The graph below represents the function f.f(x)
if g is a quadratic function with a positive leading coefficient and a vertex at (0,3), which statement is true?
А.
The function fintersects the x-axis at two points, and the function g never intersects the x-axis.
B
The function fintersects the x-axis at two points, and the function g intersects the x-axis at only one point.
c.
Both of the functions fand g intersect the x-axis at only one point.
D
Both of the functions fand g intersect the x-axis at exactly two points.
Answers
Answer: А.
The function f intersects the x-axis at two points, and the function g never intersects the x-axis.
Step-by-step explanation:
In the graph we can see f(x), first let's do some analysis of the graph.
First, f(x) is a quadratic equation: f(x) = a*x^2 + b*x + c.
The arms of the graph go up, so the leading coefficient of f(x) is positive.
The vertex of f(x) is near (-0.5, -2)
The roots are at x = -2 and x = 1. (intersects the x-axis at two points)
Now, we know that:
g(x) has a positive leading coefficient, and a vertex at (0, 3)
As the leading coefficient is positive, the arms go up, and the minimum value will be the value at the vertex, so the minimum value of g(x) is 3, when x = 0.
As the minimum value of y is 3, we can see that the graph never goes to the negative y-axis, so it never intersects the x-axis.
so:
f(x) intersects the x-axis at two points
g(x) does not intersect the x-axis.
The correct option is A.
Answer:
The answer is A.) The function f intersects the x-axis at two points, and the function g never intersects the x-axis.
Step-by-step explanation:
I took the test and got it right.
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A. 2Fe + 3CI2 - 2FeCI3 ........
Answers
The height and length of the box to the nearest tenth will be 10.6 inch and 7.4 inch respectively.
Explanation
Suppose, the height of the box is inch
As the length of the box is 3.2 in. less than the height, so the length will be:
Given that, the width of the box is 2.3 inch. and the volume is 180.4 inch³
Formula for Volume of a box:
So, the equation will be....
Now using quadratic formula......
(Negative value of is ignored as the height can't be negative)
So, the height to the nearest tenth will be 10.6 inch and the length will be:
Answers
b = 4√3
using Pythagoras' identity in the given triangle
c² = a² + b² ( substitute c = 2b and a = 12 into the equation )
(2b)² = 12² + b²
4b² = 144 + b² ( subtract b² from both sides )
4b² - b² = 144
3b² = 144 ( divide both sides by 3 )
b² = 48 ( take the square root of both sides )
b = √48 = √( 16 × 3 ) = √16 × √3 = 4√3 ' exact value '
Answers
Answer:
3.15
Step-by-step explanation:
15.75 divided by 5 gets you 3.15
Answers
Answer:
3.2 so they would each get around 3 slices!
Answer:
3.2
Step-by-step explanation:
so 3 slices for each
Which equation models the data in the table?
y = 6 sine (StartFraction pi Over 6 EndFraction x) + 2
y = 6 sine (StartFraction pi Over 6 EndFraction x) + 4
y = 4 sine (StartFraction pi Over 6 EndFraction x) + 6
y = 4 sine (StartFraction pi Over 6 EndFraction x) + 10
Answers
Modeling the data in the table is done via the equation y = 4 sine (pi/6x) + 6.
What is a cyclic pattern?
Over a period of years, a cyclical pattern recurs with considerable regularity. Cyclical patterns are distinct from seasonal patterns in that they last across a number of years as opposed to only one year for seasonal trends.
Given, The table shows the height of water in feet at different times. The water rises and falls in a cyclical pattern.
Table:
12 AM 6
3 AM 10
6 AM 6
9 AM 2
12 PM 6
from the general formula of wave
y = A sin(bx + c)
Substituting values in the equation from the graph attached below:
6 = A sin(0*b + c)......(1)
10 = A sin3b + c...(2)
6 = A sin6b + c......(3)
2 = A sin9b +c........(4)
Since -c/b is a phase shift of the graph
Thus
-c/b = 6
c = -6b
from equations 2 and 1
2* 6 = Asin(-3b) = -Asin3b
2 * 6 = Asin(-6b) = -Asin6b
2* 6/6 =sin6b/sin3b
1 = Cos3b
Thus b = π/6
from substitution in equations 3
6 = A sin6b + c
=> 6 = Asin 6* pi/6 + c
=> c = 6
from substitution in equations 2
10 = A sin3b + c
A = 4
therefore, The equation that models data in the table is y = 4 sine (pi/6x) + 6.
Learn more about cyclic patterns here:
#SPJ3
Answer:
c
Step-by-step explanation: