triangle IJK with vertices I(-9-8),J(-5-6),and K(-7-3) is drawn on the coordinate grid below. what is the area in square units of triangle IJK
Answers
Here, we want to calculate the area of the given triangle
Mathematically, the product of the height and base of a triangle divided by 2 gives its area
Now, as we can see the shape, while IJ represents the base, KJ represents the height
We need to calculate the distance between these points before we can get the area of the triangle
To get the distances between the points, we have to use the distance formula
We can proceed with this as follows;
[tex]\begin{gathered} D\text{ = }\sqrt[]{(_{}x_2-x_1)^2+(y_2-y_1)^2} \\ \\ \text{For IJ} \\ (x_1,y_1)\text{ = (-9,-8)} \\ (x_2,y_2)\text{ = (-5,-6)} \\ |IJ|\text{ = }\sqrt[]{(-5+9)^2+(-6+8)^2} \\ |IJ|\text{ = }\sqrt[]{16\text{ + 4}} \\ |IJ|\text{ = }\sqrt[]{20} \\ \\ \text{For KJ} \\ (x_1,y_1)\text{ = (-7,-3)} \\ (x_2,y_2)\text{ = (-5,-6)} \\ |KJ|\text{ = }\sqrt[]{(-5+7)^2+(-6+3)^2} \\ |KJ|\text{ = }\sqrt[]{4+9} \\ |KJ|\text{ = }\sqrt[]{13} \end{gathered}[/tex]Thus, we have the area of the triangle as follows;
[tex]\begin{gathered} \text{Area = }\frac{1}{2}\times base\times height \\ \\ \text{Area = }\frac{1}{2}\times\sqrt[]{20}\times\sqrt[]{13\text{ }}=\frac{\sqrt[]{260}}{2}\text{ = }\frac{2\sqrt[]{65}}{2}\text{ = }\sqrt[]{65\text{ }}\text{ square units} \end{gathered}[/tex]Related Questions
Stanley bought sneakers, a pair of pants, a t-shirt and a jacket for $535.00. The sneakers cost 5 less than the jacket, the pants cost $50 less than the jacket, and the t-shirt cost $10 less than three times the jacket. Find the cost of each item.
Answers
The cost of Sneakers, pair of pants, Jacket and T-shirt are $95, $50, $100 and $290 respectively.
This can be solved by forming linear equations. A linear equation is the one which can be represented in the form ax + b = 0 where a, b are coefficients and x is the independent variable. Let us assume the cost of Sneakers be 's', cost of Pants be 'p', cost of Jacket be 'j' and cost of t-shirt be 't'.
The cost of all the items is equal to $535
s + p + j + t = $535 ......(1)
Sneakers cost $5 less than the jacket
s = j - $5 ......(2)
Pants cost $50 less than the jacket
p = j - $50 ......(3)
T-shirt cost $10 less than three times the jacket
t = 3j - $10 ......(4)
Putting the values of equation (2), (3) and (4) in equation (1)
j - $5 + j - $50 + j + 3j - $10 = $535
6j = $535 + $65
=> 6j = $600
=> j = $100 which is the cost Jacket.
Now, s = $100 - $5 = $95 which is the cost of Sneakers.
p = $100 - $50 = $50 which is the cost of pair of pants.
t = $300 - $10 = $290 which is the cost of t-shirt.
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Find the constant of proportionality for the proportional relationship between weight and cost shown in the table. Then find the cost of 10 oz of green beans. Cost of Green Beans Weight (oz) Cost($) 8 1.12 12 1.68 16 2.24 The constant of proportionality is $0.14 per ounce. The cost of 10 oz of green beans is $ VE S 4.1 More 10 Enter your answer in each of the answer boxes. Next Back of 16 Question 1 Review progress
Answers
A worker in an assembly line takes 7 hours to produce 31 parts. At that rate, how many parts can she produce in 28 hours?
Answers
Answer:
124
Step-by-step explanation:
Since the amount of time is being multiplied by 4, the number of parts will also be multiplied by 4.
[tex]31(4)=124[/tex]
What is the Expanded form of 45,803
Answers
Answer: 40000
+ 5000
+ 800
+ 3
Step-by-step explanation:
The expanded form splits the number, and it represents the number in units, tens, hundreds and thousands form.
