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Lorico [155]
1 year ago
12

Solve the equation by first using a sum-to-product formula. (enter your answers as a comma-separated list. let k be any integer.

round terms to three
Mathematics
1 answer:
kykrilka [37]1 year ago
8 0

Solutions of the equation are 22.5°, 30°.

The given equation is sin(5θ) - sin(3θ) = cos(4θ)

We take left side of the equation

sin(5θ) - sin(3θ) = 2cos ((5θ+3θ)/2) (sin(5θ-3θ)/2)

=2cos4θsinθ  [From sum-product identity]

Now we can write the equation as

2cos(4θ)sin(θ) = cos(4θ)

2cos(4θ)sinθ - cos(4θ) = 0

cos(4θ)[2sinθ - 1] = 0

cos(4θ) = 0

4θ = 90°

θ = 90/4

θ = 22.5°

and (2sinθ - 1) = 0

sinθ = 1/2

θ = 30°

Therefore, solutions of the equation are 22.5°, 30°

For more information about trigonometric identities, visit

brainly.com/question/24496175

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What are the solutions to the equation (2x - 5) (3x - 1) = 0
SCORPION-xisa [38]

Answer:

x = 5/2 & x = 1/3

Step-by-step explanation:

Create two equations and solve

1) 2x-5 = 0 & 2) 3x-1 = 0

1) 2x = 5

x = 5/2

2) 3x = 1

x = 1/3

You create two equations as you want the left hand side (LHS) to equal 0 (RHS), thus if one of the brackets becomes 0 it will result in the whole LHS beocming 0 as the brackets are being multiplied (anything multiplied by 0 = 0)

6 0
3 years ago
Trevor’s total employment compensation is $33,500. If Trevor has no job expenses and his gross pay is $28,600, then his total em
svetoff [14.1K]

The equation be x/100 * 28,600 = 33,500, then we get 17%.

Trevor's total employee benefits exists 17.1% of his gross pay.

Therefore, the correct answer is option d. 17.1.

<h3>How to find Trevor's total employee benefits?</h3>

If you would like to know Trevor's total employee advantages, you can estimate this utilizing the subsequent steps:

To find the percentage of the total employee benefits x% of $28,600 exists $33,500.

To estimate the value of x, bring the variable to the left side and bring all the remaining variables to the right side. Simplify the values to estimate the result.

x/100 * 28,600 = 33,500

x = 33,500 * 100 / 28,600

x = 117.13% = 117%

117% - 100% = 17%

x = 17%

The correct result would be 17%.

Trevor's total employee benefits exists 17.1% of his gross pay.

Therefore, the correct answer is option d. 17.1.

To learn more about the value of x refer to:

brainly.com/question/12862290

#SPJ9

6 0
1 year ago
Read 2 more answers
[50 points!]
marshall27 [118]

Answer:

1/3

Explanation:

P(Freshman | Boy)

  • Freshman = 4
  • Boy = 12

⇒ Probability = Number of favorable outcomes ÷ Total number of possible outcomes

  • P(Freshman | Boy) = freshman/total boys
  • P(Freshman | Boy) = 4/12
  • P(Freshman | Boy) = 1/3
4 0
2 years ago
Read 2 more answers
Carlos is going to an amusement park for his 11th birthday with his 2 yr old brother and parents. His parents brought $100 to sp
amm1812
They have $49.00 left for desert because a ticket is $15 for each person 7 and older. So 15 × 3 people = $45.00. $1.50 per slice and they got 4 slices so 1.50 × 4 = $6.00. $45.00 + $6.00 = $51.00. $100 - $51 = $49.00
8 0
3 years ago
Which set of numbers may represent the lengths of the sides of a triangle?
Nataly [62]

Answer:

B. (5,12,13)

Step-by-step explanation:

The only answer with two side lengths that are greater than the largest side length.

3 0
2 years ago
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