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docker41 [41]
1 year ago
14

Suppose angles a and B are the two acute angles in a right triangle and that b < a. Apply the relationship between sine and c

osine todetermine which statements are correct.sin(6x - 10) = cos(4x + 10)A)x = 9B)a = 46°a = 48°D)B = 42°E)B = 44
Mathematics
1 answer:
Valentin [98]1 year ago
5 0

The right statements are: A, B and E

Sin(A)=cos(B)

then we check if using x=9 this holds true:

sin(6x-10)=cos(4x+10)

sin((6*9)-10) = sin(44º)

cos(4x+10)=cos(46)

Sin(44)=0.694=cos(46)

then a is true

Now, we know that b

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The sum of four consecutive odd integers is three more than five times the least of the integers. Find the integers.
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Answer:

<h3>              9, 11, 13, 15</h3>

Step-by-step explanation:

{k - some integer}

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5(2k+1)  - five times the least

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2k+3+2 = 2k+5  - the next odd consecutive integer (third)

2k+5+2 = 2k+7  - the last odd consecutive integer (fourth)

2k+1+2k+3+2k+5+2k+7 - <u>the sum of four odd consecutive integers</u>

2k+1 + 2k+3 + 2k+5 + 2k+7 = 5(2k+1) + 3

8k + 16 = 10k + 5 + 3

     - 10k       -10k

-2k + 16 = 8

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      -2k = -8  

    ÷(-2)    ÷(-2)  

      k = 4

2k+1 = 2•4+1 = 9

2k+3 = 2•4+3 = 11

2k+5 = 2•4+5 = 13

2k+7 = 2•4+7 = 15  

Check: 9+11+13+15 = 48;  48-3 = 45;  45:5 = 9 = 2k+1

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