k is equal to 2, and the function g(x) is obtained by shifting the graph of f(x) two units to the left.
What is function?A function in mathematics is a relationship between a set of inputs (also known as the domain) and a set of outputs (also known as the range), where each input is connected to each output inexactly.
It can be compared to a machine that processes inputs and outputs in accordance with predetermined rules or algorithms.
In order to model real-world scenarios, carry out calculations, and examine mathematical relationships, functions are used.
They are frequently depicted through graphs or algebraic equations.
Since g(x) = f(x + k), we need to find the value of k that will shift the graph of f(x) to the graph of g(x). To do this, we can use the fact that g(x) = f(x + k) and the values in the table to determine the value of k.
When x = -1, g(x) = 5 = f(-1 + k). Since f has a point at (-1, 3), we know that f(-1) = 3.
Therefore, we have:
5 = f(-1 + k) = f(-1) + k = 3 + k
Solving for k, we get:
k = 5 - 3 = 2
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Complete the steps to solve the equation 2x2 + 12x-42=0 by completing the square.
2x² + 12x-42 = 0
Answer:
2(-3±√120)
Step-by-step explanation:
quadratic formula
what is 1 and 2/3 simplified
Answer:
The improper/exact form=5/3 and the decimal form is 1.(6) (which is the 6 repeated)
Step-by-step explanation:
Technically, you can't simplify 1 2/3, but these are just two ways you could change it into.
Two cylinders are shown below. Find the volume of each cylinder. Use 3.14 for π
π
. Round your answers to the nearest hundredth.
Answer: cylinder a is 12.45cm^3
cylinder b is 49cm^3
Step-by-step explanation: been through this my guy it was a struggle frl but bro igy frls
can someone please help me solve this?! it’s homework so it’s urgent!
Answer:
31
Step-by-step explanation:
The coordinates of point A are (-6,4). The coordinates of point B are (3, 4). Which expression represents the distance, in units, between points A and B?
A. |-6| + |3|
C. |-6| + |-4|
B. |3| - |-6|
D. |4| - |-6|
Answer:
a
Step-by-step explanation:
6 - 6=0 the 0-3 -3 total of 9 and 6 + 3 is equal to 9
what is the length of the line
Step-by-step explanation:
rise = height = 5 units run = base = 2
Use Pythagorean theorem
L^2 = 5^2 + 2^2
L^2 = 29
L = sqrt (29)
why does it make sense that fraction are about division?
Answer:
Step-by-step explanation:
Fractions represent a division problem where the numerator is divided by the denominator. For example, the fraction 3/4 represents the division of 3 by 4, which can be written as 3 ÷ 4. This is why it makes sense that fractions are about division.
Furthermore, fractions are used to represent parts of a whole or a group. When we divide a whole into equal parts, we are essentially dividing the whole into groups, with each group having the same size. For example, if we divide a pizza into 8 equal slices, each slice represents 1/8th of the pizza. We can also think of this as dividing the pizza into 8 equal groups, with each group having one slice.
Therefore, fractions are a natural way to represent division, as they allow us to express how many parts we have out of a whole or a group, and how big each part is relative to the whole or group.
Marcus saw the factorization shown below in his textbook, but part of the factorization was covered by a drop of ink. What expression was covered by the drop of ink?
-24x^5-16x^3=-8x^3(?+2)
The missing expression that was covered by the drop of ink is simply 3[tex]x^{2}[/tex].
What is Algebraic expression ?
An algebraic expressiοn is a statement in mathematics that can cοntain variables, integers, οperatοrs (including additiοn, subtractiοn, multiplicatiοn, and divisiοn), as well as grοuping symbοls like brackets.
The given expression is:
-24[tex]x^{5}[/tex] - 16[tex]x^{3}[/tex] = -8[tex]x^{3}[/tex] (? + 2)
To find the missing expression, we need to isolate the unknown factor, denoted by the question mark (?). We can begin by factoring out the common term of -8x³ from the left side of the equation:
-8[tex]x^{3}[/tex](3[tex]x^{2}[/tex] + 2) = -8[tex]x^{3}[/tex](? + 2)
Now, we can divide both sides by -8[tex]x^{3}[/tex], which gives:
3[tex]x^{2}[/tex] + 2 = ? + 2
Subtracting 2 from both sides yields:
3[tex]x^{2}[/tex] = ?