MARKING BRAINLIEST What are the lengths of the major and minor axes of the ellipse?
(x−3)212+(y+4)224=1
Drag a value to the boxes to correctly complete the table.
Answers
The lengths of the major and minor axis of the ellipse, are; 4√6 and 4√3 respectively.
What is an ellipse in coordinate geometry?An ellipse describes the locus of a point on a curve, such that the sum of the distance between two focal points from the points on the curve is a constant.
The function of the ellipse can be calculated as follows;
[tex]\dfrac{(x-h)^2}{a^2} + \dfrac{(y-k)^2}{b^2} =1[/tex]
Where (h, k) = The coordinates of the center of the ellipse
a = The length of the semi-major axis
b = The length of the semi-minor axis
Now,
[tex]\dfrac{(x-3)^2}{12} + \dfrac{(y+ 4)^2}{24} =1[/tex]
By comparison, we have;
(h, k) = (3, -4)
a = √(24) = 2√6
b = √(12) = 2√3
The length of the major axis is 2a
The length of the minor axis is 2b
The length of the major axis will be;
2a = 2 × 2√6 = 4√6
The length of the minor axis will be;
2b = 2 × 2√3 = 4√3
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Two trains for Palwal leave Kanpur at 10 am and 10:30 am and travel at the speeds of 60Kmph and 75Kmph respectively. After how many kilometers from Kanpur will the two trains be together?
Answers
Answer:
150 km
Step-by-step explanation:
You want to know the number of kilometers each train has traveled when they meet. The first goes 60 km/h and has a half-hour head start. The second goes 75 km/h.
SetupAt t hours after 10 am, the distance of the first train from Kanpur will be ...
distance = speed × time
distance = 60t
At t hours after 10 am, the distance of the second train from Kanpur will be ...
distance = 75(t -1/2) . . . . . . the distance is 0 at 10:30 am, 1/2 after 10 am
These distances will be equal when ...
60t = 75(t -1/2)
SolutionThe time at which the trains meet will be the solution to the above equation.
60t = 75t -37.5 . . . . eliminate parentheses
0 = 15t -37.5 . . . . . . subtract 60t
0 = t -2.5 . . . . . . . . . divide by 15
2.5 = t . . . . . . . . . the trains meet 2.5 hours after the first one leaves
The distance traveled by each of the trains is the same at that time. It will be the distance traveled by the first train:
60t = 60(2.5) = 150 . . . . km
The two trains will be together 150 km from Kanpur.
One ounce is 28.35 grams. Convert16 ounces into grams. Round to nearest tenth
Answers
16 ounces is equivalent to 453.6g when rounding to nearest tenth.
What is rounding off ?
Rounding off means a number is made into simpler form by keeping its value fixed but closer to the next number.
To round off the number to the nearest tenth we need to look at the hundredths place digit. If the digit is 1, 2, 3, 4 then we don't have to do anything, if the digit is 5, 6, 7, 8, 9 we must round up.
here the given data is :
1 ounce = 28.35 grams
Conversion of ounce to grams :
This is the conversion of a mass unit from ounce to grams. Given that 1 ounce is equal to 28.35 grams, let us calculate how grams would be in 16 ounces.
The easiest way about this is simply multiply 16 by 28.25g
1 ounce = 28.35 grams
16 ounce = x
x = 16 x 28.25
x= 453.6 g
From the calculations above, 16 ounces is equivalent to 453.6g.
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Last year, Tammy opened an investment account with $8200 . At the end of the year, the amount in the account had decreased by 7.5% . How much is this decrease in dollars? How much money was in her account at the end of last year?
Answers
1. The decrease in dollars in Tammy's investment account, based on a 7.5 percent decrease, is $615.
2. The balance in Tammy's investment account at the end of last year was $7,585.
What is the percentage?The percentage is the proportion of a value in relation to another.
Percentages show how much a variable is contained in another.
The percentage gives the fractional value of the decrease in the investment account.
Initial investment = $8,200
Decrease in investment = 7.5%
Decrease in dollars = $615 ($8,200 x 7.5%)
Balance = $7,585 ($8,200 - $615)
Thus, we can conclude that Tammy's investment account decreased by $615, representing a 7.5% decrease.
