Algebra 2

Some people advise that in very cold weather, you should keep the gas tank in your car more than half full. Lou's car had 5.6

Rasek [7]

26.98. You have the following information given in the problem above:

- Lou filled the tank with gas that cost $3.80 per gallon.

- Lou's car had 5.9 gallons in the 13-gallon tank.

2. Therefore, if he filled the tank, you can calculate the total amount of money Lou spent, by subtracting 13 gallons and 5.9 gallons and multiplying the result by $3.80.

8 0

2 years ago

How do you find the quotient of 5/2 ÷ 1/4 ?

anastassius [24]

The answer is to what is 5/2 divided by 1/4 is 10

3 0

3 years ago

Would appreciate the help !

aleksandr82 [10.1K]

This is one pathway to prove the identity.

Part 1

$\frac{\sin(\theta)}{1-\cos(\theta)}-\frac{1}{\tan(\theta)} = \frac{1}{\sin(\theta)}\\\\\frac{\sin(\theta)}{1-\cos(\theta)}-\cot(\theta) = \frac{1}{\sin(\theta)}\\\\\frac{\sin(\theta)}{1-\cos(\theta)}-\frac{\cos(\theta)}{\sin(\theta)} = \frac{1}{\sin(\theta)}\\\\\frac{\sin(\theta)*\sin(\theta)}{\sin(\theta)(1-\cos(\theta))}-\frac{\cos(\theta)(1-\cos(\theta))}{\sin(\theta)(1-\cos(\theta))} = \frac{1}{\sin(\theta)}\\\\$

Part 2

$\frac{\sin^2(\theta)}{\sin(\theta)(1-\cos(\theta))}-\frac{\cos(\theta)-\cos^2(\theta)}{\sin(\theta)(1-\cos(\theta))} = \frac{1}{\sin(\theta)}\\\\\frac{\sin^2(\theta)-(\cos(\theta)-\cos^2(\theta))}{\sin(\theta)(1-\cos(\theta))} = \frac{1}{\sin(\theta)}\\\\\frac{\sin^2(\theta)-\cos(\theta)+\cos^2(\theta)}{\sin(\theta)(1-\cos(\theta))} = \frac{1}{\sin(\theta)}\\\\$

Part 3

$\frac{\sin^2(\theta)+\cos^2(\theta)-\cos(\theta)}{\sin(\theta)(1-\cos(\theta))} = \frac{1}{\sin(\theta)}\\\\\frac{1-\cos(\theta)}{\sin(\theta)(1-\cos(\theta))} = \frac{1}{\sin(\theta)}\\\\\frac{1}{\sin(\theta)} = \frac{1}{\sin(\theta)} \ \ {\checkmark}\\\\$

As the steps above show, the goal is to get both sides be the same identical expression. You should only work with one side to transform it into the other. In this case, the left side transforms while the right side stays fixed the entire time. The general rule is that you should convert the more complicated expression into a simpler form.

We use other previously established or proven trig identities to work through the steps. For example, I used the pythagorean identity $\sin^2(\theta)+\cos^2(\theta) = 1$ in the second to last step. I broke the steps into three parts to hopefully make it more manageable.

3 0

2 years ago

Each year Lizzie’s school purchases student agenda books, which are sold in the school store. This year, the school

mrs_skeptik [129]

First divide $1,137.50 by 350 to figure out how much each book costs. Then divide $1,500 by 350 to see how much the school should add to the price of each agenda book to make the total profit. So the answer should be: (1137.50/350)+(1500/350)=minimum price

5 0

3 years ago

Read 2 more answers

Points A, B, C, D, E, and F are located on the number line. A number line going from Negative 1 and StartFraction 3 Over 8 EndFr

telo118 [61]

Answer:

The true statements are;

Point D represents a number less than the number Point C represents

Point E represents the smallest number of all the numbers represented by points

Step-by-step explanation:

The given information are;

The number line with points are

$-1\frac{3}{8} , -1\frac{1}{4} , -1\frac{1}{8} , -1..., \frac{3}{8}$

In decimal format, with Microsoft Excel and Word, we have;

-1.375, -1.25, -1.125, -1, -0.875, -0.75, -0.625, -0.5, -0.375, -0.25, -0.125, 0, 0.125, 0.25, 0.375

We have, E = -1.25, B = -1, D = -0.875, C = -0.25, A = 0, F = 0.25

The correct options are;

Point D = -0.875 < Point C = -0.25

Point E = -1.25 which is the second number on the number line and the smallest number of the numbers represented by points

8 0

3 years ago