Answer: Function g reflected function f across the x-axis.
For function g, as x approaches negative infinity, g(x) approaches negative infinity.
Function f is symmetrical about the point (4,6).
The correct options are Option A and Option C : Function g is reflected of function f across the x-axis. and as x approaches to the -∞, g approaches to the -∞.
Here given that the function g(x)= -(x-4)²+6
vertex of the graph of the function g is
dg/dx=0
⇒2(x-4)=0
⇒x-4=0
⇒x=4
putting x=4 in g(x) , g(4)= -(0-0)²+6=6
Hence the vertex of the graph of g is (4,6).
The parent function is f(x)= x²
here the vertex of the function is (0,0).
Option A: This option is true as the graph of function g is the inverse image of f. So, Function g is reflected of function f across the x-axis.
Option B: This option is incorrect. as the vertex of the function f is transformed to (4,6) which is the vertex of g(x).
Option C: This option is true because
[tex]\lim_{x \to- \infty} g(x)[/tex]
= [tex]\lim_{x \to- \infty} -(x-4)^2+6\\[/tex]
= -(∞-4)²+6
=-∞²+6
=-∞
Hence as x approaches to the -∞, g approaches to the -∞
Option D. This option is incorrect because
if the function is always decreasing its derivative is negative for all x∈R
dg/dx<0
⇒2(x-4)<0
⇒x-4<0
⇒x<4
so the function is decreasing for x<4 not for all x.
Option E: This option is incorrect. because g is not always rather it is positive for 4-√6 < x < 4+√6
g(x)>0
⇒-(x-4)²+6 >0
⇒-(x-4)²>-6
⇒(x-4)²<6
⇒|x-4|<√6
⇒4-√6<x<4+√6
so, g(x) is positive for 4-√6 < x < 4+√6
Option E:
This option is incorrect as g(x) is symmetrical about line x=4.
Therefore the correct options are Option A and Option C : Function g is reflected of function f across the x-axis. and as x approaches to the -∞, g approaches to the -∞.
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Archbridge Bus Company have a very small road on the exit of their bus garage. This means they need to be aware of when this road will be used by multiple buses. The 157 bus leaves every 33 minutes. The 183 bus leaves every 6 minutes. All buses start service at 9:00. Apart from when the buses leave at 9:00, at what time will both be leaving the garage at the same time?
Enter the equation of the line in slope-intercept form. Slope is 4, and (3,4) is on the line. The equation of the line is y=
Answer:
y= 4x - 8
Step-by-step explanation:
hope this helps :)
3/4 + (-2 1/2) on a number line.. select the location on the number line to plot the sum.. HURRYYYYY
Answer:
the answer is -1 3/4
Step-by-step explanation:
Find the coordinates of the midpoint of the segment with endpoints (-8,5) and (4, -3)
Answer:
[tex]MP= (-2,1 )[/tex]
Step-by-step explanation:
[tex]MP= (\frac{x_1+x_2}{2} )(\frac{y_1+y_2}{2} )\\MP= (\frac{-8+4}{2} )(\frac{5+-3}{2} )\\MP= (\frac{-4}{2} )(\frac{2}{2} )\\MP= (-2,1 )[/tex]
What is the answer to X(x+7)
Answer:
[tex] \boxed{ \bold{ \boxed {\huge{ \sf{ {x}^{2} + 7x}}}}}[/tex]
Step-by-step explanation:
[tex] \sf{x(x + 7)}[/tex]
Distribute x through the parentheses
[tex] \dashrightarrow{ \sf{x \times x + x \times 7}}[/tex]
[tex] \dashrightarrow{ \boxed{ \sf{ {x}^{2} + 7x}}}[/tex]
Hope I helped!
Best regards! :D
scientist measured water pressures of different depths she measured the table showing her findings the X values represents the deepest death matters the Y value represents the pressure in atmospheres
Answer:10,2
Step-by-step explanation:
Answer:
the answer you are looking for is A
Step-by-step explanation:
Determine whether the equation is always, sometimes, or never true. 6(x + 1) = 2(5 + 3x)
Answer:
never true
Step-by-step explanation:
6(x + 1) = 2(5 + 3x)
distribute
6x + 6 = 10 + 6x
combine like terms by subtracting 6x and 6 from both sides
0 = 4
that is not a true statement, so this equation is never true
inverse sin of 13/7?
