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2 years ago

Please help with all of question 4.

Mathematics

1 answer:

olga55 [171]2 years ago

6 0

Answer:

Step-by-step explanation:

Combine like terms: Like terms have same variable with same power and to combine the like terms, add/subtract the co efficient of the variables.

<h3>Perimeter:</h3>

Perimeter = sum of all sides

a) Perimeter of ΔABC = AB + BC + CA

= x + 14 + x + 14 + x + 14

= x + x + x + 14 + 14 + 14 {Combine like terms}

= 3x + 42

b) EF = DI - GH

= 2x + 3 - x

= 2x - x + 3

= x + 3

c) FG = HI - ED

= 12 + 2x - (x + 5)

= 12 + 2x - x - 5 {To open the brackets, (-1) is distributed to x and 5}

= 12 - 5 + 2x - x

= 7 + x

d) Perimeter of DEFGHI = DE + EF + FG + GH + HI + ID

= x + 5 + x + 3 + 7 +x + x + 12 +2x + 2x + 3

= x +x + x + x + 2x + 2x + 5 + 3 + 7 + 3 + 12

= 8x + 30

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Can someone check this one for me , thank you!

Rudik [331]

Answer:

Step-by-step explanation:

Using sum/difference to product identity

• sin x - sin y = 2 cos( $\frac{x+y}{2}$ ) sin ( $\frac{x-y}{2}$ )

with x = 4Θ and y = 2Θ

Then

sin(4Θ) - sin(2Θ)

= 2 cos( $\frac{4o+2o}{2}$ ) sin( $\frac{4o-2o}{2}$ )

= 2cos(3Θ)sinΘ → C

8 0

3 years ago

let sin(θ) =3/5 and tan(y) =12/5 both angels comes from 2 different right trianglesa)find the third side of the two tringles b)

statuscvo [17]

In a right triangle, we haev some trigonometric relationships between the sides and angles. Given an angle, the ratio between the opposite side to the angle by the hypotenuse is the sine of this angle, therefore, the following statement

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

Describes the following triangle

To find the missing length x, we could use the Pythagorean Theorem. The sum of the squares of the legs is equal to the square of the hypotenuse. From this, we have the following equation

$x^2+3^2=5^2$

Solving for x, we have

$\begin{gathered} x^2+3^2=5^2 \\ x^2+9=25 \\ x^2=25-9 \\ x^2=16 \\ x=\sqrt[]{16} \\ x=4 \end{gathered}$

The missing length of the first triangle is equal to 4.

For the other triangle, instead of a sine we have a tangent relation. Given an angle in a right triangle, its tanget is equal to the ratio between the opposite side and adjacent side.The following expression

$\tan (y)=\frac{12}{5}$

Describes the following triangle

Using the Pythagorean Theorem again, we have

$5^2+12^2=h^2$

Solving for h, we have

$\begin{gathered} 5^2+12^2=h^2 \\ 25+144=h^2 \\ 169=h^2 \\ h=\sqrt[]{169} \\ h=13 \end{gathered}$

The missing side measure is equal to 13.

Now that we have all sides of both triangles, we can construct any trigonometric relation for those angles.

The sine is the ratio between the opposite side and the hypotenuse, and the cosine is the ratio between the adjacent side and the hypotenuse, therefore, we have the following relations for our angles

$\begin{gathered} \sin (\theta)=\frac{3}{5} \\ \cos (\theta)=\frac{4}{5} \\ \sin (y)=\frac{12}{13} \\ \cos (y)=\frac{5}{13} \end{gathered}$

To calculate the sine and cosine of the sum

$\begin{gathered} \sin (\theta+y) \\ \cos (\theta+y) \end{gathered}$

We can use the following identities

$\begin{gathered} \sin (A+B)=\sin A\cos B+\cos A\sin B \\ \cos (A+B)=\cos A\cos B-\sin A\sin B \end{gathered}$

Using those identities in our problem, we're going to have

$\begin{gathered} \sin (\theta+y)=\sin \theta\cos y+\cos \theta\sin y=\frac{3}{5}\cdot\frac{5}{13}+\frac{4}{5}\cdot\frac{12}{13}=\frac{63}{65} \\ \cos (\theta+y)=\cos \theta\cos y-\sin \theta\sin y=\frac{4}{5}\cdot\frac{5}{13}-\frac{3}{5}\cdot\frac{12}{13}=-\frac{16}{65} \end{gathered}$

4 0

1 year ago

Question 7 of 12<br> 64 =<br> O A. 9<br> OB. 7<br> C. 8<br> O D. 16<br> Pleaseee

sasho [114]

Answer:7

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

3 gallons But in pints

MakcuM [25]

Answer: 24 pints

Step-by-step explanation:

multiply the volume value by 8

3*8=24

8 0

3 years ago

How many square inches in a foot

Cloud [144]

Answer:

There are 144 square inches in a square foot.

Step-by-step explanation:

A square foot is a square that is 1 foot by 1 foot. Since there are 12 inches in 1 foot, and to get the area you need to multiple 2 adjacent sides together, you do 12 times 12 which is 144 square inches. Many people have the misconception that a square foot has 12 square inches, but this is wrong since a square foot has dimensions of 12 inches by 12 inches, but when you multiply them together, you can see that the answer is actually 144.

5 0

3 years ago

Please help with all of question 4.​

Please help with all of question 4.