The graph of g(x) = f(–2x) will be a horizontally stretched and reflected version of the graph of the parent function f(x) = x^3. The reflection occurs over the y-axis, and the stretch is by a factor of 1/2.
Explanation:The student's question involves a transformation of a cubic parent function. The original function, f(x) = x3, represents a standard cubic graph, which is symmetric about the origin and increases from negative infinity to positive infinity as x does the same. The transformation g(x) = f(–2x) modifies the parent function in two notable ways. First, the multiplication by –2 reflects the graph over the y-axis (because of the negative sign) and also stretches it horizontally by a factor of 1/2 (because the absolute value of the number is greater than 1).
To visualize this, if we consider specific points on the graph of f(x) such as (1,1), (2,8), and (3,27), you would find their corresponding points on g(x) at (-0.5,1), (-1,8), and (-1.5,27), respectively. This indicates that every point on g(x) is twice as far from the y-axis as it is on f(x), and on the opposite side due to the reflection.
The effect of this transformation demonstrates the result of horizontal stretching and reflection when contrasts with the original function f(x), providing insight into how linear transformations affect the shape and position of graphs.
Which of the following expressions results in 0 when evaluated at x = 3?
Answer:
You need to provide the expressions you have to choose from.
Step-by-step explanation:
let f(7)=12 and g(2)=7 what is the value of (f•g)(2)
Final answer:
The value of (f•g)(2), given f(7)=12 and g(2)=7, is 12. This is found by first applying g to 2 to get 7, and then applying f to get f(7), which equals 12.
Explanation:
The question pertains to the composition of functions and the use of the chain rule in calculus. Given that f(7)=12 and g(2)=7, we need to find the value of (f•g)(2). The notation (f•g)(x) means we first apply g to x, and then apply f to the result of g(x). Therefore, to find (f•g)(2), we first find g(2), which is 7, and then find f(g(2)) which is f(7). Since we know that f(7)=12, the value of (f•g)(2) is therefore 12.
PLEASE HELP IT'S SO IMPORTANT PLZ
create word problems that required multi-step mathematical thinking, such as the solution of the equation is then used to determine the actual solution of the question, and SOLVE IT.
Will this help?
Answers:
1. $8 left
2. 4 minutes
3. 9 balloons
Questions
1. Craig has a twenty dollar bill. He buys six squirt guns
for $2 each. How much money did Craig have left?
2. Lauren and Gina's mother told her daughters they can
swim in the pool for 20 minutes. First, they swam laps in
the pool for 7 minutes. Then they swam underwater for
one minute. Then they played water polo for 8 minutes.
How much longer can they stay in the pool?
3. Maria invited 4 of her friends over for a water balloon fight in
the backyard. At the start of the game, Maria gave each of
her friends 2 water balloons. She had one water balloon for
herself. How many water balloons did they have altogether?
A parallelogram is always which of these?
A. rhombus
B. quadrilateral
C. rectangle
D. square
A group of middle school boys have a mean height of 167 cm and a range of 164 cm to 169 cm. A group of high school boys have a mean height of 180 cm and a range of 175 cm to 183 cm. Which statement BEST compares the two groups of boys?
Answer:
C
Step-by-step explanation:
The high school boys vary in height more than the middle school boys.
middle school boys range = 169 − 164 = 5 cm
high school boys range = 183 − 175 = 8 cm
The range for both conditions is 5 cm and 8 cm respectively.
What is the range?The difference between the highest and lowest value data points of the provided data is known as the range in mathematics.
In statistics, the mean is the product of all the values in a set of data divided by the total number of values in the data for a given set of observations.
The high school boys vary in height more than the middle school boys.
Middle school boys range = 169 − 164 = 5 cm
High school boys range = 183 − 175 = 8 cm.
To know more about the range follow
https://brainly.com/question/2264373
#SPJ6
What is an equation of the line that passes through the points (7, -6) and (3, -6)
Answer:
y=-6
Step-by-step explanation:
What is the probability of getting a head with the flip of a coin?
