Quadrilateral KLMN is a rectangle. The coordinates of L are L(1,-4) and the coordinates of M are M(3,-2) find the slopes of side
s KL,LM,MN,and NK
2 answers:
We can start by finding the gradient of LM
Two perpendicular lines will meet the requirement
×
=-1
Two parallel lines have equal gradients
NM is perpendicular to LM, hence the gradient of NM is -1
KN is a line that is parallel to NM, hence the gradient is 1
KL is perpendicular to LM, hence the gradient of KL is -1
Two perpendicular lines will meet the requirement
Two parallel lines have equal gradients
NM is perpendicular to LM, hence the gradient of NM is -1
KN is a line that is parallel to NM, hence the gradient is 1
KL is perpendicular to LM, hence the gradient of KL is -1
Answer:
The slope of LM is 1, slope of KL is -1, slope of MN is -1 and the slope of NK is 1.
Step-by-step explanation:
It is given that quadrilateral KLMN is a rectangle and the coordinates of L are L(1,-4) and the coordinates of M are M(3,-2).
If a line passing though two points, then the slope of the line is
The slope of LM is
The slope of LM is 1.
Two consecutive sides of a rectangle are perpendicular and the product of slopes of two perpendicular lines are -1.
The slope of KL is -1.
The opposite sides of a rectangle are parallel and the slope of parallel lines are same.
Therefore, the slope of MN is -1 and the slope of NK is 1.
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Answer:
z=-3.79
Step-by-step explanation:
1) Data given and notation
represent the mean average amount of money on deposit in savings account for the sample
represent the population standard deviation for the sample
sample size
represent the value that we want to test
represent the significance level for the hypothesis test.
z would represent the statistic (variable of interest)
represent the p value for the test (variable of interest)
2) State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the mean for the amount of money on deposit in savings account differs from 7500, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:
(1)
z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
3) Calculate the statistic
We can replace in formula (1) the info given like this:
4)P-value
Since is a two-sided test the p value would be:
5) Conclusion
If we compare the p value and the significance level given we see that
so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the average amount of money deposit in savings account its significantly different from 7500 tons at 1% of signficance.
Let's start with what we know:
Smaller canvas:
Length (
) = 3ft
Width (
) = 5ft
Larger canvas:
Length (
) = ?
Width (
) = 10ft
Since these are similar rectangles, we can cross-multiply to calculate the missing length. Here's that formula:
So let's plug it all in from above:
Now we cross multiply by multiplying the top-left by the bottom-right and vice versa:
Now divide each side by 5 to isolate
The 5s on the right cancel out, leaving us with:
So the length of the larger canvas is 6 ft
Smaller canvas:
Length (
Width (
Larger canvas:
Length (
Width (
Since these are similar rectangles, we can cross-multiply to calculate the missing length. Here's that formula:
So let's plug it all in from above:
Now we cross multiply by multiplying the top-left by the bottom-right and vice versa:
Now divide each side by 5 to isolate
The 5s on the right cancel out, leaving us with:
So the length of the larger canvas is 6 ft