Matthew invested $2,000 in a compound interest account for 3 years. The interest rate was 5%. How much money would it be in the end of third year in Mattew's account?

$2,315.25

Step-by-step explanation:

2000 x 0.05 = 100

2000 + 100 = 2100

After year one: 2100

2100 x 0.05 = 105

2100 + 105 = 2205

After year two: 2205

2205 x 0.05 = 110.25

2205 + 110.25 = 2315.25

After year three: 2315.25

Part A: Triangle ABD is similar to Triangle ACD

Part B: Using HL Theorem, we can determine these 2 right triangles to be similar

Part C: DA = 3

Step-by-step explanation:

We can use HL (Hypotenuse-Leg) Theorem to help determine similarity. Since DA perpendicular bisects BC, we know that it forms the altitude and forms right triangles, which gives us legs and a hypotenuse,

To find DA, we are given right triangle ACD. We know that one leg, CD, is equal to 4. We also know that 3-4-5 is a Pythagorean Triple, so DA would be 3 and AC would be 5.