what is 3 to the power of -4 as a fraction?

Step-by-step explanation:

[tex]\large\underline{\sf{Solution-}}[/tex]

[tex]\rm \longmapsto\:3cot\theta = 4[/tex]

[tex]\rm\implies \:cot\theta = \dfrac{4}{3} [/tex]

Now, Consider

[tex]\rm \longmapsto\:\dfrac{3sin\theta + 4cos\theta }{3sin\theta - 4cos\theta } [/tex]

[tex]\rm \:  =  \: \dfrac{sin\theta \bigg[3 + 4\dfrac{cos\theta }{sin\theta } \bigg]}{sin\theta \bigg[3 - 4\dfrac{cos\theta }{sin\theta } \bigg]} [/tex]

[tex]\rm \:  =  \: \dfrac{3 + 4cot\theta }{3 - 4cot\theta } [/tex]

[tex]\rm \:  =  \: \dfrac{3 + 4 \times \dfrac{4}{3} }{3 - 4 \times \dfrac{4}{3} } [/tex]

[tex]\rm \:  =  \: \dfrac{3 + \dfrac{16}{3} }{3 - \dfrac{16}{3} } [/tex]

[tex]\rm \:  =  \: \dfrac{\dfrac{9 + 16}{3} }{ \dfrac{9 - 16}{3} } [/tex]

[tex]\rm \:  =  \: \dfrac{25}{ - 7} [/tex]

[tex]\rm \:  =  \: - \: \dfrac{25}{7} [/tex]

Hence,

[tex]\rm \longmapsto\:\boxed{\tt{ \dfrac{3sin\theta + 4cos\theta }{3sin\theta - 4cos\theta } = - \frac{25}{7} \: }} \\ [/tex]

Additional Information:-

Relationship between sides and T ratios

sin θ = Opposite Side/Hypotenuse

cos θ = Adjacent Side/Hypotenuse

tan θ = Opposite Side/Adjacent Side

sec θ = Hypotenuse/Adjacent Side

cosec θ = Hypotenuse/Opposite Side

cot θ = Adjacent Side/Opposite Side

Reciprocal Identities

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

sin θ = 1/cosec θ

cos θ = 1/sec θ

tan θ = 1/cot θ

Co-function Identities

sin (90°−x) = cos x

cos (90°−x) = sin x

tan (90°−x) = cot x

cot (90°−x) = tan x

sec (90°−x) = cosec x

cosec (90°−x) = sec x

Fundamental Trigonometric Identities

sin²θ + cos²θ = 1

sec²θ - tan²θ = 1

cosec²θ - cot²θ = 1

Answer:

2/9 < 11/18 < 2/3 < 5/6

Answer:

23

Step-by-step explanation:

69 divided be 3

= 23

step 2

23 + 23 = 46 ( Alvin age)

step 3

69 -46= 23 Elga age

Answer:

Elga's age is 23

Step-by-step explanation:

To solve this, we need to make our equation.

2x+x=69

In this equation, 2x is Alvin's age, while Elga's age is x. The 69 is the sum of their ages.

Combine the like terms in this equation.

3x=69

Divide both sides by 3

3/3x=69/3

x=23

Elga's age is 23, but we still need to check to make sure we are correct.

To do this, plug in 23 for x.

2(23)+23=69

46+23=69

69=69

Do we get a true statement? Yes, so we are correct.

Answer:

Well to calculate percentage decrease

(Starting value- ending value / starting value)* 100

so 30-18=12

12/30= 2/5

2/5*100= 200/5

40 percent

Now thats the amount lost so

100%-40%=60%

60% reduction

Answer:

15 minutes

Step-by-step explanation:

725 - 710 = 15

PLEASE MARK ME BRAINLIEST!!!!

Step-by-step explanation:

3x3x3x3x3x3 = 3^6

3x3x3 = none

6x6x6 = 6^3

6+6+6 = 6x3

3 + 6 = none

3+3+3+3+3+3 = none

Answer:

For box 3^6:

3×3×3×3×3×3

For box 6^3:

6×6×6

For box 6×3:

6+6+6

3+3+3+3+3+3

For None:

6+3

3×3×3

Hope this helps! Brainliest would be really appreciated!

