The cross section of the satellite dish is an illustration of a quadratic function
The quadratic function that models the cross-section is y = 1/6(x^2 - 9)
<h3>How to determie the equation of the cross-section?</h3>
The given parameters are:
Width = 6 feet
Depth = 1.5 feet
Express the width the sum of two equal numbers
Width = 3 + 3
The above means that, the equation of the cross section passes through the x-axis at:
x = -3 and 3
So, we have:
y = a(x - 3) * (x + 3)
Express as the difference of two squares
y = a(x^2 - 9)
The depth is 1.5.
This is represented as: (x,y) =(0,-1.5)
So, we have:
-1.5 = a(0^2 - 9)
Evaluate the exponent
-1.5 = -9a
Divide both sides by -9
a = 1/6
Substitute 1/6 for a in y = a(x^2 - 9)
y = 1/6(x^2 - 9)
Hence, the quadratic function that models the cross-section is y = 1/6(x^2 - 9)
Read more about quadratic functions at:
brainly.com/question/1497716
Answer:
see explanation
Step-by-step explanation:
(a)
Given
x² + 5x + 6
Consider the factors of the constant term ( + 6) which sum to give the coefficient of the x- term ( + 5)
The factors are 3 and 2, since
3 × 2 = 6 and 3 + 2 = 5, hence
x² + 5x + 6 = (x + 3)(x + 2) ← in factored form
(b)
To solve
x² + 5x + 6 = 0 ← use the factored form, that is
(x + 3)(x + 2) = 0
Equate each factor to zero and solve for x
x + 3 = 0 ⇒ x = - 3
x + 2 = 0 ⇒ x = - 2
Answer:
The probability that the pair consists of a female junior and a male sophomore is 0.096
Step-by-step explanation:
No of male juniors=4
No of female juniors=10-4=6
No of female sophomores=5
No of male sophomores=13-5=8
As per question,
Probability that the pair consists of a female junior and
a male sophomore =
=0.096
Therefore, the probability that the pair consists of a female junior and a male sophomore is 0.096
Answer:
C) 0.19
Step-by-step explanation:
A correlation coefficient is a measure of how well the line of best fit fits the data. The higher the correlation coefficient, up to 1.0 or -1.0, the better the fit. A positive correlation coefficient means an increasing data set, while a negative correlation coefficient means a decreasing data set.
We can see that this line of best fit is increasing, so our correlation coefficient will be positive.
However we can also see that the points are fairly scattered; this means this is not a very good fit. This means that 0.19 is the better fit.
Before we do any solving, we need to simplify both sides.
On the left, we can simplify -2x + 3x - 5 to x - 5.
On the right, we can simplify 6 - 21 to -16.
So we have x - 5 = -16.
Solving from here, we add 5 to both sides to get x = -11.
