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3 years ago

Find the length of the missing side. the triangle not drawn to scale. (Image attached)

Mathematics

2 answers:

3241004551 [841]3 years ago

6 0

Answer: 8

Step-by-step explanation:

The triangle shown in the image attached is a right triangle.

Therefore, to calculate the missing lenght of the triangle you can apply the Pythagorean Theorem, which is shown below:

$a^2=b^2+c^2$

Where <em>a</em> is the hypotenuse and <em>b</em> and <em>c</em> are the legs.

The problem gives you the value of the hypotenuse and the value of one leg. Therefore, you must solve for the other leg from $a^2=b^2+c^2$ , as following:

$17^2=15^2+c^2\\c=\sqrt{17^2-15^2}\\c=8$

Therefore, the lenght of the missing side is: 8

svetlana [45]3 years ago

4 0

Answer:

The value of third side= 8 units

Step-by-step explanation:

It is given a right angled triangle with base = 15 and hypotenuse = 17

We have to find the height of given triangle.

<u>Points to remember</u>

By Pythagorean theorem

Base² + Height² = Hypotenuse²

<u>To find the third side</u>

Here base = 15 and hypotenuse = 17

We have,

Base² + Height² = Hypotenuse²

Height² = Hypotenuse² - Base² = 17² - 15² = 64

Height = √64 = 8 units

Therefore the value of third side = 8 units

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Step-by-step explanation:

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3 years ago

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Answer:

Step-by-step explanation:

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3 years ago

Comparing Leaking Pool Problem

Blababa [14]

Answer:

<em>Pool 1 leaks faster than pool 2.</em>

Step-by-step explanation:

<u>Rates of change</u>

The rate of change (ROC) is a measure that compares two quantities, usually to know how fast one variable changes in time.

We are given two rates of change for two pools that are leaking. The first one loses 2/3 gallon in 15 minutes, and the other loses 3/4 gallon in 20 minutes.

To compare them, we are required to express time in hours. Recall one hour has 60 minutes, or equivalently, one minute has 1/60 hours. Converting both times, we have:

15 minutes = 15/60 = 1/4 hours

20 minutes = 20/60 = 1/3 hours

Now compute both rates of change:

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$\displaystyle ROC_1=\frac{2/3}{1/4}=\frac{8}{3}\approx 2.67\ gal/h$

Pool 2:

$\displaystyle ROC_2=\frac{3/4}{1/3}=\frac{9}{4}= 2.25\ gal/h$

Comparing both ratios, it's clear pool 1 leaks faster than pool 2.

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3 years ago

The director of an animal shelter need to raise more than $50,000 during a fundraiser. Write an inequality that represents the a

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Answer:

m > 50,000

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3 years ago

How to solve these 3 problems

Bingel [31]

Answer:

a. decay; b. growth; c. decay; d. neither
r = 4; a = 1; y = 1·4^x
a. an = 3(5^(n-1)); b. f(x) = (3/5)(5^x); c. exponential growth; d. y-intercept: 3/5; first term: 3.

Step-by-step explanation:

There are two kinds of exponential problems here.

exponential functions of the form f(x) = a·b^x
exponential sequences of the explicit form an = a1·r^(n-1)

The second problem gives you a table that suggests the sequence form, but it asks for the exponential function form. The third problem does something similar.

In an exponential function of the form f(x) = a·b^x, the function grows if b>1 and decays if b<1. Using this check, we can easily answer ...

a. 0.4 < 1 . . . decay

b. 1.3 > 1 . . . growth

c. 1/2 < 1 . . . decay

d. 1 = 1 . . . neither growth nor decay; the function is constant: j(x) = 1.

The value of x is given starting at 1, so we can consider this a geometric sequence. The common ratio is r = 16/4 = 4. The first term is a1 = 4, so the explicit formula for the sequence is ...

an = 4·4^(n-1)

When this is expanded to get rid of the constant in the exponent, we have ...

an = 4·(4^n)·(4^-1) = 1·4^n

We recognize this form as matching the functional form f(x) = a·r^x. The multiplier of the exponential factor is a=1. In summary, ...

r = 4; a = 1; f(x) = 1·4^x

The first term of this geometric sequence is a1 = 3. The common ratio is r = 15/3 = 5. Using the explicit formula, we have ...

a. explicit form: an = 3·5^(n-1)

Using the method of question 2 to write the functional form, we find ...

an = 3(5^n)(5^-1) = (3/5)(5^n)

b. functional form: f(x) = (3/5)(5^x)

c. function family: exponential growth functions

d. y-intercept: (3/5) . . . . read this from the f(x) form

1st term: the first term listed in the given sequence is 3

_____

<em>Additional comment</em>

The "y-intercept" of a sequence is irrelevant (undefined), as the sequence term numbering starts with 1, not 0. The domain of the explicit formula is <em>natural numbers</em>, which does not include 0.

Similarly, the "first term" of a function f(x) needs further definition. Here, we've answered the question by saying the first term is f(1). There is no conventional definition of a "first term" for a continuous function.

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2 years ago