[tex]3(23+18) < 6a \\ 41 < 2a \\ a > 41/2\implies a > 20.5[/tex]
Hope this helps.
Answer: a >41/2
Step-by-step explanation: Step 1: Simplify both sides of the inequality.
123<6a
Step 2: Flip the equation.
6a>123
Step 3: Divide both sides by 6.
6a/6>123/6
a>41/2
Graph -3x2+12y2=84 . What Are The Domain And Range?
The domain and range of the given graph function is R.
The equation -3x^2 + 12y^2 = 84 represents an ellipse in the coordinate plane. The standard form of an ellipse is (x^2/a^2) + (y^2/b^2) = 1, where a and b are the lengths of the semi-major and semi-minor axis, respectively.
To put the given equation in standard form, we need to divide both sides by 84, and divide the x^2 and y^2 by the square of their respective coefficient:
(-3/84)x^2 + (12/84)y^2 = 1
This gives us x^2/ (84/-3)^2 + y^2/ (84/12)^2 = 1
Which gives us x^2/28 + y^2/7 = 1
This means that the semi-major axis has a length of 2sqrt(7) and the semi-minor axis has a length of sqrt(7).
The domain of this function is all real numbers, because the x values can take any real value.
The range of this function is also all real numbers, because the y values can take any real value, within the boundaries of the ellipse.
So, the domain and range of the function -3x^2 + 12y^2 = 84 is all real numbers.
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The graph at the right illustrates the rate at which Dave and Joe are saving money.
a. Estimate the solution to the system.
b. Explain what this means in the context of
the saving money scenario.
This problem can be solved using a system of equations.
What is the system of equations?
A set or group of equations that are solved collectively is referred to as a system of equations. Both algebraic and graphical solutions are possible for these equations. The point of intersection of two lines represents the system of equations' solution.
Line 1
Taking two points on this line (0,300) and (4,450)
Equation of line y = mx+c
m = [tex]\frac{450 - 300}{4 - 0}[/tex] = 37.5
y = 37.5x + c
Substituting (0,300) in the above equation
300 = 37.5 * 0 + c
c = 300
Line equation y = 37.5x + 300
Line 2
Taking two points on this line (0,400) and (5,500)
m = [tex]\frac{500 - 400}{5 - 0}[/tex] = 20
y = 20x + c
Substituting (0,400) in the above equation
400 = 250* 0 + c
c = 400
Line equation y = 20x + 400
a) The solution of the system is when both lines coincide
37.5 x + 300 = 20x + 400
17.5 x = 100
x = 5.7
y = 20 * 5.7 + 400 = 514
Therefore the solution of the system is ( 5.7 , 514)
b) In terms of saving money scenario. This means that Dave and Joe have the same amount of savings at this point.
Therefore these are the solutions to the above system of equations.
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For which interval is the function constant?
(−∞,−6)
(2,∞)
(−6,0)
(0,2)
The function is constant in the interval (-6 to 0).
The correct option is (C).
What is a Function?In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
If the value of one of the variables does not alter the value of the other, the function is said to be constant.
As we can see, the function is constant in the range from x=-6 to 0, because the value of y in the function does not change as the value of x changes (-6 to 0).
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in 1986 one of the first video games, the Nintendo, sold for $180. Similar to many items, its value depreciated over time.
The depreciated value in 1990 will be $146.6.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that in 1986 one of the first video games, the Nintendo sold for $180. The depreciation rate per year is 5%.
The price after 1990 will be calculated as,
Price = 180 x ( 0.95 )⁵
Price = $146.6
The complete question is given below.
In 1986 one of the first video games, the Nintendo sold for $180. The depreciation rate per year is 5%. What is the cost at the end of 1990.
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f(x)=2x-3, find f(-4)
Answer:
f(- 4) = - 11
Step-by-step explanation:
substitute x = - 4 into f(x) , that is
f(- 4) = 2(- 4) - 3 = - 8 - 3 = - 11
Answer:
f(-4)=-11
Step-by-step explanation:
f(x)=2x-3
Let x=-4
f(-4)=2(-4)-3
= -8-3
= -11
The row-echelon form of the augmented matrix of a system of equations is given. Find the solution of the system.
x2 = 3/5, x1 = 9/4, and x3 = 2/3 of the row-echelon form of the augmented matrix are the answers to the equations.
what is unitary method ?The unit technique is a method of problem-solving where you first calculate the value of a single unit, then multiply that value to get the answer. Simply expressed, a single unit value is extracted from a specified multiple using the unit method. For instance, 40 pens will set you back 400 rupees, or $1.01. The method used to accomplish this might be standardized. a solitary nation. anything has a distinctive component. (Mathematics, Algebra) Its adjoint and reciprocal are equivalent. (Linear Algebra, Mathematical Analysis, Mathematics of Matrix or Operators)
given
Replace the variable in the equation with the given integer.
