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Law Incorporation [45]
3 years ago
5

Line l passes through the points (1, 3) and (2, 5), and

Mathematics
1 answer:
vfiekz [6]3 years ago
4 0

Answer:

-3

Step-by-step explanation:

I'm going to find both equations first.

Slope for line l can be found by doing

 (1  ,  3)

- (2 ,  5)

-------------

  -1      -2          so slope is -2/-1 or just 2

y=mx+b is a linear equation with slope m and y-intercept b

y=2x+b  now we need b

3=2(1)+b  plug in a point on the line

3=2+b

so b=1

The equation for line l is y=2x+1

The other equation line m has the slope given which is 1 so this equation will be of the form y=1x+b

to find this b (this y-intercept) use the point that you know is on the line

4=1(1)+b  

so b=3

so line m is y=1x+3 or y=x+3

So we want to find when y=2x+1 and y=x+3 intersect

Replace first y with the 2nd y which is x+3

x+3=2x+1

subtract x on both sides

  3= x+1

subract 1 on both sides

 2=x

 x=2

y=2x+1

y=2(2)+1

y=4+1

y=5

So the intersection is (2,5)

So a=2 and b=5

a-b =2-5=-3

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Let's say the point is C, so C partitions AB into two pieces, where AC is at a ratio of 3 and CB is at  a ratio of 7, thus 3:7,

\bf \left. \qquad  \right.\textit{internal division of a line segment}
\\\\\\
A(5,10)\qquad B(20,25)\qquad
\qquad 3:7
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{ C=\left(\cfrac{\textit{sum of "x" values}}{\textit{sum of ratios}}\quad ,\quad \cfrac{\textit{sum of "y" values}}{\textit{sum of ratios}}\right)}\\\
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3 years ago
Connor has a collection of dimes and quarters with a total value of $6.30. The number of dimes is 14 more than the number of qua
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Connor has 14 quarters and 28 dimes.

Step-by-step explanation:

Given,

Worth of coins = $6.30 = 6.30*100 = 630 cents

We know that,

1 quarter = 25 cents

1 dime = 10 cents

Let,

Quarter = x

Dime = y

According to given statement;

25x+10y=630    Eqn 1

The number of dimes is 14 more than the number of quarters

y = x+14    Eqn 2

Putting value of y from Eqn 2 in Eqn 1

25x+10(x+14)=630\\25x+10x+140=630\\35x=630-140\\35x=490

Dividing both sides by 35

\frac{35x}{35}=\frac{490}{35}\\x=14

Putting x=14 in Eqn 2

y=14+14\\y=28

Connor has 14 quarters and 28 dimes.

Keywords: linear equation, substitution method

Learn more about substitution method at:

  • brainly.com/question/4354581
  • brainly.com/question/4361464

#LearnwithBrainly

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