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Please!!Find the value of each variable. Write theequations and solve showing ALL the work.If an answer is not a whole number, leaveit in simplest radical form.
Answers
The greater triangle and the smaller ones (the two triangles inside the original one, that share the side y) are similar triangles, then we can formulate the following expressions:
• For the larger triangle and the triangle on the left
[tex]\frac{z}{9}=\frac{5}{z}[/tex]From this equation, we can solve for z, to get:
[tex]\begin{gathered} \frac{z}{9}\times z=\frac{5}{z}\times z \\ \frac{z\times z}{9}=5\times\frac{z}{z} \\ \frac{z^2}{9}=5\times1 \\ \frac{z^2}{9}=5 \\ z^2=5\times9 \\ z^2=45 \\ z=\sqrt[]{45} \\ z=3\sqrt[]{5} \end{gathered}[/tex]Then, z equals 3√5
• Similarly, with the larger triangle and the one on the right:
[tex]\begin{gathered} \frac{x}{9}=\frac{4}{x} \\ \end{gathered}[/tex]From this expression, we can solve for x, like this:
[tex]\begin{gathered} \frac{x}{9}=\frac{4}{x} \\ \frac{x^2}{9}=4 \\ x^2=4\times9 \\ x^2=36 \\ x=\sqrt[]{36} \\ x=6 \end{gathered}[/tex]Then, x equals 6
• With the triangles on the right and on the left:
[tex]\frac{y}{4}=\frac{5}{y}[/tex]Solving for y, we get:
[tex]\begin{gathered} \frac{y}{4}=\frac{5}{y} \\ \frac{y^2}{4}=5 \\ y^2=5\times4 \\ y^2=20 \\ y=\sqrt[]{20} \\ y=2\sqrt[]{5} \end{gathered}[/tex]Then, y equals 2√5
Which graph shows a proportional relationship between the number of hours of renting a pair of roller skates and the total amount spent to
rent the roller skates?
Answers
Answer:
You were right. The answer is (C)
Step-by-step explanation:
Remember, the line always goes up in the top right corner, also the first dot is 2,20, to 4,40, to 6,60, and last 8,80 which is the number of the same total amount and number of hours.
Y=-3/2x-1. Graph integers?
Answers
The graph of the figure is attached below.
Given equation of line:-
y = (-3/2)x - 1
First we will find the x and y intercepts of the line to plot in the line.
Putting x = 0 to find the y-intercept, we get,
y = (-3/2)(0) - 1
y = -1
Hence, the coordinates of the point are (0,-1).
Putting y = 0 to find the x-intercept, we get,
0 = (-3/2)x - 1
1 = (-3/2)x
x = -2/3
Hence, the coordinates of the point are (-2/3,0).
We can find another point on the line.
Putting x = 2, we get,
y = (-3/2)(2) - 1
y = -3 - 1
y = -4
Hence, the coordinates of the point are (2,-4).
Plotting these in a graph, we can get a straight line.
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in the standard (x y) coordínate plane what’s the slope of a line that’s perpendicular to
Answers
Answer:
A line perpendicular to another has a slope that is the negative reciprocal of the slope of the other line.
are all angles are congruent to one another
Answers
Answer:
Step-Congruent angles are frequently used in the world of architecture, construction, design, and art. Congruent angles have the same angle measure. For example, a regular pentagon has five sides and five angles, and each angle is 108 degrees. Regardless of the size or scale of a regular polygon, the angles will always be congruent.
Find the height h of the solid. h I B = 147 cm2 Volume 1323 cm h= cm
Answers
Answer:
h = 9 cm
Explanation:
The volume of the solid can be calculated as:
[tex]V=B\cdot h[/tex]So, we can replace the value of the Volume by 1323 cm³ and B by 147 cm² as:
[tex]1323cm^3=147cm^2\cdot h[/tex]Then, dividing by 147 into both sides, we get:
[tex]\begin{gathered} \frac{1323cm^3}{147cm^2}=\frac{147cm^2\cdot h}{147cm^2} \\ 9\text{ cm = h} \end{gathered}[/tex]Therefore, the height h of the solid is 9 cm.
