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OLEGan [10]
3 years ago
14

Solve the following absolute value equation. If needed, write your answer as a fraction reduced to lowest terms. Please explain

your answer |y−43|−|y−35| =0
Mathematics
1 answer:
Mashutka [201]3 years ago
8 0

Answer:

y = 39

Step-by-step explanation:

|y−43|−|y−35| =0

add |y−35| to each side

|y−43|= |y−35|

This tells us that y must be between 35 and 43

That means |y−35| is positive so we can remove the absolute value signs

|y−43|  is negative so we negate each term ( or multiply by -1)

-y+43 = y - 35

Add y to each side

y-y+43 = y+y-35

43 = 2y -35

Add 35 to each side

43+35 = 2y

78 = 2y

Divide by 2

78/2 = 2y/2

39 = y

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vladimir2022 [97]
Either one at any given time could be equal to zero. So
x + 2 = 0
x = - 2

x - 18 = 0
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I've enclosed a graph of this so you can see that the answers I've given are the ones expected.

6 0
3 years ago
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QUESTION 9
Ratling [72]
The first one is (v+6)(v-6)
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3 years ago
Consider the graph of the line y = x – 4 and the point (−4, 2).
Hitman42 [59]

Answer:

a. The slope  of a line parallel to the given line is 1

b. A point on the line parallel to the given line, passing through (−4, 2), is  (1,7)

c. The slope of the line perpendicular to the given line is -1

d. A point on the line perpendicular to the given line, passing through (−4, 2), is (3,-5)

Step-by-step explanation:

The equation of the line in Slope-intercept form  is:

y=mx+b

Where m is the slope and b is the y-intercept.

a. For the line y = x - 4

You can identify that:

m=1

 By definition, two lines are parallel if they have the same slope. Then, the  slope of a line parallel to the given line is:

m=1

b. The equation of the line in Point-slope form is:

y -y_1 = m(x - x_1)

Where m is the slope and (x_1,y_1)  is a point of the line.

Given the point (-4,2), substitute this point and the slope of the line into the equation:

 y -2 = (x +4)

Give a value to "x", substitute it into this equation and solve for "y":

For x=1 :

y -2 = (1 +4)

y= 5+2

y= 7

Then, you get the point (1,7)

c. The slopes of perpendicular lines are negative reciprocals, then the  slope of a line perpendicular to the given line is:

m=-\frac{1}{1}\\\\m=-1

d. Given the point (-4,2), substitute this point and the slope of the line into the equation:

 y -2 = -1(x +4)

 y -2 = -(x +4)

Give a value to "x", substitute it into this equation and solve for "y":

For x=3 :

y -2 = -(3 +4)

y= -7+2

y= -5

Then, you get the point (3,-5)

8 0
3 years ago
a bottle of cola has 39 grams of sugar. a bottle of diet cola contains no sugar. if you drink two bottles of regular cola and on
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The answer is the temperature goes down 2.8° every hour and the expression is x=-11.2/4 because 4 is how many hours between 6pm and 10pm and its -11.2 because that was how much the temperature dropped from 6pm to 10pm
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