Answer:
0.03213586
Step-by-step explanation:
what is the value of y?
Answer:
y +43⁰ +123⁰ =180⁰
=) y +160⁰ =180⁰
=) y = 20⁰
Answer:
Y = 34
Step-by-step explanation:
y + 43 + 123 = 180
y + 146 = 180
180 - 146. = y = 34
Y = 34
A scale factor of 3 was applied to this figure. What would be the new length of the height and width of the triangle?
Answer:
height: 9 units
width: 9 units
Step-by-step explanation:
Simplify the expression. 40 – 2 • 3²
i don't get it (solve)
If lines Joined each given point on the graph to the origin, which points would be on lines that represent a unit rate greater than the one represented in the table? х,у 5,11 10,22 15,33
Answer
I think first 3
Step-by-step explanation:
A slope is also known as the gradient of a line. The points that would be on lines that represent a unit rate greater than the one represented in the table are the first three points.
What is Slope?A slope also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.
slope = (y₂-y₁)/(x₂-x₁)
The slope of the function that the table represents is 2.2.
Also, the slope of the different points and the origin will be shown on the points that would be on lines that represent a unit rate greater than the one represented in the table are the first three points.
Hence, the points that would be on lines that represent a unit rate greater than the one represented in the table are the first three points.
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. an 8 degree rise in temperature
That's increased level of warming
How many solutions does the following equation have?
3z + 9 + 142 = 4z + 5
Choose 1 answer:
A.No solutions
B.Exactly one solution
C.Infinitely many solutions
Answer:
Step-by-step explanation:
3z + 9 + 142 = 4z + 5
3z + 151 = 4z + 5
-z + 151 = 5
-z = -146
z = 146
answer is B
exactly one solution
20 points!!!! please help fast!!!!
Answer:
0 m/s
Step-by-step explanation:
The line is flat so there is no movement
Answer:
b
Step-by-step explanation:
on this graph a horizantal line means no speed because there is no change in distance
A letter in the word ACCEL is chosen. What is the theoretical probability of choosing a C?
Answer:
there are 5 letters in all and 2 c's.. 2/5 2 out of every 5 times
is negative 31 an integer
Answer:
yes
Step-by-step explanation:
all numbers are integers
Find the length of side CB in the following right triangle
Round your answer to the nearest tenth.
Answer:
6cm
Step-by-step explanation:
a2 + b2 = c
(1.4)2 + (2)2 = c
1.96 + 4 = 5.96
=5.96cm (round it)
final answer = 6cm
Answer:
CB = 1.4 cm
Step-by-step explanation:
Given is a right angled triangle.
[tex] {x}^{2} + {1.4}^{2} = {2}^{2} \\ {x}^{2} + 1.96= 4 \\ {x}^{2} = 4 - 1.96 \\ {x}^{2} = 2.04 \\ x = \sqrt{2.04} \\ x = 1.42828569 \\ x \approx 1.4[/tex]
CB = 1.4 cm
I not sure how to find the value of the letters
Answer:
a = 31°
b = 66°
Step-by-step explanation:
Reason for the answer to a:
It is an alternate angle. So, a = 31°.
Reason for the answer to b:
It is also an alternate angle. So, b = 35° + 31° = 66°.
What is the answer to -4x = 12
Steps to solve:
-4x = 12
~Divide -4 to both sides
x = -3
Best of Luck!
Answer:
x=-3
Step-by-step explanation:
-x=12/4
-x=3
×=-3
yesterday jack drove 33 1/2 miles. He used 1 1/4 gallons of gasloine
!!50 POINTS!!
What are the measures of
Step-by-step explanation:
It A because Acute is smaller then Obtuse that what I look at
Answer:
It A
Step-by-step explanation:
Can I please get brainliest?
16.3 ÷ (−7.89)? It says im in highschool but im in middle school 7th grade!
Answer:
The answer is -2.066 rounded up from the thousandths
Step-by-step explanation:
It is a bit difficult to divide by such an exact value, but I hope this helps!
someone.. anyone ? and tell me if the answer is 7: 13 because I'm guessing it is either 7:13 or 7:20
Answer:
The ratio is 7:13
Step-by-step explanation:
Pls help I am so confused
Find the square root of 784 using prime factorization.
