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)
A^2 + b^2= c^2
(a,b,c are right triangle sides)
Answer:
D.
Step-by-step explanation:
n is between -3 and 1, with 3 and 1 not included.
You need open dots on -3 and 1, and shading in between.
Answer: D.
Answer:
Step-by-step explanation:
The standard equation for a circle is given by:
Where (h, k) is the center and r is the radius.
We know that the center is (-4, 8). So, substitute -4 for h and 8 for k:
Simplify:
Now, we will need to find r.
We know that it passes through the point (-2, -1). So, we can substitute -2 for x and -1 for y and solve for r. So:
Evaluate:
Square:
Add:
So, r squared is 85.
We don’t actually have to solve for r itself, since we will have to square it anyways.
So, we have:
Substituting 85 for r squared, we get:
And we have our equation.
Answer: 46 degrees
Step-by-step explanation: First you need to find the value of the vertical angle which is 180-(85+53) which is 42 degrees. Since vertical angles are congruent, you can say that 180-(42+92) is equal to x. When you solve it, you get x=46 which is your answer
