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3 years ago

Solve for x in the diagram.

Mathematics

2 answers:

Kazeer [188]3 years ago

7 0

It is a right triangle so,

a² + b² = x²
9² + 12² = x²
225 = x²
√225 = x
15 = x

Hope this helps :)

Leokris [45]3 years ago

6 0

As you can see, the answer is 15

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Prove that sin3a-cos3a/sina+cosa=2sin2a-1

Sloan [31]

Answer:

$\frac{sin(3a)-cos(3a)}{sin(a)+cos(a)} =2sin(2a)-1$

Step-by-step explanation:

we are given

$\frac{sin(3a)-cos(3a)}{sin(a)+cos(a)} =2sin(2a)-1$

we can simplify left side and make it equal to right side

we can use trig identity

$sin(3a)=3sin(a)-4sin^3(a)$

$cos(3a)=4cos^3(a)-3cos(a)$

now, we can plug values

$\frac{(3sin(a)-4sin^3(a))-(4cos^3(a)-3cos(a))}{sin(a)+cos(a)}$

now, we can simplify

$\frac{3sin(a)-4sin^3(a)-4cos^3(a)+3cos(a)}{sin(a)+cos(a)}$

$\frac{3sin(a)+3cos(a)-4sin^3(a)-4cos^3(a)}{sin(a)+cos(a)}$

$\frac{3(sin(a)+cos(a))-4(sin^3(a)+cos^3(a))}{sin(a)+cos(a)}$

now, we can factor it

$\frac{3(sin(a)+cos(a))-4(sin(a)+cos(a))(sin^2(a)+cos^2(a)-sin(a)cos(a)}{sin(a)+cos(a)}$

$\frac{(sin(a)+cos(a))[3-4(sin^2(a)+cos^2(a)-sin(a)cos(a)]}{sin(a)+cos(a)}$

we can use trig identity

$sin^2(a)+cos^2(a)=1$

$\frac{(sin(a)+cos(a))[3-4(1-sin(a)cos(a)]}{sin(a)+cos(a)}$

we can cancel terms

$=3-4(1-sin(a)cos(a))$

now, we can simplify it further

$=3-4+4sin(a)cos(a))$

$=-1+4sin(a)cos(a))$

$=4sin(a)cos(a)-1$

$=2\times 2sin(a)cos(a)-1$

now, we can use trig identity

$2sin(a)cos(a)=sin(2a)$

we can replace it

$=2sin(2a)-1$

so,

$\frac{sin(3a)-cos(3a)}{sin(a)+cos(a)} =2sin(2a)-1$

7 0

3 years ago

Read 2 more answers

Carrie wished to build a rectangular dog run along theside of her garage. The garage will serve as one side of the fence. If she

Nat2105 [25]

Given:

Carrie has 180 ft of the fencing and wishes the fence to be 4times as long as it is wide.

To Find:

The area in square feet that the fencing encloses.

Answer:

The fence encloses 3600 sq ft.

Step-by-step explanation:

Let x denote the length of the dog run and y denote the width of the dog run.

Given that the garage wall serves as one side of the dog run, we are left with 3 other sides to instal the fence.

Carrie has 180ft of fencing with her, so the sum of the lengths of the 3 sides has to be equal to 180. We can represent this in the form of an equation as

$x+y+y=180\\\\x+2y=180\\\\x=180-2y$

We are also given that Carrie wishes the fence to be 4 times as long as it is wide.

So,

$x=4y$

Replacing this value into the first equation, we have

$4y=180-2y\\\\
6y=180\\\\
y=30$

Therefore,

$x=(4)(30)=120$

Thus, the length of the dog run is 120ft and the width is 30ft.

The area enclosed will be equal to the length multiplied with the width. So,

$(120)(30)=3600$

The fence encloses 3600 sq ft.

4 0

3 years ago

Megan has $45.12 in her purse. She spends $7.89 for lunch and $21.25 for a pair of sunglasses.

tekilochka [14]

Answer:

15.98 dollars

Step-by-step explanation:

its really easy

we need to subtract the total amount that she has spent from the total amount that she had in her purse

the total amount in Megan's purse=$45.12

total amount that Megan spent=$7.89+$21.25 =$29.14

now,

the exact amount that Megan has left = $45.12-$29.14=$15.98

5 0

2 years ago

I need help with number 16 i need the answer by 8:45 please. Thank you

Nadusha1986 [10]

Type o ( ii) = 6 . 25

Type A ( l^A l ^A or l ^A i ) = 18 . 75

Type B ( l ^b l^b or l ^ bi ) = 18.75

Type AB ( l ^ A l^ B) = 56.25

3 0

3 years ago

To simplify expressions, we often ___ like terms.

tekilochka [14]

Answer: combine

Step-by-step explanation:

When you combine like terms, it shortens or simplified the equation

Example: 2x-5+15

Combine actual numbers -5 and 15.

2x+10

6 0

3 years ago