Answer:
first check the smallest number that divide 784
i.e 2
784/2 = 392/2= 196/2 =98/2 =49/7=7
we get
748= 2*2*2*2*7*7
for square root take one out of 2 same number
square root of 784= 2*2*7 = 28
Answer:
28
Step-by-step explanation:
784=2×2×2×2×7×7⇒784 =2×2×7=28
Which statement describes the inverse of m(x) = x2 – 17x?
Answer:
The correct option is;
[tex]The \ domain \ restriction \ x \geq \dfrac{17}{2} \ results \ in \ m^{-1}(x) = \dfrac{17}{2} \pm \sqrt{x + \dfrac{289}{4} }}[/tex]
Step-by-step explanation:
The given information is that m(x) = x² - 17·x
The above equation can be written in the form;
y = x² - 17·x
Therefore;
0 = x² - 17·x - y
From the general solution of a quadratic equation, 0 = a·x² + b·x + c we have;
[tex]x = \dfrac{-b\pm \sqrt{b^{2}-4\cdot a\cdot c}}{2\cdot a}[/tex]
By comparison to the equation,0 = x² - 17·x - y, we have;
a = 1, b = -17, and c = -y
Substituting the values of a, b and c into the formula for the general solution of a quadratic equation, we have;
[tex]x = \dfrac{-(-17)\pm \sqrt{(-17)^{2}-4\times (1) \times (-y)}}{2\times (1)} = \dfrac{17\pm \sqrt{289+4\cdot y}}{2}[/tex]
Which can be simplified as follows;
[tex]x = \dfrac{17\pm \sqrt{289+4\cdot y}}{2}= \dfrac{17}{2} \pm \dfrac{1}{2} \times \sqrt{289+4\cdot y}} = \dfrac{17}{2} \pm \sqrt{\dfrac{289}{4} +\dfrac{4\cdot y}{4} }}[/tex]
And further simplified as follows;
[tex]x = \dfrac{17}{2} \pm \sqrt{\dfrac{289}{4} +y }} = \dfrac{17}{2} \pm \sqrt{y + \dfrac{289}{4} }}[/tex]
Interchanging x and y in the function of the inverse, m⁻¹(x), we have;
[tex]m^{-1}(x) = \dfrac{17}{2} \pm \sqrt{x + \dfrac{289}{4} }}[/tex]
We note that the maximum or minimum point of the function, m(x) = x² - 17·x found by differentiating the function and equating the result to zero, gives;
m'(x) = 2·x - 17 = 0
x = 17/2
Similarly, the second derivative is taken to determine if the given point is a maximum or minimum point as follows;
m''(x) = 2 > 0, therefore, the point is a minimum point on the graph
Therefore, as x increases past the minimum point of 17/2, m⁻¹(x) increases to give;
[tex]The \ domain \ restriction \ x \geq \dfrac{17}{2} \ results \ in \ m^{-1}(x) = \dfrac{17}{2} \pm \sqrt{x + \dfrac{289}{4} }}[/tex] to increase m⁻¹(x) above the minimum.
Answer:
b
Step-by-step explanation:
edge 2021
Please help me to solve the question!
Answer: (x - 3)² + (y + 0.5)² = 3.25 → [tex](x-3)^2+\bigg(y+\dfrac{1}{2}\bigg)^2=\dfrac{13}{4}[/tex]
Step-by-step explanation:
Concentric means they have the same center but different radii.
The equation of a circle is: (x - h)² + (y - k)² = r² where
(h, k) is the center of the circler is the radius of the circleComplete the square to find the center of the circle
x² - 6x + _____ + y² + y + _____ = 1 + ____ + ____
↓ ↓
-6/2 = -3 1/2 = 1/2
Equation: (x - 3)² + (y + 1/2)² = r²
Since the circle passes through point (x, y) = (4, -2), input that into the equation to find r².
(x - 3)² + (y + 1/2)² = r²
(4 - 3)² + (-2 + 1/2)² = r²
(1)² + (-3/2)² = r²
1 + 9/4 = r²
13/4 = r²
Equation: (x - 3)² + (y + 1/2)² = 13/4 → [tex](x-3)^2+\bigg(y-\dfrac{1}{2}\bigg)^2=\dfrac{13}{4}[/tex]
In decimal form: (x - 3)² + (y + 0.5)² = 3.25
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