Answer:
Yes, because 52 + 122 = 132.
Step-by-step explanation:
A line through a point on a circle is tangent at the point if it is perpendicular to the radius drawn to the point of tangency. The Pythagorean Theorem only works for right triangles.
1. Rational
2. No Rational
3. Rational
4. Rational
5. Rational
6. No Rational
7. Rational
8.
Answer:
Step-by-step explanation:
We are given that a and b are rational numbers where 
and x is irrational number .
We have to prove a+bx is irrational number by contradiction.
Supposition:let a+bx is a rational number then it can be written in 
form
where 
where p and q are integers.
Proof:
After dividing p and q by common factor except 1 then we get
r and s are coprime therefore, there is no common factor of r and s except 1.
where r and s are integers.
When we subtract one rational from other rational number then we get again a rational number and we divide one rational by other rational number then we get quotient number which is also rational.
Therefore, the number on the right hand of equal to is rational number but x is a irrational number .A rational number is not equal to an irrational number .Therefore, it is contradict by taking a+bx is a rational number .Hence, a+bx is an irrational number.
Conclusion: a+bx is an irrational number.
Answer:
Answer is in the explanation
Step-by-step explanation:
I don't know exactly word from word what your choices look like...
but I can describe per each box what happened in my own words:
First box: They multiply first equation by 3 and the second equation by 2 to obtain the equations in that first box.
Second box: They subtracted the two equations in the first box to obtain 1x+0y=2 which means 1x=2 or x=2 (this is called solving a system by elimination
Third box: They used their first original equation (before the multiplication manipulation) and plug in the value they got for x which was 2 giving them 3(2)-2y=10
Fourth box: They simplified the equation 3(2)-2y=10 by performing the multiplication 3(2) giving them 6-2y=10
Fifth box: They subtracted 6 on both sides giving them -2y=4
Sixth box: They divided both sides by -2 giving them y=-2
I will summarize then what I wrote above:
1st box: Multiplication Property of Equality
2nd box: Elimination
3rd box: Substitution (plug in)
4th box: Simplifying
5th box: Subtraction Property of Equality
6th box: Division Property of Equality
Short side length = x
Medium side = x + 7
Long side = 5x
Total 49, so
x + x + 7 + 5x = 49
If you combine like terms:
7x + 7 = 49
Subtract 7 from both sides
7x = 42
Divide both sides by 7
x = 6 inches
