Mr. and mrs. jefferson have a total of $5170 in a bank. at the end of the month, mr. jefferson deposit $450 into his account and mrs. jefferson deposit $626 into her account they now have an equal amount of money in their accounts. how much money did each of them have at first?
the correct answer option is a. –7.12, 1.12.
we are given the following equation and we are to solve it using the quadratic formula:
re-arranging this equation in order of decreasing power:
using the quadratic formula:
substituting the given values in the formula to get:
the rule is that for any triangle, the three angles always add to 180 degrees
so a+b+c = 180
replace a with 65, replace b with 3x-10 and replace c with 2x to get this new updated equation: 65 + 3x-10 + 2x = 180
now let's isolate x
65 + 3x - 10 + 2x = 180
5x + 55 = 180 combine like terms
5x + 55 - 55 = 180 - 55 subtract 55 from both sides
5x = 125
5x/5 = 125/5 divide both sides by 5
x = 25
we can stop here since your teacher only wants to know the value of x.
if you're curious how to find the other angles, then replace x with 25 and compute
angle b = 3x - 10 = 3*25 - 10 = 75 - 10 = 65 degrees
angle c = 2*x = 2*25 = 50 degrees
therefore, the three angles of the triangle are a = 65, b = 65, c = 50. as a check, they should add to 180. it turns out they do since a+b+c = 65+65+50 = 130 + 50 = 180. therefore, the answer is confirmed.
note: since angles a and b are both the same at 65 degrees, this means the triangle is isosceles (the sides opposite the congruent angles are congruent sides). we do not have enough info to actually find the length of any of the three sides.
diameter = 256 after 8 hours.
at time 0 the diameter is 1, at time 1 hour the diameter is 2, at time 2 hours the diameter is 4 and so on.
the equation of the graph is d = 2^t where d = the diameter and t = time in hours. this is exponential growth.
so after 8 hours the diameter = 2^8
= 256 (answer).