Algebra Answers

3.5 Multiply 62 by 35, firstly by breaking down 35 in its terms (30+5) and secondly by breaking down 35 in its factors (5×7). Show all your steps

Solve the inequalities. Give your answer in interval notation, and indicate the answer geometrically on the real-number line.

a) t + 6 ≤ 2 + 3t

b) 3(2 – 3x) > 4(1 – 4x) 

`Q2. CASE STUDYI ndia is competitive manufacturing locationdue to the low cost of manpower and strongtechnical and engineering capabilitiescontributing to higher quality production runs.The production of TV sets in a factoryancreases every year. It produced 1160000 setsin 2018, 2000000 sets in 2020and 2200000sets in 2021.Based on the above infor mation, answer thefollowing questions:1. Find the total production in the year 2018and 2019.2. In which year, the production was 2 millionsets?3. Find the difference of the production in theyear 2018 and 2020.4. Write 2200000 in words according to HindA rabic number system.

1. There are 49 dogs signed up for a dog show. There are 36 more small dogs than large dogs. How many small dogs have signed up to compete? 

This question comes directly from a second grader's math homework.

1. Show that if 5/3< 2x< 11/3, then x∈{y∈R such that |y- 4/3| < 1/2}

2. Draw the graph of the function f, defined by f(x)= |x-6| + |5 - x| ; x∈ [2,8]

The second term of an arithmetic progression is four times the fifth term, and the first term is 10. Find the common difference, and hence the sum of the first 12 terms.

Are there any values of p such that p²+48 is equal to -14p?

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?