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2 years ago

Find the quotient of 2,300 and (0.4 · 10^-8). In your final answer, include all of your calculations.

Mathematics

1 answer:

Alex777 [14]2 years ago

8 0

Answer:

5.75x10^11

Step-by-step explanation:

quotient of 2,300 and (0.4x10^-8) is

2,300 ÷ (0.4x10^-8)

2300 = 2.3x10^3

We now have

2.3x10^3 / 0.4x10^-8

= (2.3/0.4) x ( 10^(3 - (-8))

= 5.75 x (10^(3+8))

= 5.75 x (10^11)

= 5.75x10^11

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FrozenT [24]

Answer:

A) Swing arcs on both sides to intersect the first two arcs created.

Step-by-step explanation:

Bisecting a segment is cutting a line into two equal parts with a line bisector.

The steps involved are;

Placing a compass on one endpoint
Opening the compass to a width larger than half of the segment
Swinging an arc on either side of the segment
While maintaining the same width, place the compass on the other endpoint
Swing arcs on both sides of the segment to intersect the first two arcs created
Using a ruler placed at the points of intersection of the arcs, draw the line bisector.

Sasha was now at step four.

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Answer:

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Step-by-step explanation:

Total fraction of money spent= $\frac{1}{3} +\frac{1}{4}$

= $\frac{7}{12}$

Actual money spent = $\frac{7}{12}$ * £636

= £371

Money he has left = £(636 - 371)

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2 years ago

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Triangle XYZ with vertices X(0, 0), Y(0, –2), and Z(–2, –2) is rotated to create the image triangle X'(0, 0), Y'(2, 0), and Z'(2

Marina86 [1]

Answer: The correct options are

(A) Rotation 90° anticlockwise.

(D) (x, y) → (–y, x).

Step-by-step explanation: Given that ΔXYZ is rotated to create the image triangle ΔX'Y'Z'.

Triangle XYZ and its image triangle X'Y'Z' are shown in the attached figure.

The co-ordinates of the vertices of ΔXYZ are X(0, 0), Y(0, -2) and Z(-2, -2).

And the co-ordinates of the vertices ΔX'Y'Z' are X'(0, 0), Y'(2, 0) and Z'(2, -2).

Option (A) Rotation 90°:

We see from the figure that if we rotate ΔXYZ is rotated 90° anticlockwise, then it will coincide with ΔX'Y'Z'.

So, rotation of 90° anticlockwise is a correct option.

Option (B) Rotation 180°:

If we rotate ΔXYZ is rotated clockwise or anticlockwise 180°, then it will NOT coincide with ΔX'Y'Z'.

So, rotation of 180° is NOT a correct option.

Option (C) Rotation 270°:

If we rotate ΔXYZ is rotated clockwise 270°, then also it will not coincide with ΔX'Y'Z'.

So, rotation of 270° clockwise is also a correct option.

Option (D) (x, y) → (–y, x):

We see that the co-ordinates of both the triangle follow the transformation

X(0, 0) ⇒ X'(0, 0)

Y(0, -2) ⇒ Y'(2, 0)

Z(-2, -2) ⇒ Z'(2, -2).

So, the transformation is (x, y) ⇒ (-y, x).

Therefore, the transformation (x, y) → (–y, x) is a correct option.

Option (E) (x, y) → (y, -x):

We see that the co-ordinates of both the triangle does NOT follow this transformation

For example, suppose this transformation is correct. Then, we have

Y(0, -2) ⇒ (-2, 0), which are not the co-ordinates of Y'.

Therefore, the transformation (x, y) → (–y, x) is NOT a correct option.

Thus, the correct options are:

(A) Rotation 90° anticlockwise.

(D) (x, y) → (–y, x).

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GalinKa [24]

Answer:

Options (3) and (6)

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Since, dilation is a rigid transformation,

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Since, sides of ΔA'B'C' = $\frac{1}{2}$ of the sides of ΔABC

Area of ΔA'B'C' = $\frac{1}{2}(\text{Area of triangle ABC})$

Area of ΔABC > Area of ΔA'B'C'

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Answer:

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4p(y-k) = (x-h)^2, where p is the distance between the vertex and the focus. Comparing

4p(y-k) = (x-h)^2 to

10(y-3) = (x-2)^2, we see that 4p = 10. Therefore, p = 10/4 = 5/2, which is the vertical distance between the focus and the vertex.

Since the coordinates of the vertex are easily read from the given equation

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all we need to do is to add p (5/2) to the y-coordinate (3);

The focus is at (2, 3 + 5/2), or (2, 11/2).

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