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3 years ago

X-45=8(2x+3)-18 what are the first steps to solving this equation

Mathematics

1 answer:

Mamont248 [21]3 years ago

3 0

Step-by-step explanation:

step one Distribute

x−45=8(2x+3)−18

x−45=16x+24−18

step two Subtract the numbers

x−45=16x+24−18

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2 years ago

There is a mound of g pounds of gravel in a quarry. Throughout the day, 300 pounds of gravel are added to the mound. Two orders

galina1969 [7]

Answer:

$g+300-700-700=1500, g=2600$

Step-by-step explanation:

At the start of the day there are g pounds of gravel in the quarry.

Then it says that there were 300 pounds added to the mound, so at this point the pounds of gravel in the mound are now g+300.

Then two orders of 700 pounds are sold and removed from the mound. That means they removed 700 pounds from the mound 2 times. Therefore at this point the pounds of gravel in the mound are now g+300-700-700.

Then it says that at this point, the amount of pounds in the mound are 1500. Hence we get

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2 years ago

Express 2x+1/(x-2)(x²+1) as a partial fraction.

Oduvanchick [21]

Answer:

Partial fraction = 1/(x-2) - x/(x^2+1)

Step-by-step explanation:

Question:

Express 2x+1/(x-2)(x²+1) as a partial fraction.

Note: it will be assumed that there was a typo in the interpretation of parentheses to mean

(2x+1) / ( (x-2)(x^2+1) )

Let

(2x+1) / ( (x-2)(x^2+1) ) = A/(x-2) + (Bx+C)/(x^2+1) .........................(0)

(2x+1) / ( (x-2)(x^2+1) ) = (A(x^2+1)+(Bx+C)(x-2)) / ( (x-2)(B/(x^2+1) )

(2x+1) / ( (x-2)(x^2+1) ) = (Ax^2+A+Bx^2+(C-2B)x-2C) / ( (x-2)(B/(x^2+1) )

(2x+1) / ( (x-2)(x^2+1) ) = ( (A+B)x^2+(C-2B)x+A-2C ) / ( (x-2)(B/(x^2+1) )

Match numerators

2x+1 = (A+B)x^2+(C-2B)x+A-2C

Match coefficients,

A+B = 0 ..................(1)

-2B+C = 2 .................(2)

A-2C = 1 ...................(3)

Solve for A, B and C

Substitute A from (1) in (3)

-B - 2C =1

transpose and solve for B

B = -2C-1 ....................(4)

Substitue B from (4) in (2)

-2(-2C-1) + C = 2

simplify

5C = 2-2 = 0

C=0 ..........................(5)

substitute (5) in (4)

B = -2C-1 = -1 ...............(6)

Substitue (6) in (1)

A+(-1) = 0

A=1 .............................(7)

Using values from (7), (6) and (5) to substitute in (0)

we get

(2x+1) / ( (x-2)(x^2+1) ) = 1/(x-2) - x/(x^2+1)

as the required partial fraction

7 0

3 years ago

Read 2 more answers