Check to see if the resulting equation is correct. The number is not a solution if it is false.
x2 = 3/5, x1 = 9/4, and x3 = 2/3 of the row-echelon form of the augmented matrix are the answers to the equations.
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Malik received a$300 gift card from his grandparents and is using it only to pay for his karate lessons, which cost $30 per month.
Write a function that describes the amount, d, in dollars, on the card after t months in both general and factored form.
Answer:
(General function) d(t) = 300 - 30t(Factored version) d(t) = 30(10 - t)Step-by-step explanation:
The amount in dollars is represented by d, and the amount of months is represented by the letter t. Using this, you can construct an equation using the given values in the form of f(x) = a - b(c). This equation represents the decrease in Malik's income after one month.
Hope this helps! :)
Last year, Ivan opened an investment account with 8600. At the end of the year, the amount in the account has decreased by 6%
The _____ describes the average distance of distribution values from the mean.
A.standard deviation
B.arithmetic average
C.mean
D.mode
E.median
Express the absolute value function f(x) = -7|x| as a piecewise-defined function.
Answer:1111
Step-by-step explanation:1111
PLEASE HELP!!
if 90° < 0 <180° and csc0 = 3, then cot0=
the value of cot∅ will be -2√2.
What is trigonometric function?
Trigonometry uses six fundamental trigonometric operations. Trigonometric ratios describe these operations. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six fundamental trigonometric functions. The ratio of sides of a right-angled triangle is the basis for trigonometric functions and identities. Using trigonometric formulas, the sine, cosine, tangent, secant, and cotangent values are calculated for the perpendicular side, hypotenuse, and base of a right triangle.
Given csc∅ = 3
This is given in 2nd qudrant (90° < 0 <180°).
Sin∅ = 1/3
cos∅ = √1-(1/3)² = -√ (8/9)
cot∅ = cos∅/Sin∅ = -2√2
Hence the value of cot∅ will be -2√2.
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If you were to graph the information provided in the table, what would be the labels for the x- and y-axes?
Answer:
The answer is right there, the left of the graph "number of burritos" is the x-axis, the y axis is the "cost"
Step-by-step explanation:
For a moving object, the force acting on the object varies directly with the object's acceleration. When a force of 81 N acts on a certain object, the acceleration of the object is 9m/2 . If the acceleration of the object becomes ms/2, what is the force?
If the acceleration of the object becomes 3 m/s^2, the force is equal to 27 Newton.
What is a direct proportion?Mathematically, a direct proportion can be represented the following mathematical expression:
y = kx
Where:
y represents the force.x represents the acceleration.k represents the constant of proportionality.Next, we would determine the constant of proportionality (k) as follows:
Constant of proportionality (k) = y/x
Constant of proportionality (k) = 81/9
Constant of proportionality (k) = 9.
For the force when the acceleration of the object becomes 3 m/s^2, we have:
y = kx
y = 9(3)
y = 27 Newton.
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Complete Question:
For a moving object, the force acting on the object varies directly with the object's acceleration. When a force of 81 N acts on a certain object, the acceleration of the object is 9 m/s^2. If the acceleration of the object becomes 3 m/s^2, what is the force?
Jacqueline, Kimberly, and Julia collect mechanical pencils. Kimberly owns two less than three times the number of mechanical pencils Jacqueline owns. Julia owns three less mechanical pencils than Jacqueline. Together, the three collectors own a total of 100 mechanical pencils. How many mechanical pencils does Kimberly own?
Kimberley owns 55 pencils.
What is the solution to a linear equation?The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.
Given: Kimberly owns two less than three times the number of mechanical pencils Jacqueline owns. Julia owns three less mechanical pencils than Jacqueline. Together, the three collectors own a total of 100 mechanical pencils. Let Jacqueline own x pencils then Kimberley owns 3x-2 and Julia owns x-3
Thus 3x-2+ x-3+x=100
5x=95
x=19
Hence, Kimberley owns 55 pencils.
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A Thermometer with an arbitrary scale of equal divisons register -10 celsius at the ice point and +110 celsius at the steam point. Compute :
A. The centigrade temperature corresponding to 20 celsius on this thermometer
B. The Fahrenheit temperature corresponding to a reading of 45 celsius on this thermometer
Answer:
Step-by-step explanation:
The range (ice to steam) of a Celsius thermometer = 100 C.
