The equation of a circle is (x - 3)2 + (y + 2)2 = 25. The point (8, -2) is on the circle.What is the equation of the line that is tangent to the circle at (8, -2)?
y = 8
x = 8
x = 3
y = 3
Answers
Answer:
2nd Option is correct.
Step-by-step explanation:
Given Equation of Circle,
( x - 3 )² + ( y + 2 )² = 25
Point on circle = ( 8 , -2 )
To find: The equation of the line that is tangent to the circle at given point.
By comparing equation of circle with standard equation of circle,
( x - h )² + ( y - k )² = r²
we get,
Coordinates of center = ( 3 , -2 )
Slope of the radius line from center to point ( 8 , -2 ) =
Since, y-coordinate of radius line is same.
⇒ This line is parallel to x-axis.
We also knows that Radius and tangent are perpendicular to each other at point of contact.
⇒ Tangent is Parallel to y-axis and passes through ( 8 , -2 )
⇒ Equation of Tangent is x = 8
Therefore, 2nd Option is correct.
Answer A
y=8
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We have,
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We need to divide the total number of patches by total number of rows to find the number of patches in each row.
Therefore, the number of patches in each row is 13.
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had 2 chocolates left. Write an equation to determine the number of
friends (f) at Mr. Arango's daughter's party. *
Answers
Answer:
Ans: 16
Step-by-step explanation:
50-2=48
48/3=16 friends
Final answer:
To determine the number of friends at Mr. Arango's daughter's party, we can set up an equation. Each friend receives 3 chocolates, and 2 chocolates are left. By solving the equation 3f + 2 = 50, we find that there were 16 friends at the party.
Explanation:
To determine the number of friends (f) at Mr. Arango's daughter's party, we can set up an equation based on the information given. Let f represent the number of friends. Each friend receives 3 chocolates, so the total number of chocolates given out is 3f. We also know that 2 chocolates are left, so we can set up the equation:
3f + 2 = 50
To solve for f, we can subtract 2 from both sides:
3f = 48
Then, we divide both sides by 3 to isolate f:
f = 16
Therefore, there were 16 friends at Mr. Arango's daughter's party.
Learn more about Equations here:
#SPJ12
Answers
(x-3+i)(x-3-i)
x^2-6x+10
Answers
Answer:
In summary:
- Axis of symmetry: Not determinable from the given information.
- X-intercepts: (-1, 0) and (1.5, 0).
- Y-intercept: Not determinable from the given information.
- Vertex: (-1, 4).
- Interval of decrease: (-∞, -1) and (1.5, ∞).
Step-by-step explanation:
To identify the axis of symmetry, x-intercepts, y-intercept, and vertex of a graph, we need to analyze the given information and graph:
1. Axis of symmetry: The axis of symmetry is a vertical line that divides the graph into two symmetric halves. It is represented by the equation x = h, where h is the x-coordinate of the vertex. Based on the given information, we don't have the equation of the graph or the value of h, so we cannot determine the axis of symmetry.
2. X-intercepts: X-intercepts are the points where the graph intersects the x-axis. These points have a y-coordinate of 0. From the given information, we have the x-intercepts as follows:
- First x-intercept: (-1, 0)
- Second x-intercept: (1.5, 0)
3. Y-intercept: The y-intercept is the point where the graph intersects the y-axis. It has an x-coordinate of 0. From the given information, we don't have the y-intercept, so we cannot determine its value.
4. Vertex: The vertex is the highest or lowest point on the graph. It has an x-coordinate and a y-coordinate. From the given information, we have the vertex as follows:
- Vertex: (-1, 4)
Now, let's determine the interval in which the function is decreasing. To do this, we need to analyze the graph and observe where the graph is sloping downwards or decreasing. From the given information, we can see that the graph is decreasing in the interval (-∞, -1) and in the interval (1.5, ∞). These intervals represent the regions on the x-axis where the function is decreasing.
Answers
Answer:
= 1/(5x+7) [ 1 over (5x + 7)] with x≠ -1.4
Step-by-step explanation:
Given the function f(x), if f(x) ≠ 0, we would have the formula as following:
+) = 1/f(x)
We have the given equation:
f(x) = (10x/2) + 7 = 5x + 7
f(x) ≠ 0 when and only when (5x + 7) ≠ 0
(5x + 7) ≠ 0
⇔ 5x ≠ 0 - 7
⇔ 5x ≠ -7
⇔ x ≠ -7 ÷ 5
⇔ x ≠ -1.4
So with x≠ -1.4, f(x) ≠ 0, we have:
= 1/f(x) = 1/ (5x + 7)
Conclusion: = 1/(5x+7) [ 1 over (5x + 7)] with x≠ -1.4