Use the graphs of f and g. Which describes the transformation from the graph of f to the graph of g?
f(x)=−4x+8f(x)=−4x+8
g(x)=−f(x)g(x)=−f(x)
1.horizontal translation 1 units left
2.vertical translation 4 units down
3.reflection in the x-axis
4.reflection in the y-axis
5.horizontal shrink by a factor of 1/4
6.horizontal stretch by a factor of 4
7.vertical shrink by a factor of 1/4
8.vertical stretch by a factor of 4
Answers
The transformation from the graph of [tex]\( f(x) = -4x + 8 \)[/tex] to [tex]\( g(x) = -f(x) \)[/tex] is a reflection in the x-axis.
The [tex]- \( f(x) = -4x + 8 \)[/tex] is a linear function with a negative coefficient in front of [tex]\( x \)[/tex], indicating a reflection in the x-axis.
When you negate f(x) to get g(x) = -f(x), it reflects the graph of f(x) in the x-axis.
So, the correct answer is: 3. Reflection in the x-axis
Related Questions
What transformation takes
f(x)=15x+3 to g(x)=5x+3 ?
Question 1 options:
a horizontal compression by a factor 1/3
a translation 6 units right
a horizontal stretch by a factor of 3
a translation 6 units down
Answers
[tex]5x + 3 = 15( \frac{1}{3} x) + 3 = f( \frac{1}{3} x)[/tex]
So [tex]g(x) = f( \frac{1}{3} x)[/tex]
When a function f(x) is transformed into f(ax) where |a| > 1, it's a horizontal compression by a factor of 1/a. But when a function f(x) is transformed into f(ax) where |a| < 1, it's a horizontal stretch by a factor of 1/a.
In this case, a = 1/3. So that's a horizontal stretch by a factor of 1/(1/3) = 3. Thus the answer choice is C.
Write a polynomial function in factored form with zeros at −2, 0, and 3.
Answers
so x(x + 2)(x - 3) = 0
x(x^2 + 2x - 3x - 6) = 0
x(x^2 - x - 6) = 0
x^3 - x^2 - 6x = 0
answer
x^3 - x^2 - 6x = 0
hope it helps
Each exterior angle of an equilateral triangle has which measure?
Answers
Answer:
60 degreesStep-by-step explanation:
Find the value of x and y.
A. X=73.3, Y=15.3
B. X=73.3, Y=20.7
C. X=100, Y=10
D. X=100, Y=26
Thank You!
Answers
Find the missing angles: you may have to find missing angles that are not labeled.
Answers
angle b +50+75 = 180 ( sum of angles in a triangle )
b= 180-50-75 =55
b= c = 55 ( vertically opposite angles )
d= 125
d= 125 - b ( supplementary angles
d= 180 - 55 = 125
Step-by-step explanation:
f = 50 (parallel lines)
180 - 50 = a (angle sum of straight line)
a = 130
50 + 75 + b = 180 (angle sum of triangle)
125 + b = 180
b = 180 - 125
= 55
c = 55 (vertically opposite angles)
e = 55 (alternate angles)
d= 180 - 55 (angle sum of straight line)
= 125
9+7r>r–3≥7r+3
Gonna' have to spam this and make it more points, PLEASEEE!, ALSO GONNA' TALK IN ALL CAPS FOR BETTER UNDERSTANDING!
Answers
A student’s construction of the perpendicular bisector of is shown below. What is the student’s error?
Answers
30 POINTS PLEASE HELP! An investment in a savings account grows to three times the initial value after t years.
If the rate of interest is 5%, compounded continuously, t = (blank) years.
