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1 year ago

What is the value of b that makes the lines, given by 3x-y=4 and 2y+4bx=1, perpendicular?

Mathematics

1 answer:

USPshnik [31]1 year ago

6 0

b = 1/6

Explanation:

3x-y=4 ...1st equation

Rewriting in slope- intercept form:

y = 3x - 4

2y+4bx=1

Rewriting in slope- intercept form:

2y = -4bx + 1

y = -4bx/2 + 1/2

Equation of line: y = mx + c

where m = slope, c = intercept

For a line to be perpendicular to another, the slope of one will be the negative reciprocal of the slope of another.

Slope of the 1st equation = 3

m = 3

reciprocal of 3 = 1/3

negative reciprocal of 3 = -1/3

Slope of the 2nd equation = -4b/2

we equate both slope:

negative reciprocal of 3 = -4b/2

-1/3 = -4b/2

cross multiply:

-1(2) = 3(-4b)

-2 = -12b

Divide both sides by -12:

-2/-12 = -12b/-12

b = 1/6

Hence, the value of b that makes the lines perpendicular is 1/6

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kakasveta [241]

5. The constant of proportionality is 1.5

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Please find attached the required graph

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The procedure for finding the answers are as follows;

5. The given data are presented as follows;

$\begin{array}{ccc}Shirts \ (s)&&Profit \ (p)\\5&&7.50\\10&&15.00\\15&&22.50\end{array}$

Where two variables, s and p are proportional, we get;

p ∝ s

Therefore;

p = C × s

C = p/s

Where;

C = The constant of proportionality

Therefore, the constant of proportionality, C, of the given variables, (number of shirts, s, and profit, p, is found as follows;

C = 7.50/5 = 15.00/10 = 22.50/15 = 1.5

The constant of proportionality, C = 1.5

The equation that relates the two values is p = 1.5×s

6. For the apples to price relationship, we have;

$\begin{array}{ccc}Apples \ (a)&&Price\ (p)\\4&&7.96\\5&&9.95\\6&&11.94\end{array}$

Therefore;

p ∝ a

p = C × a

C = p/a

Plugging in the values gives;

C = 7.96/4 = 9.95/5 = 11.94/6 = 1.99

The constant of proportionality, C = 1.99

Therefore, the equation relating the two values is p = 1.99 × a

7. The given data is presented in a tabular form as follows;

$\begin{array}{ccc}Number \ of \ pens &&Cost\ \\1&&52\\2&&54\\3&&56\\4&&58\end{array}$

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From the graph of the data, created with MS Excel, the y-intercept is 50 which is not equal to zero, therefore, the relationship between the data is not a proportional relationship

8. The given data is presented in a tabular form as follows;

$\begin{array}{ccc}Number \ of \ Minutes&&Words \ Typed\ \\1&&50\\2&&90\\3&&140\\4&&180\end{array}$

From the graph of the data, we have that the y-intercept of the line of best fir is 5, therefore, the relationship is not a proportional relationship

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5 0

3 years ago

write an equation to represent"three consecutive integers is 12 less than 4 times the middle integer'

Sever21 [200]

Consider that the three consecutive integers are:

least integer = n

middle integer = n + 1

greatest integer = n + 2

THe expression "three consecutive integers is 12 less than 4 times the middle integer" can be written as follow:

n + (n + 1) + (n + 2) = 4(n +1) - 12

In order to find the numbers, proceed as follow:

n + (n + 1) + (n + 2) = 4(n +1) - 12 cancel parenthesis

n + n + 1 + n + 2 = 4n + 4 - 12 simplify like terms

3n + 3 = 4n - 8 subtract 4n and 3 both sides

3n - 4n = - 8 - 3

-n = -11

n = 11

Hence, the three consecutive integers are:

n = 11

n + 1 = 12

n + 2 = 13

5 0

1 year ago

Please help the image is below!

Arte-miy333 [17]

Answer:

18.84

Step-by-step explanation:

Diameter = 12

Circumference of a circle = πD

= 3.14* 12

=37.68

Since its a semicircle, (that's half of a circle), divide the result by 2

= 37.68/2

= 18.84

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galben [10]

Answer:

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Step-by-step explanation:

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3 years ago