Answer:
K = 43
Step-by-step explanation:
We'll begin by determining the gradient of the equation 5y + 4x = 8. This can be obtained as follow:
5y + 4x = 8
Rearrange
5y = 8 – 4x
5y = –4x + 8
Comparing 5y = –4x + 8 with y = mx + c, the gradient m is –4
Next, we shall determine the gradient of the line perpendicular to the line with equation 5y = 8 – 4x.
This can be obtained as follow:
For perpendicular lines, their gradient is given by:
m1 × m2 = – 1
With the above formula, we can obtain the gradient of the line as follow:
m1 × m2 = – 1
m1 = –4
–4 × m2 = – 1
Divide both side by –4
m2 = –1/–4
m2 = 1/4
Finally, we shall determine the value of k as follow:
Coordinate => (k, 4) and (3, –6)
x1 coordinate = k
y1 coordinate = 4
x2 coordinate = 3
y2 coordinate = –6
Gradient (m) = 1/4
m = (y2 – y1) / (x2 – x1)
1/4 = (–6 – 4) / (3 – K)
1/4 = –10 /(3 – K)
Cross multiply
3 – K = 4 × –10
3 – K = –40
Collect like terms
– K = – 40 –3
–k = –43
Divide both side by – 1
K = –43/–1
k = 43
The equation of line perpendicular to given line through (-6,7) is:
Further explanation:
Given equation of line is:
The co-efficient of x is the slope of given line.
Let m1 be the slope of given line
and
m2 be the slope of line perpendicular to given line
Then
Product of slopes of perpendicular lines is -1
The equation of new line can be written as:
Putting m2
To find the value of b, we will put (-6,7) in equation
Putting the values of b and m in general equation
Keywords: Slope, Point-slope form, perpendicular lines
Learn more about perpendicular lines at:
#LearnwithBrainly
Minimum required sample size for a desired margin of error and confidence level when it is a proportion problem: n = (z2÷margin of error2)*p-hat*q-hat
The maximum value of p-hat*q-hat occurs where p-hat = .5 (found by taking the derivative of (p-hat)*(1-p-hat) and setting it equal to 0 to find the maximum. n = ( 2.5762( for 99% confidence interval)÷.0482 )*.5*.5 = 720.028 or 721
Answer:
--3 ±sqrt((-3)^2 -4(4)(-9))
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2(4)
Step-by-step explanation:
4x^2-5=3x+4
We need to get this in standard form to answer the question
Subtract 3x from each side
4x^2-3x-5=3x-3x+4
4x^2-3x-5=+4
Subtract 4 from each side
4x^2-3x-9 =0
a = 4
b = -3
c = -9
-b ±sqrt(b^2 -4ac)
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2a
--3 ±sqrt((-3)^2 -4(4)(-9))
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2(4)
