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Law Incorporation [45]
3 years ago
15

If square ABCD is dilated by a scale factor of 1 3 with a dilation center at vertex A, by what factor does the area of the squar

e decrease? A) 1 9 B) 1 2 C) 2 D) 4
Mathematics
1 answer:
svetoff [14.1K]3 years ago
4 0

Assuming you meant to say "scale factor 1/3", then the answer is A) 1/9

This is because we simply square the scale factor to get

(1/3)^2 = (1/3)*(1/3) = 1/9

----------

For example, let's say we had a square that was 18 by 18. Its area would be 18*18 = 324 square units.

Now reduce each side by the scale factor 1/3 getting the new length 18*(1/3) = 6. The new area is 6*6 = 36

Compare 36 and 324 to see that 36/324 = 1/9. The new area is 1/9th of the old one

new area = (1/9)*(old area)

You might be interested in
The focus of a parabola is (0, -3) and the directrix is y = 3. What is the equation of the parabola?
OleMash [197]

Answer:

The equation of the parabola is y = -12\cdot x^{2}.

Step-by-step explanation:

Since the directrix is of the form y = a, the parabola is vertical. The vertex of the parabola (V(x,y)) is the midpoint between the focus (F(x,y)) and a point of the directrix (P(x,y)), that is to say:

V(x,y) = \frac{1}{2}\cdot F(x,y) + \frac{1}{2}\cdot P(x,y) (1)

If we know that F(x,y) = (0, -3) and P(x,y) = (0, 3), then the coordinates of the vertex of the parabola:

V(x,y) = \frac{1}{2}\cdot (0, -3) + \frac{1}{2}\cdot (0, 3)

V(x,y) = (0, 0)

The vertex factor (p) is the distance of the focus with respect to the vertex:

p = \sqrt{[F(x,y)-V(x,y)]\,\bullet \,[F(x,y)-V(x,y)]} (2)

If we know that F(x,y) = (0, -3) and V(x,y) = (0, 0), then the vertex factor is:

p = \sqrt{0^{2}+(-3)^{2}}

p = -3

The equation of the parabola in the vertex form is described below:

y - k = 4\cdot p \cdot (x-h)^{2} (3)

Where:

x - Independent variable.

y - Dependent variable.

h, k - Coordinates of the vertex.

If we know that (h,k) = (0, 0) and p = -3, then the equation of the parabola is y = -12\cdot x^{2}.

6 0
2 years ago
What is the missing term? (10x-4x^2)-(7x+?)=3x-6x^2
mafiozo [28]
The answer is 2x<span>^2
Because everything on the right of the minus sign will turn negative

</span>
6 0
3 years ago
Read 2 more answers
Find the greatest common factor of the following monomials 14b and 20b^6
belka [17]
The greatest common factor is 2b
3 0
3 years ago
What is the interquartile range of the data set?
pychu [463]
The interquartile range of the data set is 30.
8 0
3 years ago
Solving systems by elimination with multiplication: 8x+7y=20 and 4x-4y=-20
borishaifa [10]
If you put 0 in the place of x or y, which every one you choose, it will cancel it or and you can just divide the number next to it by the answer (-20, 20). Take it one step at a time, don't try to do both at the same time.
3 0
3 years ago
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