Consider the linear system of equations. y = –x + 9 y = 0.5x – 6 If the solution is (a,–1), what is a? a =
1 answer:
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<h2>Answer:</h2>
Figure B
<h2>Step-by-step explanation:</h2>The Pythagorean Theorem is , where c is the longest side of the triangle (the hypotenuse).
To find the side length of each square, you have to square root the area of each square. This means that Figure A has side lengths of 3, 6 and 8 units. Figure B has side lengths of 5, 12 and 13 units.
In Figure A, if the triangle is right-angled, the equation must be correct. 9 + 36 = 45. 45 is not equal to 64, so the triangle is not right-angled.
In Figure B, if the triangle is right-angled, the equation must be correct. 25 + 144 = 169. 169 is 13 squared, so the triangle is right-angled.
Alternatively, as you are already given the square values for each side length, there is no need to square root and square again. You can just test if the two smaller areas equal the larger area, but the explanation above uses a more detailed example of the Pythagorean Theorem.
Answer: the equation of the standard parabola
1)
The equation of the standard parabola
2) (x+5)^2 = 16(y-2)
Step-by-step explanation:
<u>Explanation </u>
<u>Parabola:-</u>
The set of points in a plane whose distance from a fixed point and a constant ratio to their corresponding perpendicular distance from a fixed straight line is a conic.
Let S be a fixed point and l be a fixed straight line from any point P,the perpendicular PM is drawn to the line 'l'
- The locus of P such that
- The fixed point 'S' is called the Focus.
- The fixed line'l 'is called the directrix of the conic
- The constant ratio is known as the eccentricity, denoted by 'e'
- If e=1 , the conic is called a parabola
1) <u> Step 1</u> :-
Given the focus S = (2,6) and directrix is x=0
we know that
now cross multiplication , we get
squaring on both sides,we get
step 2:-
now using distance formula is
Given S =(2,6) and P(x,y) be any point on parabola
........(1)
Now using perpendicular distance formula
let P(x , y ) be any point on the parabola
Given the directrix is x =0 and P(x,y) be any point on parabola
......(2)
equating equation(1) and equation (2), on simplification
we get .....(3)
- apply
now the equation (3) is
now the standard form of parabola is
<u>Final answer</u>:-
2) <u> Explanation:-</u>
<u>step 1:</u>
Given vertex of a parabola is A(-5,2) and its focus is S(-5,6)
here the given points of 'x'co- ordinates are equal
- Therefore the axis AS is parallel to y- axis
now the standard equation of parabola
now you have to find' a' value
Given vertex of a parabola is A(-5,2) and its focus is S(-5,6)
The distance of
on simplification we get a =4
<u>Final answe</u>r :-
the vertex (h,k) = (-5,2) and a=4
The standard parabola is