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4 years ago

What is three-fourths plus one-third

Mathematics

2 answers:

jekas [21]4 years ago

4 0

Answer: the answer is one and one twelfth.

Step-by-step explanation:

FromTheMoon [43]4 years ago

3 0

To answer you gotta find a common denominator first . For this it will probably be twelve . Which gives you 9/12+4/12 which equates to 13/12 or 1 1/12

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If cos() = − 2 3 and is in Quadrant III, find tan() cot() + csc(). Incorrect: Your answer is incorrect.

nydimaria [60]

Answer:

$\tan(\theta) \cdot \cot(\theta) + \csc(\theta) = \frac{5 - 3\sqrt 5}{5}$

Step-by-step explanation:

Given

$\cos(\theta) = -\frac{2}{3}$

$\theta \to$ Quadrant III

Required

Determine $\tan(\theta) \cdot \cot(\theta) + \csc(\theta)$

We have:

$\cos(\theta) = -\frac{2}{3}$

We know that:

$\sin^2(\theta) + \cos^2(\theta) = 1$

This gives:

$\sin^2(\theta) + (-\frac{2}{3})^2 = 1$

$\sin^2(\theta) + (\frac{4}{9}) = 1$

Collect like terms

$\sin^2(\theta) = 1 - \frac{4}{9}$

Take LCM and solve

$\sin^2(\theta) = \frac{9 -4}{9}$

$\sin^2(\theta) = \frac{5}{9}$

Take the square roots of both sides

$\sin(\theta) = \±\frac{\sqrt 5}{3}$

Sin is negative in quadrant III. So:

$\sin(\theta) = -\frac{\sqrt 5}{3}$

Calculate $\csc(\theta)$

$\csc(\theta) = \frac{1}{\sin(\theta)}$

We have: $\sin(\theta) = -\frac{\sqrt 5}{3}$

So:

$\csc(\theta) = \frac{1}{-\frac{\sqrt 5}{3}}$

$\csc(\theta) = \frac{-3}{\sqrt 5}$

Rationalize

$\csc(\theta) = \frac{-3}{\sqrt 5}*\frac{\sqrt 5}{\sqrt 5}$

$\csc(\theta) = \frac{-3\sqrt 5}{5}$

So, we have:

$\tan(\theta) \cdot \cot(\theta) + \csc(\theta)$

$\tan(\theta) \cdot \cot(\theta) + \csc(\theta) = \tan(\theta) \cdot \frac{1}{\tan(\theta)} + \csc(\theta)$

$\tan(\theta) \cdot \cot(\theta) + \csc(\theta) = 1 + \csc(\theta)$

Substitute: $\csc(\theta) = \frac{-3\sqrt 5}{5}$

$\tan(\theta) \cdot \cot(\theta) + \csc(\theta) = 1 -\frac{3\sqrt 5}{5}$

Take LCM

$\tan(\theta) \cdot \cot(\theta) + \csc(\theta) = \frac{5 - 3\sqrt 5}{5}$

6 0

3 years ago

X + 2y = 5<br> y = 6x + 3

ki77a [65]

Answer:

x = −1/13 and y = 33/13 or 2 7/13

Step-by-step explanation:

x+2y=5

x+2(6x+3)=5

x+12x+6=5

13x+6=5

-6 -6

13x= -1

/13 /13

y=6x+3

y=6(-1/13)+3

y= 33/13

y= 2 7/13

5 0

3 years ago

Subtracting Rational Numbers Simplify –3 – 1.

aksik [14]

Answer:

-4

Explanation:

when subtracting a positive integer from a negative, the answer becomes smaller. If the question were to ask -3-(-1) negative 3 minus negative 1, the subtraction sign becomes a addition sign, and you add 1 to -3.

7 0

3 years ago

Read 2 more answers

James earned $25 selling lemonade. If 80% of this was profit, how much did james spend initially on ingredients?

Y_Kistochka [10]

Set the equation to look like

20/100 = x/25

Then multiply to get

500 = 100x
500/100 = x
5 = x

Therefore James spent 5 dollars initially on ingredients.

3 0

3 years ago

Whats 100000x41 pleaseeeee

almond37 [142]

The answer is 410,000

8 0

4 years ago