So since the vertex falls onto the axis of symmetry, we can just solve for that to get the x-coordinate of both equations. The equation for the axis of symmetry is 
, with b = x coefficient and a = x^2 coefficient. Our equations can be solved as such:
y = 2x^2 − 4x + 12: 
y = 4x^2 + 8x + 3: 
In short, the vertex x-coordinate's of y = 2x^2 − 4x + 12 is 1 while the vertex's x-coordinate of y = 4x^2 + 8x + 3 is -1.
First, you must find the width of GHJK. Since the area of it is 84m², divide 84 by 7.
84÷7=12
So the width of GHJK is 12m.
Next, find the scale of GHJK to LMNP. Since the height of both are already available, you can divide 21÷7 to get 3
This means that to get the width of LMNP you must multiply the width of GHJK by 3.
12×3=36.
Now, to get the area of LMNP, multiply 21 by 36.
21×36=756
So, the area of LMNP is 756m². (Don't forget the units!>
The maximum possible area would have a length of 24 feet and width of 12 feet.
<h3>What is an
equation?</h3>
An equation is an expression that shows the relationship between two or more numbers and variables.
An independent variable is a variable that does not depend on other variables while a dependent variable is a variable that depends on other variables.
Let x represent the length and y represent the width, hence:
Since beth has 48 ft fencing and cover 3 sides, hence:
x + 2y = 48
x = 48 - 2y (1)
Also:
Area (A) = xy
A = (48 - 2y)y
A = 48y - 2y²
The maximum area is at A' = 0, hence:
A' = 48 - 4y
48 - 4y = 0
y = 12 feet
x = 48 - 2(12) = 24
The maximum possible area would have a length of 24 feet and width of 12 feet.
Find out more on equation at: brainly.com/question/2972832
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Answer:
one that fits
Step-by-step explanation:
#Bird+10 so #dog=2(#birds+10)
Answer:
Step-by-step explanation:
We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
µ = 17
For the alternative hypothesis,
µ < 17
This is a left tailed test.
Since the population standard deviation is not given, the distribution is a student's t.
Since n = 80,
Degrees of freedom, df = n - 1 = 80 - 1 = 79
t = (x - µ)/(s/√n)
Where
x = sample mean = 15.6
µ = population mean = 17
s = samples standard deviation = 4.5
t = (15.6 - 17)/(4.5/√80) = - 2.78
We would determine the p value using the t test calculator. It becomes
p = 0.0034
Since alpha, 0.05 > than the p value, 0.0043, then we would reject the null hypothesis.
The data supports the professor’s claim. The average number of hours per week spent studying for students at her college is less than 17 hours per week.
