A <span>counterclockwise rotation of 270º about the origin is equivalent to a </span><span>clockwise rotation of 90º about the origin.
Given a point (4, 5), the x-value, i.e. 4 and the y-value, i.e. 5 are positive, hence the point is in the 1st quadrant of the xy-plane.
A clockwise rotation of </span><span>90º about the origin of a point in the first quadrant of the xy-plane will have its image in the fourth quadrant of the xy-plane. Thus the x-value of the image remains positive but the y-value of the image changes to negative.
Also the x-value and the y-value of the original figure is interchanged.
For example, given a point (a, b) in the first quadrant of the xy-plane, </span><span>a counterclockwise rotation of 270º about the origin which is equivalent to a <span>clockwise rotation of 90º about the origin will result in an image with the coordinate of (b, -a)</span>
Therefore, a </span><span>counterclockwise rotation of 270º about the origin </span><span>of the point (4, 5) will result in an image with the coordinate of (5, -4)</span> (option C)
The independent events are illustrations of probability, and the value of P(B) is 0.40
<h3>How to determine the value of P(B)?</h3>
The given parameters are:
P(A) = 0.50
P(A and B) = 0.20
Two events A and B are independent, if
P(A and B) = P(A) * P(B)
So, we have:
0.50 * P(B) = 0.20
Divide both sides by 0.50
P(B) = 0.40
Hence, the value of P(B) is 0.40
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Rule: If x-k is a factor of p(x), then p(k) = 0. This is a special case of the remainder theorem.
Using that rule, we can see that x+5 is really x-(-5) so k = -5.
Therefore,
p(k) = 0
p(-5) = 0
so the answer is choice D.
Answer:
B, C, E, F
Step-by-step explanation:
The following relationships apply.
- the diagonals of a parallelogram bisect each other
- the diagonals of a rectangle are congruent
- the diagonals of a rhombus meet at right angles
- a rectangle is a parallelogram
- a parallelogram with congruent adjacent sides is a rhombus
__
CEDF has diagonals that bisect each other, and it has congruent adjacent sides. It is a parallelogram and a rhombus, but not a rectangle. (B and C are true.)
ABCD has congruent diagonals that bisect each other. It is a parallelogram and a rectangle, but not a rhombus. (There is no indication adjacent sides are congruent, or that the diagonals meet at right angles.) (E and F are true.)
The true statements are B, C, E, F.
Since these angles clearly form a circle and a circle is 360 degrees,
120-x+2x+16+3x-72=64+4x=360. Subtracting 64 from both sides, we get
4x=296 and by dividing both sides by 4 we get x=74
