Reuben will rent a car for the weekend. he can choose one of two plans. the first has no initial fee but costs $0.90 per mile driven. The second plan has an initial fee of $65 and costs an additional $0.70 per mile driven. How many miles would Reuben need to drive for the two plans to cost the same? ​

Answer:

1) [tex]\frac{\sin x}{1-\cos x} = \csc x + \cot x[/tex]

2) [tex]\frac{\sin x}{1-\cos x} = \frac{1}{\sin x} + \frac{\cos x}{\sin x}[/tex]

3) [tex]\frac{\sin x}{1-\cos x} = \frac{1+\cos x}{\sin x}[/tex]

4) [tex]\frac{\sin x}{1-\cos x} = \frac{\sin x \cdot (1+\cos x)}{\sin^{2}x}[/tex]

5) [tex]\frac{\sin x}{1-\cos x} = \frac{\sin x\cdot (1+\cos x)}{1-\cos^{2}x}[/tex]

6) [tex]\frac{\sin x}{1-\cos x} = \frac{\sin x\cdot (1+\cos x)}{(1+\cos x)\cdot (1-\cos x)}[/tex]

7) [tex]\frac{\sin x}{1-\cos x} = \frac{\sin x}{1-\cos x}[/tex]

Step-by-step explanation:

Now we proceed to show all steps needed to demonstrate the trigonometric identity:

1) [tex]\frac{\sin x}{1-\cos x} = \csc x + \cot x[/tex] Given.

2) [tex]\frac{\sin x}{1-\cos x} = \frac{1}{\sin x} + \frac{\cos x}{\sin x}[/tex] Identities for cosecant and cotangent functions.

3) [tex]\frac{\sin x}{1-\cos x} = \frac{1+\cos x}{\sin x}[/tex]             [tex]\frac{a}{b}+\frac{c}{b} = \frac{a+c}{b}[/tex]

4) [tex]\frac{\sin x}{1-\cos x} = \frac{\sin x \cdot (1+\cos x)}{\sin^{2}x}[/tex] Existence of additive inverse/Modulative property.

5) [tex]\frac{\sin x}{1-\cos x} = \frac{\sin x\cdot (1+\cos x)}{1-\cos^{2}x}[/tex]    Fundamental trigonometric identity.

6) [tex]\frac{\sin x}{1-\cos x} = \frac{\sin x\cdot (1+\cos x)}{(1+\cos x)\cdot (1-\cos x)}[/tex]   Factorization.

7) [tex]\frac{\sin x}{1-\cos x} = \frac{\sin x}{1-\cos x}[/tex] Existence of additive inverse/Modulative property/Result.

Step-by-step explanation:

[tex] {x}^{2} - 8x + 15 = 0 \\ (x - 3)(x - 5) = 0 \\ x = 3 \: or \: x = 5[/tex]

Answer:

Los números son

7 y 8

Explicación paso a paso:

Si el número menor es "x"  , el mayor es "x + 1"

entonces

( x + 1 )² - x² = 15

x² + 2x + 1 -x² = 15

2x + 1 = 15

2x = 15 - 1

2x = 14

x = 14/2

x = 7  (  número menor )

x + 1  = 7 + 1

x + 1 = 8 ( número mayor )

Answer:

A. 1

Step-by-step explanation:

its A

Answer:

Some

Step-by-step explanation:

the mean absolute deviation would intersect and would there for be some but at far enough apart to not be a lot

Answers,

1. 23

2. 79

3. 53

4. 26

5. 13

6. 11

How I did this,

What I did was subtract 8 from 31 to get ( e ) by itself.

This subject will get harder so I reccomend you focus on school and learn how to do this.

Answer:

18x^(2)+39x+15 over 3x+5 -----> 6x+3

35x^(2)-5x-30 over 5x-5 -------> 7x+6

15x^(2)-44x+21 over 5x-3 ------> 3x-7

Step-by-step explanation:

Plato Gang

9514 1404 393

Answer:

  720

Step-by-step explanation:

The LCM of these numbers will have every factor that is part of these numbers.

  16 = 2^4

  30 = 2 × 3 × 5

  36 = 2^2 × 3^2

So, the LCM will have factors of 2^4, 3^2, and 5:

  LCM(16, 30, 36) = 2^4 × 3^2 × 5 = 720

720 = 16×45 = 30×24 = 36×20

The least common multiple is 720.

