The answer is (3,-4). On a graph you see it is right in the middle. Hope this helps.
The graph shows the plans for a fence that Macy is building around her vegetable garden. Each unit on the graph represents 5 fee
1 answer:
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The distance from point A(−9,−3) to the line y = x−6 is 8.5 units
<u>What is slope ?</u>
A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).
step 1
Find the slope of the perpendicular line to the given line
y=x-6 ---> given line
The slope is m=1
Remember that
If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)
m1*m2 = -1
we have
m1=1
substitute
(1)*m2 = -1
so
m2 = -1
step 2
Find the equation of the perpendicular line to the given line
The equation in point slope form is
y-y1=m(x-x1)
we have
m=-1
(x1,y1)=(−9,−3)
substitute
y+3=-1(x+9)--> equation in point slope form
y+3= -x-9
y= -x-12---> equation in slope intercept form
step 3
Find the intersection point between the given line and the perpendicular line to the given line
we have the system of equations
y = x−6.
y= -x-12
Solve the system by graphing
The intersection point is (-3,-9)
see the attached figure
step 4
we know that
The distance between the point A and the point (-3,-9) is the same that the distance between point A and the line y=x-6
the formula to calculate the distance between two points is equal to
d=√[(y2-y1)² + (x2-x1)²]
substitute the values
d=√[(-9+3)² + (-3+9)²]
d= √72 units
simplify
d= 6√2 = 8.5 units
To learn more about the slope from the given link
#SPJ1
Answer:
464 students will score between 48 and 75. Using the z-distribution, we measure how many standard deviations each score is from the mean, then find the p-value associated with each score to find the proportion, and from the proportion, we find how many out of 1000.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation
, the z-score of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
It assumes the scores are normally distributed with a mean score of 75 and a standard deviation of 15.
This means that
How many students will score between 48 and 75?
First we find the proportion, which is the pvalue of Z when X = 75 subtracted by the pvalue of Z when X = 48. So
X = 75
has a p-value of 0.5
X = 48
has a p-value of 0.0359
1 - 0.0359 = 0.4641
Out of 1000:
0.4641*1000 = 464
464 students will score between 48 and 75. Using the z-distribution, we measure how many standard deviations each score is from the mean, then find the p-value associated with each score to find the proportion, and from the proportion, we find how many out of 1000.