Answer:
(x + 5)² + (y + 8)² = 49
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
here (h, k) = (- 5, - 8), so
(x - (-5))² + (y - (- 8))² = r², that is
(x + 5)² + (y + 8)² = r²
The radius is the distance from the centre to a point on the circle
Use the distance formula to calculate r
r = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (- 5, - 8) and (x₂, y₂ ) = (2, - 8)
r = 
= 
= 
= 7
r = 7 ⇒ r² = 7² = 49
Hence
(x +5)² + (y + 8)² = 49 ← equation of circle
Answer:
3 < x < 13
Step-by-step explanation:
<u>Triangle Inequality Theorem</u>
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
Let x be the length of the unknown side.
Therefore, x will either be the longest side or one of the shorter sides.
Therefore:
x < 5 + 8
⇒ x < 13
And:
8 < 5 + x
⇒ 3 < x
So the range of possible values of the third side is <u>greater than 3</u> and <u>less than 13</u>: 3 < x < 13
Answer:
cot²x
Step-by-step explanation:
Using the identity
sin²x + cos²x = 1, then
1 - sin²x = cos²x
1 - cos²x = sin²x
Thus
= 
= cot²x
Answer:
6 integers
Step-by-step explanation:
Its divisible by 1 and 5 and 10 ( as its ends in 0)
It is even so its divisible by 2.
Its digits do not add up to a number divisible by 3 so 3,6 and 9 are not factors. Its divisible by 4 and 8 . Not divisible by 7.
S0 answer is 6 integers between 1 and 10
Answer:
w≠-7
Step-by-step explanation:
w-2
---------
w+7
The denominator cannot be zero, so
w+7 cannot be zero
w+7≠0
Subtract 7 from each side
w+7-7 ≠0-7
w≠-7
