Ask question

Ask question

All categories

Thepotemich [5.8K]

2 years ago

14

5(x + 3) + 9 = 3 (x - 2) + 6 Please Show Work.

2 answers:

snow_lady [41]2 years ago

8 0

5(x + 3) + 9 = 3 (x - 2) + 6

5x + 15 + 9 = 3x - 6 + 6

5x + 24 = 3x

5x - 3x = -24

2x = -24

x = -24/2

x = - 12

Olin [163]2 years ago

4 0

Remove parentheses

Eliminate the opposite calculate the sum

Answer -12

You might be interested in

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

Can someone plz help this is like my 5th time putting up this question!!!

serg [7]

Answer:

the table should be 25,98,173,248

3 0

2 years ago

<img src="https://tex.z-dn.net/?f=What%20are%20the%20domain%20and%20range%20of%20the%20function%20f%28x%29%3D%5Cfrac%7B3%7D%7B4%

jeka57 [31]

The domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that f takes.

8 0

3 years ago

34(4a + 12) = 21 a = <br> please find my answer

noname [10]

Answer: a = 2,84

Step-by-step explanation:

34(4a + 12) = 21 a =

136a + 408 = 21

136a = -408 + 21

136a = - 387

a = <u>- 387 </u>

136

a = - 2,84

8 0

2 years ago

Can anyone help me on this? also pls use step by step thank you

Lisa [10]

Answer:

1000 = 125 /65536

Step-by-step explanation:

Rewrite the expression using the negative exponent rule and then Raise

2 to the power of 21 . Cancel the common factor of 32. Combine 125 and 1 /65536

7 0

2 years ago

Read 2 more answers