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Nastasia [14]
3 years ago
5

Two similar triangles have a scale factor of 2 : 3. For numbers 7a – 7d, determine whether each statement about the triangles is

true or false.
7a. The ratio of their perimeters is 2 : 3. True or False
7b. The ratio of their areas is 4 : 6. True or False
7c. Their perimeters could be 14 cm and 21 cm. True or False
7d. Two corresponding sides could be 6 in and 7 in. True or False
Mathematics
2 answers:
grigory [225]3 years ago
7 0

Answer:

Step-by-step explanation:

7a. perimeter=3 sides added so the ratio is the same

The ratio of their perimeters is 2 : 3.

True

7b. area= sidexside so the ratio is 2x2:3x3 = 4:9

The ratio of their areas is 4 : 6.

False

7c. 14:21 =2:3

Their perimeters could be 14 cm and 21 cm.

True

7d. 6:7 <> 2:3

Two corresponding sides could be 6 in and 7 in.

False

postnew [5]3 years ago
6 0

Answer:

Step-by-step explanation:

Two similar triangles have a scale factor of 2 : 3.

7a. The ratio of their perimeters is 2 : 3.

As the sides are 2 : 3, the perimeters which are sums of all sides will also be 2 : 3

True

7b. The ratio of their areas is 4 : 6. True or False

As the sides are 2 : 3, the areas which are the products of two sides will be in the ratio of 2*2 : 3*3 = 4 : 9

False

7c. Their perimeters could be 14 cm and 21 cm. True or False

As the perimeter ratio for 14cm and 21 cm is 14 : 21 = 2 : 3 which complies with 7a. So they could be the perimeters.

True

7d. Two corresponding sides could be 6 in and 7 in. True or False

As the corresponding sides of 6in and 7in, the ratio is 6 : 7 and is different from 2 : 3.  So they cannot be corresponding sides.

False

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A device produces random 64-bit integers at a rate of one billion per second. After how many years of running is it unavoidable
nikitadnepr [17]

Answer:

3171 × 10^(44) years

Step-by-step explanation:

For each bit, since we are looking how many years of running it is unavoidable that the device produces an output for the second time, the possible integers are from 0 to 9. This is 10 possible integers for each bit.

Thus, total number of possible 64 bit integers = 10^(64) integers

Now, we are told that the device produces random integers at a rate of one billion per second (10^(9) billion per second)

Let's calculate how many it can produce in a year.

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(10^(9) billion per second) × 31,536,000 seconds = 3.1536 × 10^(16)

Thus;

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(10^(64))/(3.1536 × 10^(16)) = 3171 × 10^(44) years

6 0
3 years ago
The admission at the movies is $5 for children and $10 for adults. The total amount collected was
sesenic [268]

Answer:

Number of children, x= 400

Number of adults, y = 100

Step-by-step explanation:

Let the number of children be x

Let the number of  adults be y

Given : Total number of people,  x + y = 500  --------(1)

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(1) => y = 500 - x

Substitute y in (2) : 5x + 10(500 - x) = 3000

                             5x + 5000 - 10x = 3000

                                -5x = 3000 - 5000

                                 -5x = -2000

                                    x = 400

Substitute x in (1) : 400 + y = 500

                                      y = 500 - 400

                                      y = 100

4 0
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kenny6666 [7]
5=8
20/5=4
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4 0
2 years ago
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Answer:

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Step-by-step explanation:

8 0
3 years ago
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