Therefore, the missing expression that was covered by the drop of ink is simply 3[tex]x^{2}[/tex].
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solve for x. round to the nearest tenth
A bag contains 42 red, 45 green, 20 yellow, and 32 purple candies. You pick one candy at random. Find the probability that it is yellow or green.
The probability to pick one candy at random that is yellow or green through which relation satisfied is [tex]\frac{65}{139}[/tex]
What about probability ?
Probability is a branch of mathematics that deals with the study of random events or experiments. It is a measure of the likelihood or chance of an event occurring, expressed as a number between 0 and 1, where 0 indicates an impossible event and 1 indicates a certain event.
The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. For example, if you roll a fair six-sided die, the probability of rolling a 3 is 1/6, since there is only one favorable outcome (rolling a 3) out of six possible outcomes (rolling any number from 1 to 6).
Probability theory is used in a wide range of fields, including statistics, economics, physics, engineering, and computer science, to model and analyze phenomena that involve uncertainty or randomness. It is also used in many practical applications, such as risk assessment, decision making, and game theory.
According to the given information:
The probability it is yellow:
[tex]\frac{20}{20+42+45+32} = \frac{20}{139}[/tex]
The probability it is green:
[tex]\frac{45}{45+20+42+32} = \frac{45}{139}[/tex]
P(green, yellow):
⇒ [tex]\frac{20}{139} + \frac{45}{139}\\\\\frac{65}{139}[/tex]
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Answer:
65/139
Step-by-step explanation:
Acellus
three-guys vending inc. supplies vended food to a large university. because students often kick the machines out of anger and frustration, management has a constant repair problem. the machines break down on an average of three per hour, and the breakdowns are distributed in a poisson manner. downtime costs the company $230/hour per machine, and each maintenance worker gets $28 per hour. one worker can service machines at an average rate of five per hour, distributed exponentially; two workers working together can service seven per hour, distributed exponentially; and a team of three workers can repair eight per hour, distributed exponentially. what is the optimal maintenance crew size for servicing the machines? and why?
This is because, in this scenario, the total cost per hour (-$432/hour) is the lowest compared to the costs of having two or three workers (-$864/hour and -$1,066/hour, respectively).
To determine the optimal maintenance crew size for servicing the machines at Three-Guys Vending Inc., we need to consider the average rate of breakdowns, downtime costs, and worker costs for each crew size.
The breakdowns are distributed in a Poisson manner, and the service rates are distributed exponentially.
1. Average breakdown rate: 3 machines/hour
2. Downtime cost: $230/hour per machine
3. Worker cost: $28/hour per worker.
Crew Size Scenarios:
A. One worker: services 5 machines/hour
B. Two workers: service 7 machines/hour together
C. Three workers: service 8 machines/hour together
First, we'll calculate the downtime and worker costs for each scenario:
A. One worker:
Downtime cost = (3 breakdowns/hour - 5 services/hour) x $230 = -$460/hour
Worker cost = 1 x $28 = $28/hour
Total cost = -$460 + $28 = -$432/hour
B. Two workers:
Downtime cost = (3 breakdowns/hour - 7 services/hour) x $230 = -$920/hour
Worker cost = 2 x $28 = $56/hour
Total cost = -$920 + $56 = -$864/hour.
C. Three workers:
Downtime cost = (3 breakdowns/hour - 8 services/hour) x $230 = -$1,150/hour
Worker cost = 3 x $28 = $84/hour
Total cost = -$1,150 + $84 = -$1,066/hour
From the calculations above, the optimal maintenance crew size for servicing the machines is one worker.
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write the expression in exponential form using a rational exponent. 3sqrt2^4
As a result, 12 is the exponential expression employing a rational exponent.
Define Logic exponent?An exponent of a fraction or rational number is said to have a rational exponent. With x as the base, p as the power, and q as the root 21, it may be represented as x(p/q). It can be transformed into the corresponding radical form,
for example, x(p/q) = (x(1/q))p = qxp 21. Similar rules apply to rational exponents and integer exponents 1.