The range of the given thermometer = 10 + 110 = 120 degrees.
So, 1 degree C ≡ 1.2 degrees on the given thermometer.
A. So, 20 degrees C ≡ 24 on given thermometer and the reading will be 24 - 10 = 14.
Which answer describes the graph of the system of equations?
The point of intersection is (0, 4).
The point of intersection is (4, 0).
The lines are parallel.
The lines coincide.
There must be several solutions for which the lines of the equation coincide for an equation system to be a dependent consistent system. D is the right answer.
What is a System of equations?The lines of the equations must be parallel to one another for a system of equations to have no meaningful solution.
Consistent Method
First, Dependent Consistent System
There must be several solutions for which the lines of the equation coincide for an equation system to be a dependent consistent system.2. Independent Consistency SystemA system of equations must have a single unique solution for which the equation's lines must intersect at a certain location in order to qualify as an Independent Consistent System.It is clear that the lines coincide if the graph of the given system of equations is drawn as shown below. Therefore, choice D is the right one.The complete question is,
Which answer describes the graph of the system of equations?
{y=4-x
{2y=8-2x
A) the point of intersection is (0,4)
B) the point of intersection is (4,0)
C) the lines are parallel
D) the lines coincide
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Answer:
d (the line coincide)
Step-by-step explanation:
we all need help
y = 4x y = -x + 3 what is one way you can use substitution to see if arabelle is correct
The solution to the equation is (3/5, 12/5)
How to determine the solution to the equationFrom the question, we have the following parameters that can be used in our computation:
y = 4x
y = -x + 3
substitute the known values in the above equation, so, we have the following representation
4x = -x + 3
Evaluate the like terms
5x = 3
So, we have
x = 3/5
This gives
y = 4 * 3/5
Evaluate
y = 12/5
Hence, the solution is (3/5, 12/5)
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Which of the following is true of z scores that fall below the mean?
O Group of answer choices
O They are negative.
O They are equal to the mode.
O They are positive.
O They are in the upper half of the distribution.
The truth of z scores that fall below the mean is - they are negative. Option(b) is the correct answer.
A z-score called a standard score gives an idea of how far from the mean a data point is. But technically it is a calculation of how many standard deviations below or above the population mean a raw score is.
A z-score can place on a normal distribution curve. Z-score ranges from -3 standard deviations up to +3 standard deviations.
A z-score is equal to 0 means that it is on the mean. A positive z-score shows the score is higher than the mean average.
A negative z-score reveals the score is below the mean average.
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Use the number line below, where RS=6y+3, ST=4y+8, and RT=61.
a. What is the value of y?
b. Find RS and ST.
Using the number line below, where RS=6y+3, ST=4y+8, and RT=61, the value of y was found to be 4.
what is line segments ?An area of a line that can connect two points is known as a line segment. A and B, the ends of this line segment, both have fixed lengths. The separation between endpoints A and B is the length of this line segment. An area or portion of a line with two endpoints is known as a line segment. A line segment has a set length as opposed to a line. Both metric measurements, such as millimeters and centimeters, as well as conventional units, such as feet or inches, can be used to measure the length of a line segment. The length of one line segment in comparison to the other when there are two can be determined just by glancing at them. The line segment CD is longer than AB, as can be seen.
given
ST = 2y + 9 RS = 7y + 3
RT = 14y - 8
S lies between R and T, hence we can deduce that:
RS plus ST = RT
Therefore, we can swap out the equations for each of the segments above to obtain:
We can now solve this for y; to do so, let's move all the phrases that begin with y to the left.
14y -7y - 2y = 3 + 9 + 8\s(14 - 7 - 2) (14 - 7 - 2)
*y = 20
5*y = 20
y = 20/5 = 4\
y = 4
The value of y was determined to be 4.
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Show that the function is 1/n.
Calcula el volumen de un prisma cuya base es un rombo de diagonales 12 y 18 cm
So on solving the provided question we can say that - Area of prism,
Area, A = 2(wl+hl+hw) = 180 sq units
what is prism?The definition of a prism in geometry is a polyhedron with an n-sided polygonal base, a second base that is a shifted copy of the first base, and n additional faces (necessarily all parallelograms), with two Connect the corresponding sides of the base. Translations of the base are all cross sections that are parallel to it. A prism is a two-sided, solid, three-dimensional object. It consists of equal cross-sections, flat sides, and identical bases. A prism has faces that are parallelograms or rectangles without bases. A prism is a homogenous, solid, transparent, refracting object enclosed by two planes that are obliquely angled to one another. Two triangular faces and three parallel rectangular faces make up a typical prism. They are constructed of either glass.
