What is the prime factors of the numbers 48
1 answer:
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<u>ANSWER: </u>
The area of the triangle bounded by the y-axis is
<u>SOLUTION:</u>
Given,
Consider f(x) = y. Hence we get
--- eqn 1
On rewriting the terms we get
4x + 7y – 63 = 0
As the triangle is bounded by two perpendicular lines, it is an right angle triangle with y-axis as hypotenuse.
Area of right angle triangle = where a, b are lengths of sides other than hypotenuse.
So, we need find length of f(x) and its perpendicular line.
First let us find perpendicular line equation.
Slope of f(x) =
So, slope of perpendicular line =
Perpendicular line is passing through origin(0,0).So by using point slope formula,
Where m is the slope and
--- eqn 2
4y = 7x
7x – 4y = 0
now, let us find the vertices of triangle, one of them is origin, second one is point of intersection of y-axis and f(x)
for points on y-axis x will be zero, to get y value, put x =0 int f(x)
0 + 7y – 63 = 0
7y = 63
y = 9
Hence, the point of intersection is (0, 9)
Third vertex is point of intersection of f(x) and its perpendicular line.
So, solve (1) and (2)
Put x value in (2)
So, the point of intersection is
Length of f(x) is distance between and (0,9)
Now, length of perpendicular of f(x) is distance between
Now, area of right angle triangle =
Hence, the area of the triangle is
Answer: The correct options are (1) (5,10), (2) (3,-3), (3) x = -1, (4) , (5) 21s and (6) 0, -1, and 5.
Explanation:
Te standard form of the parabola is,
.....(1)
Where, (h,k) is the vertex of the parabola.
(1)
The given equation is,
Comparing this equation with equation (1),we get,
and
Therefore, the vertex of the graph is (5,10) and the fourth option is correct.
(2)
The given equation is,
To make perfect square add , i.e.,
. Since there is factor 3 outside the parentheses, so subtract three times of 9.
Comparing this equation with equation (1),we get,
and
Therefore, the vertex of the graph is (3,-3) and the fourth option is correct.
(3)
The given equation is
To make perfect square add , i.e.,
. Since there is factor 4 outside the parentheses, so subtract three times of 1.
Comparing this equation with equation (1),we get,
and
The vertex of the equation is (-1,3) so the axis is x=-1 and the correct option is 2.
(4)
The given equation is,
To make perfect square add , i.e.,
.
Therefore, the correct option is 4.
(5)
The given equation is,
It can be written as,
It is a downward parabola. so the maximum height of the function is on its vertex.
The x coordinate of the vertex is,
Therefore, after 21 seconds the projectile reach its maximum height and the correct option is first.
(6)
The given equation is,
Use factoring method to find the factors of the equation.
Equate each factor equal to 0.
Therefore, the zeros of the given equation is 0, -1, 5 and the correct option is 2.
Answer:
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