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vesna_86 [32]
3 years ago
11

What is the simplified form of (x+9)/8 minus (x+3)/(x+2)?

Mathematics
2 answers:
Murrr4er [49]3 years ago
6 0
Here is the work to help you understand the problem.
\frac{x+9}{8}-\frac{x+3}{x+2}

\mathrm{Find\:the\:least\:common\:denominator\:} \ \textgreater \  8\left(x+2\right)

\mathrm{Adjust\:Fractions\:based\:on\:the\:LCD} \ \textgreater \  \frac{\left(x+9\right)\left(x+2\right)}{8\left(x+2\right)}-\frac{\left(x+3\right)\cdot \:8}{8\left(x+2\right)}

\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}: \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}

\frac{\left(x+9\right)\left(x+2\right)-8\left(x+3\right)}{8\left(x+2\right)}

Expand \left(x+9\right)\left(x+2\right)-8\left(x+3\right)

\left(x+9\right)\left(x+2\right)
\mathrm{Distribute\:parentheses\:using}: \left(a+b\right)\left(c+d\right)=ac+ad+bc+bd
Where\; a=x,\:b=9,\:c=x,\:d=2

x\cdot \:x+x\cdot \:2+9\cdot \:x+9\cdot \:2 \ \textgreater \  \mathrm{Add\:similar\:elements:}\:2x+9x=11x

xx+11x+2\cdot \:9 \ \textgreater \  \mathrm{Apply\:exponent\:rule}: \:a^b\cdot \:a^c=a^{b+c}

xx=\:x^{1+1}=\:x^2 \ \textgreater \  x^2+11x+2\cdot \:9 \ \textgreater \  \mathrm{Multiply\:the\:numbers:}\:9\cdot \:2=18

x^2+11x+18 \ \textgreater \  x^2+11x+18-8\left(x+3\right)

-8\left(x+3\right) \ \textgreater \  \mathrm{Distribute\:parentheses\:using}: \:a\left(b+c\right)=ab+ac
Where\;a=-8,\:b=x,\:c=3

-8\cdot \:x-8\cdot \:3 \ \textgreater \  \mathrm{Multiply\:the\:numbers:}\:8\cdot \:3=24 \ \textgreater \  -8x-24

x^2+11x+18-8x-24 \ \textgreater \  \mathrm{Group\:like\:terms} \ \textgreater \  x^2+11x-8x+18-24

\mathrm{Add\:similar\:elements:}\:11x-8x=3x \ \textgreater \  x^2+3x+18-24

\mathrm{Add/Subtract\:the\:numbers:}\:18-24=-6 \ \textgreater \  x^2+3x-6

\frac{x^2+3x-6}{8\left(x+2\right)}

Hope this helps!
matrenka [14]3 years ago
5 0
The simplified form of (x+9)/8 - (x+3)/(x+2) is:

x^2+3x-6 over 8 (x+2)

Work:

1. (x+9)(x+2) - (x+3) x 8 over 8 (x+2)

2. (x+9)(x+2) - 8(x+3) over 8(x+2)

3. x^2 + 2x + 9x + 18 - 8x -24 over 8(x+2)

4. x^2 + (2x + 9x - 8x) + (18 - 24) over 8(x+2)

= x^2+3x-6 over 8 (x+2)

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Angles that measure between 0 and 90 degrees are called_?
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Answer:

Acute angles.

Step-by-step explanation:

Acute angles are from 0-90 degrees.

Hope this helps :)

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Finn and Ellie sell oranges at a produce stand. Finn earns $5 for each crate of oranges he sells. At the end of the week, Ellie
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Number of crates of oranges finn sold
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What is x and y? 2x-2y=-4 2x+y=11 Is there infinitely many solutions, 1 solution, or no solution? solve by elimination.
Kaylis [27]

Let's solve your system by substitution.

2x−2y=−4;2x+y=11

Rewrite equations:

2x+y=11;2x−2y=−4

Step: Solve2x+y=11for y:

2x+y=11

2x+y+−2x=11+−2x(Add -2x to both sides)

y=−2x+11

Step: Substitute−2x+11foryin2x−2y=−4:

2x−2y=−4

2x−2(−2x+11)=−4

6x−22=−4(Simplify both sides of the equation)

6x−22+22=−4+22(Add 22 to both sides)

6x=18

6x/6 = 18/6

(Divide both sides by 6)

x=3

Step: Substitute3forxiny=−2x+11:

y=−2x+11

y=(−2)(3)+11

y=5(Simplify both sides of the equation)

Answer:

x=3 and y=5

5 0
2 years ago
A three digit divisible by 3,5 and 6
kondaur [170]
Your answer is three hundred and thirty six (336)
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In 1906 Kennelly developed a simple formula for predicting an upper limit on the fastest time that humans could ever run distanc
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Answer / Step-by-step explanation:

(1) Given t = 0.0588s ¹.¹²⁵

where s is the distance and t is the time to run that distance.

The second portion asks us to find the derivative of the equation when our s value is equal to 20 and interpret.

(2) First, we try to convert the unit from miles to meters

Therefore, 1 mile = 1609 meters

Then,

         t = 0.0588 ( 1609 ) ¹.¹²⁵

             =238 . 09

This gives us the instantaneous rate of change of seconds between every 20 meters ran.

The last portion asks us to compare this estimate to current world records. And have they been surpassed?

As of today, the fastest official record for a standard mile is held by a man from Morocco named Hichan El Guerrouj. The time was recorded at 3.43 minutes in Rome, Italy on July 7th, 1999.

Now, keep in mind that this is almost a full minute slower than the estimated time. However, how do these projections hold up against Usain Bolt, the man that is considered the fastest man in the world ?

Although, Usain Bolt does run long distances, he holds records in nearly every sprinting event that he has ever competed in.

Hence, Kennelly's estimate for the fastest mile is 238.09

(3) Now, noting that since dt / ds = 0.0588 ( 1.25 ) s  ⁰.¹²⁵

Then,

           dt / ds I 100 = 0.0588 (1.25) (20)  ⁰.¹²⁵

                              = 0.1176

6 0
3 years ago
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