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3 years ago

LINE PERPENDICULAR TO Y=1/5X+5 WITH THE POINT (-6,0)?????

2 answers:

4 0

<span>y=1/5x+5 with the point (-6, 0)

The line perpendicular to this line will have a slope that's the negative reciprocal of this one. So if the slope here is 1/5 (based on y=mx+b, where m is the slope), then the perpendicular slope would be -5/1.

So now that you have the point and the slope, use the point-slope formula.
y - y</span>₁ = m(x - x₁)
m = -5
(x₁, y₁) = (-6, 0)

y - 0 = -5(x + 6)
y = -5x - 30

y = -5x - 30 is the line perpendicular to y=1/5x+5.

EastWind [94]3 years ago

3 0

You need to flip the slope (or number in front of the x) and sign of it to do the perpendicular part. This should give you: y=-5x+b. Now put the -6 in for the x, and the 0 in for the y. Simply solve for an answer of -30=b. Your final answer is: y=-5x-30

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One positive number is 14 less than another positive number. If the reciprocal of the smaller number is added to five times the

Kipish [7]

Let's call the two numbers $s$ and $l$ .

Given these variables, we can say: $s = l - 14$ , based on the first sentence in the problem.

Also, remember that the reciprocal of a number is simply 1 divided by the number. Thus, we can say that:

$\dfrac{1}{s} + 5\Big( \dfrac{1}{l} \Big) = \dfrac{1}{4}$

To solve, we can simply substitute $l -14$ in for $s$ in the second equation and solve.

$\dfrac{1}{l - 14} + \dfrac{5}{l} = \dfrac{1}{4}$

Set up

$\dfrac{l}{l(l - 14)} + \dfrac{5(l - 14)}{l(l - 14)} = \dfrac{1}{4}$

Get terms on the left side to a common denominator for easier addition

$\dfrac{l + 5l - 70}{l(l - 14)} = \dfrac{1}{4}$

Simplify

$4(6l - 70) = l(l - 14)$

Cross multiplication ( $\frac{a}{b} = \frac{c}{d} \Rightarrow ad = bc$ )

$24l - 280 = l^2 - 14l$

Simplify

$l^2 - 38l + 280 = 0$

Subtract $24l - 280$ from both sides of the equation

$(l - 10)(l - 28) = 0$

Factor left side of the equation

$l = 10, 28$

Zero Product Property

Now, notice that we have found two solutions, but the problem is only asking for one. This <em>likely </em>means that one of our solutions is extraneous. Let's take a look. Remember that the smaller positive number is equal to 14 less than the larger number. However,

$s = 10 - 14 = -4$ ,