(Select all that are correct) which statements describe key features of function g if g(x) = f(x + 2)
a. y-intercept at (0,4)
b. domain of {x|-♾️< x <♾️}
c. horizontal asymptote of y = 0
d. horizontal asymptote of y=2
e. y-intercept at (0,1)
Answer:
Y-intercept (0,1) / Domain (-infinite,infinite) / horizontal asymptote y=0
The y-intercept is: (0,1)
The domain is [tex]\{x|-\infty < x < \infty\}[/tex]
The horizontal asymptote is [tex]y = 0[/tex]
The given parameters from the complete question are:
[tex]f(x) = 2^{x-2}[/tex]
[tex]g(x) = f(x + 2)[/tex]
First, we calculate the function of g(x)
[tex]g(x) = f(x + 2)[/tex]
Calculate f(x + 2)
[tex]f(x) = 2^{x-2}[/tex]
[tex]f(x + 2) = 2^{x+2-2}[/tex]
[tex]f(x + 2) = 2^x[/tex]
So:
[tex]g(x) = 2^x[/tex]
Start by calculating the y intercept:
This means, we calculate the g(x) when [tex]x=0[/tex]
[tex]g(x) = 2^x[/tex]
[tex]g(0) = 2^0[/tex]
[tex]g(0) =1[/tex]
The above computation means (a) is incorrect; but (e) is correct.
Next, calculate the domain of g(x)
[tex]g(x) = 2^x[/tex]
Some features in a function that limit the x values are: roots, fractions, etc.
[tex]g(x) = 2^x[/tex] does not have any restricting value of x.
This means the value of x ranges from negative infinity to positive infinity.
Hence, the domain is: [tex](-\infty,\infty)[/tex]
The above computation means (b) is correct
Next, calculate the horizontal asymptote.
To do this, we plot the graph of g(x) --> see attachment
Then we trace a horizontal line from the horizontal part of the curve of g(x) till it gets to the y-axis.
From the attached graph of g(x), the line touches the y-axis at [tex]y = 0[/tex]
So, the horizontal asymptote is: [tex]y = 0[/tex]
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Lyla is rounding some numbers to the nearest tenth. Select the number that will have an 8 in the tenths place after rounding.
A. 5.74
B. 6.08
C. 7.79
D. 8.86
Answer:
c
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
if u round 7.79 it will be 8 because 7 is greater than 5
what is what3 2/3 - 3/5 as a fraction plz give awnser
Answer:
55/15-9/15=46/15 or 3 1/15
Step-by-step explanation:
Answer:
46/15 or 3 1/5
Step-by-step explanation:
Hope this helps and have a Great Day :)Type your solution as an ordered pair.
Answer and Step-by-step explanation:
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Hi there! This is what the graph should look like: (Look at the picture attached)
We can see that the solution to the equation is (3, -2) because this is where the lines intersect.
*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^
#teamtrees #WAP (Water And Plant)
A cookie factory puts 2/5 of a barrel of flour into each batch of cookies. How much flour will the factory use for 5 batches?
Answer:
they would use 2 barrels of flour. or 10/5
Step-by-step explanation:
Answer:
2 barrels
Step-by-step explanation:
Just multiply 2/5 by 5
Hope it helps ^,^
What is the product?
(6) (negative 12)
–82
–72
72
82
Answer:
-72 is the answer.........
I need help with this, please!
Answer:g(x)=-x/2-6
Step-by-step explanation:plug it in
Plz help me answer this question
Answer: 4/5 - 2
Step-by-step explanation:
Simply put it into a graphing calculator
2x+10=6(x-1) What does x equal
Answer:
x=4
Step-by-step explanation:
2x+10=6(x-1)
2x+10=6x-6
10=6x-2x-6
10=4x-6
16=4x
4=x
A dolphin jumps 54 times in a 6 hour period. At this rate, how many jumps would be expected in a 2 hour period?
if the original price was $19.99, estimate the new price by first rounding the original price
Answer: $20.00
Step-by-step explanation:
Answer:
When rounded the answer will be $20.00.
Step-by-step explanation:
A swimming pool that holds 10,000 gallons of water is being filled at a rate of 600 gallons per hour. The function h(x)=600x represents the amount of water in the pool after x hours. Find h(3.25).
Answer:
16.6
Step-by-step explanation:
In 3.5 hours, a total of 1950 gallons of water will be filled in swimming pool.
What is the general form of a linear function?The general form of a linear function is given as follows -
y = kx
or
y = kx + c
Given is a swimming pool that holds 10,000 gallons of water is being filled at a rate of 600 gallons per hour. The function h(x)=600x represents the amount of water in the pool after [x] hours.
