Answer:
Q7. 11.3 inches (3 s.f.)
Q8. 96.2 ft
Q9. 36.4cm
Step-by-step explanation:
Q7. Please see attached picture for full solution.
Q8. Let the length of a side of the square be x ft.
Applying Pythagoras' Theorem,
Thus, the perimeter of the square is
Q9. Equilateral triangles have 3 equal sides and each interior angle is 60°.
Since the perimeter of the equilateral triangle is 126cm,
length of each side= 126÷3 = 42 cm
The green line drawn in picture 3 is the altitude of the triangle.
Let the altitude of the triangle be x cm.
sin 60°= 
(to 3 s.f.)
Therefore, the length of the altitude of the triangle is 36.4cm.
Answer:
See below.
Step-by-step explanation:
Part A:
For Dog walking, he earns $30 for 5 hours of work.
He earns $36 for 6 hours of work.
$30/5 hours = $6/hour
$36/6 hours = $6/hour
He earns $6/hour dog walking.
For 8 hours, he earns 8 hours * $6/hour = $48
To earn $66, he works 66/6 = 11 hours.
5 30
6 36
8 48
11 66
Part B:
He earns $7/hour for yard work, so multiply the number of hours by 7 to find the money he earns.
Table for yard work
Hours Money
5 $35
6 $42
8 $56
Part C:
For 5 hours, he earns $35 for yard work and $30 as a dog walker.
$35 - $30 = $5
Answer:
40
Step-by-step explanation:
(2/5)*n - 6 = 10 Add 6 to both sides
(2/5)*n - 6 + 6 = 10 + 6 Combine
(2/5)*n = 16 Multiply both sides by 5/2
(5/2)(2/5)n = 16*(5/2)
n = 80 / 2
n = 40
Answer:
Step-by-step explanation:
(a+ b)² = a² + b² + 2ab
(2x + y)² = (2x)² + y² + 2*2x *y
= 4x² + y² + 4xy
(a- b)² = a² + b² - 2ab
(3x - 2y)² = (3x)² + (2y)² - 2*3x *2y
= 9x² + 4y² - 12xy
(a - b)(a +b) = a² - b²
(x - 4y(x + 4y) = x² - (4y)²
= x² - 16y²
(2x + y)² - (3x - 2y)² + (x - 4y)(x +4y)
= 4x² + y² + 4xy - (9x² + 4y² - 12xy) + x² - 16y²
= 4x² + y² + 4xy - 9x² - 4y² + 12xy + x² - 16y²
= 4x² - 9x² + x² + y² - 4y² - 16y²+ 4xy + 12xy
= -4x² - 19y² + 16xy
