Since 30² = 900 and 40² = 1600, between 30 and 40 of the numbers Grogg enters will reduce to integers. Now just find which count is correct. We don't have to look far:
31² = 961
32² = 1024
so there 31 of the outputs of √1, √2, √3, ..., √1000 are integers.
<em><u>Question:</u></em>
Point R divides in the ratio 1 : 3. If the x-coordinate of R is -1 and the x-coordinate of P is -3, what is the x-coordinate of Q?
<em><u>Answer:</u></em>
x-coordinate of Q is 5
<em><u>Solution:</u></em>
Given that,
Point R divides in the ratio 1 : 3
Which means,
Point R divides the line segment PQ internally
The x-coordinate of the point which divides the line segment in ration m:n internally is given as:

Where,
= x-coordinate of point dividing the segment R = -1
= x-coordinate of P = -3
= x-coordinate of Q = ?
m : n = 1 : 3
m = 1
n = 3
Therefore,

Thus x-coordinate of Q is 5
Answer:
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Step-by-step explanation:
Answer:
Matrix transformation = ![\left[\begin{array}{ccc}-1&0\\0&1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-1%260%5C%5C0%261%5Cend%7Barray%7D%5Cright%5D)
Vertices of the new image: P'= (5,-2), Q'= (6,-3), R'= (2,-3)
Step-by-step explanation:
Transformation by reflection will produce a new congruent object in different coordinate. Reflection to y-axis made by multiplying the x coordinate with -1 and keep the y coordinate unchanged. The matrix transformation for reflection across y-axis should be:
.
To find the coordinate of the vertices after transformation, you have to multiply the vertices with the matrix. The calculation of the each vertice will be:
P'=
= (5,-2)
Q'=
= (6,-3)
R'=
= (2,-3)