A) 0/2
B) 1/4
C) 1/2
D) 2/2
Answer:
1/2
Step-by-step explanation:
there is two side of a coin, so there is a 1/2 chance that you will head heads.
A coin has two sides, one side is heads, and the other is tails. Since there are 2 sides the probability of getting either heads or tails is 1/2. Therefore, the probability of flipping a coin and getting heads is C) 1/2.
Best of Luck!
What is the answer 2-2n=3n+17
Answer:
n=-3
Step-by-step explanation:
2-2n=3n+17
Add 2n to each side
2-2n+2n=3n+2n+17
2 = 5n+17
Subtract 17 from each side
2-17 = 5n+17-17
-15 = 5n
Divide by 5
-15/5 = 5n/5
-3 =n
Answer:
n = -3
Step-by-step explanation:
2 - 2n = 3n + 17
Collect the like terms
-2n - 3n = 17 - 2
-5n = 15
Divide both sides by -5
n = 15/-5
n = -3
1) Write in the formula. What equals the perimeter P of the rectangle wich is 25 cm wide. (show the length with the letter b.) 2) Calculate the perimeter of the rectangle when its length is equal to:
a) 45 cm; b) 0.25 m; c) 650 mm; d) 3 m by 9 cm; e) 3 dm.
Please I really need help
Answer:
1)P = 2 x(L+l) = 2 x (25+L)
2) Maintaing L= 25 cm
P= 2x (25+45) = 140 cm²
P= 2x (25+0,25m) =2x(25+25)= 100 cm²
P= 2x (25+650 mm) =2x(25+65)= 180 cm²
d) ambigous
P= 2x (25+3dm) = 2x (25+30)=110 cm²
Step-by-step explanation:
a group of rangers work 5 days per week. it takes them 4 days to plant trees on 1/2 acre.what is the unit rate per week
The unit rate at which the group of rangers plants trees is 5/8 of an acre per week, which is found by calculating the daily acreage planted and then multiplying by the number of workdays in a week.
Explanation:To determine the unit rate per week of the group of rangers planting trees, we need to calculate how much of an acre they can plant in a standard work week. As it takes them 4 days to plant trees on 1/2 acre, they will plant 1/2 acre in every 4 days of work. Since they work 5 days per week, we can adjust the ratio to calculate the weekly rate:
1/2 acre in 4 days is equivalent to (1/2 acre)/(4 days).Now, find out how much is planted in 1 day: (1/2 acre)/(4 days) = 1/8 acre in 1 day.Finally, multiply by 5 to get the weekly amount: (1/8 acre) * 5 days = 5/8 acre per week.Therefore, the unit rate at which the group of rangers plants trees is 5/8 of an acre per week.
Below is a drawing of a wall that is to be covered with either wallpaper or paint. The wall is 8 ft. high and
16 ft wide. The window, mirror, and fireplace are not to be painted or papered. The window measures 18 in wide
and 14t. high. The fireplace is sit wide and 3 it. High while the mirror above the fireplace is 4 ft. wide and 2 ft.
high. Note: this drawing is not to scale)
How many square feet of wallpaper are needed to cover the wall?
84 sq. ft of the wall has to be covered with paint or wallpaper.
Step-by-step explanation:
Step 1: Find the area of wallpaper to be covered by calculating the area of the wall and subtracting the areas of the window, mirror and fireplace from it. All are rectangular in shape with are given by A = length × widthArea of the wall = 8 × 16 = 128 ft²
Area of the window = 18/12 × 14 = 1.5 × 14 = 21 ft² (since 1 ft = 12 in)
Area of the fireplace = 5 × 3 = 15 ft²
Area of the mirror = 4 × 2 = 8 ft²
Step 2: Calculate the area to be painted or covered with wallpaperArea of the wall to be covered with paint or wallpaper = 128 - (21 + 15 + 8)
= 128 - 44
= 84 ft²
Answer:
84 ft²
Step-by-step explanation:
Step 1: Find the area of the wall.
