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oee [108]
3 years ago
11

How is solving a literal equation similar to solving a standard equation??

Mathematics
1 answer:
timama [110]3 years ago
8 0

Sometimes you have a formula, such as something from geometry, and you need to solve for some variable other than the "standard" one. For instance, the formula for the perimeter P of a square with sides of length s is P = 4s. You might need to solve this equation for s, so you can plug in a perimeter and figure out the side length.

This process of solving a formula for a given variable is called "solving literal equations". One of the dictionary definitions of "literal" is "related to or being comprised of letters", and variables are sometimes referred to as literals. So "solving literal equations" seems to be another way of saying "taking an equation with lots of letters, and solving for one letter in particular."

At first glance, these exercises appear to be much worse than your usual solving exercises, but they really aren't that bad. You pretty much do what you've done all along for solving linear equations<span> and other sorts of equation; the only substantial difference is that, due to all the variables, you won't be able to simplify your answers as much as you're used to. </span>
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Rewrite the expression $6j^2 - 4j 12$ in the form $c(j p)^2 q$, where $c$, $p$, and $q$ are constants. What is $\frac{q}{p}$
solniwko [45]

Rewrite the expression  6j^2 - 4j + 12$ in the form $c(j + p)^2 + q$, where $c$, $p$, and $q$ are constants. What is $\frac{q}{p}$

The ratio of \frac{q}{p}  = - 34

How to solve such questions?

Such Questions can be easily solved just by some Algebraic manipulations and simplifications. We just try to make our expression in the form which question asks us. This is the best method to solve such questions as it will definitely lead us to correct answers. One such method is completing the square method.

Completing the square is a method that is used for converting a quadratic expression of the form ax^{2} + bx + c to the vertex form

a(x - h)^{2} + k. The most common application of completing the square is in solving a quadratic equation. This can be done by rearranging the expression obtained after completing the square: a(x + m)^{2} + n, such that the left side is a perfect square trinomial

$6j^2 - 4j +12$

=  $6(j^2 - \frac{2}{3} j )+12$

= $6(j^2 - \frac{2}{3} j  +  \frac{1}{9}  )+\frac{102}{9}                   (Completing Square method)

=6( j- \frac{1}{3} )^{2}  +  \frac{34}{3}

On comparing with the given equation we get

p = - \frac{1}{3}     and q = \frac{34}{3}

∴ \frac{q}{p} = \frac{\frac{34}{3} }{\frac{-1}{3} }

= - 34

Learn more about completing the square method here :

brainly.com/question/26107616

#SPJ4

7 0
2 years ago
Out of 28 students in a class, 7 have blue eyes. What is the probability a student picked at
mars1129 [50]

Answer:

3/4

Step-by-step explanation:

7/28 have blue eyes

So 28-7=21

21/28 don't have blue eyes

21/28 simplified=3/4

7 0
3 years ago
Read 2 more answers
Twice the difference of a number and six is the same as twelve . Write into algebraic equation
DiKsa [7]

Answer:

2(n-6)=12

(I went too far in my explanation; I'm not going to erase it because I think it is important to have an example on solving these)

Step-by-step explanation:

Twice the difference of a number and 6 is the same as 12.

Twice means 2 times

Difference means the result of subtracting something.

is the same as means equal to (=).

So we are given 2(n-6)=12.

You can start by dividing 2 on both sides are distributing 2 to terms in the ( ).

I will do it both ways and you can pick your favorite.

2(n-6)=12

Divide both sides by 2.

 n-6  =6

Add 6 on both sides

 n     =12

OR!

2(n-6)=12

Distribute 2 to both terms in the ( )

2n-12=12

Add 12 on both sides

2n    =24

Divide both sides by 2

n       =12

4 0
3 years ago
Need help pls math plsssssssssssssssssssdssssssssssszzssszzzzzzzxxxxxxcgvvhvib
Svetradugi [14.3K]

Step-by-step explanation:

area of a parallelogram is b×h

2.4×1=2.4cm²

I would appreciate if my answer is chosen as a brainliest answer

7 0
2 years ago
O log2 3x + log2 3=2
ipn [44]

Answer:

\large\boxed{x=\dfrac{4}{9}}

Step-by-step explanation:

\log_23x+\log_23=2\\\\\bold{DOMAIN}:\\3x>0\to x>0\\\\\text{Use}\ \log_ab+\log_ac=\log_a(bc)\\\\\log_2\bigg[(3x)(3)\bigg]=2\\\\\log_29x=2\qquad\text{use}\ \log_ab=c\iff a^c=b\\\\\log_29x=\log_22^2\\\\\log_29x=\log_24\iff9x=4\qquad\text{divide both sides by 9}\\\\\dfrac{9x}{9}=\dfrac{4}{9}\\\\\boxed{x=\dfrac{4}{9}}\in \bold{DOMAIN}

8 0
3 years ago
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