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3 years ago

Solve the linear equation.

Mathematics

1 answer:

Nataliya [291]3 years ago

8 0

$7x+10=\dfrac{1}{3}(12x-3)+14x\qquad\text{use distributive property}\\\\7x+10=\dfrac{1}{3}\cdot12x-\dfrac{1}{3}\cdot3+14x\\\\7x+10=4x-1+14x\\\\7x+10=18x-1\qquad\text{substitute 10 from both sides}\\\\7x=18x-11\qquad\text{subtract 18x from both sides}\\\\-11x=-11\qquad\text{divide both sides by (-11)}\\\\\boxed{x=1}$

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What is the solution to this equation? X/4 =-12

Natasha2012 [34]

Answer:

C. x=-48

Step-by-step explanation:

x/4=-12

multiply both sides by 4

4x/4=4 (-12)

simplify

x=-48

7 0

3 years ago

A gallon of gas cost $2.16. Rob buys 13.5 gallons of gas. How much did he pay?

pashok25 [27]

Answer:

$29.16

Step-by-step explanation:

Each gallon of gas is $2.16.

13.5 gallons of gas is 2.16 (13.5) = $29.16.

4 0

3 years ago

Read 2 more answers

17) Solve the system as matrix equations using inverses. 17) A company produces three models of MP3 players, models A, B, and C.

Vinvika [58]

Answer:

Model A=30, Model B: 20, Model C: 45

Step-by-step explanation:

Let x be the amount of type A mp3 produced, and the amount of model B mp3's produced and z the amount of model C mp3 produced.

Since in total there are 303 hours for electronics work, then:

$3.2x+5.4y+2.2z=303$

Since in total there are 393 hours for assembly, then:

$2.8x+2.4y+5.8z=393$

Since in total there are 416 hours for quality assurance, then:

$4.4x+3.4y+4.8z=416$

Then, the linear system associated to the problem is

$3.2x+5.4y+2.2z=303\\2.8x+2.4y+5.8z=393\\4.4x+3.4y+4.8z=416$

with coefficient matrix $A=\left[\begin{array}{ccc}3.2&5.4&2.2\\2.8&2.4&5.8\\4.4&3.4&4.8\end{array}\right]$ and vector of constant terms $b=\left[\begin{array}{ccc}303\\393\\416\end{array}\right]$

Since the determinant of A is equal to 36.704 then A is invertible.

Then for solve the system $Ax=b$ , is enough find the inverse of A and operate

$Ax=b\\A^{-1}Ax=A^{-1}b\\x=A^{-1}b$

Using Octave we obtain that

$A^{-1}=\left[\begin{array}{ccc}-0.22&-0.50 &0.71\\0.33&0.15&-0.34\\-0.028& 0.35&-0.20\end{array}\right]$

Then

$x=A^{-1}b=\left[\begin{array}{ccc}30\\20\\45\end{array}\right]$

This means that 30 mp3's of model A, 20 of model B and 45 of model C must be produced

8 0

3 years ago

Select the postulate that is illustrated for the real numbers. 3x + 3 = 3(x + 1) The commutative postulate for multiplication Mu

fredd [130]

Distributive postulate.

The expression 3x + 3 = 3(x + 1) is an example of a distributive postulate. It says that multiplying a number by a group of numbers added together is the same as doing each multiplication separately.

4 0

3 years ago

Substitute x=y+1 into the expression 3x -1 and determine the first step

Kruka [31]

Answer: the solution becomes 3=y+1-1

Step-by-step explanation:

The first step is to combine like terms meaning you subtract 1-1. Then you are left with 3=y.

8 0

3 years ago