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Vikentia [17]
3 years ago
11

If a line through the origin has a slope of 2, what is the slope of the line through the origin that is perpendicular to

Mathematics
1 answer:
Dmitriy789 [7]3 years ago
6 0

Answer:

-\frac{1}{2}

Step-by-step explanation:

We have the slope value of the first line, we will call this m_{1}

so  m_{1}=2

And we use the <u>condition </u>so that two lines are perpendicular: the product of the two slopes must be equal to -1.

That is, if the slope of the first line is m_{1} and the slope of the second line is m_{2}:

m_{1*}m_{2}=-1

we know that m_{1}=2, so:

2m_{2}=-1

and clearing for m_{2}:

m_{2}=-\frac{1}{2}

the slope of the line perpendicular to the line with a slope of 2 is: -\frac{1}{2}

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7 0
2 years ago
Dina wants to make 15 3/4 cups of strawberry drink by mixing water and strawberry syrup with a ratio of 2 1/4 cup of water for e
bekas [8.4K]

Answer:

The water she need is 7\frac{7}{8} \ cups. and strawberry syrup 11\frac{13}{16}\ cups.

Step-by-step explanation:

Given:

Dina wants to make 15 3/4 cups of strawberry drink by mixing water and strawberry syrup with a ratio of 2 1/4 cup of water for every 3/4 cup of syrup.

Now, to find the quantity of water and syrup she need to use.

As given in question ratio so:

Strawberry syrup = 2 1/4 = 9/4.

Water = 3/4.

Total cups of strawberry drink = 15 3/4 = 63/4.

Let the strawberry syrup be \frac{9}{4} x.

And let the water be \frac{3}{4} x.

According to question:

\frac{9x}{4} + \frac{3x}{4}=\frac{63}{4}.

<em>On adding the fractions:</em>

⇒\frac{9x+3x}{4} =\frac{63}{4}

⇒\frac{12x}{4} =\frac{63}{4}

<em>Multiplying both sides by 4 we get:</em>

⇒12x=63

<em>Dividing both sides by 12 we get:</em>

⇒x=\frac{63}{12}

<em>Dividing numerator and denominator by 3 on R.H.S we get:</em>

⇒x=\frac{21}{4}

Now, putting the value of x on ratios:

Strawberry syrup =  \frac{9}{4}\times x=\frac{9}{4}\times\frac{21}{4}

                             =  \frac{189}{16}

                             =  11\frac{13}{16}\ cups  

Water = \frac{3}{4}\times x =\frac{3}{4} \times\frac{21}{4}

          = \frac{63}{8}

          = 7\frac{7}{8} \ cups.

Therefore, the water she need is 7\frac{7}{8} \ cups. and strawberry syrup 11\frac{13}{16}\ cups.

4 0
3 years ago
-5x-(-7-4x)=-2(3x-4) true?
qwelly [4]

Answer:

x=1/5

Step-by-step explanation:

-5x-(-7-4x)=-2(3x-4)

-5x+7+4x=-6x+8

-5x+4x+7=-6x+8

-x+7=-6x+8

-x-(-6x)+7=8

-x+6x+7=8

5x+7=8

5x=8-7

5x=1

x=1/5

8 0
2 years ago
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