5x^2+3xy-25x-15y= 5x^2-25x+3xy-15y=
5x(x-5)+3y(x-5)=
= (x-5)(5x+3y)
Answer:
x = 14
< A = 58 degrees
< B = 52 degrees
< C = 70 degrees
Step-by-step explanation:
Recall that the addition of the three internal angles of a triangle must render 180 degrees, then we can write:
<A + <B + <C = 180
and now replace with the algebraic expressions given for each angle:
2(x + 15) + 3 x + 10 + 5 x = 180
eliminate parenthesis
2 x + 30 + 3 x + 10 + 5 x = 180
combine like terms
10 x + 40 = 180
subtract 40 from both sides
10 x = 140
divide both sides y 10 to isolate x
x = 14
Now that we know x, we can calculate each of the angles using the fiven expressions:
< A = 2 (x + 15) = 2 (14 + 15) = 2 * 29 = 58 degrees
< B = 3 x + 10 = 3 * 14 + 10 = 52 degrees
< C = 5 x = 5 * 14 = 70 degrees
a +b = 7
a-b = 3
Rewrite the second equation as a = 3+b
Replace a in the first equation with that:
3+b + b = 7
Simplify:
3 +2b = 7
Subtract 3 from both sides:
2b = 4
Divide both sides by 2:
b = 4/2 = 2
Now replace b in the first equation with 2 to solve for a:
a + 2 =7
a = 7-2 = 5
so you now have a and b.
Now solve the given equation:
2^a * 2^b
2^5 * 2^2
32*4
128
The answer is 128.
Answer:
the desired range is 2 < t < 12.
Step-by-step explanation:
If the third side is 12 (the sum of 5 and 7), we don't really have a triangle, since the 5-unit and 7-unit sides add up to 12 and lie on the third side (of length 12).
Since triangle ABC is acute, all its angles are between 0 and 90 degrees. So the third side can be 12 but not greater. The smallest possible length of the third side is 2, since 5 + 2 = 7.
Thus, the desired range is 2 < t < 12.
Answer: 56
Step-by-step explanation:
