Describe a sequence of transformations that transforms the graph of the parent function f into the graph of the function g.
f(x)= x
g(x)= -3(x-4)+1
Step-by-step explanation:
Parent function f(x) = x
g(x)= -3(x-4) + 1
If any number added or subtracted with x then graph moves left or right
Here 4 is subtracted from x, so graph move 4 units to the right
If any number added or subtracted at the end then graph move up or down
Here 1 is added at the end, so graph move 1 unit up.
g(x) = -f(x), for negative sign the graph reflects across x axis
We have negative sign at first, so the graph reflects over x axis
The graph of [tex]\( g(x) \)[/tex] is the result of these transformations applied to the graph of the parent function [tex]\( f(x) \)[/tex].
The sequence of transformations that transforms the graph of the parent function [tex]\( f(x) = x \)[/tex] into the graph of the function [tex]\( g(x) = -3(x-4)+1 \)[/tex] involves a reflection across the x-axis, a horizontal shift, a vertical stretch, and a vertical shift.
1. Reflection across the x-axis: The negative sign in front of the function[tex]\( g(x) \)[/tex]indicates a reflection across the x-axis. This means that for every point \( (x, y) \) on the graph of [tex]\( f(x) \)[/tex], there will be a corresponding point [tex]\( (x, -y) \)[/tex] on the graph of [tex]\( g(x) \)[/tex].
2. Horizontal shift: The expression [tex]\( (x-4) \)[/tex] inside the function [tex]\( g(x) \)[/tex]indicates a horizontal shift to the right by 4 units. This means that every point on the graph of [tex]\( f(x) \)[/tex] is moved 4 units to the right along the x-axis to get the graph of [tex]\( g(x) \).[/tex]
3. Vertical stretch: The coefficient 3 in [tex]\( -3(x-4) \)[/tex] indicates a vertical stretch by a factor of 3. This means that for every point [tex]\( (x, y) \)[/tex] on the graph of the reflected function[tex]\( -f(x) \)[/tex], the y-coordinate is multiplied by 3 to get the corresponding point [tex]\( (x, 3y) \)[/tex] on the graph of [tex]\( g(x) \)[/tex].
4. Vertical shift: Finally, the[tex]\( +1 \)[/tex] at the end of the function [tex]\( g(x) \)[/tex]indicates a vertical shift upwards by 1 unit. This means that every point on the graph of [tex]\( -3f(x-4) \)[/tex] is moved 1 unit up along the y-axis to get the graph of [tex]\( g(x) \).[/tex]
Putting it all together, the sequence of transformations is as follows:
- Start with the parent function [tex]\( f(x) = x \).[/tex]
- Reflect the graph across the x-axis to get [tex]\( -f(x) \).[/tex]
- Shift the graph 4 units to the right to get [tex]\( -f(x-4) \).[/tex]
- Stretch the graph vertically by a factor of 3 to get [tex]\( -3f(x-4) \).[/tex]
- Shift the graph 1 unit upwards to get [tex]\( -3f(x-4) + 1 \),[/tex] which is the function [tex]\( g(x) \)[/tex].
Therefore, the graph of [tex]\( g(x) \)[/tex] is the result of these transformations applied to the graph of the parent function [tex]\( f(x) \)[/tex].
Given the ordered pairs A (-6, 4) and B(8, 9). Show all work!
a. Find the equation of the line through AB.
b. Find the equation of the line parallel to line AB and passes through the point (14, -6).
c. Find the equation of the line perpendicular to line AB and passes through the point (-5, -10).
Answer:
Step-by-step explanation:
Two points A and B are given
Using two point formula for straight lines we get
[tex]\frac{x+6}{8+6} =\frac{y-4}{9-4} \\5(x+6) = 14(y-4)\\5x+30 = 14y-56\\5x-14y+86 =0[/tex]
b) A line parallel to AB would be of the form
5x-14y +k=0
Since the line passes through (14,-6) substitute to get k
5(14)-14(-6)+k=0 Or k = -154
Line is 5x-14y-154 =0
c) A line perpendicular to AB would have form as
14x+5y =k1
Substitute (-5,-10) to get k
14(-5)+5(-10) =k1
Or k1 = -120
Hence equation is 14x+5y = -120
It costs $2.25 to buy 9 pieces of candy. Which shows the unit price per piece of candy?
