Answer:
x = 33
Step-by-step explanation:
Answer: $7,488
Step-by-step explanation:
For answer B:
The formula for the new balance would be A=P(1 + r)t
A = new balance
P = principal balance -> $900
r = rate (in decimal form)
t = time in years -> 8 years
To find the rate, convert 4% to decimal
4/100 = 0.04
A=P(1+ r)t
A=900(1+0.04)8
A=900(1.04)8
A=$7,488
Given:
The vertices of a triangle are R(3, 7), S(-5, -2), and T(3, -5).
To find:
The vertices of the triangle after a reflection over x = -3 and plot the triangle and its image on the graph.
Solution:
If a figure reflected across the line x=a, then
The triangle after a reflection over x = -3. So, the rule of reflection is
The vertices of triangle after reflection are
Similarly,
And,
Therefore, the vertices of triangle after reflection over x=-3 are R'(-9,7), S'(-1,-2) and T'(-3,-5).
Lets call those two unknown numbers a, b and write the info in the problem as equations:
a*b = 30
a + b = 40
lets solve for a in the second equation and substitute in the first:
<span>a + b = 40
</span>a = 40 - b
therefore:
<span>a*b = 30
</span>(40 - b)b = 30
40b - b^2 = 30
b^2 - 40b + 30 = 0
if we apply the general quadratic equation to solve we have:
b = (40 +- √(1600 - 120))/2
b = (40 +- √(1480<span>))/2
</span>b = (40 +- 38.47)/2
There are two solutions:
<span>b1 = (40 + 38.47)/2
</span><span>b1 = 39.24
b2 = (40 - 38.47)/2
</span>b2 = 0.765
lets use the second solution <span>b2 = 0.765, and substitute in the first equation to find a:
</span><span>a*b = 30
</span>a*0.765 = 30
a = 30/0.765
a = 39.216
so the numbers are 39.216 and 0.765