The linear function that represents the amount of water in the pool after [x] hours is given by -
h[x] = 600x
Now, for x = 3.5, the amount of water in the pool will be -
h[3.25] = 600 x 3.25 = 1950 gallons of water.
Therefore, in 3.5 hours, a total of 1950 gallons of water will be filled in swimming pool.
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The elevations, in feet, of three citites are marked on the number line shown below. The point 0 on the number line represents sea level. Which statement is true?
Answer:
cityQ
Step-by-step explanation:
City Q is located at the sea level
The statement that should be true is
City P is above sea level and City Q is below sea level.
What is the number line?The word "number line" in mathematics refers to a straight line where a number should be positioned at similar intervals or segments along with its length.
Given:
The point 0 on the number line represents sea level.
As, It should be presented in a horizontal style and be infinitely in any direction.
As a result, option c should be the statement that is true. City Q is below sea level, but City P is above it.
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through (4,-3) parallel to y=-2x
Answer:
y = -2x + 5
Step-by-step explanation:
Parallel lines have the same slope, so the line's slope would be -2.
Because we have a coordinate point and the slope of the line, we can figure out the equation by using the point slope formula:
( y - y1 ) = m( x - x1 )
( y - ( - 3 ) ) = -2 ( x - 4 )
y + 3 = -2x + 8
y = -2x + 5
The equation of the line is y = -2x + 5
Una recta que pasa por los puntos A (2,1) y B (6,3) y otra recta pasa por A y por el punto (0,y) ¿Cuánto vale y, si ambas rectas son perpendiculares?
The translation of the question given is
A line that passes through the points A (2,1) and B (6,3) and another line passes through A and through the point (0, y). What is y worth, if both lines are perpendicular?
Answer:
y = 5
Step-by-step explanation:
Line 1 that passes through A (2,1) and B (6,3)
Slope (m1) = 3-1/6-2 = 2/4 = 1/2
y - 1 = [tex]\frac{1}{2}[/tex] ( x -2)
2y - 2 = x- 2
y = [tex]\frac{x}{2}[/tex]
Line 2 passes through A (2,1) and (0,y)
slope (m2) =[tex]\frac{y-1}{-2}[/tex]
Line 1 and Line 2 are perpendicular
m1*m2 = -1
[tex]\frac{1}{2}[/tex] * [tex]\frac{y-1}{-2}[/tex] = -1
y-1 = 4
y = 5
slope = -2
Equation of Line 2
Y-1 = -2(x-2)
y -1 = -2x +4
2x +y = 5
Which of the following quadratic equations has no real solution?
A) x^2-6x-2=0
B) 4x^2+4x+1=0
C) x^2+3x-5=0
D) 2x^2-4x+3=0
If I charged 30$ a hair cut the whole year how many customers would I need to have to get 17,510$ and how many times would my customers have to see me within that year
Answer: Around 584 people would have to get a haircut at 30$, if you are looking for 17,510$
Step-by-step explanation:
Rewrite, using the distributive property. -3(20 + -29d) = [?] + [ ]d
Answer:
-60+87d
or
87d-60
Step-by-step explanation:
-3(20+-29d)=
-60+87d
The image below shows the download speed of three different companies. Use the information to answer the questions.
Complete questions 1-5 in order.
1) What is the download speed in MB per minute for AT&T?
2) What is the download speed in MB per minute for Bidmore?
3) What is the download speed in MB per minute for Comcast?
4) Who has the best download speed? Explain your choice.
5) All these equations show proportional relationships. Bid more's graph is shown, what would the other two graphs look like for AT&T and Comcast?
They will go through _________and be a __________line.
Answer:
1) The download speed for AT&T is 1,800
2) The download speed for Bidmore is 1,500
3) The download speed for Comcast is 1,680
4) AT&T has the best download speed out of the three.
5) They will go through the origin and be a proportional line.
Step-by-step explanation:
Plz answer correctly! thnx! :)
WHOEVER ANSWERS FIRST GETS BRAINLEST!
The number p of pennies in Jorge's bank is one fourth the number of nichels, The wokal
number of coins in the bank is 25,
Which equation could be used to find m?
n= 25
06 A-' = 25
+ 2n = 25
Answer:
C
Step-by-step explanation:
The value of x + x(xx) when x = 2 is:
Answer:
10
Step-by-step explanation:
X+x(xx)
X+x(x^2)
X+x^3
2+2^3
10
Answer:
10.
Step-by-step explanation:
2 + 2 x (2x2)
= 2 + 2 x 4
= 2 + 8
= 10
Hope that helped, :)
The ratio of boys to girls in a class is 2:3. There are 30 students in the class. How many more girls than boys are there?
