MATHEMATICS HIGH SCHOOL

Explain why the sine of an acute angle of a right triangle is equal to the cosine of its complement

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Answer 1
Answer: to see this relationship, all you need to know is some basic trig. 

consider triangle ABC. the sin(β)=b/c ; cos(α)=b/c, therefore sin(β)=cos(α). also, since this is a right triangle, β and α are complements

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Area of 6m circle to the nearest tenth use 3.14 for pi.

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The area of the circle would be 113.1.
Hope it helped!
A = πr²
A = (3.14)(6)²
A = (3.14)(36)
A = 113.04cm²

The first four terms of a sequence are shown below: 7, 4, 1, -2 Which of the following functions best defines this sequence? A.f(1) = 7, f(n + 1) = f(n) + 3; for n ≥ 1 B.f(1) = 7, f(n + 1) = f(n) - 3; for n ≥ 1 C.  f(1) = 7, f(n + 1) = f(n) - 4; for n ≥ 1 D.f(1) = 7, f(n + 1) = f(n) + 4; for n ≥ 1

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Answer:

Option (B) is correct.

The sequence that best defines the function is f(1) = 7, f(n + 1) = f(n) - 3; for n ≥ 1

Step-by-step explanation:

Given sequence 7 ,4, 1,-2

We have to choose a function from given options that best defines this sequence.

Let f(n) denotes the value at nth position,

Like f(1) = 7 , so here, n= 1.

Since next term is 4 = f(2)

4 can be written as 7 - 3 = f(1) -3

Next term is 1 = f(3)

1 can be written as 4-1 = f(2) - 3

Next term is -2 = f(4)

-2 can be written as 1-3 = f(3) - 3

Thus, following the sequence and writing in general form for n

f(n+1) = f (n) -3 , n ≥ 1

Thus, option (B) is correct.

The sequence that best defines the function is f(1) = 7, f(n + 1) = f(n) - 3; for n ≥ 1
answer is B.f(1) = 7, f(n + 1) = f(n) - 3; for n ≥ 1

f(1) = 7
f(2) = 7 -3 = 4
f(3) = 4 -3 = 1
f(4) = 1 -3 = -2

Jessica took out a, $84,000 loan to buy her grandmother a house. After 10 years, she had paid $31.500 in interest. What was herinterest rate?

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3.75%
_________
please mark brainliest if correct

Divide using synthetic division(45x^(5)+6x^(4) +3x^(3) +8x+12) ÷ (3x-2)

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Answer:

15x4  +  12x3  +  9x2  +  6x  +  20/3  +  76/3(3x−2)

How many solutions does the following system of equations have?y=5/2x+2
2y=5x+4

One

Two

Zero

Infinitely many

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We will use a method of substitution.
y = 5/2 x + 2 
2 y = 5 x + 4   ⇒  2 ( 5/2 x + 2 )= 5 x + 4
5 x + 4 = 5 x + 4
0 x = 0            ⇒  x, y ∈ R
Answer: D)   
This system has infinitely many solutions.

Mr. Swanson has $350 to order music books for the new school year. Music books cost $10 each and come in packages of 5. Mr. Swanson orders 6 packages.

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Answer:

Total cost he paid was = 300

Step-by-step explanation:
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