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3 years ago

What is 44/12 in simplest form?

2 answers:

7 0

The numerator and denominator when both divided by 4 results in the fraction 11/3. To simplify this further, you can turn it into a mixed number which is 3 2/3

vekshin13 years ago

5 0

The answer is 3and 2/3

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which shows the students in order from greatest test score to lease test score Alex 0.95 Octavia 16/20 Tonya 9/10 Wilson 0.87

Nonamiya [84]

Answer:

Alex (0.95), Tonya (0.90), Wilson (0.87), Octavia (0.80)

Step-by-step explanation:

To solve this, we have to convert all of the scores into either a decimal or a fraction. In this case, I will be solving all of them into decimals since it is easier.

Alex: 0.95

Octavia: 16/20 = 0.80

Tonya: 9/10 = 0.90

Wilson: 0.87

Therefore, we can order these from greatest score to least score.

Alex (0.95), Tonya (0.90), Wilson (0.87), Octavia (0.80)

4 0

3 years ago

<img src="https://tex.z-dn.net/?f=prove%20that%5C%20%20%5Ctextless%20%5C%20br%20%2F%5C%20%20%5Ctextgreater%20%5C%20%5Cfrac%20%7B

inysia [295]

$\large \bigstar \frak{ } \large\underline{\sf{Solution-}}$

Consider, LHS

$\begin{gathered}\rm \: \dfrac { \tan \theta + \sec \theta - 1 } { \tan \theta - \sec \theta + 1 } \\ \end{gathered}$

We know,

$\begin{gathered}\boxed{\sf{ \:\rm \: {sec}^{2}x - {tan}^{2}x = 1 \: \: }} \\ \end{gathered} \\ \\ \text{So, using this identity, we get} \\ \\ \begin{gathered}\rm \: = \:\dfrac { \tan \theta + \sec \theta - ( {sec}^{2}\theta - {tan}^{2}\theta )} { \tan \theta - \sec \theta + 1 } \\ \end{gathered}$

We know,

$\begin{gathered}\boxed{\sf{ \:\rm \: {x}^{2} - {y}^{2} = (x + y)(x - y) \: \: }} \\ \end{gathered} \\$

So, using this identity, we get

$\begin{gathered}\rm \: = \:\dfrac { \tan \theta + \sec \theta - (sec\theta + tan\theta )(sec\theta - tan\theta )} { \tan \theta - \sec \theta + 1 } \\ \end{gathered}$

can be rewritten as

$\begin{gathered}\rm\:=\:\dfrac {(\sec \theta + tan\theta ) - (sec\theta + tan\theta )(sec\theta -tan\theta )} { \tan \theta - \sec \theta + 1 } \\ \end{gathered} \\ \\ \\\begin{gathered}\rm \: = \:\dfrac {(\sec \theta + tan\theta ) \: \cancel{(1 - sec\theta + tan\theta )}} { \cancel{ \tan \theta - \sec \theta + 1} } \\ \end{gathered} \\ \\ \\\begin{gathered}\rm \: = \:sec\theta + tan\theta \\\end{gathered} \\ \\ \\\begin{gathered}\rm \: = \:\dfrac{1}{cos\theta } + \dfrac{sin\theta }{cos\theta } \\ \end{gathered} \\ \\ \\\begin{gathered}\rm \: = \:\dfrac{1 + sin\theta }{cos\theta } \\ \end{gathered}$

<h2>Hence,</h2>

$\begin{gathered} \\ \rm\implies \:\boxed{\sf{ \:\rm \: \dfrac { \tan \theta + \sec \theta - 1 } { \tan \theta - \sec \theta + 1 } = \:\dfrac{1 + sin\theta }{cos\theta } \: \: }} \\ \\ \end{gathered}$

$\rule{190pt}{2pt}$

5 0

3 years ago

What number must you add to complete the square? x2 + 14x = -5

ale4655 [162]

None of them will get into a negative number. When you have like "2x" is the number twice, right? Some number has to be negative

3 0

4 years ago

Read 2 more answers

How much water should be added to 3 gallons of pure alchohol in order to obtain a solution that is 15% alchohol?

lidiya [134]

say we're going to add "x" gallons of water, now how many gallons of alcohol is in pure water? well 0%, and 0% of "x" is (0/100) * x = 0.

the 3 gallons we know are 100% alcohol, how many gallons of alcohol is in it? well (100/100) * 3 = 3.

the resulting mix will have x + 3 gallons total and it's going to be 15% alcohol, how many gallons of alcohol is that? (15/100) * (x+3).

now, the amount of alcohol never increased, so the original 3 gallons of only alcohol will remain even after the water has been added, so.

$\begin{array}{lcccl} &\stackrel{solution}{quantity}&\stackrel{\textit{\% of }}{amount}&\stackrel{\textit{gallons of }}{amount}\\ \cline{2-4}&\\ \textit{pure water}&x&0.00&0\\ \textit{pure alcohol}&3&1.00&3\\ \cline{2-4}&\\ mixture&x+3&0.15&0.15(x+3) \end{array} \begin{array}{llll} \\[3em] \leftarrow \textit{this amount}\\\\ \leftarrow \textit{must be equal to this one} \end{array} \\\\\\ 3 = 0.15(x+3)\implies 3=0.15x+0.45\implies 2.55=0.15x \\\\\\ \cfrac{2.55}{0.15}=x\implies 17=x$

5 0

2 years ago

I need help ASAP due in an hour <br><br>only the highlighted ones plz:)

kolbaska11 [484]

Answer:

15.

a) 9

b) (x + 3)(x + 3) or (x + 3) ^ 2

16.

a) 121

b) (x + 11)(x + 11) or (x + 11) ^ 2

17.

a) 81

b) (x + 9)(x + 9) or (x + 9) ^ 2

7 0

3 years ago