Answer:
A. Alternate Exterior Angles Theorem
Step-by-step explanation:
The Alternate Exterior Angles Theorem states that when two parallel angles are cut by a transversal, the resulting alternate exterior angles are congruent.
∠2 & ∠7 both follow this rule.
A=P (1+r/n)^nt
A= Total amount invested, P=principal amount, r=Interest rate, n=number of time in a year when the interest is earned (for annual, n=1; for semi-annual, n=2, ...), t = time in years
In the current scenario, case 1, n=2; case 2, n=1 and A1=A2, t1=t2
Therefore,
800(1+0.0698/2)^2t = 1000(1+0.0543/1)t
Dividing by 800 on both sides;
(1+0.0349)^2t = 1.25(1+0.02715)^t
(1.0349)^2t = 1.25(1.02715)^t
Taking ln on both sides of the above equation;
2t*ln (1.0349)= ln 1.25 + t*ln (1.02715)
2t*0.0343 = 0.2231+ t*0.0268
0.0686 t = 0.2231+0.0268 t
(0.0686-0.0268)t = 0.2231
0.0418t=0.2231
t=5.337 years
Therefore, after 5.337 years or 5 years and approximately 4 months, their value of investments will be equal.
This value will be,
A=800(1+0.0698/2)^2*5.337 = $1,153.76
To find the ordered pair solution, you need to find the zero(s) (which are the x-values for which y is equal to zero). This is called the Zero Product Property. Here's the math:
-2x-y=4 convert the equation into slope form
-y=2x+4 multiply both sides by -1
y=-2x-4 convert into factored form
y=-2(x+2) now, we need to find what x equals that makes y equal zero
0=-2(x+2) replace y with zero
0/-2=x+2 divide both sides by -2
-2=x x=-2 when y=0
Therefore, the zero of the equation (aka the solution) is the ordered pair (-2,0).
Answer: (-2,0)
If you have access to a graphing calculator, you can just convert the equation to y=mx+b form and enter it as a function. The solution is wherever the graph intercepts the x-axis. Hope this helps!
E and pi are 2 famous examples
Eight cats for every three goats is a ratio between the cats and goat, so it would be 8:3
