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 -∞.
Learn more about quadratic function
here: https://brainly.com/question/9643976
#SPJ10
What is the answer when you Simplify 6(x + 4).
Answer:
6x + 24
Step-by-step explanation:
Distributive property: a (b + c) = ab + ac.
6 (x + 4) = 6x + 6(4) = 6x + 24.
plz help will mark brainliest
What will be the coordinates of the upper-right vertex of
the next largest (fourth) square in the pattern?
(5,5)
(7,7)
(8,8)
(16, 16)
Answer:8,8
Step-by-step explanation:
Took the test on edge
Answer:
C. (8, 8)
Step-by-step explanation:
Edge 2022. ^
Mickey is looking for his ties and finds out he have 20 shirts for every 4 ties if he has 30 shirts how many ties does he have
Answer:
Step-by-step explanation:
6 ties
Half of 20 is 10, and half of 4 is 2
Therefore, 4+2=6
Answer:
6 ties
Step-by-step explanation:
Please help urgent easy question,just no 8
Answer:
Ruby is 11. Tanya is 14.
Step-by-step explanation:
Let Ruby's age eight years ago be x.
Tanya's age eight years ago = 2x.
Ruby's age now = x + 8
Tanya's age now = 2x + 8
Total age = [tex]x+8+2x+8=25[/tex]
[tex]3x+16=25[/tex]
Subtract 16 from both sides:
[tex]3x+16-16=25-16[/tex]
[tex]3x=9[/tex]
Divide both sides by 3:
[tex]\frac{3x}{3} =\frac{9}{3}[/tex]
[tex]x=3[/tex]
Ruby's age now [tex]=x+8=3+8=11[/tex]
Tanya's age now [tex]=2x+8=2(3)+8=6+8=14[/tex]
Answer:
Tanya is 14; Ruby is 11.
Step-by-step explanation:
Let T represent Tanya's current age and let R represent Ruby's current age.
We know that their ages add up to 25. So:
[tex]T+R=25[/tex]
8 years ago, Tanya was twice as old as Ruby. In other words, Tanya's current age minus 8 is the same as Ruby's current age minus 8 times 2. So:
[tex]T-8=2(R-8)[/tex]
We have a system of equations. We can solve by substitution. From the first equation, subtract R from both sides:
[tex]T=25-R[/tex]
Substitute this into the second equation:
[tex](25-R)-8=2(R-8)[/tex]
On the left, subtract. On the right, distribute:
[tex]17-R=2R-16[/tex]
Add 16 to both sides. The right side cancels:
[tex]33-R=2R[/tex]
Add R to both sides. The left cancels:
[tex]33=3R[/tex]
Divide both sides by 3:
[tex]R=11[/tex]
So, Ruby is currently 11 years old.
So, Tanya is currently 25-11 or 14 years old.
Check:
8 years ago, Ruby was 11-8 or 3 years old.
8 years ago, Tanya is 14-8 or 6 years old.
Tanya's age of 6 is 2 times Ruby's age of 3 so our answer is correct.
The area of a square poster 26 inch. 2. Find the length of one side of the poster to the nearest tenth of an inch.
Answer:
6.5 inches
Step-by-step explanation:
Divide 26 by 4
26/4=6.5
The length of one side of the poster to the nearest tenth of an inch is 5.1 inches.
What is the area of a square?The area of a square can be calculated as the square of the sides of a given figure.
The area of a square = side x side
Given; The area of a square poster 26 inch
We need to find the length of one side of the poster to the nearest tenth of an inch.
The area of a square would be S^2
26 = S^2
s = sqrt(26) = 5.099
Then rounded to nearest tenth = 5.1 inches
Hence, the length of one side of the poster to the nearest tenth of an inch is 5.1 inches.
Learn more about the area here;
https://brainly.com/question/1658516
#SPJ2
Evaluate -R -Y for R=-2 and Y:-7
5
Step-by-step explanation:
-2 - (-7)
you have to do the opposite of the sign and switch the last number from negative to positive.
A passenger car weighs 4.5x10 units. Which unit of measure was used? grams ounces O pounds 0 tons
Answer:
C, pounds
Step-by-step explanation:
grams and ounces are automatically out because they just don't make sense, and a car can't weigh 4500 tons, it would be too heavy to drive.
hope this helps!!!