Answers
A = A₀ × (1+growth rate)ⁿ
Where:
A = The final value after 'n' years
A₀ = The initial value
Growth rate = 5% = 0.05
We know that final value = 3 × Initial value
So that's A = 3A₀
Substitute this expression into the formula, we have
3A₀ = A₀ (1+0.05)ⁿ
3A₀ ÷ A₀ = (1.05)ⁿ
3 = (1.05)ⁿ
from here we can use the trial and error method:
take n = 1, then (1.05)¹ = 1.05
take n = 2, then (1.05)² = 1.1025
take n = 3, then (1.05)³ = 1.16
take n = 5, then (1.05)⁵ = 1.3
take n = 10, then (1.05)¹⁰ = 1.6
take n = 20, then (1.05)²⁰ = 2.7
take n = 30, then (1.05)³⁰ = 4.3 ⇒ too big
take n = 25, then (1.05)²⁵ = 3.4
take n = 24, then (1.05)²⁴ = 3.2
take n = 23, then (1.05)²³ = 3.1
take n = 22, then (1.05)²² = 2.9
so, the number of years it takes for the account to grow three times the initial value after 23 years.
Find the side length of a square with the same perimeter as a equilateral triangle with side 7 cm.
Answers
Since it's a equilateral triangle, which means all the sides of the triangle is the same length.
Perimeter of triangle = 7 x3
= 21
And there r 4 sides in a square,
So just divide 21 by 4
21 ÷ 4 = 5.25
So the answer is 5.25 cm
Final answer:
The side length of a square with the same perimeter as an equilateral triangle with side 7 cm is 5.25 cm.
Explanation:
To find the side length of a square with the same perimeter as an equilateral triangle with sides of 7 cm, first calculate the perimeter of the triangle, which is 7 cm x 3 = 21 cm. Since a square has four equal sides, divide the perimeter by 4 to get the side length of the square. Thus, the side length would be 21 cm ÷ 4 = 5.25 cm.
The noise rating of an air conditioner is 50 decibels, and the noise rating of a washing machine is 65 decibels. Determine how many time greater the washing machine's intensity of sound is.
Use the formula , β = 10log I/I 0 where β is the sound level in decibels, I is the intensity of sound you are measuring, and Io is the smallest sound intensity that can be heard by the human ear (roughly equal to 1 x 10^-12 watts/m2).
The washing machine's intensity of sound is (blank) times greater than that of the air conditioner.
Answers
[tex]10 log \frac{I_{1}}{I_{0}}=50 \\\\ log \frac{I_{1}}{I_{0}}=5 [/tex]
The decibels of the washing machine is 65. Its intensity of sound, I₂, is given by
[tex]10log \frac{I_{2}}{I_{0}}=65 \\\\ log \frac{I_{2}}{I_{0}}=6.5 [/tex]
Therefore
[tex] \frac{I_{1}}{I{0}}=10^{5} \\\\ \frac{I_{2}}{I_{0}}=10^{6.5} \\\\ \frac{I_{2}}{I_{1}}= \frac{10^{6.5}}{10^{5}}=10^{1.5}= 31.6[/tex]
Answer:
The washing machine's sound intensity is 31.6 times greater than that of the air conditioner.
Answer:
the answer is 31.6 on PLATO
Solve the system by substitution, show all steps.
-x-y-z=-8
-4+4y+5z=7
2x+2z=4
Answers
z=-x+2
plug into the second equation -4+4y+5(-x+2)=7
-4+4y-5x+10=7
4y-5x=1
y=5/4x+1/4
plug both of these into the first equation x+y+z=8
x+5/4x+1/4+(-x+2)=8
5/4x+2.25=8
5/4x=5.75
x=4.6
now plug back into the substitution equations.
