What is 7/20 written as a decimal? _______
1 answer:
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Answer:
a). Center of the circle = (-2, 5)
b). Equation of the line ⇒ y =
Step-by-step explanation:
Equation of the circle is,
x² + 4x + y²- 10y + 20 = 30
a). [x² + 2(2)x + 4 - 4] + [y²- 2(5)y + 25] - 25 + 20 = 30
[x² + 2(2)x + 4] - 4 + [y² - 2(5)y + 25] - 25 + 20 = 30
(x + 2)² + (y - 5)²- 29 + 20 = 30
(x + 2)² + (y - 5)²- 9 = 30
(x + 2)² + (y - 5)² = 39
By comparing this equation with the standard equation of a circle,
Center of the circle is (-2, 5).
b). A point (2, 10) lies on this circle.
Slope of the line joining this point to the center (-2, 5),
=
=
Let the slope of the tangent which is perpendicular to this line is ''
Then by the property of perpendicular lines,
Now the equation of the line passing though (2, 10) having slope
y - y' =
y - 10 =
y - 10 =
y =
y =
Therefore, equation of the line will be, y =
Answer:
Options A and D are correct choices.
Step-by-step explanation:
We have been given an inequality and we are asked to find the correct options from our given choices.
Let us solve inequalities in our given options one by one to see which of these matches with our given inequality.
(A)
We can see that option A gives the same answer as our given inequality, therefore, option A is the correct choice.
(B)
This inequality represented in option C gives solution that x should be greater than or equal to -7, which is opposite to our given inequality, therefore, option B is incorrect.
(C)
Dividing inequality by a negative number swaps inequality sign.
This inequality gives solution that x should be greater than or equal to -7, which is opposite to our given inequality, therefore, option C is incorrect.
(D)
Dividing inequality by a negative number swaps inequality sign.
We can see that option D gives the same answer as our given inequality, therefore, option D is the correct choice.