Answer:
the standard form of a quadratic equation is ax² + bx + c
the vertex form is a(x - h) + k where h & k are the x and y coordinates
to get from standard form to vertex form, you would have to follow this formula to find h:
-b/2a
plug in the values, and you will get the value of h.
to get k, you plug in the value you have just found in the above formula into the original equation, and that is the value of k.
the a in the vertex form is the value of a in the standard form
so an example of this would be: x² + 2x + 4 where a = 1, b = 2 c = 4
to get this into vertex form we will use the formula -b/2a and solve:
-2/2(1) --> -2/2 = -1
now we plug in the value we found into the original equation wherever x is
(-1)² + 2(-1) + 4 --> 1 - 2 + 4 = 3
we have both h and k, and we will put this into vertex form:
a(x - h)² + k turns into ---> (x + 1)² + 3
why x+1 and not x-1? the original equation has a negative sign, and the result we have is negative. this conflicts with the original equation and is therefore turned into a positive 1
where did a go? since a = 1, we do not need to write it, if a was equal to 2 then we would write the 2 in front
line b
line c
line d
The line which represents the direct variation equation y = 1/2 x is: line c.
We know that every straight line has the equation
y = (slope) x + (y-intercept) .
Here, we have, this line y = 1/2 x,
the equation doesn't show any y-intercept.
The y-intercept is zero,
meaning that the line crosses the y-axis at the place where y=0.
That's the origin where the x- and y-axes cross.
so, we get, the line goes through the origin.
from the given graph we get,
There are only two lines there that go through the origin,
so one of those is the answer to the question.
Now, we have to find the slope of a line.
we know that,
If the slope of a line is positive, that means it rises as it goes.
If the slope of a line is negative, that means it falls as it goes.
The equation of the line is [ y = 1/2 x ].
The slope is 1/2 .
That's positive.
The line on the graph slopes up.
so, we get,
In the picture, that can only be line 'c' .
Hence, The line which represents the direct variation equation y = 1/2 x is: line c.
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P=A+B+C+D
B. 8
C. 9
D. 12
The number of boxes of tiles is 6. The correct option is A.
The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the circle in a two-dimensional plane is called as the area of the circle.
Given that a circular playground for a daycare centre is to be covered with square tiles that are 9 inches on each side. The circle has a diameter of 12 ft. The tiles are packaged in boxes of 25 tiles.
The area of the circle is,
A = π x r²
A = π x 6²
A = 113 square ft
The area in square inches is,
A = 113 x 12 = 1356 square inches
The number of tiles will be,
Number = 1356 / 9
Number = 150
The number of boxes,
N = 150 / 25
N = 6 boxes
Therefore, the number of boxes will be 6.
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