z=-x+2= -4.6+2= -2.6
y=5/4x+1/4=5.75+1/4=6
the answer is (4.6, 6, -2.6)
Answer:
In Point Form: (x,y,z)= (3,6,-1)
In Equation Form: x=3, y=6, z=-1
Step-by-step explanation:
1) Solve for x
2x+2z=4 (Subtract 2z from both sides)
-2z -2z
2x= 4-2z (Divide 2 from both sides)
/2 /2
x=2-z
2) Substitute 2-z for x in
-x-y-z=-8
-(2-z)-y-z=-8
-2+z-y-z=-8 (Combine Like Terms)
-2-y=-8 (Add 2 to both sides)
+2 +2
-y=-6 (Divide -1 from both sides)
/-1 /-1
y=6
3) Substitute 2-z for x & 6 for y in
-4x+4y+5z+=7
-4(2-z)+4(6)+5z=7 (Get rid of parentheses)
-8+4z+24+5z=7 (Combine Like Terms)
9z+16=7 (Subtract 16 from both sides)
-16 -16
9z+=-9 (Divide 9 from both sides)
/9 /9
z=-1
4) Now find x by substituting -1 for z in
x=2-z
x=2-(-1)
x=2+1
x=3
Therefore the answer is:
In Point Form: (x,y,z)= (3,6,-1)
In Equation Form: x=3, y=6, z=-1
a jar of coins contains dimes pennies and quarters there are 88 pennies in a jar. There are 5 dimes for every 4 pennies and there are 7 quarters for every 11 dimes how many coins are in the jar? A 180 B 258 C 268 D 350
Answers
Answer:
c 268
Step-by-step explanation:
i did the test on the home school time for learning
∠1 is a complement of ∠4, and m∠1=33∘m. Find m∠4.
Answers
This means that if ∠1 is complementary to ∠4, then
∠1 + ∠4 = 90°
33 + x = 90
x = 57
m∠4 = 57°
m∠1=33∘
then m<4 = 90 - 33 = 57
answer
m<4 = 57
Solve the system:
p-3q=-1
-5p+16q=5
a. (2,1)
b.(3,3)
c. (-1,0)
d.(5,2)
Answers
Answer: The correct option is
(c) (-1, 0).
Step-by-step explanation: We are given to solve the following system of equations :
[tex]p-3q=-1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\-5p+16q=5~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
From equation (i), we have
[tex]p-3q=-1\\\\\Rightarrow p=3q-1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)[/tex]
Substituting the value of p from equation (iii) in equation (ii), we get
[tex]-5(3q-1)+16q=5\\\\\Rightarrow -15q+5+16q=5\\\\\Rightarrow q=5-5\\\\\Rightarrow q=0.[/tex]
From equation (i), we get
[tex]p=3\times0-1=-1.[/tex]
Thus, the required solution is (p, q) = (-1, 0).
Option (c) is CORRECT.
How do you write this number in standard form
15,000+7000+400+9
Answers
A scuba diver used the expression below to describe his position in relation to sea level.
2 + (–20) + 8
Which statement could describe the diver’s movements?
Starting on a platform 2 feet above sea level, dive down to a location that is 18 feet below sea level, and then rise 8 feet.
Starting on a platform 2 feet above sea level, dive down to a location that is 20 feet below sea level, and then rise 8 feet.
Starting 2 feet below sea level, dive down 20 more feet, and then rise to a location that is 8 feet below sea level.
Starting 2 feet below sea level, dive down 18 more feet, and then rise to a location that is 8 feet below sea level.
Answers
starting on a platform 2 ft above sea level....so it is 2
dive down 20 ft....so this is below sea level...so it is -20
rise 8 ft...so it is 8
so ur answer is : 2nd answer choice
Answer:
Starting on a platform 2 feet above sea level, dive down to a location that is 20 feet below sea level, and then rise 8 feet.
Step-by-step explanation:
A scuba diver used the expression below to describe his position in relation to sea level.
2 + (–20) + 8
positive number is the feet above the sea level
negative number is the feet below the sea level (deep)
starting at 2 , 2 feet above sea level then down the sea 20 feet down,
finally rise 8 feet above the sea level
So, Starting on a platform 2 feet above sea level, dive down to a location that is 20 feet below sea level, and then rise 8 feet.
The test that gives a list of the possible rational zeros of a polynomial function is called the test.
