displaystyle \frac{7}{16} + \cos ^{2} ( \theta) = 1[/tex]

move left hand side expression to right hand side and change its sign:

[tex] \displaystyle \cos ^{2} ( \theta) = 1 - \frac{7}{16} [/tex]

simplify Substraction:

[tex] \displaystyle \cos ^{2} ( \theta) = \frac{9}{16} [/tex]

square root both sides:

[tex] \displaystyle \cos ^{} ( \theta) = \pm\frac{3}{4} [/tex]

since in unit circle cos is x and P belongs to Q:IV negative cos isn't applicable

hence,

[tex] \displaystyle x = \frac{3}{4}[/tex]

Answer:

A) 67.4 m

Step-by-step explanation:

Let "x" represent how many meters above the lake is the man

Reference angle = 32°

Opposite = x

Hypotenuse = 129.5 m

Apply ye trigonometric function SOH:

Sin 32° = Opp/Hyp

Son 32 = x/129.5

129.5 × sin 32° = x

x = 68.6245447

This is close to A) 67.4 m

Answer:

Which of the following relations is a function- A

Determine which relation is a function- A

Step-by-step explanation:

A function is a type of relationship where x's do not repeat. So, to solve find where each y has a unique x value. In the first question, A is correct because the x values; -3, 0, 2; never repeat. Then, on the next question A is correct because it is a relation written in slope-intercept form, which is a type of function notation.

Answer: [tex]3x^{-2.5}[/tex]

Step-by-step explanation:

Given

Expression is

[tex]\dfrac{12\sqrt{x}}{4x^3}[/tex]

Using exponent property [tex]x^a\cdot x^b=x^{a+b}[/tex]

Writing expression in the form of [tex]k\cdot x^n[/tex]

[tex]\Rightarrow \dfrac{12\sqrt{x}}{4x^3}=\dfrac{3\times 4}{4}\times \dfrac{x^{0.5}}{x^3}\\\\\Rightarrow \dfrac{3\times 4}{4}\times x^{0.5-3}\\\\\Rightarrow 3x^{-2.5}[/tex]

Answer:

-9 + 4i

Step-by-step explanation:

The additive inverse ("opposite") of a complex number a + bi  is  -a - bi.

Just use the opposites of  a  and  b.

Answer:

8x=104

Step-by-step explanation:

The answer above is the question simplified down

Step-by-step explanation:

A 106 offered history to students

Answer:

I believe the answer is B) All real numbers

Answer:

D, 225

Step-by-step explanation:

Because this equation already has a1, it's useless to test with that, so instead solve for a2.

You would have a2 - 5a1, which would get you a2 = 5(9) because we already know what a1 is, which is 9. a2 = 45

Now we have a2, which is 45, so now we solve for a3

We would have a3 = 5a2 = a3 = 5(45) which is 225 which is a3

Also thanks for the fat 18 points dude, you really put 36 points into this one big value hope this one helped you a lot

Answer:

D.2, 4, 6, 8, ...

Step-by-step explanation:

This is linear because all successive terms in the numerical pattern have the same difference between them.

Answer: The sample space S for a probability model is the set of all possible outcomes. For example, suppose there are 5 marbles in a bowl. One is red, one is blue, one is yellow, one is green, and one is purple.

Step-by-step explanation: Hope this helped :)

Answer:

V = 577 cubic cm

Step-by-step explanation:

V(cyl) = Area of Base x Height

Area of Base = πr²

r = 7/2 or 3.5

h = 15

V = π(3.5)²(15)

V = 577

Answer:

52.9

??

Step-by-step explanation:

Answer:

Explanation:

hope it will helps please heart my answer!

Answer:

The formula for the area of the base of a cylinder is π r²

Answer:

u mad bruv? xD  Xd DxD XDXDXDdd

Step-by-step explanation:

Answer:

C. make purchases

Step-by-step explanation:

took the test

Answer:

She saved $46

Step-by-step explanation:

1. Price for 3 adults would be $144

2. Price for 4 children would be $104

3. Total price for individual tickets would be $248

4. She bought 1 of [Combo 1] and 1 of [Combo 2]

5. Therefore, she paid $202

6. She saved $46

Answer:

[tex]45\:\mathrm{in}[/tex]

Step-by-step explanation:

The volume of a square pyramid is given by [tex]V=\frac{1}{3}\cdot s^2\cdot h[/tex]. Substituting given values, we have:

[tex]3,840=\frac{1}{3}\cdot 16^2\cdot h,\\h=\frac{3,840\cdot 3}{256}=\boxed{45}[/tex]

Answer:

30 in.

Step-by-step explanation:

[tex]h=3\frac{V}{a^{2} }[/tex]

[tex]h=3\frac{3840}{16^{2} }[/tex]

45.12

That is not an option, so go with the closest one 30 in.

Step-by-step explanation:

The model will contain 1 ten and 4 ones in each group.

Answer:

a = 3/4.

Step-by-step explanation:

2a/3 - 1/6 = 1/3

Multiply thru by the LCD 6:

4a - 1 = 2

4a = 3

a = 3/4.

Answer:

49 is your answer :)

Step-by-step explanation:

Have a nice dayyy <3

Answer:

16n + 7

Step-by-step explanation:

Answer:

7 + 16n

Step-by-step explanation:

The use of more than indicates addition.