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2 years ago

Rectangle ABCD was dilated to create rectangle A'B'C'D' using point R as the center of dilation.

Mathematics

2 answers:

Slav-nsk [51]2 years ago

8 0

Answer:

Step-by-step explanation:

kati45 [8]2 years ago

3 0

Answer:

The value of RD' is 5 units.

Step-by-step explanation:

It is given that rectangle ABCD was dilated to create rectangle A'B'C'D' using point R as the center of dilation.

The scale factor is the proportion of side length of image and side length of preimage.

$k=\frac{\text{lenght of image}}{\text{lenght of preimage}}$

$k=\frac{B'C'}{BC}$

$k=\frac{4}{12}$

$k=\frac{1}{3}$

Scale factor is also defined as

$k=\frac{RD'}{RD}$

$\frac{1}{3}=\frac{RD'}{15}$

Multiply both sides by 15.

$RD'=5$

Therefore the value of RD' is 5 units.

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Suppose that the universal set is U={1,2,3,4,5,6,7,8,9,10}. Express each of the following subsets with bit strings (of length 10

Vladimir [108]

Answer:

0011100000

1010010001

0111001110

Step-by-step explanation:

As the question is not complete, Here is the complete question.

Suppose that the universal set is U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Express each of these sets with bit strings where the ith bit in the string is 1 if i is in the set and 0 otherwise.

a) {3, 4, 5}

b) {1, 3, 6, 10}

c) {2, 3, 4, 7, 8, 9}.

So, we need to express a) b) and c) into bit strings.

Firstly, number of elements in the universal set represent the number of bits in the bit string.

Secondly, 1 = yes element is present in both universal set as well as in sub set.

0 = No, element is not present in sub set but present in universal set.

Hence, we have:

a) Sub set {3,4,5} = 0011100000 (As there are 3 1's which means only 3,4,5 are present in both universal set and subset.

Similarly,

b) Sub set {1, 3, 6, 10} = 1010010001

c) Sub set {2, 3, 4, 7, 8, 9} = 0111001110

5 0

2 years ago

A group of friends wants to go to the amusement park. They have $469.75 to spend on parking and admission. Parking is $10.75, an

attashe74 [19]

Answer:

Step-by-step explanation:

469.75-10.75 =

459 ÷ 38.25 =

8 0

1 year ago

If e = 9 cm and f = 40 cm, what is the length of g?

rewona [7]

(9,40,41) is a Pythagorean Triple, farther down the list than teachers usually venture.

Answer: D. 41 cm

There's a subset of Pythagorean Triples where the long leg is one less than the hypotenuse,

a^2+b^2 = (b+1)^2

a^2 + b^2 = b^2 + 2b +1

a^2=2b+1

So we get one for every odd number, since the square of an odd number is odd and the square of an even number is even.

b = (a^2 - 1)/2

a=3, b=(3^2-1)/2=4, c=b+1=5

a=5, b=(5^2-1)/2 =12, c = 13

a=7, b=24, c=25

a=9, b=40, c=41

a=11, b=60, c=61

a=13, b=84, c=85

It's good to be able to recognize Pythagorean Triples when we see them.

Otherwise we'd have to work the calculator:

√(9² + 40²) = √1681 = 41

8 0

2 years ago

"From 1990 to 2000 The population of city A rose from 12,000 to 28,000 and the population of city B rose from 18,000 to 24,000.

Virty [35]

Answer:

The year 1996

With population of both 21600

Step-by-step explanation:

From 1990 to 2000 = 10 years

So city A grew from 12000 to 28000 that is city A had an increase of 16000 in 10 years.

While city b grew from 18000 to 24000 , that's an increase of 6000 in 10 years to.

For city A

10 years= 16000

1 year = 16000/10

1 year = 1600

For city B

10 years = 6000

1 year = 6000/10

1 year = 600

So we are to find what year the both cities had same population.

12000 + x1600 = y

18000 + x600 = y

X is the year difference

Y is the population at that year

Eliminating y gives

6000= x1000

X= 6

If x is 6

18000+3600= y

21600= y

So 6 years + 1990 = 1996

4 0

2 years ago

The graph represents function 1, and the equation represents function 2: A coordinate plane graph is shown. A horizontal line is

vladimir2022 [97]

Answer:

Step-by-step explanation:

5 0

2 years ago