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3 years ago

7

The least common multiple of two integers is 240, and the greatest common divisor is 24. Given that one of the integers is 48, w

hat is the other integer?

1 answer:

djverab [1.8K]3 years ago

7 0

Answer:

120

Step-by-step explanation:

The computation of the other integer is shown below:

The Factor of 48 is 2^4 × 3

Also the greatest common divisor is 24,

This results that the second number also contains the factors 2^3 and 3 but not a fourth 2.

Now when there is a division of 240 by 48 so the number comes is 5

Now the second number factors are 2^3 and 3 that represents that it is under the factors of 48 but the factor 5 would arise from the second number

So, the other number is 120

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Intersection of the first two lines:

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Multiply the first equation by 4 and the second by 5:

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Subtract the two equations:

$(20x - 8y + 12)-(20x - 15y + 5)=0 \iff 7y+7=0 \iff y=-1$

Plug this value for y in one of the equation, for example the first:

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So, the first point of intersection is $(-1,-1)$

We can find the intersection of the other two lines in the same way: we start with

$\begin{cases}x=y\\x=3y+4\end{cases}$

Use the fact that x and y are the same to rewrite the second equation as

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And since x and y are the same, the second point is $(-2, -2)$

So, we're looking for a line passing through $(-1,-1)$ and $(-2, -2)$ . We may use the formula to find the equation of a line knowing two of its points, but in this case it is very clear that both points have the same coordinates, so the line must be $y=x$

In the attached figure, line $5x - 2y + 3 = 0$ is light green, line $4x - 3y + 1 = 0$ is dark green, and their intersection is point A.

Simiarly, line $x=y$ is red, line $x = 3y + 4$ is orange, and their intersection is B.

As you can see, the line connecting A and B is the red line itself.

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Find the x-intercepts for the parabola defined by the equation below. y = x2 + 9x + 14

faltersainse [42]

Answer:

x - intercepts are (-7,0) and (-2,0)

A is the correct option.

Step-by-step explanation:

We have been given the equation of the parabola $y=x^2+9x+14$

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A is the correct option.

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