Proving Triangles Similar CFU

blondinia [14]

Look at the picture.

ΔABD and ΔBCD are similar, therefore:

$\dfrac{y}{5}=\dfrac{11}{y}\ \ \ |\cross\ multiply\\\\y^2=55\to y=\sqrt{55}$

Use Pythagorean theorem:

$x^2=5^2+(\sqrt{55})^2\\\\x^2=25+55\\\\x^2=80\to x=\sqrt{80}\\\\x=\sqrt{16\cdot5}\\\\x=\sqrt{16}\cdot\sqrt5\\\\\boxed{x=4\sqrt5}$

6 0

3 years ago

Which question could be answered by the organized list shown? Select two answers.

umka2103 [35]

Answer:

A and E

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

1-i need to mix 25% mineral spirits to the varnish i am using what ratio of spirit to varnish am i using? 2-if i use 240 ml of v

zhenek [66]

Answer:

(1) The required ratio of spirit to varnish is 1:3.

(2) You need 80 ml of mineral spirit.

(3) The ratio of tapestries' heights to width is 3:2.

Step-by-step explanation:

(1) If you need to mix 25% mineral spirit to the varnish, then the solution would contain 25% mineral spirit and 75% varnish.

So, $\frac{spirit}{varnish}=\frac{25}{75}$

$=\frac{1}{3}$

Thus, The required ratio of spirit to varnish is 1:3.

(2) If you use 240ml of varnish, then this quantity is 75% of the total solution or ration of varnish to the total solution will be 3:4.

Let $x$ be the quantity of total solution.

Then, $240:x=3:4$ .

⇒ $\frac{240}{x}=\frac{3}{4}$

⇒ $3x=240*4$

⇒ $x=\frac{240*4}{3}$

⇒ $x=320$

That is, total solution is 320 ml.

Now, Spirit = Total solution - Varnish

⇒Spirit = 320ml-240ml

⇒Spirit = 80ml

Hence, if you use 240 ml of varnish, you need 80 ml of mineral spirit.

(3) Robison's tapestries all measure 1.5m long and 1m wide. First, we express dimensions in whole numbers by multiplying them by 10.

Then, dimensions are 15m long and 10m wide.

Now, Height : Width = 15:10

⇒ $\frac{Height}{Width} =\frac{15}{10}$

⇒ $\frac{Height}{Width} =\frac{3}{2}$

Hence, the ratio of tapestries' heights to width is 3:2.

8 0

3 years ago

Simplify completely 12 times x to the third power minus 4 times x to the 2nd power plus 8 times x all over negative 2 times x.

Alenkinab [10]

The answer is: -6x^2+2x-4

5 0

3 years ago

A discuss moves from P1 (4,8) to P2 (15,17). What is the lincar displacement in the horizontal and vertical directions? What is

Yakvenalex [24]

Answer:

The horizontal displacement is 11 units, the vertical displacement is 9 units, and the projection angle is 39.3 degrees.

Step-by-step explanation:

We can start using the definition of displacement in one dimension between any 2 points which is the difference between them, so we have

$\Delta s = s_2-s_1$

And apply it to get the horizontal and vertical displacements.

Once we have found them, we can use trigonometric functions to find the projection angle with respect the horizontal.

Linear displacements.

Using the definition of displacement, we can write the horizontal displacement as

$\Delta x = x_2-x_1$

So we can use the given points $P1:(x_1,y_2) \text{ and } P_2: (x_2,y_2)$ on the displacement formula

$\Delta x = 15-4\\\Delta x = 11$

In the same manner we can look at the y components of those points to find the vertical displacement

$\Delta y = 17-8\\\Delta y =9$

Thus the horizontal displacement is 11 units and the vertical displacement is 9 units.

Projection angle.

The projection angle with respect the horizontal is the angle that is made between the line that connects the points P1 and P2 and the horizontal, so we can use the linear displacements previously found to write

$\tan(\theta) = \cfrac{\Delta y}{\Delta x}$

Solving for the angle we get

$\theta = \tan^{-1}\left(\cfrac{\Delta y}{\Delta x}\right)$

Replacing values

$\theta = \tan^{-1}\left(\cfrac{9}{11}\right)$

Which give us

$\theta = 39.3^\circ$

So the projection angle is 39.3 degrees.

7 0

3 years ago