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Nezavi [6.7K]
4 years ago
14

2. Aladdin has some lamps. When Aladdin buys three more lamps and adds to the double of the number of lamps he has, the total nu

mber of lamps goes up to 15.
(a) Form an equation for the above, considering x as the number of lamps that Aladdin has.
Mathematics
2 answers:
Irina18 [472]4 years ago
5 0

Answer:

x=6

Step-by-step explanation:

Let the number of lamp Aladdin has=x

Aladdin buys <u>three more lamps</u> and <u>adds to the double</u> of the number of lamps he has.

  • Double the number he already has=2x
  • Three more lamps added to the double=2x+3
  • The total number of lamps goes up to 15.

Therefore:

2x+3=15

Subtract 3 from both sides

2x+3-3=15-3

2x=12

Divide both sides by 2

x=6

Aladdin has <u>6 lamps</u> initially.

Mazyrski [523]4 years ago
3 0

Answer:

The equation for the number lamps Aladdin have;

2x + 3 = 15

To solve for x;

2x = 15-3

x = 12/2 = 6

Aladdin have 6 lamps earlier.

Step-by-step explanation:

Let x be the number of lamps Aladdin have before;

When Aladdin buys three more lamps and adds to the double of the number of lamps he has, the total number of lamps goes up to 15.

2x + 3 = 15

To solve for x;

2x = 15-3

x = 12/2 = 6

Aladdin have 6 lamps earlier.

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Solve the following system of equations by substitution. Show all steps.
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Answer:

Given system of equations:

\begin{cases}f(x)=-x^2+2x+3\\g(x)=-2x+3\end{cases}

To solve by substitution, equate the equations and solve for x:

\begin{aligned}f(x) & = g(x)\\\implies -x^2+2x+3 & = -2x+3\\-x^2+4x & = 0\\x^2-4x & = 0\\x(x-4) & = 0\\\implies x & = 0\\\implies x-4 & = 0 \implies x=4\end{aligned}

Therefore, the x-values of the solution are x = 0 and x = 4.

To find the y-values of the solution, substitute the found values of x into the functions:

f(0)=-(0)^2+2(0)+3=3

g(0)=-2(0)+3=3

f(4)=-(4)^2+2(4)+3=-5

g(4)=-2(4)+3=-5

Therefore, the solutions to the given system of equations are:

(0, 3) and (4, -5)

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2 years ago
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posledela
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Step-by-step explanation:

The mean distance of the Earth from the sun is 93 million miles.

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Irina-Kira [14]

Answer:

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If we express the percentage x% in the form of ratio then it can be written as \frac{x}{100}.

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Let the number is given by x.

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