Answer:
D. g(x) = 3·x²
Step-by-step explanation:
The given parent function, f(x) = x²
The graph of the function, g(x) is narrower than the graph of the function f(x)
Therefore, the coefficient of the quadratic function is larger than 1
The given point on the parabola, g(x) = (1, 3)
Therefore. when x = 1, g(x) = 3
However, when x = 1, f(x) = 1
Therefore, given that g(x) = a·f(x), we get;
a = g(x)/(f(x)) = 3/1 = 3
g(x) = 3·x²
Answer: 9.
Step-by-step explanation:
8 5/6 is a mixed number with a whole number and a fraction. We want to round to the nearest whole number without the fraction.
First, we convert the mixed fraction to an improper fraction or fraction like this:
((8 x 6)+5)/6 = 53/6
Then, we divide the numerator by the denominator from the previous step:
53/6 = 8.83
Now we have one decimal number. Round using the following rules:
If the number to the right of the decimal point is .5 or higher, then add 1 to the left of the decimal point.
If the number to the right of the decimal point is less than .5, then leave the number to the left of the decimal point as is.
.83 is .5 or higher. Thus, we add 1 to the left of the decimal point. 8 5/6 rounded to the nearest whole number is therefore the answer will be 9.
Given:
A rope tied from a tent pole to a stake in the ground forms 55 degrees angle with the ground.
The pole is 3 feet from the stake.
To find:
The length of the rope to the nearest tenth of a foot.
Solution:
First draw a diagram according to the given information as shown below.
We know that, in a right angled triangle,
In triangle ABC,
Therefore, the length of the rope is 5.2 foot.
Answer:
The correct answer is A..
Step-by-step explanation:
From the Invertible Matrix Theorem (IMT) we have a set of equivalent conditions to determine if a square matrix is invertible or not. In particular, it says that a square matrix of dimension tex]n\times n[/tex] is invertible if and only if, its columns span the vector space tex]R^n[/tex].
In the particular case of this exercise we have a matrix of dimension tex]5\times 5[/tex]. So, by the Invertible Matrix Theorem its columns must span the vector space tex]R^5[/tex]. Now, according to the statement of the exercise this condition does not hold. Hence, the given matrix cannot be invertible.