With a rational exponent, the expression 3√24 can be expressed exponentially as follows:
3√2⁴= 3(2²)
= 3(2²) = 12
As a result, 12 is the exponential expression employing a rational exponent.
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your house is located at (0,0) to get from your house to school, you walk 2 blocks east and 1 block south. what ordered pair corresponds to the location of your school? b.
The ordered pair of the location of the school from the house is found to be (2,1).
It is said that the house is located at (0,0).
We can assume this point to be the origin so we can see that the house is located at the origin and the school is located 2 blocks east and one block south.
Now in the ordered pair the first term represents the X co-ordinate and the second term represents the Y co-ordinate.
As we are moving to the right we can say that we are moving towards the positive x axis and we are moving 1 block south, we can say that we are moving towards the positive y axis.
Han the corresponding ordered pair to the location of the school will be (2,1).
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sean prefers apples to clementines, and he prefers clementines to pears. if sean is rational, what would he choose if offered pears or apples?
Sean would choose apples over pears if he were offered both, based on his preference order of apples > clementines > pears and the assumption that his preferences are transitive.
Sean's preference order for fruits is: apples > clementines > pears. As a rational decision-maker, Sean would choose the option that he prefers the most. In this case, since he prefers apples over clementines and pears, if he were offered pears or apples, he would choose apples.
This decision is based on the assumption that Sean's preferences are transitive, meaning that if he prefers A to B and B to C, then he would prefer A to C. Therefore, choosing apples over pears is the most rational decision for Sean, based on his given preference order.
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here's another one we're doing
When we simplify an equatiοn and end up with a cοntradictiοn like this, it means that the equatiοn has nο sοlutiοn.
What is system οf linear equatiοns?The intersectiοns οr meetings οf the lines οr planes that represent the linear equatiοns are knοwn as the sοlutiοns οf linear equatiοns. The set οf values fοr the variables in every feasible sοlutiοn is knοwn as a sοlutiοn set fοr a system οf linear equatiοns.
Nοt a Sοlutiοn
If there is nο intersectiοn οf any lines, οr if the graphs οf the linear equatiοns are parallel, then the system οf linear equatiοns cannοt be sοlved.
The equatiοn 5 + 9z = 9z can be simplified as fοllοws:
5 + 9z = 9z
5 = 0
This is a cοntradictiοn since 5 cannοt be equal tο 0. Therefοre, there is nο sοlutiοn fοr this equatiοn.
In general, when we simplify an equatiοn and end up with a cοntradictiοn like this, it means that the equatiοn has nο sοlutiοn.
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A family is purchasing concrete in order to create a foundation for a rectangular outdoor patio. The rectangular patio is to be 30-feet wide and 17-feet long. To meet specifications, the concrete must be poured to a depth of .25 feet. Large amounts of concrete can be purchased by the cubic foot. How many cubic feet of concrete will it take to construct the patio? Round your answer to the nearest tenth.
Step-by-step explanation:
L X W X D = cubic feet volume
17 X 30 X .25 = 127. 5 ft^3
Please help! Urgent
Cartridges come in different sizes and shapes, and the amount of liquid ink
They can hold varies depending on the model and manufacturer.
Of course, I am here to help.
However, to better assist you, I will need more information regarding your urgent situation.
Once I have a better understanding of your situation, I can provide you with a more tailored and effective response.
In the meantime, I recommend taking a few deep breaths and staying calm.
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which recursive definition could be used to generate the sequence (3,6,3,6,3)
Answer: a1 = 3 and an = an-1 + 3(-1)n
Step-by-step explanation:
* start off with the first term being a1 = 3
* add on 3 to get to 6 as the second term
* add on -3, to get back to 3 once more
* add on the general term 3*(-1)^n (bc the pattern continues like, forever)
* term is found by a(n) = a(n-1) + 3*(-1)^n
I think This is correct as I found a similar brainly post
3) Texas enforces a 6% sales tax on items $75 and over. What would be a) the total tax and b)) the total cost on a purchase of items that cost $64, $78, $102 and $28 helppp pls
The vector u has magnitude 3 and direction 160°. If vector v = 2u, then what is
the magnitude and direction of vector v?
In response to the stated question, we may state that As a result, vector v has a magnitude of 6 and a direction of 160°.
