Answer:
They use the same triangle but in different sizes to make the big triangle.
Step-by-step explanation:
1. 11663
2. 98
3. 46 days
4. 1121
5. 29 pounds
The friend would be incorrect. The antelope running 60 feet per second will be safe if the cheetah running at 90 feet per second is 650 feet behind it. To prove this, we can calculate the time it takes for the cheetah to reach the initial position of the antelope which is 650 ft from its initial position. We do as follows:
time to reach 650 ft = 650 ft / 90 ft/s = 7.22 s
After 7.22 s, the antelope would be,
distance of the antelope = 60 ft /s (7.22 s) = 433.33 ft
It would be 433.33 ft away from its initial position. So, the cheetah would not be able to reach the antelope when it travels 650 ft.
Answer:
Option D
Step-by-step explanation:
Option A
x² - 3x² + 2x² = 0
Therefore, the given polynomial has no roots.
Option B
x² + 2x + 8
By quadratic formula,
x = 
= 
Therefore, roots are imaginary and for a polynomial with degree 1 or more than 1, both the roots can't be imaginary.
So the polynomial can't have exactly two roots.
Option C
99x³ - 33x + 1
Since the polynomial is of degree 3, so it will have three roots.
Therefore, the polynomial will not have exactly 2 roots.
Option D
√2x - 3x² + 7√2
By quadratic formula,
x = 
x = 
There are exactly two real roots.
Therefore Option D is the answer.
Option E
4x + 11x - 111
Since this polynomial is of a degree 1.
There will be only one root.
Answer:
y ≈ 16.33
Step-by-step explanation:
∆SPQ is a 30-60-90 right triangle
PS:QS:PQ = 1:2:√3
QS/PQ = 2/√3
QS/PQ = QS/10
QS/10 = 2/√3 Multiply each side by 10
QS = 20/√3
∆RSQ is a 45-45-90 right triangle.
∴ RS = QS = 20/√3
RS² + QS² = QR²
(20/√3)² + (20/√3)² = y²
400/3 + 400/3 = y²
800/3 = y² Take the square root of each side
y = √(800/3)
= 20√(2/3)
= (20√6)/3
≈ 16.33
