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notsponge [240]
2 years ago
14

Can anyone help me with this? I know that angle B is 90°

Mathematics
1 answer:
sergey [27]2 years ago
3 0

Answer:

angle c is 58 degrees and and angle a is 42 degrees

Step-by-step explanation:

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1.    An AP has a common difference of 3.  Given that the nth term is 32, and the sum of the first n terms is 185, calculate the
netineya [11]

Answer:

The value of n is 10

Step-by-step explanation:

The formula of the nth term of the arithmetic progression is a_{n} = a + (n - 1)d

  • a is the first term
  • d is the common difference between each 2 consecutive terms
  • n is the position of the term

The formula of the sum of nth terms is S_{n} = \frac{n}{2} [2a + (n - 1)d]

∵ An AP has a common difference of 3

∴ d = 3

∵ The nth term is 32

∴ a_{n} = 32

→ Substitute them in the 1st rule above

∵ 32 = a + (n - 1)3

∴ 32 = a + 3(n) - 3(1)

∴ 32 = a + 3n - 3

→ Add 3 to both sides

∴ 35 = a + 3n

→ Switch the two sides

∴ a + 3n = 35

→ Subtract 3n from both sides

∴ a = 35 - 3n ⇒ (1)

∵ The sum of the first n terms is 185

∴ S_{n} = 185

→ Substitute the value of S_{n} and d in the 2nd rule above

∵ 185 = \frac{n}{2} [ 2a + (n - 1)3]

∴ 185 = \frac{n}{2} [2a + 3(n) - 3(1)]

∴ 185 = \frac{n}{2} [2a + 3n - 3]

→ Multiply both sides by 2

∴ 370 = n(2a + 3n - 3)

∴ 370 = 2an + 3n² - 3n

→ Substitute a by equation (1)

∴ 370 = 2n(35 - 3n) + 3n² - 3n

∴ 370 = 70n - 6n²+ 3n² - 3n

→ Add the like terms in the right side

∵ 370 = -3n² + 67n

→ Add 3n² to both sides

∴ 3n² + 370 = 67n

→ Subtract 67 from both sides

∴ 3n² - 67n + 370 = 0

→ Use your calculator to find n

∴ n = 10 and n = 37/3

∵ n must be a positive integer ⇒ 37/3 neglecting

∴ n = 10

∴ The value of n is 10

4 0
2 years ago
The length of a rectangular book is 2 times its width. The perimeter of the book is 42 inches. Write a system of
wel

Answer:

Mark me as brainlist

Step-by-step explanation:

P = Perimeter            

L = Length          

W = Width

Perimeter of rectangle = L + L + W + W        

or P = 2L + 2W

You know:

P = 36 inches

L = 2W          [length is(=) 2 times it's width]

W = ?

P = 2L + 2W    

Substitute/plug in what you know, plug in 2W for L since L = 2W

36 = 2(2W) + 2W         Simplify

36 = 4W + 2W

36 = 6W        Divide 6 on both sides

6 = W              Now that you know the width, you can find the length:

L = 2W

L = 2(6)

L = 12

L = 12 in

W = 6 in

PROOF

P = 2(12) + 2(6)

P = 24 + 12

P = 36

7 0
2 years ago
Simplify 4x-3(x-2). I'm stuck xD
alexira [117]

Answer:

Simplified = x + 6

4 0
2 years ago
Read 2 more answers
Solve the following<br> 5 3/4 + (6 2/3 - 4 5/6) =
chubhunter [2.5K]

Answer:

7 5/12

Step-by-step explanation:

first, subtract 4 5/6 from 6 2/3 by converting 6 2/3 to 6 4/6

5 3/4 + (6 4/6 - 4 5/6) = 5 3/4 + 1 4/6

* I borrowed 6/6 or '1' from the 6 and made 4/6 into 10/6

5 3/4 equals 5 9/12 and 1 4/6 equals 1 8/12

adding them gives you:

6 17/12 which is the same as 6 + 1 5/12, or 7 5/12

4 0
2 years ago
How do I write an equation of a line in slope intercept from
BabaBlast [244]

Answer:

You would use the formula y=mx+b, where m is the slope and b is the y intercept.

Step-by-step explanation:

If the slope was 1/2 and the y intercept was 2, it would be y=1/2x+2

4 0
3 years ago
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