A 25¢ per piece
B 50 ¢ per piece
C 35¢ per piece
D 5¢ per piece
ASAP! ☹☹☹☹☹☹☹☹☹
Answer:
A 25¢ per piece
Step-by-step explanation:
To find the unit price, we take the dollar amount and divide by the number of pieces
$2.25 / 9 pieces
$.25 per piece
The multiplication of two or more quantities may be expressed as the ? of the same quantities.
Answer:
sum
Step-by-step explanation:
We have that, 'The multiplication of two or more quantities may be expressed as the repeated addition of the same quantities'.
i.e. multiplication of two or more terms is equal to adding as many copies of one of them.
i.e. a × b = a + a + ... ( 'b' number of times ) = b + b + .... ( 'a' number of times )
For example,
2 × 4 = 8
2 × 4 = 2 + 2 + 2 + 2 = 8 i.e. adding 2 four times
2 × 4 = 4 + 4 = 8 i.e. adding 4 two times
or
3 × 7 = 21
3 × 7 = 3 + 3 + 3 + 3 + 3 + 3 + 3 = 21 i.e. adding 3 seven times
3 × 7 = 7 + 7 + 7 = 21 i.e. adding 7 three times.
Hence, 'The multiplication of two or more quantities may be expressed as the repeated addition of the same quantities'.
The multiplication of two or more quantities can be expressed as the product of the same quantities in mathematics.
Explanation:Multiplication is a fundamental arithmetic operation that combines two or more numbers to find their total value. It represents repeated addition and is denoted by the "×" or "*" symbol. For example, multiplying 5 by 3 results in 5 * 3 = 15, indicating that the value is added five times.
In mathematics, the multiplication of two or more quantities may be expressed as the product of the same quantities. For example, if you multiply 2 by 3, the product is 6. This concept of multiplication applies to all quantities, whether they are numbers or variables.
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If an object traveled 230 miles at a rate of 25 miles per hour, how long (in hours) did it take to travel this distance?
Answer:
9.2 hours for the total drive
To determine how long it took for an object to travel 230 miles at 25 miles per hour, divide the distance by the speed, which results in 9.2 hours.
This problem is a straightforward application of the formula for calculating time when distance and speed are known. The formula is Time = Distance ÷ Speed.
In this case, the distance (d) is 230 miles and the speed (v) is 25 miles per hour. Using the formula:
Therefore, it took 9.2 hours for the object to travel a distance of 230 miles at a speed of 25 miles per hour.
The gasoline tank in Deborahs car holds 13.2 gallons. When her gas gauge says that the tank is 1/4 full, how many gallons of gasoline does the tank have?
Answer:
3.3
Step-by-step explanation:
To find the amount of gasoline when Deborah's tank is 1/4 full, divide the tank's full capacity (13.2 gallons) by 4, which results in 3.3 gallons of gasoline in the tank at 1/4 full.
To find out how many gallons of gasoline Deborah's car has when the tank is 1/4 full, we need to calculate 1/4 of the total capacity of the tank. Since the tank holds 13.2 gallons when full, the amount of gasoline at 1/4 full is calculated as follows:
Divide the full tank capacity by 4 to find 1/4 of the tank's capacity: 13.2 gallons / 4 = 3.3 gallons.Therefore, when Deborah's gas gauge indicates that the tank is 1/4 full, it contains 3.3 gallons of gasoline.
artaud noticed that if he takes the opposite of his age and adds 40, he gets the number 28. how old is artaud?
let's say Artaud's age is "x", its opposite will then be -x, so
[tex]\bf \stackrel{\textit{opposite of his age plus 40}}{-x+40}~~\stackrel{is}{=}~~28\implies -x+40-28=0 \\\\\\ -x+12=0\implies \boxed{12=x}[/tex]
Answer:
12 years old
Step-by-step explanation:
28 - 40 = -12
Note that -12 is the opposite of 12.
