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3 years ago

If 3 times a number minus 2 equals 13, what is the number? A. –6 B. 5 C. 2 D. 4

2 answers:

OverLord2011 [107]3 years ago

8 0

3x - 2 = 13

Add 2 on both sides

3x - 2 + 2 = 13 + 2
3x = 13 + 2
3x = 15

Divide both sides by 3.

3x/3 = 15/3

x = 15/3

x = 5

Your final answer is A. 5<span>.</span>

rosijanka [135]3 years ago

4 0

It is very important to read and understand the words of the problem before getting down to solving the given question. Numerous information's of immense importance are already given in the question. Those information's will come in handy while solving the question.
Let us assume the unknown number to be = x
Then
3x - 2 = 13
3x = 13 + 2
3x = 15
Dividing both sides of the equation by 3, we get
(3/3) * x = 15/3
1 * x = 5
x = 5
So the unknown number is 5. I hope the procedure is not very tough for you to understand.

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4 years ago

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3 years ago

The line y = hx - 2 where h > 0 meets the curve 3y² = 9x² - 6x + 1.

I am Lyosha [343]

Answer:

h=6

Step-by-step explanation:

since $y =hx -2$ is an equation for a line which intersects with the curve $3y^2 = 9x^2 - 6x +1$ . The point of intersection, let's say $(x_1,y_1)$ , should satisfy the two equations. As a result, the value of y in the second equation can be replaced with the value of y in the first equation as the following,

$3y^2 = 3(hx-2)^2 = 9x^2 - 6x +1\\3(h^2x^2 -4hx + 4) = 9x^2 - 6x + 1\\3h^2 x^2 -12hx +12 = 9x^2 - 6x +1$

therefore, the latter equation can be rewritten in a quadratic equation form as the following,

$(9 - 3h^2) x^2 + (12h-6)x + (1-12) = (9 - 3h^2) x^2 + (12h-6)x -11$ = 0

if the line is tangent to the curve, it means that the line touches the curve at one point, therefore the discernment of the second order equation will be equal to zero for the famous quadratic equation solution.

$b^2 -4ac =0$

where $a=9-3h^2, b=12h-6$ and $c=-11$ , as a result, the following equations can be deduced,

$(12h-6)^2 - 4*(9-3h^2)*(-11) = (144h^2 -144h +36) - (36 -12h^2)*(-11)=\\(144-(-12)*(-11)h^2 ) -144h +36 -(36*(-11)) =\\12 h^2 -144h +432 =0$

therefore, dividing both sides by 12

$h^2 -12 +36 =0\\(h-6)^2 =0\\h=6$

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2 years ago