Answers
Answer:
rational zero
Step-by-step explanation:
Which system is represented by the graph?
a. y > 2x
x + 2y ≤ –8
b. y ≥ 2x
x + 2y < –8
c. y < 2x
x + 2y ≥ –8
d. y ≤ 2x
x + 2y > –8
Answers
The correct answer is option A
See the graph below
To determine the system of two inequalities which is represented by the graph, you have to do such steps:
1 step. The dashed blue line represents sign > or <. The line has the equation y=2x, then the inequality should be y>2x or y<2x. Since point (-1,1) belongs to the blue shaded region, then the inequallity y>2x is true.
2 step. The solid red line represents sign ≤ or ≥. The line has the equation x+2y=-8, then the inequality should be x+2y≤-8 or x+2y≥-8. Since the origin (0,0) doesn't belong to the red shaded region, then the inequallity x+2y≤-8 is true.
Thus, the system is
[tex]\left\{\begin{array}{l}y>2x\\x+2y\le-8.\end{array}\right.[/tex]
Answer: correct choice is A.
Find an equation for a line that passes through the point (0, –3) and parallel to another line whose slope is 1.2.
Answers
y=1,2x+b
Now, we can plug in the point to solve for the intercept.
-3=1.2(0)+b
-3=0+b
b= -3
Finally, we can fill in the equation with all the information we've uncovered.
y=1.2x - 3
Final answer:
The equation of the line that passes through the point (0, -3) and is parallel to another line with a slope of 1.2 is y = 1.2x - 3.
Explanation:
To find an equation for a line that passes through the point (0, –3) and is parallel to another line with a slope of 1.2, we use the fact that parallel lines have the same slope. Since a line's equation can be written in the form y = mx + b, where m is the slope and b is the y-intercept, and we already know the slope (m = 1.2) and the y-intercept (b = -3, since the line passes through (0, -3)), our equation becomes:
y = 1.2x - 3
This means that any line parallel to one with a slope of 1.2 and passing through (0, -3) will also have a slope of 1.2, but the y-intercept will be unique to the point it passes through.
An aluminum recycling center pays0.08 per pound for cans how much will make receive for 21.5 pounds of cans
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Kevin earns $15 per hour for working 8 hours then he earns $18 per hour for working overtime for 4 hours a day what is the average time he works
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HELP PLEASE!!!!!
Find the radius of a circle if a central angle of 3π/2 intercepts an arc of 26.4 centimeters.
0.19 cm
3.14 cm
5.6 cm
Find the measure of a central angle that intercepts an arc of 81.5 cm in a circle whose radius is 16.3 cm.
5 rad16 rad65 radFind the arc length intercepted by a central angle of 3π/4 radians in a circle whose radius is 18.4 inches.
13.8π15.2π24.5πAnswers
26.4=r*0.081
therefore,. r=26.4/0.081=325.9cm
this is the answer if the given angle was in degree.
if the angle is in radian then,
26.4=r*3π/2
r=5.6 cm
all the best
Answer:
Find the radius of a circle if a central angle of 3π/2 intercepts an arc of 26.4 centimeters.
Ans: 5.6 cm
Find the measure of a central angle that intercepts an arc of 81.5 cm in a circle whose radius is 16.3 cm.
Ans: 5 rad
Find the arc length intercepted by a central angle of 3π/4 radians in a circle whose radius is 18.4 inches.
Ans: 13.8π
Select the postulate that is illustrated for the real numbers.
6 + 0 = 6
The commutative postulate for multiplication
Multiplication by one
The addition inverse postulate
Commutative postulate for addition
The distributive postulate
The additive identity postulate
The multiplication inverse
Answers
Answer:
The additive identity postulate
Step-by-step explanation:
6 + 0 = 6
Any number added with zero, we get the same number.
That is, a + 0 = a, where "a" is any real number.