Artaud is 12
x-3y=1 and 7x+2y=7 he decided to solve for y in the second equation because it had the smallest number as a coefficient. Max told him that there was a more efficient way. What reason can Max give for his statement?
Answer:
I would solve for x in the first equation. X in the first equation has a coefficient of 1, unlike y in the second equation which has a coefficient of 2. I do not have to divide to solve for my variable.
Step-by-step explanation:
I would solve for x in the first equation. X in the first equation has a coefficient of 1, unlike y in the second equation which has a coefficient of 2.
x-3y =1
Add 3y to each side
x = 1+3y
Then substitute this into the second equation.
Max would have to subtract 7x from each side and then divide by 2
7x+2y =7
2y = -7x+7
y = -7x/2 + 7/2
This makes the math complicated when it is substituted into the first equation because we are multiplying by 3. We will have fractions.
Answer:
Jerry solved the system of equations.
x minus 3 y = 1. 7 x + 2 y = 7.
As the first step, he decided to solve for y in the second equation because it had the smallest number as a coefficient. Max told him that there was a more efficient way. What reason can Max give for his statement?
The variable x in the first equation has a coefficient of one so there will be fewer steps to the solution.
The variable x in the second equation has a coefficient of 7 so it will be easy to divide 7 by 7.
The variable y in the second equation has a coefficient of 2 so it will be easy to divide the entire equation by 2.
The variable x in the second equation has the largest coefficient. When dividing by 7, the solution will be a smaller number.
correct answer is AAAAA
The 7th grade students at Palm Coast Middle School made some apple pies for a bake sale. The school cafeteria also donated 9 pies toward the effort. All the pies at the sale were cut into 8 pieces. If at least 224 pieces of pie were sold in all, how many pies did the students bake?
Answer:
19 i think
Step-by-step explanation:
Answer:
The students baked at least 19 pies.
Step-by-step explanation:
We know that each of the pies were cut into 8 pieces. Since the students sold at least 224 pieces of pie, we can use these equations to figure out how many pies were sold and how many were made by the students.
Total number of pies = total number of slices sold/number of slices per pie
Total number of pies = 224/8
Total number of pies = 28
Pies made by students= total number of pies-pies made by school cafeteria
Pies made by students= 28-9
Pies made by students= 19
what is 1+2+3+4+5+6+7+8+9+10
Answer:
55
Step-by-step explanation:
Add from left to right
1+2+3+4+5+6+7+8+9+10
3 +3+4+5+6+7+8+9+10
6+4+5+6+7+8+9+10
10+5+6+7+8+9+10
15+6+7+8+9+10
21+7+8+9+10
28+8+9+10
36+9+10
45+10
55
Find the product 284 times 36
Your answer to 284*36 will be 10,224.Hope this helps!
Please mark brainliest!!!!!!!!
Answer:
10,224
I just entered 284*36 into my calculator haha
Fred brown and his sister, Nancy, each have $15 in the bank. Every week Nancy plans to add $3 to her account. Fred who loves to spend money when he has it, plans to add $1 to his account each week. How many weeks will it take Nancy’s account to have TWICE as much money as Fred’s account?
