Answer:
- dimensions: 12 ft by 5 ft
- area: 60 ft²
Step-by-step explanation:
Let x represent the shorter dimension in feet. Then the longer one is x+7 and the Pythagorean theorem tells us the relation of these to the diagonal is ...
x² + (x+7)² = 13²
2x² +14x + 49 = 169 . . . . eliminate parentheses
x² +7x -60 = 0 . . . . . subtract 169 and divide by 2
(x +12)(x -5) = 0 . . . . factor the equation
x = -12 or +5 . . . . . . . only the positive value of x is useful here.
The short dimension is 5 ft, so the long dimension is 12 ft. The area is their product, 60 ft².
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<em>Comment on finding the area</em>
The quadratic equation above can be rearranged and factored as ...
x(x +7) = 60
Since the dimensions of the garden are x and (x+7), this product is the garden's area. This equation tells us the area is 60. We don't actually have to find the dimensions.
Answer:
A. 4(x - 4) + 2(3x² + 3x - 20)
C. (11x² + 7x - 55)-(5x² - 3x + 1)
F. (3x² + 5x - 28) + (3x² + 5x - 28)
Step-by-step explanation:
Given:
(3x-7)(2x+8)
= 6x² + 24x - 14x - 56
=6x² + 10x - 56
A. 4(x - 4) + 2(3x² + 3x - 20)
= 4x - 16 + 6x² + 6x - 40
= 6x² + 10x - 56
B. (3x² + 5x - 28) - (2x² + 4x + 28)
= 3x² + 5x - 28 - 2x² - 4x - 28
= x² + x - 56
C. (11x² + 7x - 55)-(5x² - 3x + 1)
= 11x² + 7x - 55 - 5x² + 3x - 1
= 6x² + 10x - 56
D. 4(x - 4) - 2(3x² + 3x - 20)
= 4x - 16 - 6x² - 6x + 40
= - 6x² - 2x + 24
E. (11x² + 7x - 55)-(5x² - 3x + 2)
= 11x² + 7x - 55 - 5x² + 3x - 2
= 11x² - 5x² + 7x + 3x - 55 - 2
= 6x² + 10x - 57
F. (3x² + 5x - 28) + (3x² + 5x - 28)
= 3x² + 5x - 28 + 3x² + 5x - 28
= 6x² + 10x - 56
It cuts the volume in half
Answer:
see explanation
Step-by-step explanation:
(a)
The angle around the centre O of the circle = 360°, then
∠ AOB = 360° - 260° = 100°
Δ AOB is isosceles ( the radii OA and OB are congruent )
The altitude from O bisects ∠ AOB , thus
y = 50°
Since the triangle is isosceles the 2 base angles are congruent, so
x = 
= 
= 40°
(b)
∠ POR = 360° - 254° = 106°
Δ POR is isosceles (the radii OP and OR are congruent ) , then
the 2 base angles are congruent , thus
a = 
= 
= 37°
