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3 years ago

Are the following equations parallel y=1/3x+6 and y=1/3x+12 ?

Mathematics

2 answers:

Mademuasel [1]3 years ago

5 0

Answer: yes

Step-by-step explanation:

They run side by side together

melamori03 [73]3 years ago

4 0

As a rule, parallel lines will always have the same slope.

However, they need to also have different y-intercepts.

Since these two lines have the same steepness or slope

and they have different y-intercepts, we say they are parallel.

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Which equation in point-slope form contains the points (6, 2) and (2, 4)?

ziro4ka [17]

Y-2 = m (x-6), where m = (2-4)/(6-2) = -2/4 = -1/2
y-2 = 1/2 (x-6)

5 0

3 years ago

Solve the equation cos (x/2) = cos x + 1. what are the solutions on the interval 0° ≤ x < 360°?

Sedbober [7]

Answer:

Step-by-step explanation:

cos (x/2)=cos x+1

cos (x/2)=2cos ²(x/2)

2 cos²(x/2)-cos (x/2)=0

cos (x/2)[2 cos (x/2)-1]=0

cos (x/2)=0=cos π/2,cos (3π/2)=cos (2nπ+π/2),cos(2nπ+3π/2)

x/2=2nπ+π/2,2nπ+3π/2

x=4nπ+π,4nπ+3π

n=0,1,2,...

x=π,3π

or x=180°,540°,...

180°∈[0,360]

so x=180°

2cos(x/2)-1=0

cos (x/2)=1/2=cos60,cos (360-60)=cos 60,cos 300=cos (360n+60),cos (360n+300)

x/2=360n+60,360n+300

x=720n+120,720n+300

n=0,1,2,...

x=120,300,840,1020,...

only 120° and 300° ∈[0,360°]

Hence x=120°,180°,300°

7 0

2 years ago

Please help!<br><br> For what value of x must ABCD be a parallelogram?<br><br> x=?

Vlad1618 [11]

Answer:

$x=3$

Step-by-step explanation:

For a shape to be a parallelogram, the angles that are across from one another have to be equal.

We can now find x by making both equations equal to each other and solving.

$11x+1=13x-5$

Solve.

$11x+1=13x-5\\6=2x\\x=3$

4 0

3 years ago

What are the vertical asymptotes of the function f(x) =5x+5/x2 + x-2

katen-ka-za [31]

let's recall that the vertical asymptotes for a rational expression occur when the denominator is at 0, so let's zero out this one and check.

$\bf \cfrac{5x+5}{x^2+x-2}\qquad \stackrel{\textit{zeroing out the denominator}~\hfill }{x^2+x-2=0\implies (x+2)(x-1)=0}\implies \stackrel{\textit{vertical asymptotes}}{ \begin{cases} x=-2\\ x=1 \end{cases}}$

5 0

3 years ago

You and your friend drive toward each other. The equation 50h=190−45h represents the number h of hours until you and your friend

Gala2k [10]

Answer:

The answer is 2 hours later.

Step-by-step explanation:

In order to find how many hours you and your friend meet, you have to solve the equation to find h :

$50h = 190 - 45h$

$50h + 45h = 190$

$95h = 190$

$h = 190 \div 95$

$h = 2$

5 0

3 years ago