Area, A = 2(wl+hl+hw)
A = 2(20 + 40 + 30)
A = 2(90)
A = 180sq units
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Noah is 1.35 meters tall. At 10 a.m., he measures the length of a tree's shadow to be 31.55 meters. He stands 26.2 meters away from the tree, so that the tip of his shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.
Answer:
3.64 meters
Step-by-step explanation:
To find the height of the tree to the nearest hundredth of a meter, you can use the principle of similar triangles.
First, we can use the Pythagorean theorem to find the length of the hypotenuse of the right triangle formed by the height of the tree, the distance between the base of the tree and the point where the shadows meet, and the length of the shadow of the tree.
c = √(a² + b²)
c = √(h² + 26.2²)
Next, we can use the similar triangles to establish a ratio between the length of the shadow and the height of the tree and the length of the shadow and the distance from the tree.
shadow tree / height tree = shadow person / height person
31.55 / h = 31.55 / 26.2
Now, we can cross-multiply and divide to solve for h
h = 31.55 * 1.35 / 26.2
h = 3.64 meters
We can round it up to the nearest hundredth of a meter:
h = 3.64 meters
Therefore, the height of the tree is 3.64 meters to the nearest hundredth of a meter.
Higher Order Thinking Lauren has a stamp collection. She gives Kristen 12 stamps and Ethan 15 stamps. Lauren has 22 stamps left. How many stamps did she have at the start?
Answer: 49 Stamps
Step-by-step explanation:
If Lauren gave Kristen and Ethan 12 stamps and 15 stamps respectively, that means that she gave them a total of 27 stamps. This leaves her with 22 stamps left. In order to find the number of stamps she had at the start, add the stamps she gave away to the stamps she had left at the end. So,
15 stamps + 12 stamps + 22 stamps = 49 stamps total at the start
Lauren had 49 stamps in the beginning. Since she gives Kristen 12 stamps, and Ethan 15 stamps, we can add both amounts to assume the total number of stamps she gave away. 15+12=27, so she gave away 27 stamps. Lauren was left with 22 stamps. We can add 22 to 27 to find out how many stamps she had in all. 27+22=49. Therefore, we can come to the conclusion that Lauren had 49 stamps at the start.
Hope this helps o(〃＾▽＾〃)o
Mindy and Troy combined ate 999 pieces of the wedding cake. Mindy ate 333 pieces of cake and Troy had \dfrac14
4
1
start fraction, 1, divided by, 4, end fraction of the total cake.
The expression is 3 + c/4 = 9 and the total pieces of care are 24.
What is an expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows:
Expression: (Math Operator, Number/Variable, Math Operator).
Given total cake eaten by mindy and troy = 9 pieces
Mindy ate = 3 pieces of cake
Troy = had ¼ of the total cake.
let there be c pieces of cake,
troy ate = c/4
Let Mindy ate be a and troy ate be b
a + b = 9
and a = 3, b = x/4
3 + c/4 = 9
c = 6 * 4
c = 24
Hence the equation is 3 + c/4 = 9 and there are 24 pieces of cake.
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the correct question is ,
Mindy and Troy combined 9 pieces of the wedding cake .Mindy ate three pieces of cake and Troy had 1/4 of the total cake
write an equation to determine how many pieces of cake (c) there were in total
Write Short note on variations ?
Using the concept of statistics, We are aware about population, sample and data, Variations refers to different forms of same thing.
What is statistics?Statistics is the branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It involves using mathematical and computational methods to describe, understand, and make inferences about data sets, and to make predictions and decisions based on that data. Statistics is the branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It involves using mathematical and computational methods to describe, understand, and make inferences about data sets, and to make predictions and decisions based on that data.
What do you mean by population and sample?In statistics, a population is the entire group of individuals or objects that have some common characteristic or that we are interested in studying. For example, the population of a country would be all its citizens, or the population of a certain species of animal would be all the individuals of that species. A sample is a smaller group of individuals or objects selected from the population in order to study or make inferences about the population as a whole.
Variation refers to the degree to which data points in a set differ from one another. In statistics, variation is used to describe the spread or dispersion of a set of data, and is an important aspect of describing and understanding the data. Variation can be measured using different statistical measures such as range, variance, and standard deviation.
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In ΔXYZ, x = 830 cm,
m
m∠Y=141° and
m
m∠Z=25°. Find the length of z, to the nearest 10th of a centimeter.
=======================================================
Explanation:
Use the two given angle measures (Y and Z) to find angle X.
X+Y+Z = 180
X+141+25 = 180
X+166 = 180
X = 180-166
X = 14
Angle X is 14 degrees.