Answer:

1 dozen = 12 units

7 dozen = 12 × 7 = 84 units

Correct unit price = 103.32 ÷ 84 = $1.23

The contractor's unit price incorrect because he did 103.32 ÷ 7 dozen.

The price he calculated is for the price for 1 dozen, not 1 unit

Step-by-step explanation:

Answer:

Answer is 33

Step-by-step explanation:

If x equals 3, then the equation simplifies to 6 squared - (9/3)

9 divided by 3 is 3, then 6 squared is 36.

36-3 = 33. Hope this helps!

Answer:

GIVEN :

SOLUTION :

[tex] \large{ \tt{A \times B = \{ \: 1 \:, 2 \: ,3 \} \: \times \: \{ \: i, \: o ,\: u \}}}[/tex]

[tex] \large{ \tt{= \{ \: (1 \:, i \: ) \: (1 \: ,o \: ) \: (1 \: ,u \: ) \: (2 \:, i) \: (2 \: ,o \: ) \: (2 \:, u) \: (3 \:, i) \: (3 \:, o) \: (3 \: ,u) \}}}[/tex]

-Hope I helped! ~

Please feel free to leave any comments if any! :)

Answer:

f(5)=14

f(3)=122

Step-by-step explanation:

Answer:

Is y

[tex]y = \sqrt{ - } 5 \times + 1[/tex]

Answer:

Hello,

Here is your answer.

Vertex: (5, -2)

Focus: (19/4, -2)

Directrix: x = 21/4

Step-by-step explanation:

Answer:

I personally have no idea how to do this but quizlet might have the answer

Sorry hope this helps though

Step-by-step explanation:

Answer:

y=4-3x

Step-by-step explanation:

Hope this helps!!!

Answer:

sry but i can't help you with it bcz i don't understand spanish can u write it in clear english

Sry

Answer:

741/10000

Step-by-step explanation:

The direct distance from the school to the library, travelled by Alice can be

found using Pythagoras's theorem.

The number of miles Britney travelled more than Alice is; 8 miles

Reason:

The distance, d, between points given their coordinates, (x₁, y₁), (x₂, y₂) can

be found with the formula;

[tex]d = \sqrt{\left (x_{2}-x_{1} \right )^{2}+\left (y_{2}-y_{1} \right )^{2}}[/tex]

The above formula can be obtained using Pythagoras's theorem.

The distances travelled by Britney are;

Distance from the school to the mall = [tex]\sqrt{(10 - 10)^2 + (6 - (-4))^2}[/tex] = 10

Distance from the mall to the library = [tex]\sqrt{(-14 - 10)^2 + (6 - 6)^2}[/tex] = 24

Total distance travelled by Britney = 24 miles + 10 miles = 34 miles

The distance travelled by Alice is from the school to the library, which

gives; Alice's distance = [tex]\sqrt{(10 - (-14))^2 + (-4 - 6)^2}[/tex] = 26

Distance travelled by Alice from the school to the library is 26 miles

The number of miles more Britney traveled is 34 miles - 26 miles = 8 miles

Therefore;

Britney traveled 8 miles more than Alice

Learn more here;

https://brainly.com/question/3508899

Answer:

[tex]-(\frac{3}{7})^3[/tex]

Step-by-step explanation:

Since we see that 3/7 is multiplied by itself three times, we can use exponents as a shorter way to write this. The expontent tells us how many times the base number, 3/7, is multiplied by itself.

[tex]-1 * (\frac{3}{7})^3[/tex]= [tex]-1 * \frac{3}{7} * \frac{3}{7} * \frac{3}{7}[/tex]

We then multiply by -1 to (3/7)^3 to get the exact answer.

