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AlekseyPX
3 years ago
7

Find the value of x for which r || S. A) 44 B) 10 C) Can't be determined. D) 14

Mathematics
2 answers:
nlexa [21]3 years ago
5 0
The answer is A because 10 and 14 don’t fit the question at all.
Elodia [21]3 years ago
4 0

Answer:

x=44

Step-by-step explanation:

For the two lines to be parallel, the two angles have to add to 180 degrees

45+3x+3 =180

Combine like terms

3x+48 = 180

Subtract 48 from each side

3x+48-48=180-48

3x=132

Divide each side by 3

3x/3 = 132/3

x =44

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<img src="https://tex.z-dn.net/?f=0.2%2810-5c%29%20%3D%205c%20-%2016" id="TexFormula1" title="0.2(10-5c) = 5c - 16" alt="0.2(10-
san4es73 [151]

We are given,

\longrightarrow 0.2(10 - 5c) = 5c - 16

Solving the parenthesis

{ \longrightarrow 0.2 \times 10 - 0.2 \times 5c = 5c - 16 }

{ \longrightarrow 2 - 1c = 5c - 16 }

{ \longrightarrow 2  + 16 = 5c + 1c }

{ \longrightarrow  18  = 6c }

Dividing both sides by 6

{ \longrightarrow  3 = c }

Hence c = 3.

8 0
3 years ago
Find the point on the parabola y^2 = 4x that is closest to the point (2, 8).
guapka [62]

Answer:

(4, 4)

Step-by-step explanation:

There are a couple of ways to go at this:

  1. Write an expression for the distance from a point on the parabola to the given point, then differentiate that and set the derivative to zero.
  2. Find the equation of a normal line to the parabola that goes through the given point.

1. The distance formula tells us for some point (x, y) on the parabola, the distance d satisfies ...

... d² = (x -2)² +(y -8)² . . . . . . . the y in this equation is a function of x

Differentiating with respect to x and setting dd/dx=0, we have ...

... 2d(dd/dx) = 0 = 2(x -2) +2(y -8)(dy/dx)

We can factor 2 from this to get

... 0 = x -2 +(y -8)(dy/dx)

Differentiating the parabola's equation, we find ...

... 2y(dy/dx) = 4

... dy/dx = 2/y

Substituting for x (=y²/4) and dy/dx into our derivative equation above, we get

... 0 = y²/4 -2 +(y -8)(2/y) = y²/4 -16/y

... 64 = y³ . . . . . . multiply by 4y, add 64

... 4 = y . . . . . . . . cube root

... y²/4 = 16/4 = x = 4

_____

2. The derivative above tells us the slope at point (x, y) on the parabola is ...

... dy/dx = 2/y

Then the slope of the normal line at that point is ...

... -1/(dy/dx) = -y/2

The normal line through the point (2, 8) will have equation (in point-slope form) ...

... y - 8 = (-y/2)(x -2)

Substituting for x using the equation of the parabola, we get

... y - 8 = (-y/2)(y²/4 -2)

Multiplying by 8 gives ...

... 8y -64 = -y³ +8y

... y³ = 64 . . . . subtract 8y, multiply by -1

... y = 4 . . . . . . cube root

... x = y²/4 = 4

The point on the parabola that is closest to the point (2, 8) is (4, 4).

4 0
3 years ago
What is the answer of: (10+2b)^2
scZoUnD [109]

Answer:

10^2+2×2b×10+2b^2 = 100+40b+2b^2

5 0
2 years ago
The expanded form of x0 is what
Anestetic [448]

Answer:

Can't really expand x and 0, so I guess it would just be x * 0

Step-by-step explanation:

explained above :)

4 0
3 years ago
Christopher has a stick that he has marked out in tenths. He has to break the stick into three pieces of which no two pieces can
ss7ja [257]

Answer:

SCREEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE

Step-by-step explanation:

REEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE

4 0
2 years ago
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