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3 years ago

Someone please let me know the answer

Mathematics

1 answer:

erastova [34]3 years ago

3 0

Answer:

The answer is 30°

Step-by-step explanation:

$when \: \: \sqrt{3} \sin( \alpha ) - \cos( \alpha ) = 0 \\ \sqrt{3} \sin( \alpha ) = \cos( \alpha ) \\ multiply \: by \: \frac{1}{ \sqrt{3} \cos( \alpha ) } \\ then \\ \frac{ \sin( \alpha ) }{ \cos( \alpha ) } = \frac{1}{ \sqrt{3} } \\ \tan( \alpha ) = \frac{1}{ \sqrt{3} } \\ then \: \alpha = 30$

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Express the ratio AC/DF in simplest form

murzikaleks [220]

Answer:

$\frac{n}{28 \: cm}$

Step-by-step explanation:

AC = n, DF = 28 cm

$\huge \red{ \frac{AC}{DF} }= \purple{ \frac{n}{28 \: cm}} \\$

5 0

3 years ago

Expand. Your answer should be a polynomial in standard form. (6x+1)(1-3x)

Ludmilka [50]

Answer:

3x-18x^2+1

Step-by-step explanation:

(6x+1)(1-3x)

6x-18x^2+1-3x

6x-3x-18x^2+1

3x-18x^2+1

Hope this helps :)

3 0

3 years ago

Read 2 more answers

Last year, there were 380 students at woodland middle school. This year, the student population will increase by 5%. What will b

olga_2 [115]

399 because 380 x .05 =19 and 19+380
=399

5 0

3 years ago

Read 2 more answers

The 16th term of an AP is three times the 5th term.If the 12th term is 20 more the 7th term.Find the first term and the common d

Vlad1618 [11]

<h3>Answer:</h3>

First term = 6
Common difference= 4

<h3>Solution:</h3>

Let's take the first term as a and the common difference be d

The formula to find the nth term of an arithmetic progression is given by :

an = a + ( n - 1 ) d

According to question, we have :

16th term of an AP is three times the 5th term.

➝ a16 = 3 ( a5 )

➝ a + ( 16 - 1 )d = 3 ( a + ( 5 - 1 )d )

➝ a + 15d = 3 ( a + 4d )

➝ a + 15d = 3a + 12d

➝ 15d - 12d = 3a - a

➝ 3d = 2a

➝ 2a = 3d

➝ a = 3d/2‎ㅤ‎ㅤ‎ㅤ⸻ ( 1 )

And, the 12th term is 20 more the 7th term.

➝ a12 - ( a7 ) = 20

➝ a + ( n - 1 )d -( a + ( n - 1 )d ) = 20

➝ a + ( 12 - 1 )d - + a + ( 7 - 1 )d ) = 20

➝ a + 11d - ( a + 6d ) = 20

➝ a - a + 11d - 6d = 20

➝ 5d = 20

➝ d = 20/ 5

➝ d = 4

Using equation ( 1 )

➝ a = 3d / 2

➝ a = ( 3 × 4 ) / 2

➝ a = 12 / 2

➝ a = 6

3 0

2 years ago

Connor gathered dry ingredients to make a large pan of brownies. He mixed1 1/4 cups of sugar, 2 2/3 cups of flour and 1 1/6 cups

sveta [45]

Answer:

5 $\frac{1}{2}$

Explanation:

1. Find a common denominator for the three fractions. A common denominator is a number all three numbers divide into evenly. The lowest common denominator for 4, 3, and 6 is 12.

2. Find the numerators. This can be done by multiplying the current numerators by however many times the old denominator goes into the new denominator.

4 goes into 12 3 times

3 goes into 12 4 times

6 goes into 12 2 times

1 x 3 = 3

2 x 4 = 8

1 x 6 = 6

So, the fractions become:

$1\frac{3}{12} + 2\frac{8}{12} + 1\frac{2}{12}$

3. Add the numerators of the new fractions and keep the denominator the same.

$4 \frac{13}{12}$

4. Convert the improper fraction to a mixed number.

$1 \frac{1}{12}$

5. Finally, add the whole numbers.

1 + 4 = 5

3 0

3 years ago

Someone please let me know the answer ​

Someone please let me know the answer