These are pretty easy but can someone answer them for me so that i could go to sleep
Hey There!! (❁´◡`❁)
The answer to this is: Map Key. Because, Large scale maps are typically used to show site plans, local areas, neighborhoods, towns etc. ... A 'small' scale map is one in which a given part of the Earth is represented by a small area on the map. Small scale maps generally show less detail than large scale maps, but cover large parts of the Earth. The answer to this is: North. Like the wind rose, the compass rose was coincidentally designed in a fashion that resembled the rose flower. It helped to orient a map in the proper reading direction and gave the relative directions for certain points on the chart. Before compass roses were used on maps, lines were drawn from central points. The answer to this is: Map. Because, a Map help you to find places where you need to go. The answer to this is: Map Key. Because, A map usually has a legend, or key, that gives the scale of the map and explains what the various symbols represent. Some maps show relief, or changes in[tex]UsedLess[/tex] elevation. A common way to show relief is contour lines, also called topographic lines. The answer to this is: Blue. Because Blue Water is mostly associated with the color blue. Uncolored versions of these symbols can be found in Earth, Air, Fire and Water Symbols. The answer to this is: Help you find directions: Because, A compass rose, sometimes called a windrose or rose of the winds, is a figure on a compass, map, nautical chart, or monument used to display the orientation of the cardinal directions (north, east, south, and west) and their intermediate points. The answer to this is: A system of vertical and horizontal lines. A grid system on a map is usually square and is represented by drawn lines on the map creating those squares. The purpose of the grid system is to give each point in the map an identifier, an address, by which we can refer to it by. The answer to this is: Map key Title, date, author, and sources usually appear on the map though not always together. The map's title tells what the map is about, revealing the map's purpose and content. For example, a map might be titled “Political Map of the World” or “Battle of Gettysburg, 1863.”Hope It Helped!~
Sorry, this take me too long to type...
Good Luck With Your Assignment!~
And, Tell me if some the answer are wrong...
[tex]UsedLess[/tex]~ (●ˇ∀ˇ●) 5(-2n+6) = 70
Please Help me! This Is algebra
Answer:
the answe is -4
Step-by-step explanation:
first you distribute the five to the numbers in the paranthesis
5(-2n+6)
-10n+30=70.
than we subtract 30 from the 30 and 70
-10n=40
Next we divide by 10 to 40 and -10n
n=-4
the reason it negative is because if you divide a negative and a positive it always make a negative.
Which fraction is equal to the decimal 0.125?
I need help now!!!!!!!
Answer:
125/1000
Step-by-step explanation:
The temperature falls 15º and then rises 18°
Answer:
3 degrees
Step-by-step explanation:
Answer:
3 more then the original number
Step-by-step explanation:
Claudia studied for 45 minutes. Crystal studied for 5 minutes. The number of minutes that Claudia studied is how many times the number of minutes that Crystal studied?
Answer:
school sucks man but you gotta do it or else you get reported to the RUSSIANS for not doing your hw so here you goo...
9
9x5=45
Work out the height of a triangle with base,
base = 6.3mm and area,
Area = 35.595mm squared.
Step-by-step explanation:
formula used is height= area×3/base
35.595×2/6.3
71.19/6.3
11.3mm2 is the answer
Answer:
[tex] \huge{ \fbox{ \sf{11.3 \: mm}}}[/tex]
Step-by-step explanation:
[tex] \underline{ \sf Given} : [/tex]
[tex] \star{ \sf{ \: Base \: of \: a \: triangle \: (b) \: = 6.3 \: mm}}[/tex]
[tex] \star{ \sf{ \: Area \: of \: a \: triangle \: (a) = 35.595 \: {mm}^{2} }}[/tex]
[tex] \star{ \sf{ \: Let \: height \: of \: a \: triangle \: be \: h}}[/tex]
[tex] \underline{ \underline{ \sf{ \: Finding \: the \: height \: of \: a \: triangle}}} : [/tex]
[tex] \boxed{ \sf{Area \: of \: a \: triangle = \frac{1}{2} * base \: * \: height}}[/tex]
[tex]\sf{Plug \: the \: values}[/tex]
[tex] \mapsto{ \sf{35.595 = \frac{1}{2} * 6.3 * h}}[/tex]
[tex] \mapsto{ \sf{35.595 = \frac{6.3h}{2} }}[/tex]
[tex] \sf{Apply \: cross \: product \: property}[/tex]
[tex] \mapsto{ \sf 6.3h = 35.595 * 2}[/tex]
[tex] \mapsto{ \sf{6.3h = 71.19}}[/tex]
[tex] \sf{Divide \: both \: sides \: by \: 6.3}[/tex]
[tex] \mapsto{ \sf{ \frac{6.3h}{6.3} = \frac{71.19}{6.3}}} [/tex]
[tex] \mapsto{ \sf{h = 11.3 \: mm}}[/tex]
The height of a triangle = 11.3 mm
Hope I helped!
Best regards! :D
~[tex] \sf{TheAnimeGirl}[/tex]
What degree does the function have?
F(x)=-2x^3+7x
Even or Odd
Answer:
The answer is Odd.
Step-by-step explanation:
I hope this helps you :)
Name the property that is being demonstrated
8-2=-2+8
Commutative Property
Associative Property
Zero Product Property
Multiplication Property of -1
Deductive Reasoning Property
Answer:
Commutative propertyStep-by-step explanation:
The "Commutative Laws" say: when we add we can swap numbers over and still get the same answer.