Answer:

me

Step-by-step explanation:

becaus im the bes guy

Step-by-step explanation:

where is x in the question

Answer:

1,-4

Step-by-step explanation:

formula for rotation of 270 is (x,y) to (y,-x)

Answer: interest rate was 6.7 %

Step-by-step explanation: 402/6000 = 0.067 = 6.7%

Answer

16/43

Step-by-step explanation:

17 Male + 27 female = 44 students

now n= 2 so first student was male so one male student was taken out of the equation so 16 male left. now left male students by remaining students  so now total left students = 43

so, prob = remaining males/remaining students=16/43

Answer:

[tex]\displaystyle \sin\left(2\sec^{-1}\left(\frac{u}{10}\right)\right)=\frac{20\sqrt{u^2-100}}{u^2}\text{ where } u>0[/tex]

Step-by-step explanation:

We want to write the trignometric expression:

[tex]\displaystyle \sin\left(2\sec^{-1}\left(\frac{u}{10}\right)\right)\text{ where } u>0[/tex]

As an algebraic equation.

First, we can focus on the inner expression. Let θ equal the expression:

[tex]\displaystyle \theta=\sec^{-1}\left(\frac{u}{10}\right)[/tex]

Take the secant of both sides:

[tex]\displaystyle \sec(\theta)=\frac{u}{10}[/tex]

Since secant is the ratio of the hypotenuse side to the adjacent side, this means that the opposite side is:

[tex]\displaystyle o=\sqrt{u^2-10^2}=\sqrt{u^2-100}[/tex]

By substitutition:

[tex]\displaystyle= \sin(2\theta)[/tex]

Using an double-angle identity:

[tex]=2\sin(\theta)\cos(\theta)[/tex]

We know that the opposite side is √(u² -100), the adjacent side is 10, and the hypotenuse is u. Therefore:

[tex]\displaystyle =2\left(\frac{\sqrt{u^2-100}}{u}\right)\left(\frac{10}{u}\right)[/tex]

Simplify. Therefore:

[tex]\displaystyle \sin\left(2\sec^{-1}\left(\frac{u}{10}\right)\right)=\frac{20\sqrt{u^2-100}}{u^2}\text{ where } u>0[/tex]

Answer:

b. it cannot be ruled out that the type of fuel is an insignificant factor in determining speed.

Step-by-step explanation:

From the question :

Let the speed of each fuel be represented as ;

u1, u2, u3

The null hypothesis, H0 ;

H0 : u1 = u2 = u3

H0 is of the notion that fuel type is not a significant factor in determining speed

The alternative hypothesis, H1;

H1 : u1 ≠ u2 ≠ u3

The alternative is the opposite of the null, fuel type is a significant factor in determining speed

If after conducting the statistical test, the null hypothesis cannot be rejected ;

Then the conclusion will be ;

There is no significant evidence to conclude that the fuel type is a significant factor in determining speed ;

Hence, fuel fuel type remains an insignificant factor in determining speed.

Answer:

The asnwer to the system of equation

x=4 y=6

Step-by-step explanation:

Answer:  1) 8x=32       2) (4,6)

Step-by-step explanation:

Hope this helps!

Mark me brainliest!

Pls and ty!

Answer:

220

Step-by-step explanation:

Area of square=8*20=160

Area of triangle=(6*20)/2=60

160+60

Answer:

220 units²

I'm sure this is the answer!

Answer:

467

Step-by-step explanation:

There were a total 1327 parking lots.

Out of these 816 were taken in the morning, 91 cars left in the afternoon, while 135 came back after lunch.

So there are,

[tex]Cars left = 1327 - (816 - 91 + 135) \\\\ = 1327 - 860\\ = 467[/tex]

Thus, there are 467 parking spots left on Monday afternoon.  

Answer:

The chances of landing on blue are 1 in 4, or one fourth. The chances of landing on red are 1 in 4, or one fourth. This problem asked us to find some probabilities involving a spinner.

Answer:

-1/3

Step-by-step explanation:

Answer:

The critical value for a 99% confidence interval is T = 2.9768

Step-by-step explanation:

We have the standard deviation of the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 15 - 1 = 14

Critical value

Now, we have to find a value of T, which is found looking at the t table, with 14 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.99}{2} = 0.995[/tex]. So we have T = 2.9768

The critical value for a 99% confidence interval is T = 2.9768

Answer:

53

Step-by-step explanation:

Because

Answer:

Step-by-step explanation:

This is already solved, and this would not be considered a inequality since it has only a equal sign.