(Explain your thinking)
Answer:
it will take 15 weeks for Nancy’s account to have TWICE as much money as Fred’s account
Step-by-step explanation:
Fred brown and his sister, Nancy, each have $15 in the bank
Initially both Fred and Nancy have $15
Every week Nancy plans to add $3 to her account
Let 'n' be the number of weeks she plans to add in her account
for 1 week, $3
For n weeks , its 3n
So amount of money in Nancy's account after 'n' weeks = 15 + 3n
Fret plans to add $1 to his account each week
for 1 week, $1
For n weeks , its 1n
So amount of money in Fred's account after 'n' weeks = 15 + 1n
Now we need to find out 'n' when
Nancy's account = 2 times of Fred's account
15 + 3n = 2(15+1n)
Distribute 2 inside the parenthesis
15 + 3n = 30 + 2n
Subtract 2n on both sides
15 + n = 30
Subtract 15 on both sides
n = 15
Hence, it will take 15 weeks for Nancy’s account to have TWICE as much money as Fred’s account
Graph the linear equation.find three points that solve the equation,then plot on the graph -3x++2y=11
[tex]-3x+2y=11\qquad\text{add 3x to both sides}\\\\2y=3x+11\qquad\text{divide both sides by 2}\\\\y=\dfrac{3}{2}x+\dfrac{11}{2}\\\\for\ x=1\to y=\dfrac{3}{2}(1)+\dfrac{11}{2}=\dfrac{3}{2}+\dfrac{11}{2}=\dfrac{14}{2}=7\to(1,\ 7)\\\\for\ x=-3\to y=\dfrac{3}{2}(-3)+\dfrac{11}{2}=-\dfrac{9}{2}+\dfrac{11}{2}=\dfrac{2}{2}=1\to(-3,\ 1)\\\\for\ x=-5\to y=\dfrac{3}{2}(-5)+\dfrac{11}{2}=-\dfrac{15}{2}+\dfrac{11}{2}=-\dfrac{4}{2}=-2\to(-5,\ -2)[/tex]
Amy has 408 beads she gives 322 beads to her sister how many beads dose amy have now
Answer:
86
Step-by-step explanation:
Subtract 322 from 408
8-2=6
we cant subtract 2 from zero so we take 1 from the next
10-2=8
3-30
86
Hope this helps! (Brainliest please!)
Which is the solution to (x-2)(x+10)=13
The solution to (x-2)(x+10)=13 is x can be either 3 or -11, therefore the problem has 2 solutions.
Answer:
x = 3 or x = -11
Hope This Helps!
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- Innverted
x − 2y = 14
x + 3y = 9
(1, 12)
(−1, −12)
(12, −1)
(12, 1)
Find the value of x and y
Answer:
x=90: y =43
Step-by-step explanation:
Given is a triangle. In ABC, AB = AC is given. also angle C = 47 is given.
AD is angle bisector of angle A
Since two sides are equal, ABC is isosceles. We have angle C = angle B
Hence angle B = 47 degrees.
Angle A = 180-(B+C) = 180-94 = 86
So angle y = 1/2 (86) = 43
Consider triangle BAD.
We have got two angles as 47 and 43.
Hence third angle is 180-(47+43) = 90
So x=90, y = 43
A rectangular playground has an area of 3,162 square meters. If the width of the rectangle is 51, find the length.
The length of the rectangular playground can be determined using the conversion of the area formula, Length = Area ÷ Width. Substituting the values provided gives us Length = 3,162 ÷ 51.
Explanation:The subject of this question is mathematics, more specifically, the topic involves calculating the dimensions of a rectangle when given the area and one side length. In this case, the student is asked to determine the length of a rectangular playground that has an area of 3,162 square meters and a known width of 51 meters.
The area of a rectangle is calculated by multiplying its length by its width, according to the formula: Area = Length x Width. This can be rearranged to find Length, resulting in: Length = Area ÷ Width.
Plugging in the values provided, we find the length by using the rearranged formula:
Length = 3,162 ÷ 51
With these calculations, we would find our answer for the length of the playground.
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Justin and Pedro each launched a toy rocket into the air. The height of Justin’s rocket is modeled by the equation h = –16t2 + 60t + 2. Pedro launched his rocket from the same position, but with an initial velocity double that of Justin’s. Which equation best models the height of Pedro’s rocket?
h(t) = at2 + vt + h0
h = –16t2 + 60t + 4
h = –32t2 + 120t + 4
h = –32t2 + 60t + 2
h = –16t2 + 120t + 2
Answer: h = -16t^2 + 120t + 2
65% of a group of people have brown eyes.
How many people are in the group if 260 people have brown eyes?
Answer:
There are 400 people in the group
Step-by-step explanation:
people with brown eyes = people * percentage with brown eyes
We know that 65 percent have brown eyes
There are 260 people with brown eyes.
