Two sides of a triangle are equal in length. The third side of the triangle is 3 more than the equal sides. If the perimeter of the triangle is 48, what is the length of the longest side?

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Answer:

[tex]L^{-1} (\frac{5s}{s^{2}+ 3 s -4 } )[/tex] =  [tex]4e^{-4t} + e^{t}[/tex]

Step-by-step explanation:

Step(i):-

Given

           [tex]L^{-1} (\frac{5s}{s^{2}+ 3 s -4 } )[/tex]

Factors of    s² + 3s - 4

               =    s² + 4s - s -4

               =   s( s +4 ) -1 (s +4)

               =   (s-1)(s+4)

  [tex]L^{-1} (\frac{5s}{s^{2}+ 3 s -4 } )[/tex]

              =    [tex]L^{-1} (\frac{5s}{s+4)(s-1) } )[/tex]

By using partial fractions

           [tex](\frac{s}{s+4)(s-1) } ) = \frac{A}{s+4} + \frac{B}{s-1}[/tex] ..(i)

                s  = A ( s-1) + B( s+4) ....(ii)

          Put s= 1  in equation (ii) , we get

             1 = B(5)

           [tex]B = \frac{1}{5}[/tex]

         s = -4 in equation (ii) , we get

        -4 = -5A

         [tex]A =\frac{4}{5}[/tex]

Step(ii):-

    now the equation (i) , we get

[tex](\frac{s}{s+4)(s-1) } ) = \frac{4}{5(s+4)} + \frac{1}{5(s-1)}[/tex]

[tex]L^{-1} (\frac{s}{s+4)(s-1) } ) = 5( L^{-1} \frac{4}{5(s+4)} + 5L^{-1} \frac{1}{5(s-1)}[/tex]                      

By using inverse Laplace transform formula

[tex]L^{-1} (\frac{1}{s-a} ) = e^{at}[/tex]

[tex]L^{-1} (\frac{1}{s-1} ) = e^{t}[/tex]

[tex]L^{-1} (\frac{1}{s+4} ) = e^{-4t}[/tex]

[tex]L^{-1} (\frac{s}{s+4)(s-1) } ) = 5( L^{-1} \frac{4}{5(s+4)} + 5L^{-1} \frac{1}{5(s-1)}[/tex]                    

                      = [tex]4e^{-4t} + e^{t}[/tex]

Answer:

Line A

Step-by-step explanation:

Line A crosses 5 at y when it hits 1 at x, meaning that constant of proportionality is 5. Trust me ; D.

Answer: 5 x 58 = 290           :)

Step-by-step explanation:

Answer:

the answer is= 2.5

Step-by-step explanation:

good luck!

Answer:

The first coordinate (usually the x-coordinate) is called the domain and the second (usually the y-coordinate) is called the range. If tou remember from earlier chapters the domain contains values that correspond to the independent variable whereas the range contains values corresponding to the dependent variable.

Step-by-step explanation:

I majored in Mathematics

Answer:

0

Step-by-step explanation:

Slope is the rise (change in y) over the run (change in x).

y=3 is simply a horizontal line.

hope this helps!

Answer:

C. the rate at the pool fills in feet per hour

Step-by-step explanation:

Given

The attached graph

Required

What does the slope represent?

The slope of any graph can be calculated using:

[tex]Slope = \frac{Rise}{Run}[/tex]

Where:

Rise = The change in the vertical axis

Run = The change in the horizontal axis within the same interval as the Rise

The vertical axis measures depth in feet and the horizontal axis measures time in hour.

So:

[tex]Slope = \frac{Depth}{Time}[/tex]

or

[tex]Slope = \frac{Feet}{Hour}[/tex]

This means that the slope measures rate in feet per hour

Answer:

False

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

The left of the number line is the domain of negative numbers. As you go left on the number line, the integers are smaller.

Answer:

57°

Step-by-step explanation:

[tex] \theta = {sin}^{ - 1} \bigg( \frac{36}{43} \bigg) \\ \\ \theta = 56.846591584 \degree\\ \\ \theta \approx 57 \degree\\ \\ [/tex]

Answer:

x+y[tex]\geq[/tex]420

18x+16.50y[tex]\geq[/tex]420

Step-by-step explanation:

Answer:

18x + 16.50y ≥ 420

Step-by-step explanation:

Answer:

-22x^8

Step-by-step explanation:

-8z^8 + (-14z^8)

z^8 = z^8

-8 - 14 = -22

-22z^8

Answer:

341.95≤x≤358.95

Step-by-step explanation:

The confidence interval formula is expressed as;

CI = xbar±(z×s/√n)

xbar is the mean sample

s is the standard deviation

z is the z score at 95% confidence interval

n is the sample size

xbar = 350kg

z = 1.96

s = 25kg

n = 30

Substitute

CI = 350±(1.96×25/√30)

CI = 350±(1.96×4.564)