Answer:
there are 18 girls
Step-by-step explanation:
for every 2 boys there are 3 girls
so then you can say 2/5 of the class are boys and 3/5 are girls
and you have to calculate 3/5 of 30 so you have to divide 5 and then multiply by 3 so 30 divided by 5 is 6 the n multiply 6 by 3 and the answer is 18.
Hope this helps
NEED HELP ASAP!!!!!!! WILL GIVE BRAINLIEST!!!!!!
Rectangle ABCD is in the coordinate plane. Which of the following is a valid definition of a reflection of rectangle ABCD?
A. Every point X on ABCD is mapped to a new point X′ such that each length from X toX′ is the same.
B. Every point X on ABCD is mapped to a new point X′ such that the distance from X to the line of reflection is the same as the distance from X′ to the line of reflection.
C. Every point X on ABCD is mapped to a new point X′ such that the coordinates of X′ are opposites of the coordinates of X.
D. Every point X on ABCD is mapped to a new point X′ such that one coordinate of X′ is the same as in X and the other coordinate of X′ is the opposite of the other coordinate in X.
The definition of a reflection of rectangle ABCD is option D:
"Every point X on ABCD is mapped to a new point X' such that one coordinate of X' is the same as in X, and the other coordinate of X' is the opposite of the other coordinate in X".
When a reflection occurs, each point on the original shape is mapped to a new location on the reflected shape.
Option A states that every point X on ABCD is mapped to a new point X' such that each length from X to X' is the same. This definition does not capture the essence of a reflection because it doesn't consider the relationship between the original shape and its reflection.
Option B states that every point X on ABCD is mapped to a new point X' such that the distance from X to the line of reflection is the same as the distance from X' to the line of reflection.
Option C states that every point X on ABCD is mapped to a new point X' such that the coordinates of X' are opposites of the coordinates of X.
Option D correctly captures the nature of a reflection. This states that each point X on ABCD is mapped to a new point X' where one coordinate of X' is the same as in X, and the other coordinate of X' is the opposite of the other coordinate in X.
Therefore, option D is the valid definition of a reflection of rectangle ABCD.
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Tasnia had a piece of ribbon that was 6 ½ yards long. She used this ribbon to make bows. Each bow was made from a piece of ribbon that was ⅓ yard long. This situation can be represented by the equation 6 ½ ÷ ⅓ = 19 ½ . Which statement best describes what the quotient 19 ½ represents?
Answer: the number of bowss that can be made.
Step-by-step explanation:
You didn't give the options but let me help out.
We are told that Tasnia had a piece of ribbon that was 6 ½ yards long and that she used this ribbon to make bows. We are further told that each bow was made from a piece of ribbon that was ⅓ yard long and that this situation can be represented by the equation 6 ½ ÷ ⅓ = 19 ½.
The quotient gotten above simply means the number of bowss that can be made.
1. Write an equivalent
expression for
3x + 12 +7x + x
Answer:
11x+12
Step-by-step explanation:
combine like terms
Lea solves the equation below by first squaring both sides of the equation.
3+2y=√-y
What extraneous solution does Lea obtain?
y=
Answer: IF YOU ARE ON KHAN ACADEMY THE ANSWER IS NOT -1
THE CORRECT ANSWER ON KHAN IS -9/4
For equation 3 + 2y = √(-y) the extraneous solution does Lea obtain is y = (-13 + √97) / 8 or y = (-13 - √97) / 8
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .
When Lea squares both sides of the equation 3 + 2y = √(-y), she gets:
(3 + 2y)² = (-y)
Expanding the left side, we get:
9 + 12y + 4y² = -y
Bringing all the terms to one side, we get a quadratic equation:
4y² + 13y + 9 = 0
We can solve this quadratic equation using the quadratic formula:
y = (-b ± √(b² - 4ac)) / 2a
Substituting the coefficients a = 4, b = 13, and c = 9, we get:
y = (-13 ± √(13² - 4(4)(9))) / 2(4)
y = (-13 ± √97) / 8
So the solutions are:
y = (-13 + √97) / 8 or y = (-13 - √97) / 8
Hence, the extraneous solution does Lea obtain is y = (-13 + √97) / 8 or y = (-13 - √97) / 8
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Gcf of 80x^3 and 30yx^2
What is -3 4/9 • 5 2/5
See attachment for answer.
The answer is -93/5.
Please help ASAP! (Photo)
Answer:a sq+ b sq= c sq
Step-by-step explanation: add a and b and the answer is c