Question

if you go to asia from the united states, then you cross an ocean.
if a vehicle is a car, then it has four wheels.
if you own a dog, then your pet is furry.
if you can stand up, then you can walk.
13.
the point ( m(-6,8) ) is the midpoint of ( overline{ab} ). the point a is has coordinates ( (-2,10) ). find the coordinates of point b.
( (2,12) )
( (-10,6) )
( (1,-6) )
( (5,-3) )

1. which of the following conjectures is false?

the sum of two even numbers is even.
the sum of two odd numbers is odd.
the product of two even numbers is even.
the product of two odd numbers is odd.

Explanation:

Step1: Use mid - point formula

The mid - point formula for two points \(A(x_1,y_1)\) and \(B(x_2,y_2)\) is \(M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\). Given \(M(-6,8)\) and \(A(-2,10)\). Let \(B=(x,y)\). Then \(\frac{-2 + x}{2}=-6\) and \(\frac{10 + y}{2}=8\).

Step2: Solve for \(x\)

From \(\frac{-2 + x}{2}=-6\), multiply both sides by \(2\): \(-2+x=-12\). Add \(2\) to both sides: \(x=-12 + 2=-10\).

Step3: Solve for \(y\)

From \(\frac{10 + y}{2}=8\), multiply both sides by \(2\): \(10 + y=16\). Subtract \(10\) from both sides: \(y=16-10 = 6\).

Step4: Check conjecture for sum of odd numbers

Let two odd numbers be \(2m + 1\) and \(2n+1\) (\(m,n\in Z\)). Their sum is \((2m + 1)+(2n + 1)=2(m + n+1)\), which is even.

Answer:

For question 13: B. \((-10,6)\)
For question 14: B. The sum of two odd numbers is odd.