Answer:
The triangle A B C will be the image of triangle of A B C in origin (0,0)
Simplifying
5x + 2(8x + -9) = 3(x + 4) + -5(2x + 7)
Reorder the terms:
5x + 2(-9 + 8x) = 3(x + 4) + -5(2x + 7)
5x + (-9 * 2 + 8x * 2) = 3(x + 4) + -5(2x + 7)
5x + (-18 + 16x) = 3(x + 4) + -5(2x + 7)
Reorder the terms:
-18 + 5x + 16x = 3(x + 4) + -5(2x + 7)
Combine like terms: 5x + 16x = 21x
-18 + 21x = 3(x + 4) + -5(2x + 7)
Reorder the terms:
-18 + 21x = 3(4 + x) + -5(2x + 7)
-18 + 21x = (4 * 3 + x * 3) + -5(2x + 7)
-18 + 21x = (12 + 3x) + -5(2x + 7)
Reorder the terms:
-18 + 21x = 12 + 3x + -5(7 + 2x)
-18 + 21x = 12 + 3x + (7 * -5 + 2x * -5)
-18 + 21x = 12 + 3x + (-35 + -10x)
Reorder the terms:
-18 + 21x = 12 + -35 + 3x + -10x
Combine like terms: 12 + -35 = -23
-18 + 21x = -23 + 3x + -10x
Combine like terms: 3x + -10x = -7x
-18 + 21x = -23 + -7x
Solving
-18 + 21x = -23 + -7x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '7x' to each side of the equation.
-18 + 21x + 7x = -23 + -7x + 7x
Combine like terms: 21x + 7x = 28x
-18 + 28x = -23 + -7x + 7x
Combine like terms: -7x + 7x = 0
-18 + 28x = -23 + 0
-18 + 28x = -23
Add '18' to each side of the equation.
-18 + 18 + 28x = -23 + 18
Combine like terms: -18 + 18 = 0
0 + 28x = -23 + 18
28x = -23 + 18
Combine like terms: -23 + 18 = -5
28x = -5
Divide each side by '28'.
x = -0.1785714286
Simplifying
x = -0.1785714286
The first figure below shows the graph for problem 5).
The second figure below shows the graph for problem 6).
Question
What is the diameter of 11.94 cm circumference
Answer:
Soln,
We know that diameter = * 2 radius
radius = 11.94/2= 5.97 half of diameter and when you multiply with 2 ,Then it comes 11.94cm
Now
Step-by-step explanation
Circumference = 2πr
11.94 = 2*22/7*r
11.94 = 6.28r
r= 11.94/6.28
therefore, r= 1.90 cm
Now
We know that diameter = * 2 radius
diameter = 1.90*2 = 3.80 cm
answer checking,
Circumference = 2πr
c= 2*22/7*1.90
therefore c = 11.94 cm
ans proved
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<h2><u>
Answer with explanation:</u></h2>
Let 
be the population mean strain in a way that conveys information about precision and reliability.
The sample mean is the best point estimate of the true population mean .
As per given , we have
Sample size : n= 12
degree of freedom : 
Sample mean : 
The true average strain in a way that conveys information about precision and reliability= 25.0
sample standard deviation : s= 3.3
Significance level : 
Since sample population standard deviation is unknown , so we use t-test.
Critical t-value for t : 
95% Confidence interval for true average strain in a way that conveys information about precision and reliability:
The 95% Confidence interval for true average strain in a way that conveys information about precision and reliability: 
We 95% confident that the true population average strain in a way that conveys information about precision and reliability lies between 22.9 and 27.1 .
