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777dan777 [17]
3 years ago
9

Express 8 sin^2x - 10sinxcosx in the form a+b sin(2x+c).

Mathematics
1 answer:
ladessa [460]3 years ago
7 0
8 sin2x - 10sinxcosx = 8*2sinXcosX-10sinXcosX = 16sinXcosX - 10sinXcosX = 6sinXcosX=3sin2x
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Compare square root of one hundred eighty and one hundred two eighths using <, >, or =.
olga2289 [7]

Converting the mixed number to a decimal, the correct comparison of the numbers is given as follows:

\sqrt{180} > \sqrt{100 \frac{2}{8}}

<h3>What is a mixed number?</h3>

A mixed number is represented by an integer part and a fractional part, as follows:

a b/c.

In which:

  • a is the integer part.
  • b/c is the fractional part.

In this problem, the numbers are given as follows:

\sqrt{180}, \sqrt{100 \frac{2}{8}}

The mixed number is:

100 and 2/8 = 100 + 0.25 = 100.25.

The square root is an increasing function, hence the higher the input, the higher the square root, as 180 > 100 the comparison is:

\sqrt{180} > \sqrt{100 \frac{2}{8}}

More can be learned about mixed numbers at brainly.com/question/1746829

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6 0
2 years ago
Charlotte’s weekly paycheck is based on the number of hours worked during the week and on the weekend. If she works 13 hours dur
Gelneren [198K]
I am setting the week hourly rate to x, and the weekend to y.  Here is how the equation is set up:

13x + 14y = $250.90
15x + 8y = $204.70

This is a system of equations, and we can solve it by multiplying the top equation by 4, and the bottom equation by -7.  Now it equals:

52x + 56y = $1003.60
-105x - 56y = -$1432.90

Now we add these two equations together to get:

-53x = -$429.30 --> 53x = $429.30 --> (divide both sides by 53) x = 8.10.  This is how much she makes per hour on a week day.

Now we can plug in our answer for x to find y.  I am going to use the first equation, but you could use either.

$105.30 + 14y = $250.90.  Subtract $105.30 from both sides --> 14y = $145.60 divide by 14 --> y = $10.40

Now we know that she makes $8.10 per hour on the week days, and $10.40 per hour on the weekends.  Subtracting 8.1 from 10.4, we figure out that she makes $2.30 more per hour on the weekends than week days.
7 0
3 years ago
Read 2 more answers
A line intersects the points
allochka39001 [22]

Answer:

The answer would be -5. Hopefully I'm not wrong.

3 0
2 years ago
SOMEONE HELP ME I GO CLASS IN 10 MINS!!
QveST [7]

Answer:

i think its mq

Step-by-step explanation:

3 0
3 years ago
Simplify the expression. Rewrite using only positive exponents.
ivanzaharov [21]

The simplification form of the provided expression is x¹⁸a³b³ option

(d) x¹⁸a³b³ is correct.

<h3>What is an integer exponent?</h3>

In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.

It is given that:

The expression:

= \rm (\dfrac{x^4a^2b^3}{x^{-2}ab^2})^3

After using the integer exponent property:

\rm =\dfrac{x^{12}a^6b^9x^6}{a^3b^6}

= a³b³x¹⁸ Or

=x¹⁸a³b³

Thus, the simplification form of the provided expression is x¹⁸a³b³ option

(d) x¹⁸a³b³ is correct.

Learn more about the integer exponent here:

brainly.com/question/4533599

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4 0
2 years ago
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