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3 years ago

11

Help Me Please I would appreciate it!!!!

1 answer:

valentina_108 [34]3 years ago

7 0

9514 1404 393

Answer:

y +2 = (1/4)(x +1)

Step-by-step explanation:

The given line is in slope-intercept form:

y = mx + b

where the slope (m) is -4 and the y-intercept (b) is +13.

For the perpendicular line, we need a slope that is the opposite reciprocal, or ...

-1/m = -1/(-4) = 1/4

A suitable form for the desired equation is the point-slope form:

y -k = m(x -h) . . . . . . line with slope m through point (h, k)

For m=1/4 and (h, k) = (-1, -2), the equation of the line is ...

y +2 = (1/4)(x +1)

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The sum of the squares of two numbers is 8 . The product of the two numbers is 4 . Find the numbers.

fenix001 [56]

Hello there.

First, assume the numbers $x,~y$ such that they satisties both affirmations:

The sum of the squares of two numbers is $8$ .
The product of the two numbers is $4$ .

With these informations, we can set the following equations:

$\begin{center}\align x^2+y^2=8\\ x\cdot y=4\\\end{center}$

Multiply both sides of the second equation by a factor of $2$ :

$2\cdot x\cdot y = 2\cdot 4\\\\\\ 2xy=8~~~~~(2)^{\ast}$

Make $(1)-(2)^{\ast}$

$x^2+y^2-2xy=8-8\\\\\\ x^2-2xy+y^2=0$

We can rewrite the expression on the left hand side using the binomial expansion in reverse: $(a-b)^2=a^2-2ab+b^2$ , such that:

$(x-y)^2=0$

The square of a number is equal to $0$ if and only if such number is equal to $0$ , thus:

$x-y=0\\\\\\ x=y~~~~~~(3)$

Substituting that information from $(3)$ in $(2)$ , we get:

$x\cdot x = 4\\\\\\ x^2=4$

Calculate the square root on both sides of the equation:

$\sqrt{x^2}=\sqrt{4}\\\\\\ |x|=2\\\\\\ x=\pm~2$

Once again with the information in $(3)$ , we have that:

$y=\pm~2$

The set of solutions of that satisfies both affirmations is:

$S=\{(x,~y)\in\mathbb{R}^2~|~(x,~y)=(-2,\,-2),~(2,~2)\}$

This is the set we were looking for.

7 0

3 years ago

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Answer:

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A line, ray, segment, or plane that intersects a segment at its midpoint is called?

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3 years ago

What is the constant of proportionality that relates the number of cookies made, y, to the number of cups of sugar used, x ? A r

dmitriy555 [2]

Answer:

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Step-by-step explanation:

Direct variation (with constant of proportionality) has the form:

$A=kB$

Where,

A & B are the 2 variables being compared
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Using cookies, $y$ , and sugar, $x$ , we can write:

$y=kx$

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3 years ago

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Step-by-step explanation:

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4 years ago