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
Answer: 10, 11, & 12
<u>Step-by-step explanation:</u>
Let x represent the age of the youngest child.
Their ages are consecutive so,
Youngest: x
Middle: x + 1
Oldest: x + 2
The age of the Youngest squared (x²) equals 8 times the Oldest [8(x + 2)] plus 4.
x² = 8(x + 2) + 4
x² = 8x + 16 + 4
x² = 8x + 20
x² - 8x - 20 = 0
(x - 10)(x + 2) = 0
x - 10 = 0 or x + 2 = 0
x = 10 or x = -2
Since age cannot be negative, x = -2 is not valid
So, the Youngest (x) is 10
the Middle (x + 1) is 11
and the Oldest (x + 2) is 12
Answer:
Average change in temperature each day = 5 degrees/day
Step-by-step explanation:
Answer:
d. 6
Step-by-step explanation:
The product of lengths to the near and far intersection points is the same for both secants:
PB×PA = PD×PC
We can use this relation to solve for x, then use the value of x to find PD.
7×12 = (3x)(7x)
4 = x² . . . . . . . . . divide by 21
2 = x . . . . . . . . . . take the square root
__
PD = 3x = 3·2
PD = 6
Combine like terms to get -4x^2-2x
