All categories

1 year ago

In the diagram below, if < A = 97 °, < B = 46 °, < D = 97 ° and < F = 37 °, we can say that

Mathematics

1 answer:

sdas [7]1 year ago

8 0

Answer:

(a) The two triangles are similar by AA

Step-by-step explanation:

Similar triangles have congruent corresponding angles and proportional corresponding side lengths.

<h3>Third angle</h3>

The third angle in triangle ABC is found using the fact that the sum of angles is 180°.

∠C = 180° -∠A -∠B

∠C = 180° -97° -46° = 37°

Two of the angles, A and C, match the measures of two of the angles in triangle DEF. The matches are ...

∠A = ∠D = 97°

∠C = ∠F = 37°

The two triangles are similar by AA.

<em>Additional comment</em>

The similarity statement can be ΔABC ~ ΔDEF.

You might be interested in

Please help i really need the points

photoshop1234 [79]

Answer:

D) dashed line, shade above

Step-by-step explanation:

The boundary line would be dashed for the reason because it is a sign without the line on the bottom, so if the sign looked like this (≥), then it would be solid. You are going to shade above because it is a greater than sign, so above! I hope this helps!

7 0

2 years ago

Suppose cos(x)= -1/3, where π/2 ≤ x ≤ π. What is the value of tan(2x). EDGE

AVprozaik [17]

Answer:

Step-by-step explanation:

We are given that:

$\displaystyle \cos x = -\frac{1}{3}\text{ where } \pi /2 \leq x \leq \pi$

And we want to find the value of tan(2<em>x</em>).

Note that since <em>x</em> is between π/2 and π, it is in QII.

In QII, cosine and tangent are negative and only sine is positive.

We can rewrite our expression as:

$\displaystyle \tan(2x)=\frac{\sin(2x)}{\cos(2x)}$

Using double angle identities:

$\displaystyle \tan(2x)=\frac{2\sin x\cos x}{\cos^2 x-\sin^2 x}$

Since cosine relates the ratio of the adjacent side to the hypotenuse and we are given that cos(<em>x</em>) = -1/3, this means that our adjacent side is one and our hypotenuse is three (we can ignore the negative). Using this information, find the opposite side:

$\displaystyle o=\sqrt{3^2-1^2}=\sqrt{8}=2\sqrt{2}$

So, our adjacent side is 1, our opposite side is 2√2, and our hypotenuse is 3.

From the above information, substitute in appropriate values. And since <em>x</em> is in QII, cosine and tangent will be negative while sine will be positive. Hence:

<h2> $\displaystyle \tan(2x)=\frac{2(2\sqrt{2}/3)(-1/3)}{(-1/3)^2-(2\sqrt{2}/3)^2}$ </h2>

Simplify:

$\displaystyle \tan(2x)=\frac{-4\sqrt{2}/9}{(1/9)-(8/9)}$

Evaluate:

$\displaystyle \tan(2x)=\frac{-4\sqrt{2}/9}{-7/9} = \frac{4\sqrt{2}}{7}$

The final answer is positive, so we can eliminate A and B.

We can simplify D to:

$\displaystyle \frac{2\sqrt{8}}{7}=\frac{2(2\sqrt{2}}{7}=\frac{4\sqrt{2}}{7}$

So, our answer is D.

7 0

3 years ago

The manager of a neighborhood plant nursery measured the height of every tree on the lot. The mean height of the trees was 75 in

zloy xaker [14]

Answer: D. skewed to the right

Step-by-step explanation:

just took it

4 0

2 years ago

How do you solve (x+4)2 ?

Savatey [412]

Answer:

find the value of x or do

(4x)2

Step-by-step explanation:

Daily fact:Noah's Ark is the vessel in the Genesis flood narrative through which God spares Noah, his family, and examples of all the world's animals from a world-engulfing flood. The story in Genesis is repeated, with variations, in the Quran, where the Ark appears as Safinat Nūḥ and al-fulk.

8 0

2 years ago

Read 2 more answers

Which measurement is the largest 6 kilometers 60 meters 600 centimeters 6000 millimeters

Tju [1.3M]

6 kilometers is the greatest,but arranging from greatest to least: 6km, 60m, 600 cm or 6000mm

60 meters = 60 meters * 1km/1000 meters = 0.06 km600 centimeters = 600 cm * 1m/100cm * 1km/1000m = 0.006 km6000 millimeters = 6000mm * 1m/1000mm * 1km/1000m = 0.006km

<span>thus arranging from greatest to least:6km, 60m, 600 cm or 6000mm</span>

4 0

2 years ago

Read 2 more answers