Algebra Answers

Example:Grade 4 patterns, functions and algebra. Conceptual understanding, procedural fluency, strategic competence, adaptive reasoning and productive disposition

1. Explain how part to part ratio occur in:

i. Geometry

ii. Algebra

iii. Probability

2. The ratio of the sides of a pentagon is 5:3:2:4:1 . The perimeter of the pentagon is 75cm. How long is the shortest side?

5+3+2+4+1, so x is?

a. 5/15 × 75/1 = 25cm

b. 2/15 × 75/1 = 10cm

c. 3/10 × 75/1 = 5cm

d. 1/5 × 75/1 = 5cm

1. A retirement account is opened with an initial deposit of $8,500 and earns 8.12% interest compounded monthly. What will the account be worth in 20 years? What if the deposit was calculated using simple interest? Could you see the situation in a graph?

2. Graph the function  and its reflection about the line y=x on the same axis, and give the x-intercept of the reflection. Prove that . [Suggestion: type  {- 7 < x < 2} {0 < y < 7} in desmos, and then type its inverse function.]

3. How long will it take before twenty percent of our 1,000-gram sample of uranium-235 has decayed? [See Section 6.6 Example 13]

The decay equation is , where t is the time for the decay, and K is the characteristic of the material. Suppose T is the time it takes for half of the unstable material in a sample of a radioactive substance to decay, called its half-life. Prove that  . What is K for the uranium-235?

how many different computer passwords are possible if 

(a) digits and letters can be repeated

(b) digits and letters cannot be repeated

Question:  3 digits followed by 2 letters

Find one-half of these fractions.

1. 1/4

2. 2/3

3. 3/4

2x^2

a^3x+5/a^3x-1

(b) For the given sequence 1/n, 1/2n, 1/4n,…  Find the 16th term. Find sum of first sixteen terms where n is your arid number i.e. 19-arid-234 take n=234