The wall is 8 ft high and 16 ft wide
A = LW
A = (16)(8)
A = 128 ft²
Step 2: Find the area of the window, fireplace, and mirror.
Window: The window measures 18 in wide and 14 ft high
18 in = 1.5 ft
A = LW
A = (14)(1.5)
A = 21 ft²
Fireplace: The fireplace is 5 ft wide and 3 ft high
A = LW
A = (3)(5)
A = 15 ft²
Mirror: The mirror above the fireplace is 4 ft wide and 2 ft high
A = LW
A = (2)(4)
A = 8 ft²
Step 3: Add all the areas of the three objects (window, fireplace, and mirror)
A = 21 + 15 + 8
A = 36 + 8
A = 44 ft²
Step 4: Subtract the total area of the objects from the area of the wall.
A = 128 ft² - 44 ft²
A = 84 ft²
Marvin washes 10 1/2 crates in 3/4 hours. At this rate how many crates can he wash in one hour?
Please help us due tomorrow 3/3/2020!!!
The circumference of a circle is 15 meters. Find the area. Use 3.14 for π.
Pls help me with this question
The solutions are £5575, £312.5 and £345 respectively.
Step-by-step explanation:
Step 1: Find the amount of Swedish kronor received by Theo in exchange for £500£1 = 11.15 kr
⇒ £500 = 500 × 11.15 = £5575
Step 2: Find the amount of Swiss francs received by Theo in exchange for £250£1 = 1.25 CHF
⇒ £250 = 250 × 1.25 = £312.5
Step 3: Find the pounds to get 407.10 euros.£1 = 1.18 euros
⇒ 407.10 euros = 407.10/1.18 = £345
how can something me nonlinear
HELP PLEASE BE QUICK
Answer:
Radius is 2 centimeters
Step-by-step explanation:
4π is the area of a circle
Area of a circle = πr^2
4π / π = πr^2 / π
sqrt(4) = sqrt(r^2)
2 = r
Answer: Radius is 2 centimeters
Charlotte wants to swim 50 miles this school year she plans to swim 1/4 miles each day how many days Will it take her to swim 50 miles
Pamelas age is. 2 times jiris age. The sum of their ages is 30.what is jiris age?
Answer:
Pamela is 20 years old
Jiris is 10 years old.
Step-by-step explanation:
The very first step is to identify your variables. Let's say that Pamela is 'P' and lets say Jiris is 'J.' The next step is to create an equation. 'The sum of their ages is 30' is something that we can use. So, P + J = 30. The next step is to see that Pamela is two times Jiris' age. So we can say that P = 2J. Now, in order to solve for one variable, we need to do some substitution. We know that P = 2J, so we can plug that into the first equation (P + J = 30). With this change, we now have, 2J + J = 30. With that, you combine like terms and solve for J to get an answer of J = 10. Now we can use that number and plug it into one of our previous equations, like P + J = 30. Now it is going to be P + 10 = 30. Solve for P and get an answer of 20 years old.
A triangle has sides with lengths of 4 meters, 5 meters, and 7 meters. Is it a right triangle
A triangle has sides with lengths of 4 meters, 5 meters, and 7 meters. It is a right triangle because the square of the largest side length is not equal to the sum of the square of the other two small side lengths and it can be determined by using the properties of the right triangle.
Given that,A triangle has sides with lengths of 4 meters, 5 meters, and 7 meters.
We have to determine,Is it a right triangle?
According to the question,To determine the right triangle following all the steps given below.
A triangle has sides with lengths of 4 meters, 5 meters, and 7 meters.
The condition for the right triangle;The square of the largest side length is not equal to the sum of the square of the other two small side lengths then it is called the right triangle.
Then,
[tex]= (4)^2+(5)^2 = 7^2\\\\= 16 +25 = 49\\\\=41\neq 49[/tex]
Hence, Yes it is a right triangle because the square of the largest side length is not equal to the sum of the square of the other two small sides lengths.