[tex]-(\frac{3}{7})^3[/tex]

Answer:

Step-by-step explanation:

Ti piacciono i banane scimmia

Answers and Step-by-step explanation:

a. The independent variable is the variable being manually changed by the experimenter. The dependent variable is the variable being affected by the independent variable. X (members joining the fitness club) is the independent variable. Y (total monthly cost) is the dependent variable.

b. The domain is 6, because x is always the domain. The range is 77, because Y is always the range. You plug in 6 (the domain which is x), and get 77.

c. Yes, this relation is a function. Relations are only not functions when one singular input (domain) goes to 2 outputs (range).

    A domain can not have multiple ranges. A range can have multiple domains though.

The y is the dependent variable and the x is the independent variable, in the equation y = 7x + 35, The domain is 6 and the range is 77 for the given equation. Yes, it is a function.

In other terms, it is a mathematical statement stating that "this is equivalent to that." It appears to be a mathematical expression on the left, an equal sign in the center, and a mathematical expression on the right.

Given:

y = 7x + 35, x members joining the fitness club and y is cost.

(a) As you can see from the equation, y depends on the value of x,

(b) Calculate the amount of x = 6 (as given)

y = 7 × 6 + 35

y = 42 + 35

y = $77

The domain of the function is 6 and the range is 77.

(c) Yes, as we put the values in x, y also changes, so it is a function.

To know more about equations:

https://brainly.com/question/12788590

#SPJ2

Answer:

Step-by-step explanation:

0.6432

Answer:

y = 0x - 5 or just y = -5

Step-by-step explanation:

use the slope intercept equation

y2 - y1

x2 - x1

- 5 - 9 = 14

-3 + 3 = 0

14 / 0 = 0

so the slope is undefined

take one of the points (let's use -3, -5) and plug that in the slope intercept form (y = mx+b)

so -5 = 0(-3)+b

0 • 3 = 0 so the b (or y intercept) equals -5

so the equation is y = -5

Answer:

[tex]\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:x=-2,\:y=2}[/tex]

Step-by-step explanation:

[tex]\begin{bmatrix}-7x-6y=2\\ 7x+4y=-6\end{bmatrix}[/tex]

[tex]\mathrm{Substitute\:}x=-\frac{2+6y}{7}[/tex]

[tex]\begin{bmatrix}7\left(-\frac{2+6y}{7}\right)+4y=-6\end{bmatrix}[/tex]

[tex]\begin{bmatrix}-2-2y=-6\end{bmatrix}[/tex]

[tex]\mathrm{For\:}x=-\frac{2+6y}{7}[/tex]

[tex]\mathrm{Substitute\:}y=2[/tex]

[tex]x=-\frac{2+6\cdot \:2}{7}\\\\x=-2[/tex]

Answer:

x ≈ 50.8°

Step-by-step explanation:

Using the sine ratio in the right triangle

sin x = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{JK}{IK}[/tex] = [tex]\frac{6.2}{8}[/tex] , then

x = [tex]sin^{-1}[/tex] ([tex]\frac{6.2}{8}[/tex] ) ≈ 50.8° ( to the nearest tenth )

[tex]\frac{2a}{3} +13, \:a=15[/tex]

Step 1: Substitute [tex]a[/tex] for 15

[tex]\frac{2(15)}{3} +13[/tex]

Step 2: Solve

15 × 2 = 30

[tex]\frac{30}{3} +13[/tex]

30 ÷ 3 = 10

[tex]10 +13[/tex]

10 + 13 = 23

The evaluation of the expression is 23.

Answer:

it is an equation that is always valid

Step-by-step explanation:

3(xy) = 3(xy)

3(xy)-(3xy) = 0

0 = 0

Answer:

x = 5

Step-by-step explanation:

X+3(2×-4)=-19

x + 3(-8) = -19

x - 24 = -19

x = 5

Answer:

20

Step-by-step explanation:

[tex]f(x) = 2|x + 6| -4[/tex]

Step 1: Substitute [tex]x[/tex] for the given function.

6 is the given function.

[tex]f(x) = 2|x + 6| -4\\=f(x) = 2|6 + 6| -4\\\\f(x) = 2|6 + 6| -4\\=24-4\\\\=20[/tex]