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3 years ago

How to solve this linear equation step by step please

Mathematics

1 answer:

mote1985 [20]3 years ago

7 0

$\bf \cfrac{3}{c^2-4c}-\cfrac{9}{2c^2+3c}=\cfrac{2}{2c^2-5c-12}\\\\\\ 
\begin{cases}
c^2-4c=&c(c-4)\\
2c^2+3c=&c(2c+3)\\\\
2c^2-5c-12=
&(2c+3)(c-4)
\end{cases}\\\\
-------------------------------\\\\
\textit{therefore, our LCD for the \underline{left-side} will have to be }\underline{c(c-4)(2c+3)}\\\\
-------------------------------\\\\$

$\bf \cfrac{3}{c(c-4)}-\cfrac{9}{c(2c+3)}=\cfrac{2}{(2c+3)(c-4)}
\\\\\\
\cfrac{3(2c+3)-9(c-4)}{c(c-4)(2c+3)}=\cfrac{2}{(2c+3)(c-4)}
\\\\\\
\cfrac{6c+9-(9c-36)}{c(c-4)(2c+3)}=\cfrac{2}{(2c+3)(c-4)}
\\\\\\
\cfrac{6c+9-9c+36}{1}=\cfrac{2[c(c-4)(2c+3)]}{(2c+3)(c-4)}
\\\\\\
-3c+45=2c\implies 45=5c\implies \cfrac{45}{5}=c\implies 9=c$

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A line is perpendicular to y = - x - 2 and intersects the point (-5, 10)

Lady_Fox [76]

Answer:

y = x + 15

Step-by-step explanation:

If two lines are perpendicular to each other, they have opposite slopes.

The first line is y = - x - 2. Its slope is -1. A line perpendicular to this will have a slope of 1.

Plug this value (1) into your standard point-slope equation of y = mx + b.

y = 1x + b or y = x + b

To find b, we want to plug in a value that we know is on this line: in this case, it is (-5, 10). Plug in the x and y values into the x and y of the standard equation.

10 = (-5) + b

Simplify.

10 = -5 + b

Now, add 5 to both sides to isolate b.

15 = b

Plug this into your standard equation.

y = x + 15

This equation is perpendicular to your given equation (y = -x - 2) and contains point (-5, 10)

Hope this helps!

6 0

3 years ago

Delta makes 12-volt car batteries. These batteries are known to be normally

blondinia [14]

Answer:

The probability that Delta car batteries last between three and four years

P(36≤X≤48) = 0.5188

The percentage of that Delta car batteries last between three and four years

P(3≤X≤4) = 52%

Step-by-step explanation:

Step(i):-

Given that the sample size n =12 -volt car batteries

Let 'X' be a Random variable in a normal distribution

Given that mean of the normal distribution = 45 months

Given that the Standard deviation of the normal distribution = 8months

Step(ii):-

Let X₁ = 3 years = 12 × 3 = 36 months

$Z_{1} = \frac{x_{1} -mean}{S.D} = \frac{36-45}{8} = -1.125$

Let X₂ = 4 years = 12 × 4 = 48 months

$Z_{2} = \frac{x_{2} -mean}{S.D} = \frac{48-45}{8} = 0.375$

Step(iii):-

The probability that Delta car batteries last between three and four years

P(36≤X≤48) = P(-1.125≤Z≤0.375)

= P(Z≤0.375) - P(Z≤-1.125)

= 0.5 +A(0.375) - (0.5-A(1.125)

= 0.5 + 0.1480 - (0.5 -0.3708)

= 0.1480 + 0.3708

= 0.5188

Final answer:-

The probability that Delta car batteries last between three and four years

P(36≤X≤48) = 0.5188

The percentage of that Delta car batteries last between three and four years

P(3≤X≤4) = 52%

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3 years ago

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3 years ago

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vlabodo [156]

Answer:

$x=55$

Step-by-step explanation:

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