Ariana has $1.40 worth of nickels and dimes. She has twice as many nickels as dimes. Determine the number of nickels and the num
1 answer:
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Answer:
The new coordinates of point D(-4, -4) after the dilation by a scale factor of 1/2 will be: D'(-2, -2)
Step-by-step explanation:
The rectangle ABCD on the grid shown is attached below.
From the grid, it is clear that the coordinates of point D are (-4, -4)
i.e. D(-4, -4)
As we are told that the figure is to be dilated from the origin.
A dilation tends to stretch or shrink the original figure, depending upon scale factor.
- If scale factor > 1, then the image gets enlarged
- If the scale factor < 1, the image gets reduction
When we dilate a figure from the origin by any scale factor, the new coordinates of the image can be obtained by multiplying the scale factor with the coordinates of the original object/figure.
As the the coordinates of point D are (-4, -4). If we dilate the figure by a scale factor of 1/2, the new new coordinates of point D would be:
P(x, y) → P'(1/2x, 1/2y)
D(-4, -4) → D'(-4/2, -4/2) or D'(-2, -2)
Therefore, the new coordinates of point D(-4, -4) after the dilation by a scale factor of 1/2 will be: D'(-2, -2)
We can use the Pythagorean Trigonometric Identity which says:
Since we need to find sin(t), we have to solve for it:
Let's plug in the given cos(t) value:
And solve sin(t):
Simplify further:
And it all simplifies down to:
Since it's in the 4th quadrant, the sin(t) value is going to be negative. So, your final answer is:
Hope this helps!
Since we need to find sin(t), we have to solve for it:
Let's plug in the given cos(t) value:
And solve sin(t):
Simplify further:
And it all simplifies down to:
Since it's in the 4th quadrant, the sin(t) value is going to be negative. So, your final answer is:
Hope this helps!
Answer:
4.57ft by 1.57 ft
Step-by-step explanation:
We are given that
Emma's square patio has been area=31 sq.ft
One dimension decrease by 1 foot and other dimension decrease by 4 feet.
We have to find the new dimensions of Emma's patio.
Let x be the side of Emma's square patio
We know that
Area of square=
ft
One dimension= ft
other dimension=
Hence, the new dimension of Emma's patio is given by
4.57ft by 1.57 ft