Find the value of 2y if 2x - y = 5 and
x + y = 4.​

Answer:

[tex]\displaystyle \cos\left(-\frac{7\,\pi}{12}\right) = \frac{\sqrt{2} - \sqrt{6}}{4}[/tex].

Step-by-step explanation:

Convert the angle [tex]\displaystyle \left(-\frac{7\, \pi}{12}\right)[/tex] to degrees:

[tex]\displaystyle \left(-\frac{7\, \pi}{12}\right) = \left(-\frac{7\, \pi}{12}\right) \times \frac{180^\circ}{\pi} = -105^\circ[/tex].

Note, that [tex]\left(-105^\circ\right)[/tex] is the sum of two common angles: [tex]\left(-45^\circ\right)[/tex] and [tex]\left(-60^\circ\right)[/tex].

By the sum-angle identity of cosine:

[tex]\cos(A + B) = \cos(A)\cdot \cos(B) - \sin(A) \cdot \sin(B)[/tex].

Apply the sum formula for cosine to find the exact value of [tex]\cos\left(-105^\circ \right)[/tex].

[tex]\begin{aligned}\cos\left(-105^\circ \right) &= \cos\left(\left(-45^\circ\right) + \left(-60^\circ\right)\right) \\ &= \cos\left(-45^\circ\right) \cdot \cos\left(-60^\circ\right)\right) - \sin\left(-45^\circ\right) \cdot \sin\left(-60^\circ\right)\right) \\ &= \frac{\sqrt{2}}{2} \times \frac{1}{2} - \left(-\frac{\sqrt{2}}{2}\right)\times \left(-\frac{\sqrt{3}}{2}\right) = \frac{\sqrt{2} - \sqrt{6}}{4}\end{aligned}[/tex].

[tex]\displaystyle \left(-\frac{7\, \pi}{12}\right) = \left(-\frac{7\, \pi}{12}\right) \times \frac{180^\circ}{\pi} = -105^\circ[/tex]. In other words, [tex]\displaystyle \left(-\frac{7\, \pi}{12}\right)[/tex] and [tex]\left(-105^\circ\right)[/tex] correspond to the same angle. Therefore, the cosine of [tex]\displaystyle \left(-\frac{7\, \pi}{12}\right)\![/tex] would be equal to the cosine of [tex]\left(-105^\circ\right)\![/tex].

[tex]\displaystyle \cos\left(-\frac{7\,\pi}{12}\right) = \cos\left(-105^\circ\right) = \frac{\sqrt{2} - \sqrt{6}}{4}[/tex].

Answer:

fndskfnzxc.,vnf

Step-by-step explanation:

fnznmsdv,ns.d,

Answer:

fwnancasca

Step-by-step explanation:

32+9

the domain of a sine function is from negative to positive infinity. The domain is written as (-∞,∞) in interval notion. It it the same thing as the domain is all real numbers.

hope this helped <3

Answer:

the domain of the function y=sin(x) ) is all real numbers (sine is defined for any angle measure), the range is −1≤y≤1 .

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

Angle-Angle-Side (AAS) congruence

HTH :)

Answer:

4

Step-by-step explanation:

The greatest common factor (GCF)

The greatest common factor of 16 and 100 is 4, and it represents the largest number that can evenly divide both 16 and 100.

Here,

To find the greatest common factor (GCF) of two numbers, we need to identify the largest number that can evenly divide both numbers.

Here's the step-by-step process to find the GCF of 16 and 100:

Step 1: List the factors of each number.

The factors of 16 are 1, 2, 4, 8, and 16.

The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100.

Prime factorization of 16:

16 = 2 * 2 * 2 * 2

Prime factorization of 100:

100 = 2 * 2 * 5 * 5

Step 2: Identify the common factors.

The common factors of 16 and 100 are 1, 2, 4.

Step 3: Find the greatest common factor.

Among the common factors, the greatest common factor (GCF) is the largest one, which is 4.

So, the GCF of 16 and 100 is 4.

In conclusion, the greatest common factor of 16 and 100 is 4, and it represents the largest number that can evenly divide both 16 and 100.

To learn more on GCF click:

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Answer:

20

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

Answer: Valentina measured incorrectly.

Step-by-step explanation: 1 feet equals to 12 inches. If you substitute this value for all the other values like 5 ft and 8 inches (Noah's measurement). Firstly, 5 multiplied by 12 is 60, then you would add 8 to it. Caleb already measured the same amount of inches as Noah so we can just leave that one. Same with Mary, 3 * 12 inches = 36 plus 32 which is also 68. Finally, we are left with Valentina in which she has 2 * 12 inches =24 plus 48 which is 72, not 68. Hence, Valentina measured incorrectly.