Let's take a look at (x + y)^2 (x - y)^2 and (x^2 + y^2)(x^2 - y^2). While Beeker believes that these two expressions are equal for all real numbers x and y Clod believes they are not! Let's get to the bottom of this!
a) Evaluate (x + y)^2 (x - y)^2 and (x^2 + y^2)(x^2 - y^2) for x = 7 and y = 11
b) For which values of x and y does (x + y)^2 (x - y)^2 equal (x^2 + y^2)(x^2 - y^2)? For which values of x and y does (x + y)^2 (x - y)^2 not equal (x^2 + y^2)(x^2 - y^2)?
Answers
From the given expression, it is found that:
a) When x = 7 and y = 11, the numeric values are given as follows:
(x + y)²(x - y)² = 5184.(x² + y²)(x² - y²) = 12240.b) They will only have the same numeric value when x = y.
How to find the numeric value of a function or of an expression?To find the numeric value of a function or of an expression, we replace each instance of the variable in the function by the desired value.
The same is true for multi-variable expressions, as each variable will have a numeric value that we will replace in the function.
In the context of this problem, the expressions are given as follows:
(x + y)²(x - y)².(x² + y²)(x² - y²).When x = 7 and y = 11, the numeric values are given as follows:
(11 + 7)²(11 - 7)² = 5184.(11² + 7²)(11² - 7²) = 12240.The notable product of the square of the sum is different of the sum of the squares, and the same holds true for the subtraction, hence both expressions will only have the same value when x = y, as factors (x - y)² and (x² - y²) will both be of 0, resulting in a multiplication of 0 in each expression and a value of 0.
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Given f(x) = ln(x), which is the correct answers ?
Answers
First, lets perform each transformation and then take a look at its graph:
1.
[tex]\begin{gathered} g(x)=-\frac{1}{2}f(x-2) \\ \\ \Rightarrow g(x)=-\frac{1}{2}\ln (x-2) \end{gathered}[/tex]The only etiquette that matches this plot is: Function decreases as x increases
2.
[tex]\begin{gathered} h(x)=f(x-\frac{1}{2}) \\ \\ \Rightarrow h(x)=\ln (x-\frac{1}{2}) \end{gathered}[/tex]The only etiquette that matches this plot is: x-intercept at (1.5 , 0)
3.
[tex]\begin{gathered} j(x)=f(x)-\frac{1}{2} \\ \\ \Rightarrow j(x)=\ln (x)-\frac{1}{2} \end{gathered}[/tex]The only etiquette that matches this plot is: Asymptote of x = 0
Find the area of this circle.Use 3.14 to approximate n.Α = πη28 inA = [ ? ] in?
Answers
To find the area of a circle given its radius,
[tex]\text{Area}=\pi\times r^2[/tex]The value of the radius r = 8 inches, and the value of pi is 3.14. Hence;
[tex]\begin{gathered} \text{Area}=3.14\times8^2 \\ \text{Area}=3.14\times64 \\ \text{Area}=200.96in^2 \end{gathered}[/tex]The area of the circle is 200.96 inches squared
What is 1/8 as a Decimal
Answers
What is the answer pleasee
Answers
The value of interior angle x for the given pentagon if found as 88 degrees.
What is termed as the pentagon?A pentagon is a two-dimensional polygon with 5 sides and 5 angles.This shape should have five sides and form a closed two-dimensional figure. A closed figure consists of each of its sides intersecting to form vertices.Five diagonals connect the five vertices to one‘s opposite vertices in a pentagon shape.Each interior angle in a regular pentagon is 108°, so each exterior angle is 72°.For the given question;
The exterior angles of the pentagon are given in figure.
Find all the interior angles for given angles using linear pair as all are straight lines.
180 - 62 = 118180 - 33 = 147180 - 114 = 66180 - 59 = 121The sum of all the interior angle of pentagon is 540.
Thus,
118 + 147 + 66 + 121 + x = 540
x = 540 - 452
x = 88
Thus, the value of interior angle x for the given pentagon if found as 88 degrees.
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URGENT!! ILL GIVE
BRAINLIEST!!!!! AND 100
POINTS!!!!!
Answers
The correct option is True, there is enough information given to say that both line are parallel.
