Answer:
Let p(x) = x3 + ax2 + bx +6
(x-2) is a factor of the polynomial x3 + ax2 + b x +6
p(2) = 0
p(2) = 23 + a.22 + b.2 +6 =8+4a+2b+6 =14+ 4a+ 2b = 0
7 +2 a +b = 0
b = - 7 -2a -(i)
x3 + ax2 + bx +6 when divided by (x-3) leaves remainder 3.
p(3) = 3
p(3) = 33 + a.32 + b.3 +6= 27+9a +3b +6 =33+9a+3b = 3
11+3a +b =1 => 3a+b =-10 => b= -10-3a -(ii)
Equating the value of b from (ii) and (i) , we have
(- 7 -2a) = (-10 - 3a)
a = -3
Substituting a = -3 in (i), we get
b = - 7 -2(-3) = -7 + 6 = -1
Thus the values of a and b are -3 and -1 respectively.
Step-by-step explanation:
Simplifying
18x + -44 = 13y + -38
Reorder the terms:
-44 + 18x = 13y + -38
Reorder the terms:
-44 + 18x = -38 + 13y
Solving
-44 + 18x = -38 + 13y
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '44' to each side of the equation.
-44 + 44 + 18x = -38 + 44 + 13y
Combine like terms: -44 + 44 = 0
0 + 18x = -38 + 44 + 13y
18x = -38 + 44 + 13y
Combine like terms: -38 + 44 = 6
18x = 6 + 13y
Divide each side by '18'.
x = 0.3333333333 + 0.7222222222y
Simplifying
x = 0.3333333333 + 0.7222222222y
6. Answer: B
Length of 1 side is 6
Perimeter is 6×6 = 36
5 times larger
Length of one side 6×5 = 30
Perimeter is the 30×6 = 180
180/36 = 5 Perimeter is 5 times greater
7. Answer: H
Find the whole number of squares in the shape given - 22 squares
22 × 10ft = 220 feet
8. Answer: F
((12-3)×3) + (4×3) = (9×3) + 12
= 27 + 12
= 39 ft^2
9. Answer: C
Answer:
The Distributive Property.
Step-by-step explanation:
4(x - 1) = 12
When distributing out the 4, it must go to all the terms within the brackets like this:
4x - 4 = 12.
4x = 16
x = 4.
Answer:
see explanation
Step-by-step explanation:
Part 1
The n th term of a geometric sequence is
= a
where a is the first term and r the common ratio
Given 
= 128, then
a
= 128, that is
32a = 128 ( divide both sides by 32 )
a = 4 ← first term
Part 2
= 4
= 4 × 1048576 = 4194304
