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Mandarinka [93]
3 years ago
12

A triangle has a perimeter of 90 centimeters write and use a linear system

Mathematics
1 answer:
lawyer [7]3 years ago
5 0

We are given sides of the triangle by expression

First side : n

Second side : m = 5n-5.

Third side : l = 5/4 m - n.

Perimeter is 90.

Therefore, first equation could be set :

n +m +l = 90   --------------equation(1)

Second equation would be

m = 5n-5        --------------equation(2)

Third equation would be

l = 5/4 m - n   --------------equation(3)

Let us solve the system of equations by substitution.

Substituting m = 5n-5 and l = 5/4 m - n in first equation.

We get

n +5n-5 +5/4 m - n= 90

Now, substituting m = 5n-5 in above equation we get

n +5n-5 +5/4 (5n-5) - n= 90

5n + 25n/4 -5 - 25/4 =90

5n + 6.25n -5-6.25 = 90.

11.25n-11.25 = 90

Adding 11.25 on both sides, we get

11.25n-11.25+11.25 = 90+11.25

11.25n = 101.25.

Dividing both sides by 11.25, we get

n=9.

Plugging n=9 in 2nd equation.

m = 5(9)-5 = 45 -5 = 40.

Plugging n=9 and m=40 in first equation, we get

9 +40 +l = 90

49 +l = 90.

Subtracting 49 from both sides, we get

49-49 +l = 90-49

l = 41.

Therefore, sides are of lengths l = 41, m= 40 and n=9.


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Answer:

22% reduction

Step-by-step explanation:

Find the percent decrease by dividing the difference in amounts by the original amount.

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115 - 90 = 25

Divide this by the original amount:

25/115

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So, the percent decrease is 21.7%. Round this to the nearest whole percentage:

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The percent reduction in fuel used was approx. 22%

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The average daily temperature, t, in degrees fahrenheit for a city as a function of the month of the year, m, can be modeled by
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The answer will be t = sin((m.\frac{\pi}{6})+55) average daily temperature, t, in degrees Fahrenheit for a city as a function of the month of the year.

<h3>What is temperature?</h3>

Temperature is the degree or intensity of heat present in a substance or object, especially as expressed according to a comparative scale and shown by a thermometer or perceived by touch.

<h3>TO SOLVE:</h3>

35cos(\frac{\pi}{6(m+3)}+55)\\\\35 cos(\frac{\pi m}{6} + 55 + \frac{\pi}{2})\\

suppose x = m.\frac{\pi}{6}+55 and \frac{\pi}{2} = 90 degree

We know, cos(x+90°) = - sin(X)

⇒ cos((m.\frac{\pi}{6})+55+90degree)degree = -sin((m.\frac{\pi}{6})+55)

⇒ t = sin((m.\frac{\pi}{6})+55)

Hence the answer will be t = sin((m.\frac{\pi}{6})+55) average daily temperature, t, in degrees Fahrenheit for a city as a function of the month of the year.

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2 years ago
Which function is equivalent to f(x) =2x² - 8x + 3?
Afina-wow [57]

Answer:

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Step-by-step explanation:

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The following double line graph represents the enrollment of students at Jefferson Middle School for 2006 through 2009. What was
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Step-by-step explanation:

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1+2-3+4+5-6+7+8-9...+97+98-99
zaharov [31]

Answer:

  1584

Step-by-step explanation:

The sum of this sequence can be found a number of ways. One way is to recast it as the series whose terms are groups of three terms of the given series.

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<h3>series of partial sums</h3>

The partial sums, taken 3 terms at a time, are

  1+2-3 = 0

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...

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So the original series is equivalent to ...

  0 +3 +6 +... +96 = 3×1 +3×2 +... +3×32 = 3×(1 +2 +... +32)

That is, the sum is 3 times the sum of the consecutive integers 1..32.

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<h3>consecutive integers</h3>

The sum of integers 1..n is given by the equation ...

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<h3>series sum</h3>

Using this to find the sum of our series, we find it to be ...

  series sum = 3 × (32)(33)/2 = 1584

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<em>Alternate solution</em>

The given series is the sum of integers 1-99, with 6 times the sum of integers 1-33 subtracted. That is, ...

  1 + 2 - 3 + 4 + 5 - 6 = 1+2+3+4+5+6 -2(3 +6) = 1+2+3+4+5+6 -6(1+2)

Continuing on to ...97 +98 -99 gives the result s(99) -6s(33).

Computed that way, we find the sum to be ...

  (99)(100)/2 -6(33)(34)/2 = 4950 -3366 = 1584

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2 years ago
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