Answer:
the last one [d)]
Step-by-step explanation:
First, we need to use the triangle inequality theorem. The sum of the lengths of the two sides must be greater than the third side.
a) 7+14=21=21 (this cannot represent a triangle)
b) 13+23=36<37 (this cannot represent a triangle)
c) 7+18=25=25 (this cannot represent a triangle)
d) 11+24=35>32 (this can represent a triangle)
d) is the answer
Hope this helps!
Answer:
2(4x + 1)(x + 1)
Step-by-step explanation:
Given
8x² + 10x + 2 ← factor out 2 from each term
= 2(4x² + 5x + 1)
To factor the quadratic
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term
product = 4 × 1 = 4 and sum = + 5
The factors are + 1 and + 4
Use these factors to split the x - term
4x² + x + 4x + 1 ( factor the first/second and third/fourth terms )
= x(4x + 1) + 1 (4x + 1) ← factor out (4x + 1)
= (4x + 1)(x + 1), thus
4x² + 5x + 1 = (4x + 1)(x + 1) and
8x² + 10x + 2 = 2(4x + 1)(x + 1) ← in factored form
By using formula given above, M= log(w/w_0), we can find
10^M= w/w_0, it means 10^M.w_0,= w
but M=6.5, so 10^6.5=3162277,66
the seismic waves of the Caracas earthquake were 3162277,66 times more powerful of the standard seismic waves
Answer:
f(x) = x² - 4x - 12
Step-by-step explanation:
f(x) = (x - 6)(x + 2)
f(x) = x² + 2x - 6x - 12
f(x) = x² - 4x - 12
Factor out the GCF of
21
b
2
c
2
from
63
b
2
c
4
+
42
b
3
c
2
.
Tap for fewer steps...
Factor out the GCF of
21
b
2
c
2
from each term in the polynomial.
Tap for fewer steps...
Factor out the GCF of
21
b
2
c
2
from the expression
63
b
2
c
4
.
21
b
2
c
2
(
3
c
2
)
+
42
b
3
c
2
Factor out the GCF of
21
b
2
c
2
from the expression
42
b
3
c
2
.
21
b
2
c
2
(
3
c
2
)
+
21
b
2
c
2
(
2
b
)
Since all the terms share a common factor of
21
b
2
c
2
, it can be factored out of each term.
21
b
2
c
2
(
3
c
2
+
2
b
)
The greatest common factor
GCF
is the term in front of the factored expression.
21
b
2
c
2
