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blsea [12.9K]
3 years ago
6

Find the exact value of sin –255°.

Mathematics
1 answer:
alekssr [168]3 years ago
8 0

Answer:

sin(-255°) = √2 + √6/4

Step-by-step explanation:

We need to find sin -255°

We know that sin(-a) = - sin(a)

so, sin(-255°) = - sin 255°

We know that 180° + 75° = 255°

Now we can write sin(255°) = sin(180° + 75°)

We can use the identity:

sin(x+y) = sin(x) cos(y)+cos(x)sin(y)

x = 180° , y = 75°

Solving,

sin(x+y) = sin(x) cos(y)+cos(x)sin(y)

sin(180° + 75°) = sin(180°) cos(75°)+cos(180°)sin( 75°)

sin(180°)  = 0

cos(75°) = √6 -√2/4

cos(180°) = -1

sin( 75°) = √2 + √6/4

Putting values,

sin(180° + 75°) = 0 (√6 -√2/4) + (-1)(√2 + √6/4)

sin(180° + 75°) = -(√2 + √6/4)

We know that sin(-255°) = -sin(255°)

Putting value of sin(255°)

sin(-255°)  = -(-(√2 + √6/4))

sin(-255°) = √2 + √6/4

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Sue has $2.80 in dimes and nickels. If she has 13 more dimes than nickels, how many of each coins does she have?
olga55 [171]
I have seen this question before and I think you meant 10 more dimes than nickels.

We can use substitution to answer this question. The value of a nickel is 5 cents, and we can use the variable n to represent the number of nickels. The value of a dime is 10 cents, and we can use the variable d to represent the number of dimes.

First lets figure out the equations.
.10d+.5n=2.80 (the number of nickels (n) multiplied by .5 will tell us their money value. Same thing for the dimes)
d-n=10 (since there are 13 more dimes than nickels, the number of dimes value (d) minus the number of nickels value (n) will give us 10)

Now lets isolate a variable in one of the equations, preferably the second one because it doesn't have any visible coefficients,

d-n=10
-n=10-d (subtracted the d from both sides)
n=-10+d (made the n positive)

Now that we have the value of n, we can plug it into the other equation.

.10d+.05n=2.80
.10d+.05(-10+d)=2.80 (we replaced the n with the value that we previously got)
.10d-.5+.05d=2.80 (did the multiplication)
.15d-.5=2.80 (combined like terms)
.15d=3.30 (added the .5 to both sides)
d=22 (divided both sides by the .15)

Now that we know that there are 22 dimes and we also know that there are 10 less nickels than dimes, so we can subtract 10 from 22 to get the number of nickels. 22-10=12

d=22
n=12


5 0
3 years ago
Emanuel is renting a car for 1week in Charleston, South Carolina. The rental car agency is charging $175 for the rental and 15%
Semenov [28]

Answer:

201.25 (im not 100% sure)

Step-by-step explanation:

If its correct please mark me as brainliest

6 0
2 years ago
Read 2 more answers
a radio station had 234 tickets to a concert. They gave away 5 times as many tickets to listeners as to employees. how many tick
RSB [31]

Answer:

39 tickets were given to the employees

Step-by-step explanation:

1. Approach

First, list the given information, then form an equation based on the given information. Finally, solve the equation with simplification and inverse operations.

2.Given

A total of 234 tickets were given away

5 times as many tickets were given away to listeners compared to employees

-Call the number of tickets given away to employees (x)

3. Form an equation

(Tickets_given_to_employees) + (Tickets_given_to_listeners) = (Total_tickets)

Substitute,

x + 5x = 234

Simplify,

6x + 234

Inverse operations,

6x = 234

/6      /6

x = 39

5 0
3 years ago
Which choice is equivalent to the expression below?
eimsori [14]

Answer:

C

Step-by-step explanation:

We have the expression:

\sqrt{-100}

Rewriting this yields:

=\sqrt{-1\cdot100}=\sqrt{-1}\cdot\sqrt{100}=i\sqrt{100}=10i

Therefore, our answer is C.

6 0
3 years ago
The coordinate −6 has a weight of 3, and the<br> coordinate 2 has a weight of 1
Damm [24]

The weight average of the coordinates is -4

<h3>How to determine the weight average?</h3>

The complete question is given as:

The coordinate -6 has a weight of 3 and the coordinate 2 has a weight of 1. And we need to calculate the weight average

The given parameters are:

  • Coordinate -6 has a weight of 3
  • Coordinate 2 has a weight of 1.

The weight average is then calculated as:

Weight average = Sum of (Weigh * Coordinate)/Sum of Weights

So, we have:

Weight average = (-6 * 3 + 2 * 1)/(3 +1)

Evaluate the products

Weight average = (-18 + 2)/(3 +1)

Evaluate the sum

Weight average = -16/4

Evaluate the quotient

Weight average = -4

Hence, the weight average of the coordinates is -4

Read more about average at

brainly.com/question/20118982

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<u>Complete question</u>

The coordinate -6 has a weight of 3 and the coordinate 2 has a weight of 1. Calculate the weight average

4 0
2 years ago
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