Answer:
x = 16
Step-by-step explanation:
If the figure is a parallelogram, the opposite sides are the same length
3x+20 = 5x-12
Subtract 3x from each side
3x+20 -3x = 5x-12-3x
20 = 2x-12
Add 12 to each side
20+12 = 2x-12+12
32 = 2x
Divide each side by 2
32/2 = 2x/2
16 =x
Answer:
-1, 4+i, 4-i
Step-by-step explanation:
x^4- 6x^3 + 2x^2 + 26x + 17
Using the rational root theorem
we see if 1, -1, -17 or 17 are roots
Check and see if 1 is a root
1^4- 6(1^3) + 2(1^2) + 26(1) + 17=0
1-6+2+26+17 does not equal 0 1 is not a root
-1
1^4- 6(-1^3) + 2(1^2) + 26(-1) + 17=0
1 +6 +2 -26+17 = 0
-1 is a root
Factor out (x+1)
(x+1) ( x^3-7x^2+9x+17)
Using the rational root theorem again on x^3-7x^2+9x+17
Checking -1
-1 -7 -9 +17=0
-1 is a root
(x+1) (x+1) (x^2-8x+17)
Using the quadratic on the last
8 ±sqrt(8^2 - 4(1)17)
--------------------------------
2
gives imaginary roots
4±i
Answer:
0.6
Step-by-step explanation:
A permutation is an arrangement of outcomes whereas a combination is a grouping of outcomes.
Order matters in case of permutations but does not matter in combinations.
Given:
Number of red marbles = 3
Number of white marbles = 2
Number of green marbles = 1
To find: probability of picking 4 marbles and getting one of each color
Solution:
Total number of outcomes = =
Number of favourable outcomes = 2 red, 1 white and 1 green marble + 1 red, 2 white and 1 green marble = =
So, probability of picking 4 marbles and getting one of each color = Number of favourable outcomes/Total number of outcomes =
Answer:
The product of 2x + y and 5x – y + 3 is 10x^2+ 3xy + 6x - y^2 + 3y
Step-by-step explanation:
The product of the two expressions can be expressed mathematically as;
(2x +y) (5x -y +3)
To obtain the product of these expressions, we simply expand the brackets as follows;
2x(5x -y +3) + y(5x -y +3)
= 10x^2 - 2xy + 6x + 5xy - y^2 + 3y
= 10x^2- 2xy + 5xy + 6x - y^2 + 3y
= 10x^2+ 3xy + 6x - y^2 + 3y
The product of 2x + y and 5x – y + 3 is thus 10x^2+ 3xy + 6x - y^2 + 3y
The interest rate offered would decrease. The federal reserve sets the rates to help prevent inflation, deflation etc