Instructions: The polygons in each pair are similar. Find the missing side length.

Two snails climbed up a tree at a constant rate. A person measured and recorded their respective distances above the ground. • S

Sophie [7]

Answer:

140 minutes

Step-by-step explanation:

Using m = (y₂ - y₁)/(x₂ - x₁) , we find the rate at which Snail A moves which is also the gradient of the line with which it moves. Given that Snail A was 12.5 inches above the ground at 10 minutes and 16 inches above the ground at 24 minutes, x₁ = 10 min, y₁ = 12.5 inches, x₂ = 24 min and y₂ = 16 inches.

So, m = (y₂ - y₁)/(x₂ - x₁)

m = (16 - 12.5)/(24 - 10) = 3.5/14 = 0.25

Also, the equation of the line,

(y - y₁)/(x - x₁) = m

(y - 12.5)/(x - 10) = 0.25

cross-multiplying, we have

y - 12.5 = 0.25(x - 10)

expanding the bracket, we have

y - 12.5 = 0.25x - 2.5

adding 12.5 to both sides, we have

y - 12.5 + 12.5 = 0.25x - 2.5 + 12.5

y = 0.25x + 10

Since Snail B started at 3 inches above the ground and climbed 0.3 inch per minute. The snails continued at the same speeds, its distance y moved is y = 0.3t + 3

We now find the time x it takes the snails to cover the same distance by equating both expressions. So,

0.25x + 10 = 0.3x + 3

collecting like terms, we have

10 - 3 = 0.3x - 0.25x

7 = 0.05x

0.05x = 7

x = 7/0.05

x = 140 minutes

5 0

3 years ago

Explain how to write a mixed number as a division expression. Drag the words to the appropriate

Andrej [43]

Answer:

improper fraction numerator

denominator as divisor

Step-by-step explanation:

that's the answers

8 0

3 years ago

Consider the following definitions for sets of characters: Digits = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 } Letters = { a, b, c, d, e,

Darya [45]

Answer:

a) Number of passwords: 2763633600

b) Number of passwords: 2487270240

Step-by-step explanation:

We have:

10 digits,

26 letters, and

4 special characters.

We have to compute the number of passwords that satisfy the following conditions:

a) Strings of length 6. Characters can be special characters, digits, or letters, with no repeated characters.

We can use the three types of characters, as long as they do not repeat.

We have a total of 10+26+4=40 characters.

This means we have 40 options for the first place, (40 - 1) for the second place (as the first place already use one of the options available), and so on up to 6 places.

We can write this as:

$C=40*39*38*37*36*35=40!/34!=2763633600$

b. Strings of length 6. Characters can be special characters, digits, or letters, with no repeated characters. The first character can not be a special character.

In this case we add a restriction: the first character can not be a special character.

Then, for the first place we have only 40-4=36 options (digits and letters).

For the second place we can use the 39 options available (digits, letters and special characters).

Then we have:

$C=36*(39*38*37*36*35)=36*(39!/34!)=2487270240$

6 0

3 years ago

Read 2 more answers

Hannah is setting up chairs for the class play. The room has 20 chairs. What are the different ways she can arrange the chairs i

andrezito [222]

Answer:

Have them 4 by 5.

Step-by-step explanation:

If you she but 5 chairs in a row, then 3 on the side of the chairs. That would create a backward "L" type of shape.

For example, (The "o" is a chair)

OOOOO

O

As you see the the top are the 5 chairs, then side are are the 4 chairs.

Then, you will do the exact same thing but on the opposite side.

Here is the next example.

OOOOOO

O O

OOOOOO

Basically, arranging the chairs 4x5, it would make a rectangle.

5 0

3 years ago

Fill in the other coordinate for the line 2x - 5y = 11: (4, )

enot [183]

2x - 5y = 11. (4, a). x = 4, y = a

Substituting into 2x - 5y = 11

2(4) - 5(a) = 11

8 - 5a = 11

-5a = 11 - 8

-5a = 3

a = 3/-5 = -3/5 =- 0.6

Other coordinate = -3/5 = -0.6

5 0

4 years ago