Answer:
(3x+4)(5x+7)
Step-by-step explanation:
15x^2
+41x+28
Factor the expression by grouping. First, the expression needs to be rewritten as 15x^2
+ax+bx+28. To find a and b, set up a system to be solved.
a+b=41
ab=15×28=420
Since ab is positive, a and b have the same sign. Since a+b is positive, a and b are both positive. List all such integer pairs that give product 420.
1,420
2,210
3,140
4,105
5,84
6,70
7,60
10,42
12,35
14,30
15,28
20,21
Calculate the sum for each pair.
1+420=421
2+210=212
3+140=143
4+105=109
5+84=89
6+70=76
7+60=67
10+42=52
12+35=47
14+30=44
15+28=43
20+21=41
The solution is the pair that gives sum 41.
a=20
b=21
Rewrite 15x^2
+41x+28 as (15x^2
+20x)+(21x+28).
(15x^2
+20x)+(21x+28)
Factor out 5x in the first and 7 in the second group.
5x(3x+4)+7(3x+4)
Factor out common term 3x+4 by using distributive property.
(3x+4)(5x+7)
Answer:
The answer to your question is the letter A) x ≥ 0.5
Step-by-step explanation:
Inequality
2(4x - 3) ≥ -3(3x) + 5x
Process
1.- Expand
8x - 6 ≥ - 9x + 5x
2.- Simplify
8x - 6 ≥ - 4x
3.- Add 6 units in both sides
8x - 6 + 6 ≥ -4x + 6
4.- Simplify
8x ≥ -4x + 6
5.- Add 4x in both sides
8x + 4x ≥ -4x + 6 + 4x
6.- Simplify
12x ≥ 6
7.- Divide by 12 both sides
12x/12 ≥ 6/12
8.- Simplify
x ≥ 1/2 or 0.5
We use 2 different rules here:
1) sum of angles in a triangle is equal to 180 degrees
2) when a triangle side is a diameter of the circle, then angle opposite to diameter is equal to 90 degrees.
so from 2) we know that B= 90
then from first one:
sum of angles = 180 = 90 + (3x + 6) + x = 96 + 4x
so 180 - 96 = 4x
so x = 84/4
x = 21
so answer is
A= 3x+ 6 = 63 + 6 = 69
B = 90
C = 21