We are looking for people
260 = people * .65
Divide each side by .65
260/.65 = people
400= people
BRAINLIEST ANSWER TO FIRST ANSWERER!!!!
What is the approximate area of the shaded sector in the circle shown below
Answers in pic
Answer:
B. 51 in²
Step-by-step explanation:
π14²= 615.752160104 (find total circle area)
30/360= 1/12 (calculate fraction size the section would be of the entire circle)
615.752160104/12= 51.3126800087 (the slice's area)
Answer:
51
Step-by-step explanation:
A school district transported a total of 409 students and teachers to a zoo in buses and vans.
-Each bus transported a total of 55 students and teachers.
-Each van transported a total of 12 students and teachers.
-There were 5 buses than vans
What is the total number of students and teachers who rode to the zoo in buses? What is the total number of students as teachers who rode to the zoo in vans?
( 18 points guaranteed)
Answer: There are 385 students and teachers who rode to the zoo in buses and 24 students and teachers who rode to the zoo in trains.
Step-by-step explanation:
Since we have given that
Total number of students and teachers = 409
Let the number of vans be x
Let the number of buses be x+5
Number of students and teachers each bus transported = 55
Number of students and teachers each van transported = 12
According to question,
[tex]55(x+5)+12x=409\\\\55x+275+12x=409\\\\67x=409-275\\\\67x=134\\\\x=\frac{134}{67}\\\\x=2[/tex]
Total number of students and teachers who rode to the zoo in buses will be
[tex]55(x+5)\\\\=55(2+5)\\\\=55\times 7\\\\=385[/tex]
Total number of students and teachers who rode to the zoo in vans will be
[tex]12x\\\\=12\times 2=24[/tex]
Hence, there are 385 students and teachers who rode to the zoo in buses and 24 students and teachers who rode to the zoo in trains.
To find the total number of students and teachers who rode to the zoo in buses, we need to determine the number of buses and multiply it by the number of students and teachers each bus transported. Each bus transported 55 students and teachers, while each van transported 12. By solving the equation using the given information, we can find the total number of students and teachers in each type of vehicle.
Explanation:To find the total number of students and teachers who rode to the zoo in buses, we need to determine the number of buses and multiply it by the number of students and teachers each bus transported.
Let x be the number of vans.
Since there were 5 buses more than vans, the number of buses can be represented as x + 5.
Each bus transports 55 students and teachers, so the total number of students and teachers in buses is (x + 5) * 55.
Each van transports 12 students and teachers, so the total number of students and teachers in vans is x * 12.
Since there were a total of 409 students and teachers, we can create an equation: (x + 5) * 55 + x * 12 = 409.
Solving this equation will give us the value of x, which represents the number of vans. Once we know x, we can calculate the total number of students and teachers who rode to the zoo in buses and vans.
A 20-foot ramp is used at the loading dock of a factory.lf the base of the ramp is placed 19 feet from the base of the dock,how high is the loading dock?
Answer:
6.24 feet (to nearest hundredth)
Step-by-step explanation:
Use the Pythagoras Theorem:-
20^2 = x^2 + 19^2 where x = height of the loading dock.
x^2 = 20^2 - 19^2 = 39
x = √39
= 6.2449 feet
The height of the loading dock is found to be approximately 6.24 feet.
To solve this problem, we will use the Pythagorean theorem, which is applicable when we have a right triangle. The theorem states:
a² + b² = c²
Here:
a is the height of the loading dock (which we need to find).
b is the base of the ramp (19 feet).
c is the length of the ramp (20 feet).
