Answer: 2/3
Step-by-step explanation:
2b 2a
----------------- + -----------------
(b+a)^2 (b^2 - a^2)
2b 2a
= ----------------- + -------------------
(b+a)(b+a) (b+a)(b-a)
2b(b - a) + 2a(b + a)
= ------------------------------------
(b+a)(b+a)(b-a)
2b^2 - 2ab + 2ab + 2a^2
= ---------------------------------------
(b+a)(b+a)(b-a)
2b^2 + 2a^2
= ------------------------
(b+a)(b+a)(b-a)
2(b^2 + a^2)
= ------------------------
(b+a)^2 (b-a)
Answer:
Numerator: 2(b^2 + a^2)
Denominator: (b+a)^2 (b-a)
Hello there! I can help you! The formula for compound interest is P(1 + r)^t, where P= principal (initial amount), r = interest rate (in decimal form), and t = time (in years). Let's do this step by step. First off, we add the rate into 1. 4% is the interest rate (0.04 in decimal form). 1 + 0.04 is 1.04. Now, what we will do is raise that number to the 2nd power, because the time that elapses is 2 years. 1.04² is 1.0816. That's that. Now, multiply 7,500 to find the total amount of money. 1.0816 * 7,500 is 8,112. There. Toby's savings account balance in 2 years is £8,112.
Note: To solve for compound interest questions like it, add 1 to the percentage rate in decimal form, raise that number to a power based on the number of years (for example, raise the number to the 7th power if we are looking for the balance after 7 years), and then multiply that number by the starting amount. After you raise the number by a power, there may be a lot of numbers behind it. Whatever you do, DO NOT delete the number. Keep it there and multiply it by the principal.
To find the area of a rectangle, multiple the width by the length.
(And simply the fractions for a simpler equation)
For piece A:
The length 1 and 3/5 can be turned into an improper fraction by multiplying 1 by the denominator (5) and adding it to the numerator (3). 1 and 3/5 = 8/5
(3/4) • (8/5) = area
Multiple the numerators with each other and the denominators with each other (3 times 8 = 24) (4 times 5 = 20)
The area of piece A is 24/20
If you do the same for piece B:
(2/5) • (21/8) = area
The answer is 42/40
1/3 of 39,900 equals 1/3*39900
(1/3)*(39900/1)= 39900/3
39900/3= 13300
Final answer: 13,300
