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victus00 [196]
2 years ago
10

2x2 - 12x + 10what are the roots​

Mathematics
1 answer:
Tcecarenko [31]2 years ago
4 0

Answer:

5 & 1

Step-by-step explanation:

We can use the quadratic formula to solve this:

Quadratic Formula = \frac{-b+-\sqrt{b^2-4ac} }{2a}

So we will have 2 answers (roots).

a is the coefficient of x^2 (2)

b is the coefficient of x (-12)

c is the constant (10)

Now, substituting, we get:

x = \frac{-b+-\sqrt{b^2-4ac} }{2a}=\frac{12+-\sqrt{(-12)^2-4(2)(10)} }{2(2)}=\frac{12+-\sqrt{64} }{4}=\frac{12+-8}{4}=\frac{12+-8}{4}=5,1

Hence the roots are 5 & 1

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Find the dot product of the position vectors whose terminal points are (14, 9) and (3, 6).
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Answer:

Step-by-step explanation:

The formula for the dot product of vectors is

u·v = |u||v|cosθ

where |u| and |v| are the magnitudes (lengths) of the vectors. The formula for that is the same as Pythagorean's Theorem.

|u|=\sqrt{14^2+9^2} which is \sqrt{277}

|v|=\sqrt{3^2+6^2} which is \sqrt{45}

I am assuming by looking at the above that you can determine where the numbers under the square root signs came from. It's pretty apparent.

We also need the angle, which of course has its own formula.

cos\theta=\frac{uv}{|u||v|} where uv has ITS own formula:

uv = (14 * 3) + (9 * 6) which is taking the numbers in the i positions in the first set of parenthesis and adding their product to the product of the numbers in the j positions.

uv = 96.

To get the denominator, multiply the lengths of the vectors together. Then take the inverse cosine of the whole mess:

cos^{-1}\theta=\frac{96}{111.64676} which returns an angle measure of 30.7. Plugging that all into the dot product formula:

u*v=\sqrt{277}*\sqrt{45}cos(30.7) gives you a dot product of 96

6 0
2 years ago
The endpoints of the diameter of a circle are (6, 0) and (-6, 0). What are the coordinates of the center of this circle?
Kay [80]

Answer:

(0,0)

Step-by-step explanation:

a diameter means The average of two measurements of the diameter taken at right angles to each other. so if you try graphing you will be able to find out its (0,0) is the center of the circle coordinates

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1 year ago
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Answer:

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Step-by-step explanation:

midpoint formula: (x1 + x2/ 2, y1 + y2/ 2)

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Hope you do well , i pray blessings and growth to you .
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