-----------
Now use the law of sines to determine side length z.
Make sure your calculator is in degree mode.
z/sin(Z) = x/sin(X)
z/sin(25) = 830/sin(14)
z = sin(25)*830/sin(14)
z = 1449.9438
z = 1449.9 cm is the final answer.
The solution is : the length of z, to the nearest 10th of a centimeter is, 1449.9 cm.
What is triangle?A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.
here, we have,
Explanation:
Use the two given angle measures (Y and Z) to find angle X.
X+Y+Z = 180
X+141+25 = 180
X+166 = 180
X = 180-166
X = 14
Angle X is 14 degrees.
Now use the law of sines to determine side length z.
z/sin(Z) = x/sin(X)
z/sin(25) = 830/sin(14)
z = sin(25)*830/sin(14)
z = 1449.9438
z = 1449.9 cm is the final answer.
Hence, The solution is : the length of z, to the nearest 10th of a centimeter is, 1449.9 cm.
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A zebra can run at a constant speed of 0.6 miles per minute. How far can a zebra run in 30 minutes?
Answer:
To find how far a zebra can run in 30 minutes, we need to multiply its speed by the amount of time it runs.
Distance = speed x time
In this case, the speed of the zebra is 0.6 miles per minute and the time it runs is 30 minutes.
Distance = 0.6 miles/min x 30 min = 18 miles
So, a zebra can run 18 miles in 30 minutes at a constant speed of 0.6 miles per minute.
Answer:
18 miles
Step-by-step explanation:
0.6 -----> 1
x -----> 30
30×0.6= 18
Ayden owns a food truck that sells tacos and burritos. He only has enough supplies to make 120 tacos or burritos. He sells each taco for $3-75 and each burrito for $6.25.
Ayden must sell no less than $530 worth of tacos and burritos each day. Also, he can sell at most 70 burritos. If a represents the number of tacos sold and y represents the number of burritos sold, write and solve a system of inequalities graphically and determine one possible solution.
Answer:
see below for a graph
(x, y) = (50, 60) . . . . one possible solution
Step-by-step explanation:
You want inequalities, their graph, and one possible solution to match the Ayden food truck scenario: a total of 120 tacos (x) or burritos (y) can be sold, with that total including at most 70 burritos. At $3.75 per taco and $6.25 per burrito, revenue must be at least $530.
InequalitiesAn inequality can be written for each constraint:
total number of tacos and burritos: x + y ≤ 120
minimum revenue: 3.75x +6.25y ≥ 530
maximum burritos: y ≤ 70
GraphThese are graphed in the attachment. The point (x, y) = (50, 60) represents one possible solution: 50 tacos and 60 burritos sold for $562.50.
Match the terms to their definition.
1 .
the number that is repeated as a factor in an exponential expression
exponent
2 .
the smaller number in an exponential expression; tells how many times a factor is repeated
base
The proper pairing is as follows:
(1) The factor in an exponential equation that is repeated: Base
(2) The smaller number indicates the number of times a factor is repeated in an exponential expression: Exponent
What are exponent and base?Exponentiation is a mathematical process that involves the base b and the exponent or power n.
It is represented as bn and is pronounced as "b to the n."
The formula for an exponential function is f (x) = ax, where x is a variable and an is a constant that serves as the function's base and must be bigger than 0.
The transcendental number e, or roughly 2.71828, is the most often used exponential function basis.
The correct matching will be as follows:
(1) The number that is repeated as a factor in an exponential expression: Base
(2) The smaller number in an exponential expression; tells how many times a factor is repeated: Exponent
Therefore, the proper pairing is as follows:
(1) The factor in an exponential equation that is repeated: Base
(2) The smaller number indicates the number of times a factor is repeated in an exponential expression: Exponent
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Use the graph to evaluate the function below for specific inputs and outputs.
Inputs and outputs are 3,-2.One point can be used to represent each set of input and output values on a graph.
Inputs and outputs are graphical in what way?One point can be used to represent each set of input and output values on a graph. The vertical axis is used to measure output values, whereas the horizontal axis is used to measure input values. On each axis, a scale that is consistent and can hold all the necessary points is drawn.
The C language provides input and output functions for carrying out the most typical operations. Three fundamental tasks are performed in every C program: taking input data, processing that data, and producing output. Data that is accepted is considered input, and data that is presented is considered output.
According to question:-
At x=-4, g(x) equals 6.
g(x)= -2 x=3
kindly examine the g(x) graph.
the value of y is equal to 6 for x=-4.
with x = 3, the value of y Equals -2.
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