Answer:
The possible lengths of the third side is all real numbers greater than 4 inches and less than 20 inches
Step-by-step explanation:
we know that
<u>The Triangle Inequality Theorem</u>. states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side
Let
x -----> the possible lengths of the third side
Applying the Inequality Theorem
1) 12+8 > x
20 > x
Rewrite
x < 20 in
2) 8+x > 12
x> 12-8
x > 4 in
therefore
4 in < x < 20 in
The possible lengths of the third side is all real numbers greater than 4 inches and less than 20 inches
Answer:
$0.18 per pencil.
Step-by-step explanation:
"Dollars per unit" means that you take the dollar amount and divide it by the amount of pencils, so you get 3.24/18, or .18.
Answer:
Y(n) = 7n + 23
Step-by-step explanation:
Given:
f(0) = 30
f(n+1) = f(n) + 7
For n=0 : f(1) = f(0) + 7
For n=1 : f(2) = f(1) + 7
For n=2 : f(3) = f(2) + 7 and so on.
Hence the sequence is an arithmetic progression with common difference 7 and first term 30.
We have to find a general equation representing the terms of the sequence.
General term of an arithmetic progression is:
T(n) = a + (n-1)d
Here a = 30 and d = 7
Y(n) = 30 + 7(n-1) = 7n + 23
Answer:
All numbers can be written as a product of the prime numbers that conform them.
A) Find two numbers with a common factor of 3 only.
for example:
2*3 = 6
7*3 = 21
Both numbers have the factor 3 in them, and because the other two numbers are primes, we can be sure that the 3 is the only common factor.
B) Write a pair of numbers with a common factor of 2, 3 and 6.
Here we can write:
2*3*2 = 12
3*2*5 = 30
Those two numbers have the common factors 6, 2 and 3.
C) Write a pair of numbers with common factors of 3, 6 and 9.
3*2*3 = 18 (has the factors 2, 3, 3*2 = 6, 3*3 = 9)
-3*2*6 = -36
Both have the common factors 3, 6 and 9 (and they share more common factors like 2, this happens because 6 = 3*2, so if 6 is a common factor, 2 also must be)
Answer:
<u>Radius: 12 units </u>
- Area: πr² = 3.14*12² = 452.16 square units
<u>Diameter: 16.8 units</u>
- Area: πd²/4 = 3.14*16.8²/4 = 221.5584 square units
<u>Radius: 3.4 units</u>
- Area: πr² = 3.14*3.4² = 452.16 square units
<u>Diameter: 10 units</u>
- Area: πd²/4 = 3.14*10²/4 = 78.5 square units
