Algebra Answers

Find the first 3 terms, in ascending powers of 𝑥, of the binomial expansion of (2−𝑥)⁴ and simplify each term.

A grandparent gives a grandchild £100 at birth, and promises to increase the gift by £5 on each subsequent birthday.

a. Show that the grandchild will receive £200 on the 20𝑡ℎ birthday.

b. If the child has saved all the money, what is the total amount at age 20?

c. By how much would the gift have to increase each year if the total at age 20 is to be £4,200?

a. Expand (𝑎+𝑏)⁵. Hence find the coefficient of 𝑥 in the expansion of (4𝑥+2/9𝑥)⁵

b. The coefficient of 𝑥² in the expansion of (1+𝑥)ⁿ is 45. Given that 𝑛 is a positive integer, find the value of 𝑛.

Straight line y = mx + k .Where coordinates (-3,4) lies on the graph, write down the value of m and k and equation

The 7th term of an AP is 15 and the fourth is 9. Find the sequence, first term and the common difference

Use Descartes' Rule of Signs to find the possible number of negative zeros of p(x)=2x5+x4+x3−4x2−x−6

Solve the following system of equations and provide a graphical representation of the solution.

y - x = 1

x² + y² = 13

On a website that sells funny T-shirts, the number of customers has been falling 10% per month. If the site had 14,000 customers this month, then how many should it expect to have 10 months from now?

1. Solve the matrix equation 4𝒳−ℬ=𝒳ℬ+2𝒜 if 𝒜=(−2141), ℬ=(71−72).

2. Calculate the inverse matrix to the matrix 𝒜=(001011111). Check whether the obtained inverse matrix is correct.

3. Solve the system of linear equations: 𝑥−2𝑦+𝑧=5,−2𝑥+3𝑦−𝑧=−8,−𝑥−𝑦+2𝑧=2.

4. Calculate the area of the flat shape bounded by the curves: 𝑦=√𝑥−1,𝑦=3−𝑥,𝑦=0.

5. Find all the extrema of the function 𝑓(𝑥)=√16−𝑥2.

6. Find the maximal intervals of convexity (concavity) of the function 𝑓(𝑥)=2𝑥+arctg(3𝑥). Find the respective inflection points.

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