Answer:
a) 75/3=25/1
Step-by-step explanation:
On a graph, the point moves down 9 points and to the right by 2
Answer: a
Step-by-step explanation: Just trust me
Ryan was 8 when his parents invested $4000 in a certificate of deposit that pays 6%. If Ryan leaves the account alone until the investment doubles, how old will he be? (Assume that the interest is not compounded.)
<span>This one has a twist to it in that it tells you that the interest is not compounded. </span>
<span>They need to earn $8,000 - $4,000 = $4,000 in interest. </span>
<span>They earn $4,000 X 6% = $240 in interest per year. </span>
<span>$4,000 / $240 = 16.67 </span>
<span>16.67 + 8 = 24.67 </span>
<span>Ryan will be 24 and 8 months old when the investment doubles. </span>
<span>2.)Benjamin has $6000 invested in two accounts. One earns 8% interest per year, and the other pays 7.5% interest per year. If his total interest for the year is $472.50, how much is invested at 8%? </span>
<span>X = the amount invested at 8% </span>
<span>($6,000 - X) = the amount invested at 7.5% </span>
<span>So: </span>
<span>.08X + .075(6,000 - X) = $472.50 </span>
<span>Now solve: </span>
<span>.08X + 450 -.075X = $472.50, this reduces to </span>
<span>.005X = $22.50, which finally reduces to </span>
<span>X = $4,500 </span>
<span>So $6,000 - X = $1,500 </span>
<span>So the answer is: $4,500 is invested at 8% </span>
<span>Test the result </span>
<span>$4,500 X 8% = $360.00 </span>
<span>$1,500 X 7.5% = $112.50 </span>
<span>$360.00 + $112.50 = $472.50, and you've proved your answer</span>
Answer:
the intersection is the point P=(x,y,z)=(8,9,14) and the line does not lie in the plane
Step-by-step explanation:
from the equation of the line
x - 1/2 = y + (3/2)/-1 = (z + 1) / 2 = t (parameter)
then the parametric equation of the line is
x= 1/2 +t
y = (3/2) + t
z = (-1) + 2*t
therefore from the equation of the plane
2x - 2y + z = 12
2*(1/2 +t) - 2[(3/2) + t] + [(-1) + 2*t] = 12
1+2*t - 3 -2*t -1 + 2*t = 12
-3 + 2*t = 12
t= 15/2
therefore there is only one intersection of the line with the plane ( then the line does not lie in the plane , since there would be infinite intersection points). The intersection is
x= 1/2 +t = 1/2 +15/2 = 8
y = (3/2) + t = (3/2) + 15/2 = 9
z = (-1) + 2*t = (-1) + 2*15/2 = 14
thus the intersection point P=(x,y,z)=(8,9,14)