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3 years ago

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Mala is y years old her sister is 4 years older than mala write an expression in simplest form that repersents the sum of the ag

es of the sisters

1 answer:

stealth61 [152]3 years ago

5 0

We are given

Mala is y years old

So, Mala =y

her sister is 4 years older than Mala

So, Sister =y+4

now, we can find sum

Sum = Mala +Sister

Sum = y +y+4

Sum = 2y+4...............Answer

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Helps, also explain how to do it I want to learn how and stop using brainy

Nutka1998 [239]

Answer:

259

Step-by-step explanation:

USE PEMDAS

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5 0

3 years ago

Given tan theta =9, use trigonometric identities to find the exact value of each of the following:_______

Ludmilka [50]

Answer:

$(a)\ \sec^2(\theta) = 82$

$(b)\ \cot(\theta) = \frac{1}{9}$

$(c)\ \cot(\frac{\pi}{2} - \theta) = 9$

$(d)\ \csc^2(\theta) = \frac{82}{81}$

Step-by-step explanation:

Given

$\tan(\theta) = 9$

Required

Solve (a) to (d)

Using tan formula, we have:

$\tan(\theta) = \frac{Opposite}{Adjacent}$

This gives:

$\frac{Opposite}{Adjacent} = 9$

Rewrite as:

$\frac{Opposite}{Adjacent} = \frac{9}{1}$

Using a unit ratio;

$Opposite = 9; Adjacent = 1$

Using Pythagoras theorem, we have:

$Hypotenuse^2 = Opposite^2 + Adjacent^2$

$Hypotenuse^2 = 9^2 + 1^2$

$Hypotenuse^2 = 81 + 1$

$Hypotenuse^2 = 82$

Take square roots of both sides

$Hypotenuse =\sqrt{82}$

So, we have:

$Opposite = 9; Adjacent = 1$

$Hypotenuse =\sqrt{82}$

Solving (a):

$\sec^2(\theta)$

This is calculated as:

$\sec^2(\theta) = (\sec(\theta))^2$

$\sec^2(\theta) = (\frac{1}{\cos(\theta)})^2$

Where:

$\cos(\theta) = \frac{Adjacent}{Hypotenuse}$

$\cos(\theta) = \frac{1}{\sqrt{82}}$

So:

$\sec^2(\theta) = (\frac{1}{\cos(\theta)})^2$

$\sec^2(\theta) = (\frac{1}{\frac{1}{\sqrt{82}}})^2$

$\sec^2(\theta) = (\sqrt{82})^2$

$\sec^2(\theta) = 82$

Solving (b):

$\cot(\theta)$

This is calculated as:

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

Where:

$\tan(\theta) = 9$ ---- given

So:

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

$\cot(\theta) = \frac{1}{9}$

Solving (c):

$\cot(\frac{\pi}{2} - \theta)$

In trigonometry:

$\cot(\frac{\pi}{2} - \theta) = \tan(\theta)$

Hence:

$\cot(\frac{\pi}{2} - \theta) = 9$

Solving (d):

$\csc^2(\theta)$

This is calculated as:

$\csc^2(\theta) = (\csc(\theta))^2$

$\csc^2(\theta) = (\frac{1}{\sin(\theta)})^2$

Where:

$\sin(\theta) = \frac{Opposite}{Hypotenuse}$

$\sin(\theta) = \frac{9}{\sqrt{82}}$

So:

$\csc^2(\theta) = (\frac{1}{\frac{9}{\sqrt{82}}})^2$

$\csc^2(\theta) = (\frac{\sqrt{82}}{9})^2$

$\csc^2(\theta) = \frac{82}{81}$

4 0

3 years ago

What’s 20 over 14 as a percentage

sergey [27]

Answer: 14 / 20 = 70%

Step-by-step explanation:

8 0

3 years ago

I need help on this specific equation: 10x+1=3x+9

Yuri [45]

Well, first you'd have to get the x by it's self.
10x+1=3x+9
Subtract 3x from each side and you'll have the x on only one side rather than two.
7x+1=9
Now I'd get rid of the 1 on the x's side. So just subtract 1 from each side.
7x=8
Then you should make it so the seven isn't there with the x either. Just divide each side by 7.
Answer: x=8/7
Each time you change something on one side, you must do the same to the other side. T find the value of a variable in an equation, simple seclude it so it's on it's own without number to make things confusing.
The answer was x=8/7 btw.

3 0

3 years ago

Read 2 more answers

How do I correctly solve this?

Gelneren [198K]

<h3>Answer: y = 14</h3>

===================================

Explanation:

The two angles involving x add up to 180 degrees. This is because they are same side interior angles (and because the horizontal lines are parallel)

So,

(angle BCF) + (angle EFC) = 180

(5x - 66) + (2x + 50) = 180

5x - 66 + 2x + 50 = 180

7x - 16 = 180

7x - 16+16 = 180+16 ... add 16 to both sides

7x = 196

7x/7 = 196/7 .... divide both sides by 7

x = 28

This will be used to help find y

Notice how the angles BCF and ACD are vertical angles, therefore they are congruent or the same measure

angle ACD = angle BCF

9y - 52 = 5x - 66

9y - 52 = 5*28 - 66 ..... replace x with 28 (since x = 28)

9y - 52 = 140 - 66

9y - 52 = 74

9y - 52+52 = 74+52 .... add 52 to both sides

9y = 126

9y/9 = 126/9 .... divide both sides by 9

y = 14

3 0

3 years ago

Read 2 more answers