Answer:
a. y + 9 + x + y + x + 4 + x + 5 = 2x + 2y + 18
b. 30.4cm
c. Area of big rectangle = 9y cm², Area of small rectangle = 4x cm²
d. a = 9y + 4x
e. a = 38.8
Step-by-step explanation:
a. Perimeter = y + 9 + x + y + x + 4 + x + 5
= x + x + y + y + 9 + 4 + 5
= 2x + 2y + 18
b. 2x + 2y + 18 = 2(3.4) + 2(2.8) + 18
= 6.8 + 5.6 + 18
= 30.4cm
c. Formula for area of rectangle: length × breadth
Area of big rectangle = 9 × y
= 9y cm²
Area of small rectangle = 4 × x
= 4x cm²
d. a cm² = (9y + 4x)cm²
e. a = 9y + 4x
= 9(2.8) + 4(3.4)
= 25.2 + 13.6
= 38.8
Answer:
According to the sum of cubes formula, Janis is correct
Step-by-step explanation:
The sum of cubes formula is given as follows;
x³ + y³ = (x + y)·(x² - x·y + y²)
The given expression is presented as follows;
27·x³ + 8
The given expression can be expressed as 27·x³ + 8 = (3·x)³ + 2³
Therefore, using the sum of cubes formula, we have;
(3·x)³ + 2³ = (3·x + 2)·((3·x)² - 3·x·2 + 2²) = (3·x + 2)·(9·x² - 6·x + 2²)
∴ 27·x³ + 8 = (3·x)³ + 2³ = (3·x + 2)·(9·x² - 6·x + 2²)
Therefore, Janis is correct, by the sum of cubes formula, we get;
27·x³ + 8 = (3·x + 2)·(9·x² - 6·x + 2²).
Answer:
First investment = $98000
Second = $413,000
Step-by-step explanation:
Given the following :
Investment 1:
Let first investment = f
Rate = 8% = 0.08
Investment 2:
$21,000 more than 4 times of investment 1:
4f + 21000
Rate = 10% = 0.1
Total annual interest earned from both :
$49,140
Interest on investment 1 + interest on investment 2 = $49,140
To solve:
Simple Interest = principal * rate * time
Time = 1 year
Total interest = (f * 0.08 * 1) + ((4f + 21000) * 0.1 * 1)
49140 = 0.08f + 0.4f + 2100
0.48f = 47040
f = 47040 / 0.48
f = 98000 = first investment
Second investment :
4f + 21000
= 4(98000) + 21000
= $413,000
