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3 years ago

How do you write 12/75 as a decimal

1 answer:

6 0

$\frac{12}{75} = \frac{4\times 3}{25\times 3} = \frac{4}{25}= \frac{4\times 4}{25\times 4} = \frac{16}{100} =\boxed {0.16}$

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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

Explain how you know that x^2-8x+20 is always positive. <br> Please help.

IRISSAK [1]

Answer:

if you rearrange to complete the square, you get (x^2-4)^2 +4

and seeing as anything squared will always be positive or zero, the lowest possible value for (x^2-4)^2 is 0, when x = 4

and 0 + 4 = 4, which is greater than 0, so positive

Step-by-step explanation:

4 0

2 years ago

I will give you brainliest I will give you five stars and I will give you a heart if you can get this correct

BigorU [14]

Answer:

the last one

Hope this helps

-mercury

7 0

2 years ago

Can someone help me in question 51 please

notka56 [123]

We know that the area of a parallelogram is the base * the height of it, so if we divide both sides by the height, then area/height=base. Therefore, we must divide the area by the height. To divide using polynomials, we first set it up similar to a regular long division problem:

______________________

2x+3 | 2x²+13x+15

Next, we take the first component of the numerator (2x² in this case) and divide it by the first component of the denominator (2x) to get x. That will form the start of our answer, and at the bottom, we will subtract our numerator by the denominator (2x+3) multiplied by the start of our answer (x). Therefore, we have

_x_____________________

2x+3 | 2x²+13x+15

-(2x²+3x)

_______________

10x+15

We then repeat the process until we finish, and whatever's left at the top is our answer. If there's something left, that's our remainder.

_x+5_____________________

2x+3 | 2x²+13x+15

-(2x²+3x)

_______________

10x+15

- (10x+15)

_________________

Therefore, our base has a length of x+5.

Feel free to ask further questions, and Happy Holidays!

3 0

2 years ago

Write an expression for 8 times r

Vlada [557]

Answer:

Step-by-step explanation:

3 0

3 years ago