We can set up the equation as follows:
a² + 19² = 20²
a² + 361 = 400
a² = 39
a = √39 ≈ 6.24 feet
Thus, the height of the loading dock is approximately 6.24 feet.
hich of the following expressions is equivalent to |x + 4| < 5? A. –5 > x + 4 < 5 B. –5 < x + 4 < 5 C. x + 4 < 5 and x + 4 < –5 D. x + 4 < 5 or x + 4 < –5 Please select the best answer from the choices provided A B C D
Answer:
option B
Given : |x + 4| < 5
A. –5 > x + 4 < 5
B. –5 < x + 4 < 5
C. x + 4 < 5 and x + 4 < –5
D. x + 4 < 5 or x + 4 < –5
In general , |x|< n where n is positive
Then we translate to -n < x < n
|x + 4| < 5
5 is positive, so we translate the given absolute inequality to
-5 < x+4 < 5
So option B is correct
if the base of the parallelogram is 1.4 inches and the hight is 1/4 inch what is the area of the parallelogram
( area = base • height )
Answer:
0.35 [tex]in^{2}[/tex]
Step-by-step explanation:
Plug it in
[tex]1.4*\frac{1}{4}[/tex]
0.35 [tex]in^{2}[/tex]
Help please?
Describe a situation that matches the equation. 34 = g + 25
A: The temperature on Monday was 25 degrees below zero and on Tuesday the temperature got up to 34 degrees. What was the increase in temperature between Monday and Tuesday?
B: The eighth-grade class has 34 students. The year before, when the students were in seventh grade, there were 25 students. How many students were added between seventh and eighth grade?
C: A person bikes 34 miles on Monday and 25 miles on Tuesday. How many miles total did the person bike?
D: Jack has 25 marbles. Mary gives him 34 marbles. How many marbles does Jack have?
Answer:
The answer is B!
Step-by-step explanation:
The equation and the equation from scenario B are both, when simplified, g = 9.
Answer:
Option B matches the equation
Step-by-step explanation:
Equation: 34 = g + 25
A:Since we are given that The temperature on Monday was 25 degrees below zero So, in given equation there should be -25 in place of 25
So, It does not matches the equation
B: The year before, when the students were in seventh grade, there were 25 students.
Let g be the no. of students added between seventh and eighth grade
So, Total students = 25+g
We are given that The eighth-grade class has 34 students.
So, equation becomes : 34=g+25
It matches the equation.
C :A person bikes 34 miles on Monday
He bikes 25 miles on Tuesday.
So, Total miles =25+34
So, It does not matches the equation
D: Jack has 25 marbles.
Mary gives him 34 marbles.
Total marbles = 25+34
So, It does not matches the equation
Hence Option B matches the equation
what is the solution to 4(x-7)=0.3(x+2)+2.11
Expand
4x - 28 = 0.3x + 0.6 + 2.11
Simplify 0.3x + 0.6 + 2.11 to 0.3x + 2.71
4x - 28 = 0.3x + 2.71
Add 28 to both sides
4x = 0.3x + 2.71 + 28
Simplify 0.3x + 2.71 + 28 to 0.3x + 30.71
4x = 0.3x + 30.71
Subtract 0.3x from both sides
4x - 0.3x = 30.71
Simplify 4x - 0.3x to 3.7x
3.7x = 30.71
Divide both sides by 3.7
x = 30.71/3.7
Simplify 30.71/3.7 to 8.3
x = 8.3
What is the slope of a line that is parallel to the line shown in this graph?
Answer:
The slope of the parallel line is 2/3
Step-by-step explanation:
Parallel lines have the same slope, so we need to find the slope of the line on the graph.
We can use the equation for the slope of a line
m = (y2-y1)/ (x2-x1)
=(2-0) /(3-0)
= 2/3
The slope of the line of the graph is 2/3 so
The slope of the parallel line is 2/3
what is the sum of 1/3(9-6m)+1/4(12m-8)
ANSWER:
EXPLANATION:
[tex]\frac{1}{3}(9-6m)+\frac{1}{4}(12m-8)\\\text{Distribute.}\\3 - 2m + 3m - 2\\\text{Simplify.}\\m + 1[/tex]
Answer:
I belive it is m +1
Step-by-step explanation:
The first hing you need to do is distribute, and then combine like terms.
The range of the following relation R:
Answer:
{- 5, - 4, 2 }
Step-by-step explanation:
the range is the corresponding values of y ( output) from the given set in ascending order without repeats