What is the GCF of 12 and 48?

< ADF measures 2x degrees and < FDC measures x + 12 degrees. What is the measure

gtnhenbr [62]

Answer:

<h2>Angle ADF is equal to 52° and angle FDC is equal to 38°.</h2>

Step-by-step explanation:

In the image attaches, you can observe that angles ADF and FDC are complementary angles, because they sum 90°.

$\angle ADF + \angle FDC = 90\°$

And we know that

$\angle ADF=2x\\\angle FDC = x+12$

Replacing these expressions, we have

$2x+x+12=90\°\\3x=90\° - 12\°\\x=\frac{78}{3}\\ x=26$

Then, we replace this value in each expression to find both angles measures.

$\angle ADF= 2(26)=52\°\\\angle FDC = 26+12=38\°$

Therefore, angle ADF is equal to 52° and angle FDC is equal to 38°.

7 0

3 years ago

Can you please answer the question?

Roman55 [17]

The <em>trigonometric</em> expression $\frac{\tan^{2} \alpha}{\tan \alpha - 1} + \frac{\cot^{2} \alpha}{\cot \alpha - 1}$ is equivalent to the <em>trigonometric</em> expression $\sec \alpha \cdot \csc \alpha + 1$ .

<h3>How to prove a trigonometric equivalence</h3>

In this problem we must prove that <em>one</em> side of the equality is equal to the expression of the <em>other</em> side, requiring the use of <em>algebraic</em> and <em>trigonometric</em> properties. Now we proceed to present the corresponding procedure:

$\frac{\tan^{2} \alpha}{\tan \alpha - 1} + \frac{\cot^{2} \alpha}{\cot \alpha - 1}$

$\frac{\tan^{2}\alpha}{\tan \alpha - 1} + \frac{\frac{1}{\tan^{2}\alpha} }{\frac{1}{\tan \alpha} - 1 }$

$\frac{\tan^{2}\alpha}{\tan \alpha - 1} - \frac{\frac{1 }{\tan \alpha} }{\tan \alpha - 1}$

$\frac{\frac{\tan^{3}\alpha - 1}{\tan \alpha} }{\tan \alpha - 1}$

$\frac{\tan^{3}\alpha - 1}{\tan \alpha \cdot (\tan \alpha - 1)}$

$\frac{(\tan \alpha - 1)\cdot (\tan^{2} \alpha + \tan \alpha + 1)}{\tan \alpha\cdot (\tan \alpha - 1)}$

$\frac{\tan^{2}\alpha + \tan \alpha + 1}{\tan \alpha}$

$\tan \alpha + 1 + \cot \alpha$

$\frac{\sin \alpha}{\cos \alpha} + \frac{\cos \alpha}{\sin \alpha} + 1$

$\frac{\sin^{2}\alpha + \cos^{2}\alpha}{\cos \alpha \cdot \sin \alpha} + 1$

$\frac{1}{\cos \alpha \cdot \sin \alpha} + 1$

$\sec \alpha \cdot \csc \alpha + 1$

The <em>trigonometric</em> expression $\frac{\tan^{2} \alpha}{\tan \alpha - 1} + \frac{\cot^{2} \alpha}{\cot \alpha - 1}$ is equivalent to the <em>trigonometric</em> expression $\sec \alpha \cdot \csc \alpha + 1$ .

To learn more on trigonometric expressions: brainly.com/question/10083069

#SPJ1

6 0

2 years ago

Sam bought 6 baseball trading cards to add to his collection. The next day his dog ate half of his collection. There are now 27

enyata [817]

He started with 42 cards.

27-6= 21

21×2= 42.

Hope this helps! :)

\(^ ◇^)/

7 0

3 years ago

Read 2 more answers

The ice cream dessert at a restaurant comes in 4 flavors:

Cloud [144]

Answer:

8 mint

5 strawberry

1 lemon

1 cookie dough

6 0

3 years ago

Help 8th grade need answers quick

yaroslaw [1]

Answer:

with what nothings there

Step-by-step explanation:

5 0

3 years ago