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MissTica
2 years ago
14

3. Consider the straight line x + y = 1 and the family of straight lines that pass

Mathematics
1 answer:
ANTONII [103]2 years ago
5 0

Answer:

  • solution: (1/(1+m), m/(1+m))
  • no solution for m = -1 (lines are parallel)

Step-by-step explanation:

Two distinct lines will always have a point of intersection, provided they are not parallel. That is, the system of equations {x +y = 1, y = mx} will have a unique solution as long as m ≠ -1.

The solution to the system can be found by substitution:

  x +mx = 1

  x(1 +m) = 1 . . . . factor out x

  x = 1/(1+m) . . . . . divide by the coefficient of x; we must have m ≠ -1

  y = m/(1+m) . . . . find the y-coordinate of the solution

The point of intersection is (1/(1+m), m/(1+m)).

__

The above solution is undefined when the denominator is zero: m = -1. There is no solution for m = -1.

You might be interested in
Convert the ratio 56: 80 to a percentage
zysi [14]
Change the ratio into a fraction

56:80  is the same as 56/80

Divide, make it a decimal

56/80 = 0.7

0.7 = 7/10 or 70/100

70/100 = 70%

70% is your answer

hope this helps
8 0
3 years ago
kevin sells beaded necklaces. Each large necklace sells for $5.70 and each small necklace sells for $4.60. How much will she ear
KIM [24]

Answer:

$56.10

Step-by-step explanation:

The first step is to multiply the values.

28.50 for large.

27.60 for small.

Add them together.

You get 56.10.

8 0
2 years ago
Read 2 more answers
If the sin P = √2/2, what is the value of cos P
ArbitrLikvidat [17]

Answer:

√2/2

Step-by-step explanation:

If sinP = √2/2,

Rationalize;

√2/2

= √2/2,*√2/√2

√4/2√2

= 2/2√2

= 1/√2

Hence sinP = 1/√2

Take sin inverse of both sies

arcsinP = arcsin1/√2

P = 45 degrees

cos P =  Cos 45

= 1/√2

= 1/√2 * √2/√2

= √2/2

Hence the value of cosP is √2/2

5 0
3 years ago
An airplane travels 640 miles from Topeka to Houston in 3.2 hours, going against the wind. The return trip is with the wind, and
Mandarinka [93]

The  airplane flies at 260 mi/h with no wind, while the rate of the wind is 60 mi/h.

<h3>What is an equation?</h3>

An equation is an expression that shows the relationship between two or more numbers and variables.

Let a represent the rate of the airplane with no wind. and b the rate of the wind, hence:

(a - b)3.2 = 640

a - b = 200   (1)

Also:

(a + b)2 = 640

a + b = 320    (2)

The solution to equation 1 and 2 is:

a = 260, b = 60

The  airplane flies at 260 mi/h with no wind, while the rate of the wind is 60 mi/h.

Find out more on equation at: brainly.com/question/2972832

#SPJ1

4 0
2 years ago
What is the equation of a line, in general form, that passes though points (-1,2) and (5,2)?
Tom [10]

Answer:

A

Step-by-step explanation:

To write the equation of the line. first calculate the slope using the slope formula.

m = \frac{y_2-y_1}{x_2-x_1} = \frac{2-2}{5--1}= \frac{0}{6} = 0

Since the slope of this line is 0, it is horizontal and has the form y=b where b is the y-coordinate. So y = 2 is the equation. In general form, it would be y-2 = 0

3 0
3 years ago
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