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dybincka [34]
3 years ago
13

Compare the average score of a student at the beginning of a month and at the end of that month, if at first, it increased by 40

%, then decreased by 25%
Mathematics
2 answers:
-BARSIC- [3]3 years ago
6 0

Answer: 5%

Step-by-step explanation:

Leno4ka [110]3 years ago
4 0

Answer:

122.5

Step-by-step explanation:

Let the student normal score be 100

In the beginning score increased by 40%

Hence score at the beginning =100+40 = 140%

Now before end score decreased by 25%

Decrease = 25% of 140 = 35

Hence score at the end of month = 140-35 = 105

Average score for the month

= Total of scores of end and beginning month /2

= \frac{140+105}{2} \\=122.5

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Write an equation of the perpendicular bisector of the segment with the endpoints (8,10) and ( -4,2).
ale4655 [162]

Answer:

The required equation is:

y = -\frac{3}{2}x+9

Step-by-step explanation:

To find the equation of a line, the slope and y-intercept is required.

The slope can be found by finding the slope of given line segment. A the perpendicular bisector of a line is perpendicular to the given line, the product of their slopes will be -1 and it will pass through the mid-point of given line segment.

Given points are:

(x_1,y_1) = (8,10)\\(x_2,y_2) = (-4,2)

We will find the slope of given line segment first

m = \frac{y_2-y_1}{x_2-x_1}\\= \frac{2-10}{-4-8}\\=\frac{-8}{-12}\\=\frac{2}{3}

Let m_1 be the slope of perpendicular bisector then,

m.m_1 = -1\\\frac{2}{3}.m_1 = -1\\m_1 = \frac{-3}{2}

Now the mid-point

(x,y) = (\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2})\\= (\frac{8-4}{2} , \frac{10+2}{2})\\=(\frac{4}{2}, \frac{12}{2})\\=(2,6)

We have to find equation of a line with slope -3/2 passing through (2,6)

The equation of line in slope-intercept form is given by:

y = m_1x+b

Putting the value of slope

y= -\frac{3}{2}x+b

Putting the point (2,6) to find the y-intercept

6 = -\frac{3}{2}(2)+b\\6 = -3+b\\b = 6+3 =9

The equation is:

y = -\frac{3}{2}x+9

7 0
3 years ago
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