Find the value of x when 3x - 6 = 2(x + 4). A) -2 B) 1 C) 2 D) 18 5 E) 14

To estimate the height of a house Katie stood a certain distance from the house and determined that the angle of elevation to th

Nata [24]

the height of the house is $408ft$ .

<u>Step-by-step explanation:</u>

Here we have , To estimate the height of a house Katie stood a certain distance from the house and determined that the angle of elevation to the top of the house was 32 degrees. Katie then moved 200 feet closer to the house along a level street and determined the angle of elevation was 42 degrees. We need to find What is the height of the house . Let's find out:

Let y is the unknown height of the house, and x is the unknown number of feet she is standing from the house.

Distance of house from point A( initial point ) = x ft

Distance of house from point B( when she traveled 200 ft towards street = x-200 ft

Now , According to question these scenarios are of right angle triangle as

At point A

⇒ $Tan32 =\frac{Perpendicular}{Base}= \frac{y}{x}$

⇒ $Tan32 = \frac{y}{x}$

⇒ $y=x(Tan32 )$ ..................(1)

Also , At point B

⇒ $Tan42 = \frac{y}{x-200}$

⇒ $y=(x-200)(Tan42)$ ..............(2)

Equating both equations:

⇒ $(x-200)(Tan42) = x(Tan32)$

⇒ $x(Tan42-Tan32)=Tan42(200)$

⇒ $x=\frac{Tan42(200)}{(Tan42-Tan32)}$

⇒ $x=653ft$

Putting $x=653ft$ in $y=x(Tan32 )$ we get:

⇒ $y=x(Tan32 )$

⇒ $y=653(Tan32 )$

⇒ $y=408ft$

Therefore , the height of the house is $408ft$ .

4 0

3 years ago

ΔA’B’C’ is a reflection of ΔABC. Which best describes the reflection?

ruslelena [56]

Answer:

A reflection over the line x=3

Step-by-step explanation:

5 0

3 years ago

A rectangular swimming pool is twice as long as it is wide. A small concrete walkway surrounds the pool. The walkway is a 2 feet

Ksivusya [100]

Answer:

The width and the length of the pool are 12 ft and 24 ft respectively.

Step-by-step explanation:

The length (L) of the rectangular swimming pool is twice its wide (W):

$L_{1} = 2W_{1}$

Also, the area of the walkway of 2 feet wide is 448:

$W_{2} = 2 ft$

$A_{T} = W_{2}*L_{2} = 448 ft^{2}$

Where 1 is for the swimming pool (lower rectangle) and 2 is for the walkway more the pool (bigger rectangle).

The total area is related to the pool area and the walkway area as follows:

$A_{T} = A_{1} + A_{w}$ (1)

The area of the pool is given by:

$A_{1} = L_{1}*W_{1}$

$A_{1} = (2W_{1})*W_{1} = 2W_{1}^{2}$ (2)

And the area of the walkway is:

$A_{w} = 2(L_{2}*2 + W_{1}*2) = 4L_{2} + 4W_{1}$ (3)

Where the length of the bigger rectangle is related to the lower rectangle as follows:

$L_{2} = 4 + L_{1} = 4 + 2W_{1}$ (4)

By entering equations (4), (3), and (2) into equation (1) we have:

$A_{T} = A_{1} + A_{w}$

$A_{T} = 2W_{1}^{2} + 4L_{2} + 4W_{1}$

$448 = 2W_{1}^{2} + 4(4 + 2W_{1}) + 4W_{1}$

$224 = W_{1}^{2} + 8 + 4W_{1} + 2W_{1}$

$224 = W_{1}^{2} + 8 + 6W_{1}$

By solving the above quadratic equation we have:

W₁ = 12 ft

Hence, the width of the pool is 12 feet, and the length is:

$L_{1} = 2W_{1} = 2*12 ft = 24 ft$

Therefore, the width and the length of the pool are 12 ft and 24 ft respectively.

I hope it helps you!

8 0

3 years ago

Can you please show me how to do:

USPshnik [31]

Step-by-step explanation:

$6\sqrt3\cdot\dfrac{\sqrt3}{3}=\dfrac{(6\sqrt3)(\sqrt3)}{3}\\\\\text{use the associative property}\ (a\times b)\times c=a\times(b\times c)\\\\=\dfrac{(6)(\sqrt3\cdot\sqrt3)}{3}\\\\\text{use}\ \sqrt{a}\cdot\sqrt{a}=a\\\\=\dfrac{(6)(\not3)}{\not3}\qquad\text{cancel 3}\\\\=6$

3 0

3 years ago

Read 2 more answers

We found in the previous task, that Chef Walton cooked 50 meals first. However, for the next dinner service, Chef Barber prepare

makkiz [27]

Answer:

Chef Barber will now cook 50 meals first and The new y-intercept will change the result.

Step-by-step explanation:

I just did on edge

8 0

3 years ago