What is termed as as the supplement angles?The term "supplementary angles" refers to a pair of angles which always add up to 180°. These two perspectives are known as supplements. When supplementary angles are combined, they form a straight angle (180 degrees). In other words, if Angle 1 + Angle 2 = 180°, angles 1 and 2 are supplementary. Angles 1 and 2 are referred to as "supplements" in this case.For the given question.
The two lines are given with angles measure from 1 to 8.
Where,
∠4 = 89°∠3 = 91°As, the sum of the angles is;
∠4 + ∠3 = 91° + 89°
∠4 + ∠3 = 180° (supplementary angles)
Thus, we can say that both lines are parallel to each other.
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help meeeeeee pleaseee !!!!
Answers
The linear equation that passes through the two points (0, 360) and (10, 560) is:
y = 20*x + 360
How to find the linear equation?Remember that the slope-intercept form of a linear equation is:
y = a*x + b
Where b is the y-intercept and a is the slope or rate of change.
If we know that the line passes through the points (x₁, y₁) and (x₂, y₂) then the slope is:
[tex]a = \frac{y_2 -y_1}{x_2 - x_1}[/tex]
Here the line must pass through (0, 360) and (10, 560), so the slope is:
[tex]a = \frac{560 - 360}{10 - 0} = 20[/tex]
And because of the point (0, 360) we can see that the y-intercept is 360, then the linear equation is:
y = 20*x + 360
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Factor 540 into product of prime factors
Answers
Step 1
Given;
[tex]540[/tex]Required; To factor it out into products of prime factors.
Step 2
A prime factor is a factor that is a prime number. In other words: any of the prime numbers that can be multiplied to give the original number is a prime factor. Examples of prime factors are; 1,2,3,5 etc. When a composite number is written as a product of all of its prime factors, we have the prime factorization of the number.
Step 3
Find the prime factor of 540
Therefore, the prime pr
Carolyn leases a new Hyundai Elantra by paying $2600 up front and $170 a month over three years. The lease also stipulates he will be charged $0.12 per mile for every mile over 36,000. If she puts 40,693 miles on the car, what will be the total cost of the lease?
Answers
4,693 x $0.12= $563.16 (cost of the mile overage)
3 years= 36 months. (Multiply 3 x 12)
Now multiply 36 x $170 a month = $6,120.
$2,600 (up front cost) + $563.16 (cost of mile overage) + $6,120 (cost over 3 years) = $9.283.16 ( answer)
radicals that have the same index and the same radicand is this true
Answers
Given the expression;
[tex]\frac{\sqrt[]{2}}{7}\times\sqrt[]{7}\times\sqrt[]{14}[/tex]Step 1:
[tex]\begin{gathered} \frac{\sqrt[]{2}}{7}\times\sqrt[]{7}\times\sqrt[]{7}\times\sqrt[]{2} \\ \end{gathered}[/tex]Step 2:
[tex]\begin{gathered} \sqrt[]{2}\times\sqrt[]{2}=2 \\ \sqrt[]{7}\times\sqrt[]{7}=7 \\ \frac{\sqrt[]{2}}{7}\times\sqrt[]{7}\times\sqrt[]{7}\times\sqrt[]{2}=\frac{2\times7}{7} \end{gathered}[/tex]Step 3:
[tex]\begin{gathered} \frac{\sqrt[]{2}}{7}\times\sqrt[]{7}\times\sqrt[]{14}=\frac{2\times7}{7} \\ \frac{\sqrt[]{2}}{7}\times\sqrt[]{7}\times\sqrt[]{14}=2 \end{gathered}[/tex]The solution is;
[tex]2[/tex]RCX)=2VX SCx) = x(RSX4=
Answers
Given the two functions:
[tex]\begin{gathered} R(x)=2\sqrt[]{x} \\ S(x)=\sqrt[]{x} \end{gathered}[/tex]We need to find (RoS)(4). THis is the functional composition. We take S(x) and put it into R(x) and then put "4" into that composed function. Shown below is the process:
[tex](RoS)(x)=2\sqrt[]{\sqrt[]{x}}[/tex]When we plug in "4", into "x", we have:
[tex]\begin{gathered} (RoS)(x)=2\sqrt[]{\sqrt[]{x}} \\ (RoS)(4)=2\sqrt[]{\sqrt[]{4}} \\ =2\sqrt[]{2} \end{gathered}[/tex]5. Higher Order Thinking Linda wants to show
skip counting by 5s from a number to get to
1,000. Write the numbers she should put on
her number line below. How do you know?
