Let <em>x</em> be the first number in the sequence. Then the first three numbers are
{<em>x</em>, <em>x</em> + 3, <em>x</em> + 6}
The next sentence says that the sequence
{<em>x</em> + 1, <em>x</em> + 9, <em>x</em> + 25}
is geometric, which means there is some fixed number <em>r</em> for which
<em>x</em> + 9 = <em>r</em> (<em>x</em> + 1)
<em>x</em> + 25 = <em>r</em> (<em>x</em> + 9)
Solve for <em>r</em> :
<em>r</em> = (<em>x</em> + 9)/(<em>x</em> + 1) = (<em>x</em> + 25)/(<em>x</em> + 9)
Solve for <em>x</em> :
(<em>x</em> + 9)² = (<em>x</em> + 25) (<em>x</em> + 1)
<em>x</em> ² + 18<em>x</em> + 81 = <em>x</em> ² + 26<em>x</em> + 25
8<em>x</em> = 56
<em>x</em> = 7
Then the three numbers are
{7, 10, 13}
Answer:
-13°F is the change in temperature.
Step-by-step explanation:
The change in temperature is,
→ -1 + x = -14
→ x = -14 + 1
→ [ x = -13 ]
Hence, -13°F is the change.
Answer:
Runner Up Amount=$16,000
Winner Amount=$64,000
Step-by-step explanation:
Amount of the college's scholarship=$80,000
The fund is being divided between the top two contestants so that the winner receives four times as much as the runner-up.
Therefore: we can say it is being divided into 5 parts where the winner gets 4 parts and the runner up gets 1 part, i.e in the ratio 4:1.
Runner Up Amount
Winner Amount
The winner gets $64,000 and the runner up gets $16,000.
Answer:
6.4 is the correct answer