Let's take a = 9, we get
9 + 0 = 9
Let's check out a few more examples:
-9 + 0 = -9
2/3 + 0 = 2/3
22 + 0 = 22
You can see any number added with 0, we get the same number.
Here 0 is additive identity, this is called additive identity postulate.
We are given 6 + 0 = 6 which illustrated by "The additive identity postulate."
Therefore, answer is "The additive identity postulate"
How do I solve this??
Answers
HELP ME PLS!!
The function graphed shows the total cost for a taxi cab ride for x miles.
Select from the drop-down menus to correctly identify the taxi cab ride information provided by the graph.
The slope is
5, 3, 2.5, 0.2
The slope represents
1)the total cost of the taxi ride
2)the total number of miles traveled
3)the cost per miles traveled
4)the initial cost of the ride
Answers
Hope this helps!
Have a great day.
~ ShadowXReaper069
The slope of the line between cost of taxi and distance is 2.5 and it represents the cost of taxi per mile of distance travelled.
What is slope of line ?
Slope of line is the angle made by the line from positive x-axis in anticlockwise direction, it also denoted the steepness of the line.
The function graphed shows the total cost for a taxi cab ride for x miles the cost in taxi is shown in y axis and the distance covered by taxi in x axis. Now, to find put the slope we must two coordinates which can be found out from the graph easy by observation as (0,3) and (2,8).
How using slope formula to find the slope of line :
[tex]\begin{aligned}\frac{y_{2}-y_{1}}{x_{2}-x_{1}}&=\frac{8-3}{2-0}\\&=\frac{5}{2}\\&=2.5\end{aligned}[/tex]
It represents the cost of taxi per mile of distance travelled.
Therefore, the slope of the line between cost of taxi and distance is 2.5 and it represents the cost of taxi per mile of distance travelled.
check and know more about slope of line here :
https://brainly.com/question/3605446
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The sum of two numbers is 62 . the larger number is 22 more than the smaller number. what are the numbers?
Answers
larger number: 22+x
x+(x+22)=62
2x+22=62
2x=62-22
2x=40
x=40/2
x=20
The smaller number is 20 and the bigger number is 22+20= 42
Hope I helped :)
Is the point (−7,1) a solution to the inequality
y < 0.5x + 9 ?
Question 1 options:
True
False
Answers
The given point (−7,1) is a solution to the inequality.
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
We must determine if the inequality holds for a certain set of ordered pairs in order to determine which ordered pairs constitute the answer to the inequality.
We have been given inequality is:
⇒ y < 0.5x + 9
To determine the point (−7,1) a solution to the inequality
Substitute x = -7 and y = 1 in the inequality, we get
⇒ y < 0.5x + 9
⇒ 1 < 0.5(-7) + 9
⇒ 1 < -3.5 + 9
Apply the subtraction operation in the above inequality, we get
⇒ 1 < 5.5
This is true.
Hence, the given point (−7,1) is a solution to the inequality.
Learn more about the inequalities here:
brainly.com/question/20383699
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You purchased a shirt on sale for $17.55. The discount on the shirt was $5.85. What was the original price of the shirt?
Which equation best models the scenario above?
x + 5.85 = 17.55
x - 5.85 = 17.55
x + 17.55 = 5.85
x - 17.55 = 5.85
Answers
The original price of the shirt is simply the sum of the purchased price and the discount price, that is:
original price = $17.55 + $5.85
original price = $23.40
The equation that best model this scenario is:
x - 5.85 = 17.55
where x is the original price
If Michelle walked 5 meters how many inches did she walk
Answers
Which of the following is a function equivalent to f(x) = 5(1.9)3x?
f(x) = 34.29x
f(x) = 5(6.86x)
f(x) = 5(6.86)x
f(x) = 328.51x
Answers
The function equivalent to f(x) = 5(1.9)3x is f(x) = 5(6.86)x.
Explanation:The function equivalent to f(x) = 5(1.9)3x is f(x) = 5(6.86)x.