8 - 2 = (8) + (-2) = (-2) + (8) = -2 + 8
Can someone please do these questions or try to find the answers to them
Answer:if you look up the name of your work sheet into google and type in answer key after it will show up w the answer key
Step-by-step explanation:
solve the equation 2w=58
Answer:
29
Step-by-step explanation:
all you do is divide.
pls help, this is timed
Answer:
x/2 + 7 = 13 is the answer
Answer: C
Step-by-step explanation: He sold half of his comic, meaning dividing whatever he had by 2. Buying 7 more and it will equal 13.
What is the simplified form of (4m2n−3)2⋅12n138m20?
The simplified form of the given expression [(4m²n⁻³)² × 12n¹³]/(8m²⁰) will be 24n⁷/m¹⁶ so option (D) will be correct.
What is an expression?A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.
An expression is a mathematical proof of the equality of two mathematical expressions.
A statement expressing the equality of two mathematical expressions is known as an equation.
Given,
⇒ [(4m²n⁻³)² × 12n¹³]/(8m²⁰)
⇒ [(16m⁴n⁻⁶) × 12n¹³]/8m²⁰
⇒ 192m⁴n⁷/8m²⁰
⇒ 24n⁷/m¹⁶
Hence "The simplified form of the given expression [(4m²n⁻³)² × 12n¹³]/(8m²⁰) will be 24n⁷/m¹⁶".
To learn more about expression,
https://brainly.com/question/14083225
#SPJ5
Is 99 squared over 3 rational or irrational
Find the x-intercept of the graph of the equation y = -2.65x + 25.
What does the x-intercept mean in terms of the situation?
Answer:
x=9.4
Step-by-step explanation:
x intercept is the point where the graph crosses the x axis and y always =0
-2.65x+25=0
-2.65x=-25
x=-25/-2.65
x=500/53
x=9.4
1. Simplify: (3x + 4y – 2z) - (-2z + 6y)
Answer: x - 2y + 2z
keep it in alphabetical order!
Step-by-step explanation:
the negative on the outside changes what is on the inside, so the new equation will be
3x + 4y - 2x + 2z - 6y
combine like terms
x - 2y + 2z
Answer: 3x +10y
Step-by-step explanation:
first you put all the common integers (i think that is what they are called) together
3x+4y+6y-2z-(-2z)
Then you add and subtract all the integers
4y+6y=10y
-2z-(-2z)=0
so the answer is
3x+ 10y
Hopefully this is the right answer
God bless you!!
What is the area of a rectangle
with a length of 5 cm and a width of
4 cm
Answer:
Area = 20 cm²
Step-by-step explanation:
Area = width * length
area = 5cm * 4cm
area = 20 cm²
Answer:
20 cm
5x4 =20
length times width
How would I start this question?
Btw I need to find the X and the Y
Answer:
you know the whole circle is 360 degrees
Step-by-step explanation:
Answer:
You know the corresponding angles, read explanation.
Step-by-step explanation:
top left is equal to bottom right
top right is equal to bottom left
top mid is equal to bottom mid
ALL amount to 360 degrees!
The current value of a baseball card is 50 times its original value v (in dollars). The baseball card is worth $62. Write and solve an equation to find the original value of the baseball card
Answer:
50v
Step-by-step explanation:
The equation would be 50v, because $62 is the original value, or v, and we are trying to find the value of the card now. Which is now 50 times the original price, $62.
13% of $67.99 please help me please
Answer:
8.8387 (round to 8.84)
Step-by-step explanation:
To find the percentage of something, convert the percent into decimal form by moving the decimal two places to the left. In this case, the decimal form of 13% is 0.13
Then, multiply this decimal by the number you need to find the percentage of. In this case, that number is 67.99
The result of .13x67.99 is 8.8387.
Answer:
$8.84
Step-by-step explanation:
1.) Start with the 13%
2.) You have 13.
3.) Move the decimal point 2 places to the left.
4.) Now you have 0.13
5.) Multiply 0.13 and 67.99
6.) This equals $8.84
Solve for x: 4.23x + 1 = 17.8929 A. 0 B. 14.6629 C. 5.23 D. 6.23 PLEASE HELP!!!
Answer:
d
Step-by-step explanation:
Which are valid rearrangements of F=95C+32? Select the two correct answers. response - incorrect 95C−F=32 F+95C+32=0 C=59(F−32) C=95(F−32) F−32=95C
Answer:
F+95C+32=0 & F−32=95C
Step-by-step explanation:
f=95c+32
Answer:
1st and the last one
Step-by-step explanation:
If c – a = b, which of the following statements is true?
A. a + b = c
B. c + b = a
C. a – c = b
D. b – c = a
If c – a = b, then true statement is A. a + b = c
What is commutative property?The commutative property states that the numbers on which we operate can be moved or swapped from their position without making any difference to the answer.
Now the given statement is,
c – a = b
adding a to both the the side
c – a + a = b + a
⇒ c = b + a
Using commutative property of addition we get,
a + b = b + a
Therefore, we get
⇒ c = a + b
Thus the true statement is A. a + b = c
To learn more about addition :
https://brainly.com/question/11066761
#SPJ6