1,000
Answers
The numbers that Linda should put on her number line are 5,10,15,20...1000 .
Integers are frequently represented as specifically labelled dots evenly spaced on a line. Despite the fact that the graphic only depicts the integers from -3 to 3, the product contains all real numbers, which continue indefinitely in each direction, as well as numbers that lie between the integers. It is frequently used to help teach simple numerals, particularly with negative numbers.
The numbers are skip counted. so each number differs from the preceding number by 5.
let us take the number counting starts from 0. so the second number will be 5+5=10
The third number 10+5 = 15 and so on and so forth.
Hence it forms an arithmetic sequence of numbers whose first term is 5 and common difference is 5.
A number line is really a picture of a stepped straight line as serves as a visual representation of real numbers in primary mathematics. Every point of a x axis is assumed to coincide to a true figure, and every decimal digits to a point.
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Astronomers discover an exoplanet (a planet of a star other than the Sun) that has an orbital period of 3.95 Earth years in its circular orbit around its sun, which is a star with a measured mass of 3.97×1030kg . Find the radius of the exoplanet's orbit.
Answers
The radius of this exoplanet's orbit is equal to 4.71 × 10¹¹ meters.
How to calculate the radius of the exoplanet's orbit?In order to calculate the radius of the exoplanet's orbit, we would apply Kepler's Third Law of planetary motion.
Mathematically, Kepler's third law of planetary motion can be calculated by using this formula:
T² = 2π√(r³/GM)
Where:
T represents the orbital period.M represents the mass.G represents the universal gravitational constant.r represents the radius.Making radius (r) the subject of formula, we have:
Radius, r = ∛(GMT²/2π)
Note: Universal gravitational constant is equal to 6.67 × 10⁻¹¹ m³kg⁻¹s⁻².
Orbital period, T = 3.95 × 365 × 24 × 60 × 60 = 341,280 seconds
Substituting the given parameters into the formula, we have;
Radius, r = ∛(6.67 × 10⁻¹¹ × 3.97×10³⁰ × (341,280)²/2 × 3.142)
Radius, r = 4.71 × 10¹¹ meters.
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Juan rides the bus to school each day. He always arrives athis bus stop on time, but his bus is late 80% of the time.Juan runs a simulation to model this using a randomnumber generator. He assigns these digits to the possibleoutcomes for each day of the week:• Let 0 and 1 = bus is on time• Let 2, 3, 4, 5, 6, 7, 8, and 9 = bus is lateThe table shows the results of the simulation.
Answers
B. 2/10 = 20%
Explanations:The total number of weeks shown in the simulation = 10
By observing the simulation, we would see that there is no 0 or 1 in group 2 and group 3. This means that Juan was late everyday of week 2 and week 3
The number of weeks that Juan was late everyday = 2
The estimated probability that Juan will be late evryday of next week = 2/10 = 20%
number in expended form
675,432
Answers
Answer: 600,000 + 70,000 + 5,000 + 400 + 30 + 2
Explanation:
Each digit forms a different number depending on its place value.
The 6 is in the hundred thousands place value, so the 6 in 675,432 corresponds to 600,000. Similar ideas apply for the other digits as well
HELP I DONT UNDERSTAND THEIS QUESTIIONS
Answers
1) f(x)-3
[tex]\begin{gathered} f(x)=2x-4 \\ \Rightarrow f(x)-3=2x-4-3 \end{gathered}[/tex]Therefore, f(x)-3=2x-4-3
2) f(x-3)
[tex]\Rightarrow f(x-3)=2(x-3)-4[/tex]Thus, f(x-3)=2(x-3)-4
3) f(-3x)
[tex]f(-3x)=2(-3x)-4[/tex]Then, f(-3x)=2(-3x)-4
4) -3f(x)
[tex]-3f(x)=-3(2x-4)[/tex]Hence, -3f(x)=-3(2x-4)