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3 years ago

Simplify the midpoint of QS.

Mathematics

1 answer:

oee [108]3 years ago

8 0

Answer:

[(a + b), c]

Step-by-step explanation:

Midpoint of a segment with extreme ends represented by ordered pairs $(x_1,y_1)$ and $(x_2,y_2)$ ,

Midpoint = $(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

It is given that extreme ends of the segment QS are Q(2b, 2c) and S(2a, 0)

Coordinates of the midpoint of QS will be,

= $(\frac{2a+2b}{2},\frac{2c+0}{2} )$

= [(a + b), c]

Therefore, ordered pair representing the midpoint of QS will be [(a + b), c].

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Find the smallest integer n for an O(xn) estimate of order of the function f(x)

alexdok [17]

Answer with explanation:

$f(x)=\frac{(x^3+x^2+5)(x^4-3x^2)}{(2x^2+2x-3)(4x^2+7)}\\\\f(x)=\frac{x^3\times (x^4-3x^2)+x^2 \times (x^4-3x^2)+5 \times (x^4-3x^2)}{2x^2\times (4x^2+7)+2x(4x^2+7)-3\times (4x^2+7)}\\\\f(x)=\frac{x^7-3x^5+x^6-3x^4+5x^4-15x^2}{8x^4+14x^2+8x^3+14 x-12x^2-21}\\\\f(x)=\frac{x^7+x^6-3x^5+2x^4-15x^2}{8x^4+8x^3+2x^2+14 x-21}$

The largest degree of numerator is 7 , while the largest degree of denominator is 4.So, as we know

$\frac{x^a}{x^b}=x^{a-b}\\\\\frac{x^7}{x^4}=x^{7-4}\\\\=x^3$

→So, order of the function is the highest degree in the function raised to power.Highest degree is 3,when you will reduce the function in Expression form.

So, Degree=3

Order=1

6 0

3 years ago

Find the length of side AB in the right triangle shown.

Bogdan [553]

Side AB is 72 cm long.

Explanation:

To find the length of side AB you have to use this formula:

${a}^{2} + {b}^{2} = {c}^{2}$

*Remember there are two legs (a and b) and a hypotenuse (c) on a triangle. The longest side will be the hypotenuse and the other two will be the legs. For this triangle the hypotenuse is side BC while the legs are sides CA and side AB.

Plug in the numbers into the equation.

${65}^{2} + {b}^{2} = {97}^{2}$
For this triangle, you were given the hypotenuse (c) and one leg (a). To find the last length solve the equation and balance it so only b is left, like this:

$4225 + {b}^{2} = 9409$

$9409 - 4225 = 5184$

Soo...

${b}^{2} = 5184$

Then to get the side length, square root 5184.

$\sqrt{5184} = 72$

So the length of the last side is 72 cm.

5 0

3 years ago

What number is the opposite of -69?<br><br> What number is the opposite of the opposite of -69?

grandymaker [24]

Answer:

69, -69

Step-by-step explanation:

If the number is positive, the opposite of it is the same number, but negative.

If the number is negative, the opposite of the number is the same number, but positive.

So, -69 would be 69.

69 is the opposite of -69, so the opposite of 69 would go back to -69.

8 0