Step-by-step explanation:
Perpendicular slopes must be opposite reciprocals of each other: m1 * m2 = –1
4x+ y= 3
y= -4x + 3
slope = -4
the new slope = 1/4
the equation formula y= mx+b
m = new slope
y = (x/4) + b
From the point given (4,-3)
y = -3. x = 4
-3 = 1 + b
b = -4
the equation =
Answer: area is 286.16 ft²
Step-by-step explanation:
Length of the sand pit is 29.2 feet and the width is 9.8 feet.
L= 29.2 ft
W = 9.8 ft
To find out the area, all we have to do is multiply the lenght by the width:
And do not forget that to calculate the area, all units must be the same and for the area, it is always the unit squared, in this case, feet square or simply (ft²).
A = l*w
A = 29.2 * 9.8 = 286.16 ft²
The number of observations for each case in a t test for dependent samples is two is the correct answer.
In this question,
The dependent t-test also called the paired t-test or paired-samples t-test compares the means of two related groups to determine whether there is a statistically significant difference between these means. Each sample must be randomly selected from a normal population and each member of the first sample must be paired with a member of the second sample.
A dependent samples t-test uses two raw scores from each person to calculate difference scores and test for an average difference score that is equal to zero.
The groups contain either the same set of subjects or different subjects that the analysts have paired meaningfully. In dependent samples, subjects in one group do provide information about subjects in other groups.
Hence we c an conclude that the number of observations for each case in a t test for dependent samples is two is the correct answer.
Learn more about dependent t-test here
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Answer:
1) x = (a+c)/b
2) The equation is correct no matter what value x takes.
Step-by-step explanation:
1) a−(a+b)x=(b−a)x−(c+bx)
<=> a - ax - bx = bx - ax - c - bx
<=> a - ax - bx - (bx - ax - c - bx) = 0
<=> a - ax - bx - bx + ax + c + bx = 0
<=> a - ax + ax - bx - bx + bx + c = 0
<=> a - bx + c = 0
<=> bx = a + c
If b ≠ 0, x = (a+c)/b
2) 2(3x−5a)+9(2a−7b)+3(5a−2x)=0
<=> 2×3x + 2×(-5a) + 9×2a + 9× (-7b) + 3×5a + 3×(-2x) = 0
<=> 6x -10a + 18a - 63b + 15a - 6x = 0
<=> (6x - 6x) + (15a - 10a + 18a) - 63b = 0
<=> 23a - 63b = 0
<=> 23a = 63b
=> a = 63b/23
with all values of x, the equation is correct.
Marcus needs to bike at least 11 miles each day.
Step-by-step explanation:
Given,
Distance to cover = 80 miles at least
Distance already biked = 25 miles
Number of days left = 5
Let,
x be the distance to cover in 5 days.
According to given statement;
Number of days left * Distance to cover + distance already bike ≥ Total distance to travel
Dividing both sides by 5
Marcus needs to bike at least 11 miles each day.
Keywords: inequality, division
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