0.77 / 0.05 = 15.4 ...so we know it is 15 nickels
15 * 0.05 = 0.75.....0.77 - 0.75 = 0.02....with 2 pennies left over
ur answer is : 15 nickels and 2 pennies left over
Knowing what the variables are means that all we have to do is substitute:
[ ( 3 ) ^2 + ( 4 ) ^2 ] / 4 - 3 =
( 9 + 16 ) / 1 =
25
1.
a^2+b^2=c^2
easy
a=a
b=13
c=21
a^2+13^2=21^2
a^2+169=441
minus 169 both sides
a^2=272
sqrt both sides
a=16.4924
D is answer
2. same thing
a=18
b=26
18^2+26^2=c^2
324+676=c^2
1000=c^2
sqrt both sides
31.6228=c
C is answer
3.
one way is to plug them in
remember that hypotonuse is longest side
A. 7^2+24^2=25^2, is that true?, yes it is treu
answer is A
4.
legs are 6 and 4
a=6
b=4
c=x
4^2+6^2=x^2
16+36=x^2
52=x^2
sqrt both sides
7.2111=x
7.2=x
5.c=20
a=x
b=14
x^2+14^2=20^2
x^2+196=400
minus 196 both sides
x^2=204
sqrt both sides
x=14.2829
x=14.3
1. D
2. C
3. A
4. 7.2
5. 14.3
Answer:
Prove set equality by showing that for any element , if and only if .
Example:
.
.
.
.
.
Step-by-step explanation:
Proof for for any element :
Assume that . Thus, and .
Since , either or (or both.)
- If , then combined with , .
- Similarly, if , then combined with , .
Thus, either or (or both.)
Therefore, as required.
Proof for :
Assume that . Thus, either or (or both.)
- If , then and . Notice that since the contrapositive of that statement, , is true. Therefore, and thus .
- Otherwise, if , then and . Similarly, implies . Therefore, .
Either way, .
Therefore, implies , as required.