What is Vector?A vector in mathematics is a mathematical object with both magnitude (or length) and direction. Vectors are frequently depicted as arrows, with the length of the arrow representing the magnitude and the direction of the arrow representing the vector's direction. A vector, for example, might represent an object's velocity, where the magnitude of the vector indicates the object's speed and the direction of the vector represents the direction of motion.
Assuming that u has a magnitude of 3 and a direction of 160°.
Vector u can be represented by its components as follows:
3 cos(160°)i + 3 sin(160°)j = u
where I and j are unit vectors pointing in the x and y directions.
We now know that vector v = 2u, implying that the magnitude of vector v is:
|v| = |2u| = 2|u| = 2(3) = 6
As a result, the magnitude of vector v is 6.
We can use the fact that vector v is in the same direction as vector u but scaled by a factor of two to determine its direction. As a result, the vector v's direction is also 160°.
As a result, vector v has a magnitude of 6 and a direction of 160°.
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The salesman has observed that many students are looking for cars that cost less
than $5,000. If he decides to also deal in cars that cost less than $5,000 and projects selling 200 of them over the next 10 years, how will the distribution be affected?
A distribution that includes more vehicles sold at lower prices and may deviate from the initial distribution as a result of the inclusion of vehicles priced under $5,000.
What is distribution?A distribution in statistics is a function that identifies all potential values for a dataset together with their frequencies or probabilities. The normal distribution, the binomial distribution and the Poisson distribution are just a few examples of frequent distribution types. Data are described and analyzed using distributions, which may offer significant insights about a dataset's central tendency, variability, and form.
The distribution will be impacted in a number of ways if the salesperson decides to also offer automobiles that cost less than $5,000 and forecasts selling 200 of them over the next ten years. In particular, it will
Growth in vehicle sales: Over the next 10 years, more vehicles under $5,000 will be sold, increasing the overall vehicle sales.
Change the distribution of prices towards lower values: By selling more automobiles at lower prices, the introduction of more affordable vehicles will change the price distribution towards lower values.
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Three ballet dancers are positioned on stage. Max is 2 feet straight behind Kenji and 4 feet directly left of Lindsey. When the music begins, Max twirls to Lindsey's position, then leaps to Kenji's position, and finally walks back to his original position. How far did Max travel? If necessary, round to the nearest tenth.
Answer: 8.5 feet
Step-by-step explanation:
To determine how far Max traveled, we can use the Pythagorean theorem to find the distances between the points.
Max twirls to Lindsey's position:
Since Max is 2 feet behind Kenji and 4 feet left of Lindsey, Max and Lindsey form a right triangle with legs of 2 feet and 4 feet. Using the Pythagorean theorem:
a² + b² = c²
2² + 4² = c²
4 + 16 = c²
20 = c²
Taking the square root of both sides:
c = √20 ≈ 4.47 feet (rounded to the nearest tenth)
Max leaps to Kenji's position:
Since Max was initially 2 feet behind Kenji, the distance between Lindsey and Kenji is also 2 feet.
Max walks back to his original position:
The distance between Max's original position and Kenji's position is 2 feet.
Adding up the distances:
4.47 feet (Max to Lindsey) + 2 feet (Lindsey to Kenji) + 2 feet (Kenji to Max's original position) = 8.47 feet
So, Max traveled approximately 8.5 feet (rounded to the nearest tenth) during his movements.
The distance Max traveled can be found by calculating the distance of each movement he makes and adding them up. First, we need to use the Pythagorean theorem to calculate the distance between Lindsey and Max:
sqrt(4^2 + 2^2) = sqrt(16 + 4) = sqrt(20) = 2*sqrt(5)
So, Max travels 2*sqrt(5) feet to get to Lindsey's position. Next, he travels the distance between Kenji and Lindsey, which is 4 feet:
distance = 4
Finally, he travels in a straight line back to his original position, which is 2 feet straight behind Kenji:
distance = 2
Adding these distances together, we get:
2*sqrt(5) + 4 + 2 = 2*sqrt(5) + 6
Rounding to the nearest tenth gives us a final answer of approximately 8.5 feet.
Yadira'smom is buying hot dogs and hot dog buns for the family barbecue.
Hot dogs come in packs of 12 and hot dog buns come in packs of 9.
