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3 years ago

Estimate: 89)364 A 4 B 270 10 D 450

Mathematics

2 answers:

Novosadov [1.4K]3 years ago

6 0

Answer:

expresión

Step-by-step explanation:

Gre4nikov [31]3 years ago

5 0

Answer:

Step-by-step explanation:

Either the question is displayed incorrectly, or some crucial information has been omitted.

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Are the triangles similar?

Fed [463]

Answer:

No, because the sides lengths are not proportional.

Step-by-step explanation:

<h3>What is the SAS similarity theorem ?</h3>

By definition, two triangles are similar if all their corresponding angles are congruent and their corresponding sides are proportional.

<h3>What is the AA similarity theorem ?</h3>

If two angles of one triangle are respectively equal to two angles of another triangle, then the two triangles are similar.

They both have an angle of 70°
This lies between sides of 6/9 and 9/18 respectively for the triangles
6/9 = 2/3 and 9/18 = 1/2
Hence, the sides are not proportional
They are not similar

8 0

2 years ago

Read 2 more answers

Two ferries travel across a lake 50 miles wide. One ferry goes 5 miles per hour slower than the other. If the slower ferry leave

Zepler [3.9K]

Answer:

Step-by-step explanation:

Let x be the speed of first ferry.

Then the speed of second slower ferry is x-5 (since 5 miles per hour slower)

Time taken by first ferry = distance/speed = $\frac{50}{x}$

Time taken by second ferry = $\frac{50}{x-5}$

Since second ferry starts one hour early, difference in times is 1 hour.

$\frac{50}{x-5}-\frac{50}{x}=1\\50x-50(x-5)=x(x-5)\\250 = x^2-5x\\x^2-5x-250 =0\\(x-10)(x+5) =0\\x=18.5, -13.5$

Speed cannot be negative.

Hence answer is speed of the first ferry = 18.5 mph

and second ferry i.e. slower ferry is = 13.5 mph

5 0

3 years ago

Solve for x<br> 3 x = − 2 <br><br> Give your answer as a fraction in its simplest form.

alexandr1967 [171]

It is -2/3
I gotchu don’t worry !

7 0

3 years ago

As the light passes from the air into the glass, it makes an angle θa in air and an angle θl in the lens material, relative to t

grin007 [14]

Answer:

The angles are related by Snell's Law of refraction.

Step-by-step explanation:

When light is incident on a medium at an angle this angle is known as angle of incidence and it undergoes refraction in the medium at an angle meaning that it deviates from it's normal path this angle of deviation measured with respect to normal is known as angle of refraction and are related by Snell's Law as under

$\mu _{air}sin(\theta _{a})=\mu _{lens}sin(\theta _{l})\\\\\therefore \frac{sin(\theta _{a})}{sin(\theta _{l})}=\mu _{lens}$

here $\mu _{lens}$ is the refractive index of material of lens and $\mu _{air}$ is the refractive index of air equaling 1

8 0

3 years ago

Given right triangle ABC, with altitude CD intersecting AB at point D. If AD = 5 and DB = 8, find the length of CD, in simplest

galben [10]

First we dra a triangle:

To prove that the triangles are similar we have to do the following:

Considet triangles ABC and ACD, in this case we notice that angles ACB and ADC are equal to 90°, hence they are congruent. Furthermore angles CAD and CAB are also congruent, this means that the remaining angle in both triangles will also be congruent, therefore by the AA postulate for similarity we conclude that:

$\Delta ABC\approx\Delta ACD$

Now consider triangles ABC and BCD, in this case we notice that angles ACB and BDC are congruent since they are both equal to 90°. Furthermore angles ABC and DBC are also congruent, this means that the remaining angle in both triangles will, once again, be congruent. Hence by the AA postulate we conclude that:

$\Delta ABC\approx\Delta BCD$

With this we conclude that traingles BCD and ACD are both similar to triangle ABC, and by the transitivity property of similarity we conclude that:

$\Delta ACD\approx BCD$

Now that we know that both triangles are similar we can use the following proportion:

$\frac{h}{x}=\frac{y}{h}$

this comes from the fact that the ratios should be the same in similar triangles.

From this equation we can find h:

$\begin{gathered} \frac{h}{x}=\frac{y}{h} \\ h^2=xy \\ h=\sqrt[]{xy} \end{gathered}$

Plugging the values we have for x and y we have that h (that is the segment CD) has length:

$\begin{gathered} h=\sqrt[]{8\cdot5} \\ =\sqrt[]{40} \\ =\sqrt[]{4\cdot10} \\ =2\sqrt[]{10} \end{gathered}$

Therefore, the length of segment CD is:

$CD=2\sqrt[]{10}$

6 0

2 years ago