CI = 350±(8.946)

CI = (350-8.946, 350+8.946)

CI = (341.05, 358.95)

Hence the 95% confidence interval for how much food the elephant eats us 341.95≤x≤358.95

Answer:

n = [tex]\frac{d-4m}{7}[/tex]

Step-by-step explanation:

Given

d = 4m + 7n ( subtract 4m from both sides )

d - 4m = 7n ( isolate n by dividing both sides by 7 )

[tex]\frac{d-4m}{7}[/tex] = n

Answer:

n = d - 4m ÷ 7

Step-by-step explanation:

d = 4m + 7n

d - 4m = 7n

7n = d - 4m

n = d - 4m ÷ 7

Thus, n = d - 4m ÷ 7

-TheUnknownScientist

Answer: 5/6

Step-by-step explanation:

Answer:

I believe the answer is 1 1/6

Step-by-step explanation:

Here is how I got 1 1/6

4 1/3 - 3 1/2

4 - 3 = 1

1/3 - 1/2 = 2/6 - 3/6 = 1/6

Answer = 1 1/6

[tex]\boxed{\boxed{\pink{\bf \leadsto Option \ A \ is \ correct .}}}[/tex]

Given that , Paul needs 27 plants to fill his garden and has $99 to spend. Lilies cost $5 each and tulips cost $2 each.

Now we need to find which set of linear equations represent the above situation. So ,

Sum of number of lilies and tulips is 27 .

[tex]\implies \bf n( Tulips) + n(Lilies ) = 27 \\\\\bf\implies \boxed{ \bf l + t = 27 }[/tex]

Now , cost of each lily is $5 and tulip is $2 . And he has $99 in total . So ,

[tex]\bf\implies n_{tulips} \times cost_{tulip} + n_{lilies} \times cost_{lilies} = Money \ that \ Paul \ has. \\\\\bf \implies t\times \$2 + l \times \$5 = \$ 99 \\\\\implies \boxed{\bf 2t + 5l =\$ 99 }[/tex]

Hence we can see that our ans matches with option (a) which is ,

[tex]\red{\bf Option \ A}\begin{cases} \bf l + t = 27 \\\\\bf 2t + 5l = 99 \end{cases}[/tex]

Answer:

answers in this order

5

4

3

2

1

6

Step-by-step explanation:

i kno that the way these numbers are are kinda sus but this is correct

hope this helps <3

Answer: 6, 5, 4

Step-by-step explanation:

The mode is the number that you see the most. 6, 5, and 4 appear 3 times in the set.

Answer:

6,5,4

Step-by-step explanation:

the all tie in repeating 3 times. The mode is what repeats the most. since 6,5,4 all repeats 3 times they tie for mode.

Answer:

where is the numberline miss

Answer:

you forgot the picture

:-(((

Answer:

so sorry i had too

Step-by-step explanation:

someone passed this to me) 90% of people marry there 7th grade love. since u have read this, u will be told good news tonight. if u don't pass this on nine comments your worst week starts now this isn't fake. apparently if u copy and paste this on ten comments in the next ten minutes you will have the best day of your life tomorrow. you will either get kissed or asked out in the next 53 minutes someone will say i love you

Answer:

Between 80 and 160

Step-by-step explanation:

this is  such a bad graph i honestly could not give you an exact answer

Answer:

21

Step-by-step explanation:

9*7 is 63 divided by 3 should get you 21.

Answer:

21

Step-by-step explanation:

Answer:

70 inches weighs 160

125-pound person is 66 inches tall

Step-by-step explanation:

Answer:

I wouldn't advise putting answers from test on brainly its against the honor of code and you will get warned.

Step-by-step explanation:

Answer:

Step-by-step explanation:

reqd. rate=(1.6)×47÷34≈2.2 questions per minute.

The required rate to complete the question in 34 minutes is given as 2.2 questions per minute.

Rate of change is defined as the change in value with rest to the time is called rate of change.

As mentioned in the question, in homework rate of doing questions is 1.6 questions per minute.
It took 47 minutes to complete the whole expression,

Total questions in the homework given by,
Total question = rate × time
Total question = 1.6 × 47
Total questions ≈ 75 questions

Now,
If the time to complete the question is 34 minutes, the rate required is given by,
Rate = total question/time

Rate = 75/34
rate = 2.2 questions per minute.

Thus, the required rate to complete the question in 34 minutes is given as 2.2 questions per minute.

Learn more about the rate of change here: https://brainly.com/question/13103052

#SPJ2

Answer:

4x(3a+2b)

Step-by-step explanation:

Answer:

4x(3a+2b)

Step-by-step explanation:

Given: 12x+8bx

Factor out x: x(12a+8b)

Factor out 4: 4x(3a+2b)

Answer:

its 5 hours i think

Step-by-step explanation:

Answer:

[tex] {x}^{2} - 11x + 37 - \frac{128}{x + 4} [/tex]