Answer:
Therefore the correct assembling is
3.∠DAC ≅ ∠BCA 3. Alternate interior Angles are Equal as AD || BC.
Step-by-step explanation:
Given:
AD ≅ BC and AD || BC
To Prove:
ABCD is a Parallelogram
Proof:
Alternate Interior Angles Theorem :
"When two parallel lines are cut by a transversal , the resulting alternate interior angles are congruent.
Here AD || BC and the transversal is AC
Statement Reasons
1. AD ≅ BC . 1. Given
2. AD || BC 2. Given
3.∠DAC ≅ ∠BCA 3. Alternate interior Angles are Equal as AD || BC.
Therefore the correct assembling is
3.∠DAC ≅ ∠BCA 3. Alternate interior Angles are Equal as AD || BC.
Answer:
The volume of the cylinder is <u>141.23 cubic feet </u>
Step by step explanation :
<u>Given</u>-
- Radius of cylinder = 3 feet
- Height of cylinder = 5 feet
Now, we know that
<h3>
</h3>
where, r is the radius of the cylinder & h is the height of the cylinder.
Now,
Volume of the cylinder = 
<h3>
</h3>
( approximately )
Answer:
Consider f: N → N defined by f(0)=0 and f(n)=n-1 for all n>0.
Step-by-step explanation:
First we will prove that f is surjective. Let y∈N be any natural number. Define x as the number x=y+1. Then x∈N, and f(x)=x-1=(y+1)-1=y. We conclude that f is surjective.
However, f is not injective. Take x1=0 and x2=1. Then x1≠x2 but f(x1)=0 and f(x2)=x2-1=1-1=0. We have shown that there are two natural numbers x1,x2 such that x1≠x2 but f(x1)=f(x2), that is, f is not injective.
Note:
If 0∉N in your definition of natural numbers, the same reasoning works with the function f: N → N defined by f(1)=1 and f(n)=n-1 for all n>1. The only difference is that you consider x1=1, x2=2 for the injectivity.
If a consistent system has an infinite number of solutions, it is dependent. When you graph the equations, both equations represent the same line. <span>If a system has no solution, it is said to be </span>inconsistent. <span>The graphs of the </span>lines<span> do not intersect, so the graphs </span>are parallel<span> and there is no solution.</span>
