The probability that the sum of the dice is 7 is 1/2 because there are only three combinations that result in the sum of 7: (1,6)(2,5) and (3,4). But there are 6 possible outcomes( this is if you don’t add reverse combinations such as 1,6 and 6,1) so the probability would be 3/6 or 1/2
Answer:
13.64 litres
Explanation
Since 1 gallon = 4.546 litres
Therefore...3 gal
; 3 × 4.546 = 13.64 litres
To find the zeros of this function, we must first set the entire function equal to 0
f(x) = x² - 2x - 15 = 0
Since this is a quadratic function, we must use the quadratic formula, which is:
![\frac{-b +/- \sqrt{b^{2} - 4(a)(c) } }{2a}](https://tex.z-dn.net/?f=%20%5Cfrac%7B-b%20%2B%2F-%20%20%5Csqrt%7Bb%5E%7B2%7D%20-%204%28a%29%28c%29%20%7D%20%7D%7B2a%7D%20)
Let's assign a, b, and c using our first function
x² means a = 1 (because it could be written as 1x²)
-2x means b = -2
-15 means c = -15
Now let's plug those in:
![\frac{-(-2) +/- \sqrt{(-2)^{2} - 4(1)(-15) } }{2(1)}](https://tex.z-dn.net/?f=%20%5Cfrac%7B-%28-2%29%20%2B%2F-%20%5Csqrt%7B%28-2%29%5E%7B2%7D%20-%204%281%29%28-15%29%20%7D%20%7D%7B2%281%29%7D%20)
which simplifies to:
![\frac{2 +/- \sqrt{(4 + 60} }{2}](https://tex.z-dn.net/?f=%20%5Cfrac%7B2%20%2B%2F-%20%5Csqrt%7B%284%20%2B%2060%7D%20%7D%7B2%7D%20)
Simplified further:
![\frac{2 +/- \sqrt{(64} }{2}](https://tex.z-dn.net/?f=%20%5Cfrac%7B2%20%2B%2F-%20%5Csqrt%7B%2864%7D%20%7D%7B2%7D%20)
![\frac{2 +/- 8 }{2}](https://tex.z-dn.net/?f=%5Cfrac%7B2%20%2B%2F-%208%20%7D%7B2%7D%20)
And divide it by the 2 on the bottom gives us:
![2 +/- 4](https://tex.z-dn.net/?f=2%20%2B%2F-%204)
2+4 = 6
2-4 = -2
So the zeros of this function are
-2 and
6
Answer:
Yes, It is a right triangle for the given vertices.
Step-by-step explanation:
Given:
Q(7, –10),
R(–3, 0),
S(9, –8)
To Find:
determine whether is a rig ht triangle for the given vertices = ?
Solution:
QR=![\sqrt{(-3-7)^2+(0-(-10))^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%28-3-7%29%5E2%2B%280-%28-10%29%29%5E2%7D)
QR=![\sqrt{(-10)^2+(10)^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%28-10%29%5E2%2B%2810%29%5E2%7D)
QR=![\sqrt{100+100}](https://tex.z-dn.net/?f=%5Csqrt%7B100%2B100%7D)
QR=
--------------------------(1)
QR=14.142136
RS=![\sqrt{(9-(-3))^2+(-8-0)^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%289-%28-3%29%29%5E2%2B%28-8-0%29%5E2%7D)
RS=![\sqrt{(12)^2+(-8)^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%2812%29%5E2%2B%28-8%29%5E2%7D)
RS=![\sqrt{144+64}](https://tex.z-dn.net/?f=%5Csqrt%7B144%2B64%7D)
RS=
---------------------------(2)
RS=14.422205
QS=![\sqrt{(7-9)^2+(-10-(-8))^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%287-9%29%5E2%2B%28-10-%28-8%29%29%5E2%7D)
QS=![\sqrt{(-2)^2+(-2)^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%28-2%29%5E2%2B%28-2%29%5E2%7D)
QS=![\sqrt{4+4}](https://tex.z-dn.net/?f=%5Csqrt%7B4%2B4%7D)
QS=
-------------------------------------(3)
QS=2.828427
According to Pythagorean Theorem,
![RS^2 = QR^ +QS^2](https://tex.z-dn.net/?f=RS%5E2%20%3D%20QR%5E%20%2BQS%5E2)
Substituting the values,
![(\sqrt{208})^2 = (\sqrt{200})^2 +(\sqrt{8})^2](https://tex.z-dn.net/?f=%28%5Csqrt%7B208%7D%29%5E2%20%3D%20%28%5Csqrt%7B200%7D%29%5E2%20%2B%28%5Csqrt%7B8%7D%29%5E2)
![208 = 200 +8](https://tex.z-dn.net/?f=208%20%3D%20200%20%2B8)
208 = 208
Pythagorean theorem is satisfied. Hence it is a right triangle.
Answer:
The correct answer is Kinetic Energy
Step-by-step explanation:
From conservation of energy a body at rest posses energy called Potential Energy under which it acquired at particular position of the body i.e at rest
Then as soon body starts moving with a certain speed "v" there is conservation of energy from Potential energy to Kinetic energy given as product of a half with mass of the body and square of its velocity.
In formular K.E= 1/2mv^2 where m stands for mass of the body and v is the speed of the body.