To know more about the Right Triangle click the link given below.
https://brainly.com/question/7894175
Sin(pi/2-x)/cot^2(pi/2-x)+1
Answer:
[tex] { \cos}^{3} x[/tex]
Step-by-step explanation:
We want to simplify:
[tex] \frac{ \sin( \frac{\pi}{2} - x) }{ { \cot}^{2} ( \frac{\pi}{2} -1 ) + 1} [/tex]
Use the Pythagorean identity:
[tex] { \csc}^{2}x = { \cot}^{2}x + 1[/tex]
We apply this property to get:
[tex] \frac{ \sin( \frac{\pi}{2} - x) }{ { \csc}^{2} ( \frac{\pi}{2} -x) } [/tex]
This gives us:
[tex]\frac{ \sin( \frac{\pi}{2} - x) }{ \frac{1}{{ \sin}^{2} ( \frac{\pi}{2} -x)} } [/tex]
We simplify to get:
[tex]\sin^{3} ( \frac{\pi}{2} -x)[/tex]
[tex](\sin ( \frac{\pi}{2} -x))^{3}[/tex]
Apply the complementary identity;
[tex](\cos x)^{3} = { \cos}^{3} x[/tex]
What is the solution to the inequality?
6x−5>−29
A.
x>−4
B.
x<4
C.
x<−4
D.
x>4
Prove algebraically what type of function this is (even, odd, or neither).
The given function is even.
Solution:
If f(-x) = f(x), then the function is even.
If f(-x) = -f(x), then the function is odd.
Given function:
[tex]f(x)=x^{6}-x^{4}[/tex]
Substitute x = -x
[tex]f(-x)=(-x)^{6}-(-x)^{4}[/tex]
[tex]=x^{6}-x^{4}[/tex]
= f(x) (given)
f(-x) = f(x)
From the definition, it is even.
Hence the given function is even.
What is the volume, in cubic m, of a cube with an edge length of 11m?
the volume of cube with edge length 11 m is [tex]Volume = 1331m^3[/tex] .
Step-by-step explanation:
Here we have a side length of a cube as 11 m . We need to find the volume of cube . Let's find out:
We know that every side of a cube is identical and equal . And volume of cube is given by formula :
⇒ [tex]Volume = (side)^3[/tex] ...........(1)
According to question we have following parameters as
[tex]side = 11m[/tex]
Putting this in (1)
⇒ [tex]Volume = (11m)^3[/tex]
⇒ [tex]Volume = 11(11)(11)m^3[/tex]
⇒ [tex]Volume = (121)(11)m^3[/tex]
⇒ [tex]Volume = 1331m^3[/tex]
Therefore , the volume of cube with edge length 11 m is [tex]Volume = 1331m^3[/tex] .
The volume of the cube is 1331 m³
Explanation:
Given:
side of the cube, a = 11m
Volume of the cube, v = ?
we know:
Volume of the cube = (a)³
V = (11m)³
V = 1331 m³
Therefore, the volume of the cube is 1331 m³
I need help with this question please
ANSWER ASAP!!!
Area of the larger circle is 9/4 πx²
Step-by-step explanation:
Step 1: Given area of the small rug = 1/4 πx² Compare this to the formula for area of a circle.⇒ 1/4 πx² = πr²
⇒ x²/4 = r²
∴ r = x/2
Step 2: Given radius of the larger circle is 3 times that of the smaller circle (r = 3x/2), find area of the larger circle.Area of the larger circle = πr² = π × (3x/2)²
= 9/4 πx²
A salesperson earns a weekly salary of $175 plus a 4% commission on the
sales of bicycles made during the week. If the salesperson's bicycle sales
for the week total $4500, how much did the salesperson earn for the week
Answer:
$355
Explanation:
See the photo attached :)
Each of the letters of the word ALABAMA are written on a piece of paper and then put into a bag. A piece of paper is drawn at random. What is the theoretical probability, as a decimal, of drawing an A? Round the decimal to the nearest hundredth.