The store does not sell parts of a pack and Yadira's mom wants the same
number of hot dogs as hot dog buns.
What is the smallest total number of hot dogs that Yadira's mom can
nurchase?
Step-by-step explanation:
To find the smallest total number of hot dogs that Yadira's mom can purchase, we need to find the least common multiple (LCM) of 12 and 9, since she wants the same number of hot dogs as hot dog buns.
The multiples of 12 are: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, ...
The multiples of 9 are: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, ...
The least common multiple of 12 and 9 is 36, since it is the smallest number that appears in both lists. Therefore, Yadira's mom should purchase 36 hot dogs (3 packs of 12) and 36 hot dog buns (4 packs of 9) for the family barbecue.
Select all the expressions that are equivalent to the number in the picture
Answer:
The expressions 10³÷10⁷, 10¹²/10¹⁶, and 10⁻²/10² are all equivalent to 10⁻⁴.
Step-by-step explanation:
When dividing exponents with the same base you subtract the exponents.
For visuals, in the equation 10³÷10⁷ it would be 10³⁻⁷ which would be 10⁻⁴ since 3 minus 7 is negative 4.
It is the same thing for 10¹²/10¹⁶, it would be 10¹²⁻¹⁶ which is equal to 10⁻⁴.
The same method can be used for 10⁻²/10² (10⁻²⁻²).
(Trig word problems)
Charlotte wants to use a sheet of fiberboard 34 inches long to create a skateboard ramp with a 20° angle of elevation from the ground. How high will the ramp rise from the ground at its highest end? Round your answer to the nearest tenth of an inch if necessary.
Answer:
The ramp will rise 11.6 inches from the ground at its highest end.
11.6 in.
Step-by-step explanation:
In this example we can use the sine function to determine how high the ramp will rise from the ground.
The definition of the sine function is
[tex]\sf \sin x= \dfrac{opposite}{hypotenuse}[/tex]
[tex]\sf \sin x= \dfrac{O}{H}[/tex]
In this case we are looking to evaluate the length of the opposite side.
We can rearrange the equation to isolate [tex]\sf O[/tex].
Multiply both sides of the equation by [tex]\sf H[/tex].
[tex]\sf H \cdot \sin x= \dfrac{O}{H} \cdot H[/tex]
Cancel the common factor of [tex]\sf H[/tex] on the right side leaves us with
[tex]\sf H \cdot \sin x= \dfrac{O}{\diagup \!\!\!\! H} \cdot \diagup \!\!\!\! H[/tex]
[tex]\boxed{\sf O= H \cdot \sin x}[/tex]
Numerical Evaluation
In this example we are given
[tex]\sf x=20\\\sf H=34[/tex]
Substituting our given values into the equation yields
[tex]\sf O= 34\cdot \sin 20[/tex]
[tex]\sf O=11.628685[/tex]
Rounding to the nearest tenth
[tex]\sf O=11.6[/tex]
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Sam can paint a house in 3 days. With Clark's help, Sam can paint
the same house in 1.2 days. How long would it take Clark to paint
the house on his own?
(A) 2 days
(B) 0.86 days
(C)1.8 days
(D) 4 days
Answer:
C
Step-by-step explanation:
Because 1.2+1.8 equal to 3.
a tire for a car is 22 inches in diameter. if the car is traveling at a speed of 90 mi/hr, find the number of revolutions the tire makes per minute.
The total number of revolutions per minute tire makes when the car is traveling at a speed of 90 mi/hr and the tire has a diameter of 22 inches is equal to approximately 1375.09.
Diameter of a car tire = 22 inches
Speed of a car = 90mi/hr
Let us first convert the speed from miles per hour to inches per minute,
Since the diameter of the tire is given in inches.
90 mi/hr
= 90 × 5280 ft/hr
= 475200 ft/hr
= 475200 × 12 in/hr
= 5,702,400 in/hr
= 95,040 in/min
Number of revolutions the tire makes per minute,
Distance the tire travels in one revolution.
The circumference of a circle is given by,
C = πd
where C is the circumference and d is the diameter.
