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UNO [17]
3 years ago
11

Help Me Please I would appreciate it!!!!

Mathematics
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.

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( 9 ) If the curve of the function f intersects the curve of the function f-1 at the point
mina [271]

Answer:

The correct answer is (b) 3.

4 0
3 years ago
A line, ray, segment, or plane that intersects a segment at its midpoint is called?
Hunter-Best [27]

A segment, ray, line, or plane that is perpendicular to a segment at its midpoint is called a perpendicular bisector. Converse of the Perpendicular. Bisector Theorem. If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.

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dmitriy555 [2]

Answer:

24


Step-by-step explanation:

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

A=kB

Where,

  • A & B are the 2 variables being compared
  • k is the constant of proportionality

Using cookies, y, and sugar, x, we can write:

y=kx

Substituting y=96 and x=4, and solving for k, we have:

96=k(4)\\\frac{96}{4}=k\\k=24

Thus, constant of proportionality is 24

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jasenka [17]

Answer: M=2n-2

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n=1

Step-by-step explanation:

5 0
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