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3 years ago

If now Lina is three times as old as Nick, and in 6 years she will be twice as old as he, how old are they now?\

Mathematics

1 answer:

Kitty [74]3 years ago

8 0

Answer:

Step-by-step explanation:

Nick's age = x years

Lina's age =3*x = 3x

After 6 years,

Lina's age = 3x + 6

Nick's age = x + 6

3x + 6 = 2*(x+6)

3x + 6 = 2*x + 2*6

3x + 6 = 2x + 12 {Subtract 6 form both sides}

3x +6 - 6 = 2x + 12 - 6

3x = 2x + 6 {subtract 2x from both sides}

3x - 2x = 2x + 6 - 2x

x = 6

Nick's age = 6 years

Lina's age =3*6 = 18 years

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Sveta_85 [38]

Answer:

#1) y = -4x + 1; #2) parallel; #3) y = -1/2x + 5/2; #4) y = 2x + 4; #5) Never

Step-by-step explanation:

#1) We want a line that passes through (1, -3) and is parallel to y = 2-4(x-1). First we simplify our equation using the distributive property:

y = 2-4(x-1) = 2-4(x) -4(-1) = 2-4x--4 = 2-4x + 4 = -4x + 6

Lines that are parallel have the same slope; this means we want a line through (1, -3) with a slope of -4. Using point-slope form,

$y-y_1=m(x-x_1)\\\\y--3=-4(x-1)\\\\y+3=-4(x)-4(-1)\\\\y+3=-4x+4\\\\y+3-3=-4x+4-3\\\\y=-4x+1$

#2) We must first write our second equation in slope-intercept form by isolating the y term:

2x+y=7

Subtract 2x from each side"

2x+y-2x = 7-2x

y = -2x+7

This means the slope is -2; the slopes are the same, so the lines are parallel.

#3) The slope of our given equation is 2. To be perpendicular, the second line must have a slope that is a negative reciprocal (flipped and opposite signs); this makes it -1/2. Using point-slope form,

$y-0=\frac{-1}{2}(x-5)\\\\y=\frac{-1}{2}(x)+\frac{-1}{2}(-5)\\\\y=\frac{-1}{2}x+\frac{5}{2}$

#4) The slope of Main Street on the diagram, found by using rise/run, is 2. This means the bike path will also have a slope of 2 in order to be parallel. The park entrance is at (0, 4). This makes the equation y = 2x+4.

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3 years ago

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Zielflug [23.3K]

Answer:

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Step-by-step explanation:

For every 90 degrees rotated, the coordinate numbers switch and one is multiplied by -1, when clockwise it's the 2nd one, and when counterclockwise, it's the 1st.

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3 years ago

Which of the following is the solution to the differentiable equation dy/dx=4x/y, where Y(2)=-2

aliya0001 [1]

First we'll substitute $\frac{dy}{dx}$ with $y'$

$y'=\frac{4x}{y}$

Then we can separate this.

$yy'=4x$

Then we'll solve this.

$yy'=4x: \frac{y^2}{2}=2x^2+c_1$

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Then we'll plug in to find the extraneous solutions (if any)

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3 years ago

Solve the system of equations: X+y+z=5 -3x-4y+4z=15 2x-y-4z=-8

atroni [7]

Answer:

(x, y, z) = (3, -2, 4)

Step-by-step explanation:

The attachment shows a solution using a graphing calculator where the first equation is solved for z, and that expression is substituted into each of the other two equations. The solution to that system is (x, y) = (3, -2). Using these values in the expression for z, we find ...

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

The solution is (x, y, z) = (3, -2, 4).

Your graphing calculator and/or online tools can give you the reduced row echelon form of the augmented matrix representing the system:

$\left[\begin{array}{ccc|c}1&1&1&5\\-3&-4&4&15\\2&-1&-4&-8\end{array}\right]$

If you're solving by hand, you can do the substitution described above to eliminate z from one equation. You can eliminate z from another equation by adding the last two:

-3x -4y +4(5 -x -y) = 15 ⇒ -7x -8y = -5

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-7(-5y -7) -8y = -5 ⇒ 27y = -54 ⇒ y = -2

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_____

Additional comment

If all that is needed is a solution, we prefer a graphical or matrix approach. These take about the same amount of time. Both require a little additional effort to determine exact values when the solutions are not integers.

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2 years ago

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Goryan [66]

42 bro it’s pretty simple just multiplication

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3 years ago