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3 years ago

What is the quotient (x3 – 3x2 + 5x – 3) ÷ (x – 1)?

Mathematics

1 answer:

11111nata11111 [884]3 years ago

3 0

Answer:

x^2 -2x +3
x^2 +2x +3

Step-by-step explanation:

The quotient in each case can be found by any of several means, including synthetic division (possibly the easiest), polynomial long division, or graphing.

1. The graph shows you the quotient is (x-1)^2 +2 = x^2 -2x +3.

2. The graph shows you the quotient is (x+1)^2 +2 = x^2 +2x +3.

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How can the Pythagorean theorem be used to find the exact values of certain "special angles"?

Reptile [31]

In a 45-45-90 triangle, the two legs are congruent. Let's call them x. The hypotenuse is equal to 1 as we're using the unit circle. The hypotenuse of the triangle is the same as the radius of the unit circle.

a = x

b = x

c = 1

Use those values in the Pythagorean theorem to solve for x.

a^2 + b^2 = c^2

x^2 + x^2 = 1^2

2x^2 = 1

x^2 = 1/2

x = sqrt( 1/2 )

x = sqrt(1)/sqrt(2)

x = 1/sqrt(2)

x = sqrt(2)/2 ... rationalizing the denominator

So this right triangle has legs that are sqrt(2)/2 units long. Once we know the legs of the triangle, we can divide them over the hypotenuse to find the sine and cosine values.

sin(angle) = opposite/hypotenuse

sin(45) = (sqrt(2)/2) / 1

sin(45) = sqrt(2)/2

and

cos(angle) = adjacent/hypotenuse

cos(45) = (sqrt(2)/2) / 1

cos(45) = sqrt(2)/2

------------------------------------------------------

For a 30-60-90 triangle, we would have

a = 1

b = x

c = 2

so,

a^2+b^2 = c^2

1^2+x^2 = 2^2

1+x^2 = 4

x^2 = 4-1

x^2 = 3

x = sqrt(3)

The missing leg is sqrt(3) units long.

Once we know the three sides of the 30-60-90 triangle, you should be able to see that

sin(30) = 1/2

sin(60) = sqrt(3)/2

cos(30) = sqrt(3)/2

cos(60) = 1/2

3 0

3 years ago

Read 2 more answers

Laura can weed the garden in 1 hour and 20 minutes and her husband can weed it in 1 hour and 30 minutes. How long will they take

Harrizon [31]

<h2>Hello!</h2>

The answer is:

It will take 42.35 minutes to weed the garden together.

To solve the problem, we need to use the given information about the rate for both Laura and her husband. We know that she can weed the garden in 1 hour and 20 minutes (80 minutes) and her husband can weed it in 1 hour and 30 minutes (90 minutes), so we need to combine both's work and calculate how much time it will take to weed the garden together.

So, calculating we have:

Laura's rate:

$\frac{1garden}{80minutes}$