Answer:A rational number is such that when you multiply it by 5/2 and add 2/3 to the product you get -7/12 . What is the number.
Step-by-step explanation:Let p/q (q ≠ 0) denote the rational number. Multiplying it by 5/2 gives (p/q)(5/2). Add 2/3 to the product and we get (p/q)(5/2) + 2/3 . The result is given to be -7/12.
∴ (p/q)(5/2) + 2/3 = -7/12 …………………………..……………………………………..(1)
Transposing 2/3 to right-hand-side and changing the sign to negative,
(p/q)(5/2) = -2/3 -7/12 = -(2/3 + 7/12) =- (2 x 4 + 7)/12 (Taking L.C.M.)
Or, (p/q)(5/2) = -(8+7)/12 = - 15/12
Multiplying both sides by 2/5,
(p/q)(5/2) x (2/5) = -15/12 . 2/5 = -(3x5)/(3x4) . 2/5 =- 5/4 .2/5
Since 2/5 is the multiplicative inverse of 5/2, 5/2 x 2/5 = 1 and we obtain
(p/q).1 = -1/4 . 2/1 = -1/2
⇒ p/q = -1/2 which is a negative rational number in which p = 1 and q = 2 ≠ 0 .
∴ the rational number = -1/2
U . v = |u| . |v| cos 60 = 10 * 8 * 0.5 = 40 This is called the scalar (or dot) product.
Answer:
Step-by-step explanation:
We can use basic probability to find the probability that this roll is not a factor of 35.
First off, we know that with a six sided die there are 6 possible things we can roll.
1, 2, 3, 4, 5, or 6
Now, what are the factors of 35? The factors of 35 will be any whole number that can be multiplied by another whole number to get 35.
- We know
, so two factors are 1 and 35. - We know
, so two factors are 5 and 7.
Therefore, the factors of 35 are 1, 5, 7, 35.
Both 5 and 7 are inside the range of 1-6. So the probability of rolling a side that's a factor of 35 will be 
since there are two factors and 6 possible options.
This means, logically, there is a 
chance of not rolling a factor of 35.
Hope this helped!
If you want me to solve for "Y" then, the answer will be,
ir if you want me to solve for "X" instead then the answer will be,
Answer:
no mistakes
Step-by-step explanation:
4 * 3^x = 324
Divide each side by 4
4/4 * 3^x = 324/4
3^x = 81
Rewriting 81 as a power of 3
3^x = 3^4
Since the bases are the same, the powers are the same
x=4
