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Ann [662]
2 years ago
10

Given that cos(30°) = cos(45°)cos(15°) + sin(45°)sin(15°), it follows that cos(30°) =

Mathematics
2 answers:
mario62 [17]2 years ago
8 0

Answer:

cos(30\°) = cos(45\°-15\°)

Step-by-step explanation:

To solve this problem you must know the formula of subtraction of angles for the function cosx.

The formula is:

cos(h-d) = cos(h)cos(d) + sin(h)sin(d)

We can write 30° as: 45° - 15°

Then:

cos(30\°) = cos(45\°-15\°)

Using the formula for subtraction of angles we have:

cos(45\°-15\°) = cos(45\°)cos(15\°) + sin(45\°)sin(15\°)

Notice that we have achieved the expression shown in the statement

Finally:

cos(30\°) = cos(45\°-15\°)

marin [14]2 years ago
6 0

Answer:

square root 3/2

Step-by-step explanation:

on usatestprep and the unit circle

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solve for each variable i don’t need work shown just the answers please thank you very much i have 2 hours to get this done
ale4655 [162]

Answer:

(a)

x = 18.5

y = 22.5

(b)

x = 10

Step-by-step explanation:

Solving (a):

7x - 19 and 3x + 14 are interior angles.

So:

7x - 19 + 3x +14 = 180

Collect like terms

7x + 3x = 180 - 14 + 19

10x = 185

x = 18.5

7x - 19 and 5y - 2 are equal angles --- corresponding angles

So:

5y - 2 = 7x - 19

Make 5y the subject

5y  = 7x - 19+2

5y  = 7x -17

Make y the subject

y = \frac{1}{5} (7x - 17)

Substitute x = 18.5

y = \frac{1}{5} (7*18.5 - 17)

y = \frac{1}{5} (112.5)

y = 22.5

Solving (b):

The triangle is right-angled.

So:

5x + 3 + 2x + 17 + 90 = 180

Collect Like Terms

5x + 2x = 180 - 90 - 17-3

7x = 70

x = 10

3 0
3 years ago
Pls help ;-; Student #3:
Setler79 [48]

Solved the inequality correctly and graphed their solution correctly.

8 0
2 years ago
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teri and her friends bought a party size sandwich that was 7/9 yard long. they ate 2/3 of a yard. what part of the yard was left
Marysya12 [62]
Teri had 7/9 of a sandwich, you need to find a common denominator for 2/3. Multiply 2/3 by 3 which is 6/9. (6/9 is how much they ate) Then you subtract 7/9 by 6/9 (7/9-6/9=1/9)
Answer:1/9 of a yard

I hope this helped.. not much of a teacher hahah :)
6 0
3 years ago
What is the height of a trapezoid with an area of 99 in.2 whose bases are 6 in. and 12 in.?
vladimir1956 [14]

Answer:

trapezoid area = ((sum of the bases) ÷ 2) • height

trapezoid area = ((6 + 12) / 2) * height

trapezoid area = 18 / 2 * height

height = 99/9 = 11

Step-by-step explanation:

7 0
2 years ago
PLEASE HELP WITH GEOMETRY IM STUCK!?}
Ilya [14]

Answer:

13.8

Step-by-step explanation:

Recall the trigonometric ratios

Sine = Opposite over Hypotenuse (SOH)

Cosine = Adjacent over Hypotenuse (CAH)

Tangent = Opposite over Adjacent (TOA)

Now lets look back at the question

We are given an angle and its adjacent side length (11) and we need to find the hypotenuse

The hypotenuse and adjacent sides corresponds with the trig function cosine so we will use cosine to solve for x

( remember that cosine = adjacent over hypotenuse )

cos(37)=\frac{11}{x}

step 1 multiply each side by x

cos(37)*x=xcos(37)\\\frac{11}{x} *x=11

now we have xcos(37)=11

step 2 divide each side by cos(37)

\frac{xcos(37)}{cos(37)} =x\\\frac{11}{cos(37)} =13.77349\\

we're left with x = 13.77439

Our last step would be to round to the nearest tenth

We would get that the answer is 13.8

3 0
2 years ago
Read 2 more answers
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