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krok68 [10]
3 years ago
13

What is the approximate length of the missing side of a

Mathematics
1 answer:
ANEK [815]3 years ago
8 0

Answer:

The approximate length of the missing side is of 5.57 cm.

Step-by-step explanation:

Pythagorean Theorem:

In a right triangle with sides a and b and hypotenuse c, the Pythagorean theorem states that:

a^2 + b^2 = c^2

In this question:

a = 15, c = 16

We want to find b. Then

a^2 + b^2 = c^2

15^2 + b^2 = 16^2

b^2 = 256 - 225

b^2 = 31

b = \sqrt{31}

b = 5.57

The approximate length of the missing side is of 5.57 cm.

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Design a Roller Coaster Portfolio
scoray [572]

1) The domain is [0,300]. The range is [0,250]

2) The slope for the initial climb is 3.57. The equation of the line is y=3.57 x

3) The rate of change of the second hill is -1.4

4) The rate of change of the third hill is -2.1

5) The blue hill is steeper

6) It is not a function

Step-by-step explanation:

1)

The domain of a function is the set of values of x (the input) for which the function itself is defined.

Instead, the range of a function is the set of values of y (the output) that the function can take.

To find the domain, we have to look at the x-axis and see for which values of x the function is defined. By looking at the graph, we see that the function is defined between

x = 0 and x = 300

So, the domain is [0,300].

To find the range, we have to look at the y-axis and see for which values of y the function has an output. By looking at the graph, we see that the function has values of y between

y = 0 and x = 250

So, the range is [0,250].

2)

The slope of a function in a certain range is given by

m=\frac{\Delta y}{\Delta x}

where

\Delta y is the change in the y-coordinate

\Delta x is the change in the x-coordinate

For the initial climb (pink line), we have:

\Delta y = 250 - 0 = 250\\\Delta x = 70 - 0 = 70

Therefore, the slope in this part is

m=\frac{250}{70}=3.57

We can now write the equation of the line in the form

y = mx + b

where b is the y-intercept: since it is zero, the line has simply the form

y=mx \rightarrow y = 3.57 x

3)

Again, to calculate the slope of the hill, we use:

m=\frac{\Delta y}{\Delta x}

where

\Delta y is the change in the y-coordinate

\Delta x is the change in the x-coordinate

For the green hill, we have:

\Delta y = 60-200 = -140

\Delta x = 300-200 = 100

So the rate of change is

m=\frac{-140}{100}=-1.4

4)

As before, the rate of change of the hill is

m=\frac{\Delta y}{\Delta x}

For the blue hill, we have:

\Delta y = 30-230 = -300

\Delta x = 200-60 = 140

So the rate of change is

m=\frac{-300}{140}=-2.1

5)

To know which hill is steeper, we need to compare the magnitude of their rate of change.

In fact, both hills have rate of change negative - because we are going down along the slope. Therefore, we have to consider the magnitude of their slope.

For the green hill:

|m| = 1.4

For the blue hill:

|m|=2.1

We see that the blue hill has a greater slope (in magnitude): therefore, the blue hill is steeper.

6)

A function is defined as a mapping (operation between two sets of variables) in which to one value of x (the input) corresponds one and only one value of y (the output).

This means that a function cannot have multiple values of y for the same x (the input).

By looking at the graph, we see that this function does not respect this criterium: in fact, we see that certain values of x give multiple values of the output, y (for instance, at x=300 the function has two values). So, this is not a function.

Learn more about functions:

brainly.com/question/3511750

brainly.com/question/8243712

brainly.com/question/8307968

#LearnwithBrainly

5 0
3 years ago
Read 2 more answers
henry can write 5 pages of his novel in 3 hours at this rate how many pages can henry write in 8 hours​
My name is Ann [436]

Answer:

Henry can write 13 pages in 8 hours.

it can also be written as 13.3

4 0
3 years ago
Read 2 more answers
+3=17
aev [14]

Answer:

1

Step-by-step explanation:

5 0
2 years ago
WILL GIVE BRAINLIEST!
siniylev [52]

Answer:

48x² + 24x + 3

Step-by-step explanation:

Width = (4x + 1) in

Length = 3 *width = 3*(4x + 1) = 3*4x + 3*1

           = (12x + 3) in

Area of rectangle = length * width

                             = (12x + 3) (4x + 1)

                             = 12x *4x  + 12x *1  + 3*4x  + 3*1

                             = 48x² + 12x + 12x + 3

                              = 48x² + 24x + 3

8 0
3 years ago
Change the width 20/16 inches to a mixed numeral in simplest form.
Iteru [2.4K]

Answer:1 and 1/4


Step-by-step explanation:

Okay, let's see the given: 20/16

So, we can take out 16 from the top to make it 1  4/16

Now, we can simplify that by dividing the top and bottom by 2: 1  2/8

We can simplify that again to get 1 1/4

So the answer is 1 and 1/4

5 0
3 years ago
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