Answer:
B. The values x = 2 and y = 5 make the equation true.
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ABC is a right triangle, so AC has length given by
Then the circumference of circle M is 
.
Answer:
Option C. x^2-18x-81
Step-by-step explanation:
A. 16a^2-72a+81
x^2-2xy+y^2=(x-y)^2
x^2=16a^2→sqrt(x^2)=sqrt(16a^2)→x=sqrt(16) sqrt(a^2)→x=4a
y^2=81→sqrt(y^2)=sqrt(81)→y=9
2xy=2(4a)(9)→2xy=72a equal to the second term of the expression, then we can factor as a perfect square trinomial:
16a^2-72a+81=(4a-9)^2
B. 169x^2+26xy+y^2
a^2+2ab+b^2=(a+b)^2
a^2=169x^2→sqrt(a^2)=sqrt(169x^2)→a=sqrt(169) sqrt(x^2)→a=13x
b^2=y^2→sqrt(b^2)=sqrt(y^2)→b=y
2ab=2(13x)(y)→2ab=26xy equal to the second term of the expression, then we can factor as a perfect square trinomial:
169x^2+26xy+y^2=(13x+y)^2
C. x^2-18x-81
a^2+2ab+b^2=(a+b)^2
This expression does not factor as a perfect square trinomial because the third term is negative (-81).
D. 4x^2+4x+1
a^2+2ab+b^2=(a+b)^2
a^2=4x^2→sqrt(a^2)=sqrt(4x^2)→a=sqrt(4) sqrt(x^2)→a=2x
b^2=1→sqrt(b^2)=sqrt(1)→b=1
2ab=2(2x)(1)→2ab=4x equal to the second term of the expression, then we can factor as a perfect square trinomial:
4x^2+4x+1=(2x+1)^2
Answer:
b = -a
Step-by-step explanation:
We know that:
On a number line, the distance between 0 and b is the same distance that between 0 and a (but b and a are in opposite sides of zero).
And we know that, for example, when:
b = 2, a = -2
Remember that the distance between two values is given by:
|n - m|
Then the distance between 0 and b is:
|0 - b|
and the distance between 0 and a is:
|0 - a|
we have:
|-b| = |-a|
|b| = |a|
But the numbers are in opposite sides of the zero, so one must be positive and the other negative, then we can conclude that:
b = -a
or
-b = a
(these are equivalent)
Then the correct option is the first option:
b = -a
