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Nana76 [90]
3 years ago
7

What is the slope of a line parallel to a line with slope of 9

Mathematics
1 answer:
marishachu [46]3 years ago
7 0

Answer:

slope of 9

Step-by-step explanation:

parallel means never touching, so it would have the same slope.

Hope this helps!

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Find the possible values of r in The inequality 5>r-3
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R - 3 < 5
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The product of 4 and a number f decreased by 2 is 15
Debora [2.8K]

Answer:  The number is:  "2 " .

__________________________________________

Step-by-step explanation:

__________________________________________

Write the expression; which is an equation, as follows:

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    " 4x − 12 = 2(-x) " ;  in which "x" represents "the number for which we shall                                       solve" .

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Note:  

If the "number" = "x" ;  the "opposite of the number"  =  " -x " ;

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Rewrite as:  " 4x − 12 = -2x " ;

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    →  Add "12" ; & add "2x" ; to EACH SIDE of the equation:

                     4x − 12 + 12 + 2x = -2x + 12 + 2x ;

          to get:    6x  = 12  ;

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Now, divide each side of the equation by "6" ;

    to isolate "x" on one side of the equation; & to solve for "x" ;

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                        6x / 6  =  12 / 6 ;

                   to get:    x = 2 .

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Answer:  The number is:  "2 " .

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Let us check our answer, by plugging in "2" for "x" in our original equation:

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       →   " 4x − 12 = 2(-x) " ;

 Let us plug in "2" for "x" ; to see if the equation holds true; that is; if both side of the equation are equal; when "x = 2" ;

       →   " 4(2) − 12 = ?  2(-2) ??

       →    8 − 12 = ?  -4 ? ;

       →    -4 = ? -4 ??  Yes!

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7 0
3 years ago
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The area of the triangle formed by x− and y− intercepts of the parabola y=0.5(x−3)(x+k) is equal to 1.5 square units. Find all p
Juliette [100K]

Check the picture below.


based on the equation, if we set y = 0, we'd end up with 0 = 0.5(x-3)(x-k).

and that will give us two x-intercepts, at x = 3 and x = k.

since the triangle is made by the x-intercepts and y-intercepts, then the parabola most likely has another x-intercept on the negative side of the x-axis, as you see in the picture, so chances are "k" is a negative value.

now, notice the picture, those intercepts make a triangle with a base = 3 + k, and height = y, where "y" is on the negative side.

let's find the y-intercept by setting x = 0 now,


\bf y=0.5(x-3)(x+k)\implies y=\cfrac{1}{2}(x-3)(x+k)\implies \stackrel{\textit{setting x = 0}}{y=\cfrac{1}{2}(0-3)(0+k)} \\\\\\ y=\cfrac{1}{2}(-3)(k)\implies \boxed{y=-\cfrac{3k}{2}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{area of a triangle}}{A=\cfrac{1}{2}bh}~~ \begin{cases} b=3+k\\ h=y\\ \quad -\frac{3k}{2}\\ A=1.5\\ \qquad \frac{3}{2} \end{cases}\implies \cfrac{3}{2}=\cfrac{1}{2}(3+k)\left(-\cfrac{3k}{2} \right)


\bf \cfrac{3}{2}=\cfrac{3+k}{2}\left( -\cfrac{3k}{2} \right)\implies \stackrel{\textit{multiplying by }\stackrel{LCD}{2}}{3=\cfrac{(3+k)(-3k)}{2}}\implies 6=-9k-3k^2 \\\\\\ 6=-3(3k+k^2)\implies \cfrac{6}{-3}=3k+k^2\implies -2=3k+k^2 \\\\\\ 0=k^2+3k+2\implies 0=(k+2)(k+1)\implies k= \begin{cases} -2\\ -1 \end{cases}


now, we can plug those values on A = (1/2)bh,


\bf \stackrel{\textit{using k = -2}}{A=\cfrac{1}{2}(3+k)\left(-\cfrac{3k}{2} \right)}\implies A=\cfrac{1}{2}(3-2)\left(-\cfrac{3(-2)}{2} \right)\implies A=\cfrac{1}{2}(1)(3) \\\\\\ A=\cfrac{3}{2}\implies A=1.5 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{\textit{using k = -1}}{A=\cfrac{1}{2}(3+k)\left(-\cfrac{3k}{2} \right)}\implies A=\cfrac{1}{2}(3-1)\left(-\cfrac{3(-1)}{2} \right) \\\\\\ A=\cfrac{1}{2}(2)\left( \cfrac{3}{2} \right)\implies A=\cfrac{3}{2}\implies A=1.5

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3 years ago
Y = f(x) = 25x<br><br> Find f(x) when x= 1/2
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Answer:

12.5

Step-by-step explanation:

f of x just means y, so you're just finding y when x = 1/2

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Answer:

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You sum the lost excess weight: 50% + 20% + 25% = 95%. Meaning that she lost 95% of the excess weight. It remained just 5% to lose.

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