Answer:
Solution: x = -2; y = 3 or (-2, 3)
Step-by-step explanation:
<u>Equation 1:</u> y = -5x - 7
<u>Equation 2:</u> -4x - 3y = -1
Substitute the value of y in Equation 1 into the Equation 2:
-4x - 3(-5x - 7) = -1
-4x +15x + 21 = -1
Combine like terms:
11x + 21 = - 1
Subtract 21 from both sides:
11x + 21 - 21 = - 1 - 21
11x = -22
Divide both sides by 11 to solve for x:
11x/11 = -22/11
x = -2
Now that we have the value for x, substitute x = 2 into Equation 2 to solve for y:
-4x - 3y = -1
-4(-2) - 3y = -1
8 - 3y = -1
Subtract 8 from both sides:
8 - 8 - 3y = -1 - 8
-3y = -9
Divide both sides by -3 to solve for y:
-3y/-3 = -9/-3
y = 3
Therefore, the solution to the given systems of linear equations is:
x = -2; y = 3 or (-2, 3)
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Answer: Answer:Median: 10.5Lower quartile: 4Upper quartile: 16Explanation:Median:First, write the observations in ascending order or descending order.The formula to calculate the median is mean of (n/2) and (n/2+1)th observations, for even number of observationsn = 12 (even)Median = Mean of (6)th and (7)th observations = 10 + 11 divided by 2 = 21/2 = 10.5Therefore the median is 10.5.After writing in ascending or descending order the first and last terms justify the lower and upper limits respectively.They are:Lower quartile: 4Upper quartile: 16Question 2.the lengths of 10 pencils, in centimeters:18, 15, 4, 9, 14, 17, 16, 6, 8, 10Type below:_________________Answer:Median: 12Lower quartile: 4Upper quartile: 18Explanation:Median:First, write the observations in ascending order or descending order.The formula to calculate the median is mean of (n/2) and (n/2+1)th observations, for even number of observationsn = 10 (even)Median = Mean of (5)th and (6)th observations = 10 + 14 divided by 2 = 24/2 = 12Therefore the median is 12.After writing in ascending or descending order the first and last terms justify the lower and upper limits respectively.They are:Lower quartile: 4Upper quartile: 18Question 3.Make a box plot to display the data set in Exercise 2.Type below:_________________Answer:The above box plot represents the lower and upper quartiles, the median.Explanation:Box plot is drawn using the number line and the rectangle which is drawn above it.The ends of the rectangles say about the lower and upper limits and the middle line indicates the median.Question 4.The numbers of students on several teams are 9, 4, 5, 10, 11, 9, 8, and 6. Make a box plot for the data.Type below:_________________Answer: Explanation:Box plot is drawn using the number line and the rectangle which is drawn above it.The ends of the rectangles say about the lower and upper limits and the middle line indicates the median.Therefore the lower and upper quartiles are 4 and 11 respectively.Median:First, write the observations in ascending order or descending order.The formula to calculate the median is mean of (n/2) and (n/2+1)th observations, for even number of observationsn = 8 (even)Median = Mean of (4)th and (5)th observations = 8 + 9 divided by 2 = 17/2 = 8.5Therefore the median is 8.5.
Step-by-step explanation:
Answer:
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Step-by-step explanation:
Center of the door
26 1/3 divided by 2
change to an improper fraction
(3*26+1)/3 =79/3
79/3 divided by 2
copy dot flip
79/3 * 1/2
79/6
change to a mixed number
13 1/6
10 1/4 divided by 2
change to an improper fraction (4*10+1)/2 = 41/4
41/4 divided by 2
copy dot flip
41/4 * 1/2 =41/8
change to a mixed number
5 1/8
the left of the bar should be 5 1/8 from the center
to find how far from the left side to place the bar
13 1/6 - 5 1/8 =
get a common denominator
13 4/24 - 5 3/24= 8 1/24 inches
Answer: place the bar 8 1/24 inches from each edge