The theoretical probability of drawing an 'A' from the word 'ALABAMA' is 0.57. This result arrives from dividing the number of 'A's (4) by the total number of letters in 'ALABAMA' (7).
Explanation:The question deals with a probability problem related to the selection of letters from the word 'ALABAMA'. The word 'ALABAMA' has 7 letters out of which 4 are 'A's. The theoretical probability is calculated as the number of successful outcomes divided by the total number of outcomes. Since we are interested in drawing an 'A', the successful outcomes are the number of 'A's which is 4, and the total outcomes are the total number of letters which is 7.
To calculate theoretical probability, you divide the number of successful outcomes by the total number of outcomes. In this case, the calculation will be 4 / 7 = 0.57 (rounded to the nearest hundredth).
So, the theoretical probability of drawing an A from the word 'ALABAMA' in decimal form, rounded to the nearest hundredth, is 0.57.
Learn more about Probability here:https://brainly.com/question/32117953
#SPJ12
Kona’s mother wanted to find out how many minutes her family spends on the phone for each call made. She put her data in a table after a week of observation as shown below. She asked Kona to make a histogram from the data.
Minutes
Number of Calls
1 - 5
2
6 - 10
5
11 - 15
6
16 - 20
10
21 - 25
7
26 - 30
2
31 - 35
1
36 - 40
0
41 - 45
2
46 - 50
1
Which chart has the correct setup for Kona’s histogram?
A 2-column table with 4 rows tilted Time on Phone. Column 1 has entries interval use, appropriate scale, vertical axis represents, horizontal axis represents. Column 2 has entries 10, 0 to 12, minutes on phone, number of calls.
A 2-column table with 4 rows tilted Time on Phone. Column 1 has entries interval use, appropriate scale, vertical axis represents, horizontal axis represents. Column 2 has entries 10, 1 to 12, number of calls, minutes on phone.
A 2-column table with 4 rows tilted Time on Phone. Column 1 has entries interval use, appropriate scale, vertical axis represents, horizontal axis represents. Column 2 has entries 5, 1 to 12, minutes on phone, number of calls.
A 2-column table with 4 rows tilted Time on Phone. Column 1 has entries interval use, appropriate scale, vertical axis represents, horizontal axis represents. Column 2 has entries 5, 0 to 12, number of calls, minutes on phone.
Answer:
D—
The histogram will have a horizontal or an x axis of time/minute intervals of the calls (5 minutes in each), and the vertical axis or y axis will be the number of calls made.
Answer:
d
Step-by-step explanation:
yo welcome
Given f(x) and g(x) = k·f(x), use the graph to determine the value of k.
g(x)
The diagram for this exercise is attached below. We have two linear functions [tex]f(x) \ and \ g(x)[/tex] and the following relationship:
[tex]g(x) = kf(x)[/tex]
From the graph, we know that:
[tex]f(-3)=1 \\ \\ g(-3)=-3[/tex]
Then, substituting into the relationship:
[tex]g(-3)=kf(-3) \\ \\ -3=k(1) \\ \\ \\ Finally: \\ \\ \boxed{k=-3}[/tex]
Will y’all help me on my last one thank you
Answer:
$6.00
Step-by-step explanation:
Let's look at our prices:
Sandwich = $3.50
Fruit cup = $1.50
Orange juice = $1.00
Now let's add them:
$3.50 + $1.50 = $5.00
$5.00 + $1.00 = $6.00
Tip: Adding money is like adding regular digits. You also regroup (like we did with 5 + 5) as normal.
Solve for x (to the nearest tenth)
Step-by-step explanation:
By Geometric mean property:
[tex]x = \sqrt{5 \times 3} \\ = \sqrt{15} \\ = 3.87298335 \\ \huge\orange {\fbox{\therefore \: x \approx \: 3.9}} [/tex]