Answer:

umm maybe 1.3

Step-by-step explanation:

Answer:

1×10 exponent 12

Step-by-step explanation:

hipe that helped

Answer:

Hi, I'm new can I get marked as Brainliest It would be highly appreciated.

Hope my answer helps :)

lets get into answering your question.

Step-by-step explanation:

1e+12

Answer:

Yea it does

Step-by-step explanation:

Answer:

x = 17

Step-by-step explanation:

We are going to call the missing angle in triangle EDC, "y"

x+y+100=4x+49+y

Eliminate the "y" on both sides

x+100=4x+49

move the x by subtracting the x on the left from the right

100= 3x +49

Move the numbers by subtracting 49 from 100

51 = 3x

Divide both sides by 3

17=x

Answer:

x=17

Step-by-step explanation:

Hello! There are a few important pieces of information you need to keep in mind before trying to solve this problem:

Now that we know these two pieces of information, we can begin to set up our problem. Because the angles in a triangle always add up to 180, we can set up the problem as follows:

x + 100° + ∠DCE = 4x + 49° + ∠ACB

Now this is where the vertical angles come in. Angles ∠DCE and ∠ACB are vertical, which makes them congruent. Since they are the same value, we can subtract them from either side of the equation. (NOTE: We can only do this because they are the same value. Subtracting angles of different values will mess up your answer!!!)

Now, we have the same problem in much simpler terms. We can now simplify it in order to get x.

4x + 49 = x + 100 (subtract 49 from both sides)

4x = x + 51 (subtract x from both sides)

3x = 51 (divide both sides by 3)

x = 17 (FINAL ANSWER)

I really hope this helped! Take care! :)

Answer:

2

Step-by-step explanation:

0.5 is the same thing as 1/2 and half of 4 is 2

Answer:

According to my calculations, it should be 5.78

Step-by-step explanation:

I just used a calculator for this :b

Answer:$5.78

Step-by-step explanation:

Just divide 7 by 40.50

Answer:

I would help you but that's cheating cause your doing a test.

Step-by-step explanation:

Answer: Maddie is nine

Step-by-step explanation:

PETER: 9

Kelly: 12

MAX: 14

Ashley: 11

Maddie: 9

Answer:

x=70 y=110 z=30 is all of the variables

Answer:

193 cm

Step-by-step explanation:

super man is 200 cm

hulk is 196 cm

tarzan 193 cm

Answer: A on Edge

Step-by-step explanation:

Answer:

Step-by-step explanation:

4015000

Answer:

Step-by-step explanation:

is this 8th grade math?

Answer:

53/54 = 106/108

Step-by-step explanation:

You can find the answer because 53/54 * 2/2 = 106/108

2/2 = 1 - right? When you multiply any number by one, it stays the same. That's how you can tell, 53/54 = 106/108.

Answer:

No it cant

Step-by-step explanation:

it would have to be 54/54 to be equal to 1.

Answer:

Step-by-step explanation:

2

The sides this polygon have is 5 sides.

A polygon is a closed figure made up of three or more line segments connected end to end.

Any closed figure made by 4 line segments joined end to end in series is called a quadrilateral.

We are given  shown in the illustration, starfish that has the shape of a pentagon.

Since a pentagon is a polygon that has 5 sides.

Therefore, the sides this polygon have is 5 sides.

Learn more about vertex and apex;

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Answer:

(x-7)^2 + y^2 = 9

Step-by-step explanation:

Equation of a circle:

(x-h)^2 + (y-k)^2 = r^2

(x-7)^2 + (y-0)^2 = 3^2

(x-7)^2 + y^2 = 9

Answer:

153.846153846

Step-by-step explanation:

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< \ just kidding its for me

Answer:

C. 0.5

Step-by-step explanation:

If point B is nearest to zero and that far from three, it is going to be 0.5. Not to mention, you can estimate that point is about a half from one.

Answer:

C

Step-by-step explanation:

A - 3.6 is ahead of C, so nope

B - -0.2 is behind A, nope

C - 0.5 works because it seems reasonably distanced (closer to 0 than 3.5)

D - 2 is closer to 3.5, but point b is closer to 0.

Also, if you divide the section between A and C by 7, you can find that 0.5 works because it should be the first section of 0.5