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3 years ago

Find the measure of the missing side. Round your answer to the nearest tenth. (PYTHAGOREAN THEOREM)

Mathematics

1 answer:

Burka [1]3 years ago

7 0

Answer:

Rounded to the nearest tenth, the length of the missing side is 5.4 in.

Step-by-step explanation:

According to the Pythagorean theorem, $a^{2}+b^{2}=c^{2}$ , where c is the length of the hypotenuse (the longest side), a and b are the lengths of the other two sides. We can use this to solve for the length of the hypotenuse of the right triangle shown in your question (the missing side):

$2^{2}+5^{2}=c^{2}$

This simplifies to $29=c^{2}$ . Now to solve for c (the length of the hypotenuse), we just take the square root of both sides of the equation and solve like so:

$\sqrt{29} =\sqrt{c^{2}}$

This simplifies to c≈5.4 in.

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On the first day of spring, an entire field of flowering trees blossoms. The population of locusts consuming these flowers rapid

adelina 88 [10]

Answer:

$L(t)=7600(5)^{t/2}$

Explanation:

Amend the typos for better understanding:

<em />

<em>On the first day of spring, an entire field of flowering trees blossoms. The population of locusts consuming these flowers rapidly increases as the trees blossom. The locust population increases by a factor of 5 every 2 days, and can be modeled by a function, L, which depends on the amount of time, t (in days). Before the first day of spring, there were 7600 locusts in the population. Write a function that models the locust population t days since the first day of spring.</em>

<em />

<h2>Solution</h2>

A function that grows with a constant factor is modeled by an exponential function of the kind:

$F(x)=A\cdot (B)^x$

Where A is the initial value, B is the constant growing factor, and x is the number of times the growing factor applies.

Since the population increases by a factor of 5 every 2 days, the power x of the exponential function is t/2, and the factor B is 5.

The initial popultaion A is 7600.

Thus, the function that models the locust population t days since the first day of spring is:

$L(t)=7600(5)^{t/2}$

6 0

4 years ago

Please help!!!!!!!!!!!!!!!

Andreas93 [3]

Answer:

a) 12/91

b) about 67 times; (66 2/3)

Step-by-step explanation:

a) total of frequencies is 90 and frequency for a 3 is 11

however, the question said if the dice is rolled once more, then that raises the 11 to 12 and the frequency total from 90 to 91

let 'x' = # of sixes rolled out of 500 times

b) 12/90 = x/500

cross-multiply:

90x = 6000

x = 66 2/3

7 0

3 years ago

HELP QUICKLY AND FAST PLS IM GIVING BRAINLIEST!!!

grigory [225]

Answer:

Step-by-step explanation:

3 0

3 years ago

The function — is used to model the height of an object projected in the air, where h(t) is the height in meters and t is the ti

MissTica

The answer choice which represents the domain and range of the function h(t) as given in the task content in which case, values are rounded to the nearest hundredth is; Domain: [0, 3.85] and Range: [0, 18.05].

<h3>What are the domain and range of the function as given in the task content?</h3>

It follows from convention that the domain of a function simply refers to the set of all possible input values for that function.

Also, the range of a function is the set of all possible output values for such function.

On this note, by observing the graph in the attached image, it follows that the Domain of the function in discuss is; [0, 3.85].

While the range is the difference between the minimum and maximum height attained and can be computed as follows;

At minimum height, t = 0; hence, h(t) = 0.

At maximum height; h'(t) = 0 where h'(t) = h'(t)=-9.74t+18.75 and hence, t = 1.92.

Hence, h(1.92) = 18.05.

The range is therefore; [0, 18.05].

Read more on domain and range;

brainly.com/question/1942755

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6 0

2 years ago

From 1990 to 2000, the population of Florida increased by 2.13% per year. The population (in millions) in the year 1990 was 16 E

belka [17]

Answer:

19 million

Step-by-step explanation:

So generally whenever we express a exponential function, it's in the form: $y=a(b)^x$

where a=initial value aka when x=0

in this case, b can be expressed as: $1+r$ , where r is the growth rate, which in this case is 2.13%, and expressing that as a decimal (divide by 100), r=0.0213, thus b=1.0213

This gives us the following equation: $y=16(1.0213)^x$

To kind of give you a intuitive reason as to why this makes sense, think of that 1.0213 wrapping around the previous value.

So when x=0, it's actually just 16, since any number (besides 0) to the power of 0, equals 1.

When x=1, we get: $1.0213(16)$ , which can be expressed as a 2.13% increase from year 0

When x=2, we get: $1.0213(1.0213(16))$ , which can be expressed as a 2.13% increase from year 1

when x=3, we get: $1.0213(1.0213(1.0213(16)))$ , which can be expressed as a 2.13% increase from year 2.

In other words, each year we're getting another 1.0213 to multiply by (very definition of an exponent).

So to calculate the population in 1997, we put in x=7, since it's 7 years after 1990

We get the following equation: $y=16(1.0213)^7$

Using a calculator this simplifies to approximately: $18.5436$

Rounding this to the nearest integer would yield 19, and since the values are expressed in millions, the answer would be 19 million

4 0

2 years ago