So the distance the tire travels in one revolution is,
d = π(22 in)
= 69.115 in
Now, the number of revolutions per minute is ,
=distance traveled per minute / distance traveled in one revolution
⇒ revolutions per minute = 95,040 in/min / 69.115 in/rev
⇒revolutions per minute ≈ 1375.09 rev/min
Therefore, the tire makes approximately 1375.09 revolutions per minute with tire of diameter of 22 inches.
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find the distance between 0,7 and 9,-6
Given:-
[tex] \textsf{(0 , 7) }[/tex][tex] \: [/tex]
[tex] \textsf{(9 , -6)}[/tex][tex] \: [/tex]
To find:-
[tex] \textsf{Distance between two points = ?}[/tex][tex] \: [/tex]
By using formula:-
[tex] \pink\bigstar \underline{{ \boxed{ \sf{ \color{lightgreen}Distance = \sqrt{( x_2 - x_1 )² + ( y_2 - y_1 )²}}}}}[/tex]
[tex] \: [/tex]
Solution:-
[tex] \sf{D = \sqrt{( x_2 - x_1 )² + ( y_2 - y_1 )²} }[/tex]
[tex] \: [/tex]
where ,
[tex] \sf \bold{0 = x_1 }[/tex][tex] \: [/tex]
[tex] \sf \bold{ 7 = y_1}[/tex][tex] \: [/tex]
[tex] \sf \bold{ 9 = x_2 }[/tex][tex] \: [/tex]
[tex] \sf \bold{ -6 = y_2}[/tex][tex] \: [/tex]
[tex] \sf \: D = \sqrt{( 9 - 0 )² + ( -6 - 7)²} [/tex]
[tex] \: [/tex]
[tex] \sf \: D = \sqrt{ ( 9 )² + ( - 13 )²}[/tex]
[tex] \: [/tex]
[tex] \sf \:D = \sqrt{ 81 + 169} [/tex]
[tex] \: [/tex]
[tex] \underline{ \underline{ \sf{ \color{hotpink} \: D = \sqrt{{250}\: }}}}[/tex]
[tex] \: [/tex]
━━━━━━━━━━━━━━━━━━━━━━━
hope it helps:)
assume a normally distributed test has a mean of 100 and standard deviation of 7. what probability of a score greater than 115? group of answer choices 1.62% 48.38% 98.38% 51.62%
If the test is normally distributed, then the probability of a score greater than 115 is (a) 1.62%.
In order to find probability of a score greater than 115 in a normally distributed test with a mean of 100 and standard deviation of 7,
First, We have to calculate z-score for 115, and
The z-score formula is ⇒ z = (x - μ)/σ,
where x = score of interest, μ = mean, and σ = standard-deviation.
In this case, we have x = 115, μ = 100, and σ = 7.
The z-score for 115 is ⇒ z = (115 - 100)/7 = 2.14
By using the normal table :
⇒ P(Z > 2.14) = 0.0162
Therefore, the required probability is 0.0162 or 1.62%, the correct option is (a) 1.62%.
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The given question is incomplete , the complete question is
Assume a normally distributed test has a mean of 100 and standard deviation of 7. What probability of a score greater than 115?
(a) 1.62%
(b) 48.38%
(c) 98.38%
(d) 51.62%
PLEASE HELP I NEED THIS ASAP PLS
The linear functions f(x) and g(x) are represented on the graph, where g(x) is a transformation of f(x):
Part A: Describe two types of transformations that can be used to transform f(x) to g(x).
Part B: Solve for k in each type of transformation.
Part C: Write an equation for each type of transformation that can be used to transform f(x) to g(x).
A. The two types of transformations that can be used to transform f(x) to g(x) are translation and reflection.
B. The value for k in the transformation is -6.
C. The equation for transforming is g (x) = f (x) - 6.
What is transformation?
Shapes on a coordinate plane can be translated, rotated, and reflected using transformations. You can rotate, translate, or reflect any line, point, or vector.
A. The two types of transformations that can be used to transform f(x) to g(x) are translation and reflection.
Translation means shifting the graph left, right, up or down.
Reflection means creating a mirror image over x - axis or y - axis.
B. Both the transformations will have the same k value.
The graph g (x) is the translation of f (x) towards left with 6 units.
So, the value of k is -6.
C. The equation for transformation is as follows:
⇒ g (x) = f (x) + k
⇒ g (x) = f (x) - 6
Hence, the required solutions have been obtained.
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