Answer:
z*(z - 3) = 520
Step-by-step explanation:
Use the following representations:
Width: W
Length: L = W + 3, or W = L - 3
Area = L*W = L*(L - 3) = 520
Equation b) is the correct one: z*(z - 3) = 520
Answer:
A: This polynomial has a degree of 2 , so the equation 12x2+5x−2=0 has two or fewer roots.
B: The quadratic equation 12x2+5x−2=0 has two real solutions, x=−2/3 or x=1/4 , and therefore has two real roots.
Step-by-step explanation:
f(x) = 12x^2 + 5x - 2.
Since this is a quadratic equation, or a polynomial of second degree, one can easily conclude that this equation will have at most 2 roots. At most 2 roots mean that the function can have either 2 roots at maximum or less than 2 roots. Therefore, in the A category, 2nd option is the correct answer (This polynomial has a degree of 2 , so the equation 12x^2 + 5x − 2 = 0 has two or fewer roots).
To find the roots of f(x), set f(x) = 0. Therefore:
12x^2 + 5x - 2 = 0. Solving the question using the mid term breaking method shows that 12*2=24. The factors of 24 whose difference is 5 are 8 and 3. Therefore:
12x^2 + 8x - 3x - 2 = 0.
4x(3x + 2) -1(3x+2) = 0.
(4x-1)(3x+2) = 0.
4x-1 = 0 or 3x+2 = 0.
x = 1/4 or x = -2/3.
It can be seen that f(x) has two distinct real roots. Therefore, in the B category, 1st Option is the correct answer (The quadratic equation 12x2+5x−2=0 has two real solutions, x=−2/3 or x=1/4 , and therefore has two real roots)!!!
Answer:
Step-by-step explanation:
To get the value of the expressions in list A and list B we will substitute y = 5 in each expression.
List A List B
1). 6 + 6y = 6 + 6(5) = 36 6y - 6 = 6(5) - 6 = 24
2). 6(y - 1) = 6(5 - 1) = 24 6(y + 1) = 6(5 + 1) = 36
3). 6y + 1 = 6(5) + 1 = 31 1 + 6y = 1 + 6(5) = 31
Therefore, (6 + 6y) is equivalent to 6(y + 1)
6(y - 1) is equivalent to (6y - 6)
(6y + 1) is equivalent to (1 + 6y)
A. Angle 3 is a vertical angle to angle 2 which means they are the same.
Angle 3 = 76 degrees
B. Angle 6 is also the same as angle 2.
Angle 6 = 76 degrees
C. Angle 8 + angle 6 form a straight line which equals 180 degrees
Angle 8 = 180 - 76 = 104 degrees
