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3 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]3 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.

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

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

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Solve the equation. Explain or show your reasoning. 1/2 x -7 = 1/3 (x-12)

Dafna11 [192]

Answer:

x = 18

Step-by-step explanation:

1: 1/2x - 7 = 1/3x - 4

2: 3/6x - 7 = 2/6x - 4

3: 3/6x = 2/6x + 3

4: 1/6x = 3

5: x = 18

6 0

3 years ago

Solve 5x − 6y = −38 3x + 4y = 0

shepuryov [24]

The answers are X=-4 and Y=3.

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3 years ago

The U.S. annual energy consumption is roughly 1 x 1020 joules per a year. If there are 350,000,000 people in the U.S., express t

AnnZ [28]

Answer with Step-by-step explanation:

Given the total energy consumption for all of the population is

$E=1\times 10^{20}Joules$

Thus energy consumed by each person per year can be obtained by dividing the total energy consumed by the total population Thus we get

$E_{per\cdot person}=\frac{1\times 10^{20}}{350\times 10^{6}}\\\\E_{per\cdot person}=28.57\times 10^{10}Joules/Year$

Now the energy consumed in each second assuming that there are 365 days in each year equals

$E_{second}=\frac{28.57\times 10^{10}}{365\times 24\times 3600}\\\\E_{second}=9059.49Joules$

4 0

3 years ago

Operations with Radical Expressions

lisov135 [29]

Answer: $30\sqrt{11}$

Step-by-step explanation:

$3\sqrt{50} * \sqrt{22}$

= $3\sqrt{5*5*2} * \sqrt{2*11}$

= $3\sqrt{5*5*2*2*11}$

= $3*5*2\sqrt{11}$

= $30\sqrt{11}$

******************************************

Answer: $6\sqrt{30}$

Step-by-step explanation:

$\sqrt{20} * \sqrt{3} * \sqrt{18}$

= $\sqrt{2*2*5} * \sqrt{3} * \sqrt{3*3*2}$

= $\sqrt{2*2*5*3*3*3*2}$

= $2*3\sqrt{5*3*2}$

= $6\sqrt{30}$

********************************************

Answer: $-\sqrt{5}$

Step-by-step explanation:

$4\sqrt{20} - 3\sqrt{45}$

= $4\sqrt{2*2*5} - 3\sqrt{3*3*5}$

= $4*2\sqrt{5} - 3*3\sqrt{5}$

= $8\sqrt{5} - 9\sqrt{5}$

= $-\sqrt{5}$

********************************************

Answer: $4\sqrt{5}$

Step-by-step explanation:

$2\sqrt{5} + 3\sqrt{5} - \sqrt{5}$

= $(2+3-1)\sqrt{5}$

= $4\sqrt{5}$

********************************************

Answer: $46\sqrt{2}$

Step-by-step explanation:

$4\sqrt{32} + 6\sqrt{50}$

= $4\sqrt{2*2*2*2*2} + 6\sqrt{2*5*5}$

= $4*2*2\sqrt{2} + 6*5\sqrt{2}$

= $16\sqrt{2} + 30\sqrt{2}$

= $46\sqrt{2}$

7 0

3 years ago

3) The Buendorf family has agreed to let their children get some animals. The kids said they

bezimeni [28]

Answer:

The possible number of goats is 6 and the possible number of chicken is 24

Step-by-step explanation:

Let

chicken=c

Goat=g

the number of chickens could be four times the number of goats

c=4g

Total number of animals=30

c+g=30

Recall, c=4g

So,

c+g=30

4g+g=30

5g=30

Divide both sides by 5

5g/5=30/5

g=6

Recall,

c+g=30

c+6=30

c=30-6

=24

c=24

The possible number of goats is 6 and the possible number of chicken is 24 making a total of 30 animals

5 0

3 years ago