Answer:
6x^2-6x-6
Step-by-step explanation:
(x^2-3x+2)+(5x^2-3x-8)
x^2+5x^2-3x+(-3x)+2+(-8)
6x^2-3x-3x+2-8
6x^2-6x+2-8
6x^2-6x-6
Answer:
Yes, the right angle is angle B
Step-by-step explanation:
we have
![A(-2, 3), B(-3,-6),C(2,-1)](https://tex.z-dn.net/?f=A%28-2%2C%203%29%2C%20B%28-3%2C-6%29%2CC%282%2C-1%29)
Plot the vertices
see the attached figure
we know that
If triangle ABC is a right triangle
then
Applying the Pythagoras Theorem
![AB^{2} =AC^{2}+BC^{2}](https://tex.z-dn.net/?f=AB%5E%7B2%7D%20%3DAC%5E%7B2%7D%2BBC%5E%7B2%7D)
the formula to calculate the distance between two points is equal to
![d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28y2-y1%29%5E%7B2%7D%2B%28x2-x1%29%5E%7B2%7D%7D)
<em>Find the distance AB</em>
![A(-2, 3), B(-3,-6)](https://tex.z-dn.net/?f=A%28-2%2C%203%29%2C%20B%28-3%2C-6%29)
substitute in the formula
![d=\sqrt{(-6-3)^{2}+(-3+2)^{2}}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28-6-3%29%5E%7B2%7D%2B%28-3%2B2%29%5E%7B2%7D%7D)
![d=\sqrt{(-9)^{2}+(-1)^{2}}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28-9%29%5E%7B2%7D%2B%28-1%29%5E%7B2%7D%7D)
![AB=\sqrt{82}\ units](https://tex.z-dn.net/?f=AB%3D%5Csqrt%7B82%7D%5C%20units)
<em>Find the distance BC</em>
![B(-3,-6),C(2,-1)](https://tex.z-dn.net/?f=B%28-3%2C-6%29%2CC%282%2C-1%29)
substitute in the formula
![d=\sqrt{(-1+6)^{2}+(2+3)^{2}}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28-1%2B6%29%5E%7B2%7D%2B%282%2B3%29%5E%7B2%7D%7D)
![d=\sqrt{(5)^{2}+(5)^{2}}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%285%29%5E%7B2%7D%2B%285%29%5E%7B2%7D%7D)
![BC=\sqrt{50}\ units](https://tex.z-dn.net/?f=BC%3D%5Csqrt%7B50%7D%5C%20units)
<em>Find the distance AC</em>
![A(-2, 3),C(2,-1)](https://tex.z-dn.net/?f=A%28-2%2C%203%29%2CC%282%2C-1%29)
substitute in the formula
![d=\sqrt{(-1-3)^{2}+(2+2)^{2}}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28-1-3%29%5E%7B2%7D%2B%282%2B2%29%5E%7B2%7D%7D)
![d=\sqrt{(-4)^{2}+(4)^{2}}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28-4%29%5E%7B2%7D%2B%284%29%5E%7B2%7D%7D)
![AC=\sqrt{32}\ units](https://tex.z-dn.net/?f=AC%3D%5Csqrt%7B32%7D%5C%20units)
Verify the Pythagoras theorem
![(\sqrt{82})^{2} =(\sqrt{32})^{2}+(\sqrt{50})^{2}](https://tex.z-dn.net/?f=%28%5Csqrt%7B82%7D%29%5E%7B2%7D%20%3D%28%5Csqrt%7B32%7D%29%5E%7B2%7D%2B%28%5Csqrt%7B50%7D%29%5E%7B2%7D)
---> is true
therefore
Is a right triangle and the right angle is B
Answer:
The first thing you do is make the denominators equal on both sides.
Step-by-step explanation:
As a example if you have the equation:
+
=
you would multiply the denominator by the smallest multiple. I would do 2 * 5= 10
this would make the equation
![\frac{x}{10} + \frac{x}{10} = ...](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B10%7D%20%2B%20%5Cfrac%7Bx%7D%7B10%7D%20%3D%20...)
next you have to do the same with the numerator.
so sence you multiplied the
by five you will get ![\frac{5}{10}](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B10%7D)
same with the other fraction except you multiplied it by two.
x 2 = ![\frac{4}{10}](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B10%7D)
next you add and simplify if needed
Answer:
0.0319
Step-by-step explanation:
To approximate this probability, we shall be using the Bernoulli approximation of the Binomial distribution.
Let p = probability of selecting a reference book = 65% = 0.65
Let q = probability of selecting other books= 1-p = 1-0.65 = 0.35
Now, we want to find the probability that all of these 8 books to be re-shelved are reference book.
We set up the probability as follows;
P(X = 8) = 8C8 •p^8•q^0
P(X = 8) = 1 * (0.65)^8 * (0.35)^0
P(X = 8) = 0.031864481289 which is 0.0319 to 4 decimal places
The one with 2 square kilometers. Each tree in population A gets 1/5(0.2) square kilometers, whereas population B gets only 2/25(0.08).