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2 years ago

Given a dilation around the origin, what is the scale factor K? Do, K = (20,16) → (-5,-4)

Mathematics

1 answer:

Rudik [331]2 years ago

5 0

Answer:

Scale factor, K = -1/4

Step-by-step explanation:

Dilation of any image changes its size and the shape remains same.

The scale factor is the ratio of dilated image to original image.

Dilation rule: (x, y) → (kx, ky), where k is the scale factor.

It means k = x₂/x₁ or y₂/y₁

K = -5/20 = -1/4 or K = -4/16 = -1/4.

<u>The negative value of scale factor (K) indicates dilations with 180 degree rotation of the dilated image.</u>

Hence the scale factor is K = -1/4.

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Work out the sum of

Sladkaya [172]

Answer: 1 and 3/70

Explanation: Find the least common denominator and then combine like terms. The LCM is 70.

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3 years ago

The size of a slow-growing bacteria strain increases continuously over time. This equation describes the predicted size of the b

Artemon [7]

Answer:

1102.8 mm^2

Step-by-step explanation:

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3 years ago

Thirty-two percent of fish in a large lake are bass. Imagine scooping out a simple random sample of 15 fish from the lake and ob

klio [65]

Answer:

Thirty-two percent of fish in a large lake are bass. Imagine scooping out a simple random sample of 15 fish from the lake and observing the sample proportion of bass. What is the standard deviation of the sampling distribution? Determine whether the 10% condition is met.

A. The standard deviation is 0.8795. The 10% condition is met because it is very likely there are more than 150 bass in the lake.

B. The standard deviation is 0.8795. The 10% condition is not met because there are less than 150 bass in the lake.

C. The standard deviation is 0.1204. The 10% condition is met because it is very likely there are more than 150 bass in the lake.

D. The standard deviation is 0.1204. The 10% condition is not met because there are less than 150 bass in the lake.

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3 years ago

Dilate the the triangle, scale factor = 3 (positive 3, ignore the

HACTEHA [7]

Answer:

The rule of dilation is $P'(x,y) = 3\cdot P(x,y)$ .

The vertices of the dilated triangle are $A'(x,y) = (-21, -18)$ , $B'(x,y) = (-15,-10)$ and $C'(x,y) = (-3,-15)$ , respectively.

Step-by-step explanation:

From Linear Algebra, we define the dilation by the following definition:

$P'(x,y) = O(x,y) + k\cdot[P(x,y)-O(x,y)]$ (1)

Where:

$O(x,y)$ - Center of dilation, dimensionless.

$k$ - Scale factor, dimensionless.

$P(x,y)$ - Original point, dimensionless.

$P'(x,y)$ - Dilated point, dimensionless.

If we know that $O(x,y) = (0,0)$ , $k = 3$ , $A(x,y) = (-7,-6)$ , $B(x,y) = (-5,-2)$ and $C(x,y) =(-1,-5)$ , then dilated points of triangle ABC are, respectively: