How do you find the length of arc and area of sector
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We are given sides of the triangle by expression
First side : n
Second side : m = 5n-5.
Third side : l = 5/4 m - n.
Perimeter is 90.
Therefore, first equation could be set :
n +m +l = 90 --------------equation(1)
Second equation would be
m = 5n-5 --------------equation(2)
Third equation would be
l = 5/4 m - n --------------equation(3)
Let us solve the system of equations by substitution.
Substituting m = 5n-5 and l = 5/4 m - n in first equation.
We get
n +5n-5 +5/4 m - n= 90
Now, substituting m = 5n-5 in above equation we get
n +5n-5 +5/4 (5n-5) - n= 90
5n + 25n/4 -5 - 25/4 =90
5n + 6.25n -5-6.25 = 90.
11.25n-11.25 = 90
Adding 11.25 on both sides, we get
11.25n-11.25+11.25 = 90+11.25
11.25n = 101.25.
Dividing both sides by 11.25, we get
n=9.
Plugging n=9 in 2nd equation.
m = 5(9)-5 = 45 -5 = 40.
Plugging n=9 and m=40 in first equation, we get
9 +40 +l = 90
49 +l = 90.
Subtracting 49 from both sides, we get
49-49 +l = 90-49
l = 41.
Therefore, sides are of lengths l = 41, m= 40 and n=9.
a. The inequality 15x+300≤750 represents the situation.
b. It means that the band can spend at most $30 on each uniform without exceeding the budget.
Step-by-step explanation:
Given,
Budget = $750
Competition fee = $300
Uniforms to make = 15
Let,
x be the amount for each uniform.
a. Write an inequality to represent this situation.
Uniforms to make * Cost per uniform + Competition ≤ Budget
15x+300 ≤ 750
The inequality 15x+300≤750 represents the situation.
b. Solve the inequality and describe what it means in the situation.
Dividing both sides by 15
It means that the band can spend at most $30 on each uniform without exceeding the budget.
Keywords: inequality, division
Learn more about inequality at:
#LearnwithBrainly
Answer:
0.75
Step-by-step explanation:
The table is not well presented (See Attachment)
There are at least two approaches to this question
Method 1:
Steps
1. Calculate the mean of reported heights
Mean of reported heights = (61+68+57.5+48.5+75+65+80+68+69+63)/10
Mean of reported heights = 655/10
Mean of reported heights = 65.5
2. Calculate the mean of measured heights
Mean of measured heights = (62 + 68 + 56.5 + 47 + 72 + 65 + 78 + 67 + 69.5 + 62.5)/10
Mean of measured heights = 647.5/10
Mean of measured heights = 64.75
3. Get their difference
Difference = Mean of reported heights - Mean of measured heights
Difference = 65.5 - 64.75
Difference = 0,75
Method 2: Calculate the mean of their difference
Mean of difference = Sum of difference / Number of observations
Mean of difference = (-1 + 0 + 1 + 1.5 + 3 + 0 + 2 + 1 – 0.5 + 0.5)/10
Mean of difference = 7.5/10
Mean of difference = 0.75
Note that in both cases, the result is 0,75.
Hence, the reported heights at the school is 0.75 greater than the actual measured height
