From the information obtained from the question, two equations can be created:
Let x and z be the two numbers (parts)
. . . . (1)
. . . . (2)
By transposing (2), make 'z' the subject of the equation
. . . . (3)
By substituting (3) into equation (1) to find a value for x
⇒
∴ either
OR
Thus x = 5 or x = 10
By substituting the values of x into (2) to find z
z + (5) = 15 OR z + (10) = 15
⇒ z = 10 OR z = 5
So, the two numbers or two parts into which fifteen is divided to yield the desired results are 5 and 10.
Answer:
ΔABC was translated right 4 units and down 4 units.
Step-by-step explanation:
A' - A = (3, -2) -(-1, 2) = (3+1, -2-2) = (4, -4)
So, the transformation is (x, y) ⇒ (x +4, y -4).
Adding these values to a coordinate pair causes it to be translated to the right 4 units (x is increased by 4) and down 4 units (y is decreased by 4).
The sides of the triangle are given as 1, x, and x².
The principle of triangle inequality requires that the sum of the lengths of any two sides should be equal to, or greater than the third side.
Consider 3 cases
Case (a): x < 1,
Then in decreasing size, the lengths are 1, x, and x².
We require that x² + x ≥ 1
Solve x² + x - 1 =
x = 0.5[-1 +/- √(1+4)] = 0.618 or -1.618.
Reject the negative length.
Therefore, the lengths are 0.382, 0.618 and 1.
Case (b): x = 1
This creates an equilateral triangle with equal sides
The sides are 1, 1 and 1.
Case (c): x>1
In increasing order, the lengths are 1, x, and x².
We require that x + 1 ≥ x²
Solve x² - x - 1 = 0
x = 0.5[1 +/- √(1+4)] = 1.6118 or -0.618
Reject the negative answr.
The lengths are 1, 1.618 and 2.618.
Answer:
The possible lengths of the sides are
(a) 0.382, 0.618 and 1
(b) 1, 1 and 1.
(c) 2.618, 1.618 and 1.
Answer:
Hi,
6
Step-by-step explanation:
the number divided by 5 has a remainder of 1 , its last digit is 1 or 6.
the number is divisible by 2, its last digit is 0 or 2,or 4, or 6 or 8.
Both conditions give : the last digit must be 6.