Heather, Ahmad, and Pablo sent a total of 76 text messages during the weekend. Pablo sent 2 times as many messages as Ahmad. Hea
2 answers:
Well, we know all three sent altogether 76 text messages
so... let us say, the amount of text for each is
Heather sent "h" amount
Ahmand sent "a" amount
and
Pablo sent "p" amount
so.. all three sent 76, meaning
h + a + p = 76
we know that, whatever "h" and "a" and "p" are
Pablo, send twice as much as Ahmad
so, if Ahmad sent "a", Pablo then sent 2 * a or 2a
Heather sent 8 less than Ahmad
so, if Ahmad sent "a", Heather then sent a - 8
thus
solve for "a", to find how many Ahmad sent
Heather sent 8 less than that
and
Pablo sent, twice as much
so... let us say, the amount of text for each is
Heather sent "h" amount
Ahmand sent "a" amount
and
Pablo sent "p" amount
so.. all three sent 76, meaning
h + a + p = 76
we know that, whatever "h" and "a" and "p" are
Pablo, send twice as much as Ahmad
so, if Ahmad sent "a", Pablo then sent 2 * a or 2a
Heather sent 8 less than Ahmad
so, if Ahmad sent "a", Heather then sent a - 8
thus
solve for "a", to find how many Ahmad sent
Heather sent 8 less than that
and
Pablo sent, twice as much
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Ooh, fun
geometric sequences can be represented as
so the first 3 terms are
the sum is -7/10
and their product is -1/125
from the 2nd equation we can take the cube root of both sides to get
note that a=ar/r and ar²=(ar)r
so now rewrite 1st equation as
subsituting -1/5 for ar
which simplifies to
multiply both sides by 10r
-7r=-2-2r-2r²
add (2r²+2r+2) to both sides
2r²-5r+2=0
solve using quadratic formula
for
so
for 2r²-5r+2=0
a=2
b=-5
c=2
so
or 
use them to solve for the value of a
try for r=2 and 1/2
or 
test each
for a=-1/10 and r=2
a+ar+ar²=
it works
for a=-2/5 and r=1/2
a+ar+ar²=
it works
both have the same terms but one is simplified
the 3 numbers are
, 
, and 
geometric sequences can be represented as
so the first 3 terms are
the sum is -7/10
and their product is -1/125
from the 2nd equation we can take the cube root of both sides to get
note that a=ar/r and ar²=(ar)r
so now rewrite 1st equation as
subsituting -1/5 for ar
which simplifies to
multiply both sides by 10r
-7r=-2-2r-2r²
add (2r²+2r+2) to both sides
2r²-5r+2=0
solve using quadratic formula
for
so
for 2r²-5r+2=0
a=2
b=-5
c=2
so
use them to solve for the value of a
try for r=2 and 1/2
test each
for a=-1/10 and r=2
a+ar+ar²=
it works
for a=-2/5 and r=1/2
a+ar+ar²=
it works
both have the same terms but one is simplified
the 3 numbers are
Answer:
Step-by-step explanation:
Given
Required
The difference quotient for h
The difference quotient is calculated as:
Calculate f(x + h)
The numerator of is:
Collect like terms
So, we have:
Rewrite as: