In interval notation, the interval of continuity of f(x) is (-∞, 2) ∪ (5, +∞)
What is continuity of a function in an interval?A function is said to be continuous in an interval if all the values in the interval satisfy the function.
How to use interval notation to indicate where ƒ(x) is continuous?Since we have the function (x² - 4)/(x² - 7x + 10), we desire to find the interval in which it is continuous. So, we proceed as follows.
For the function f(x) = (x² - 4)/(x² - 7x + 10) to be continuous, then the denominator (x² - 7x + 10) ≠ 0
So, solving this inequality, we have
x² - 7x + 10 ≠ 0
x² - 2x - 5x + 10 ≠ 0
Factorizing, we have that
x(x - 2) - 5(x - 2) ≠ 0
(x - 2)(x - 5) ≠ 0
x - 2 ≠ 0or x - 5 ≠ 0
x ≠ 2 or x ≠ 5
Also, since the coefficient of x² is positive the function f(x) tends to ±∞.
So, the interval of continuity of f(x) is 2 < x and x > 5
So, the interval of continuity of f(x) is (-∞, 2) ∪ (5, +∞)
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I am stuck on this homework question can anyone help ?
Answer:
10 cases
Step-by-step explanation:
We are given the equation: y = -0.25x + 85, where y is the # of cases, and x is the # of students who received the vaccine.
The question asks for the # of cases if 300 students received the vaccine. Since we know that 300 students received the vaccine, we can plug that in for x in the equation above, since x is that unit:
y = -0.25(300) + 85
Now, we can solve:
y = 10
Therefore, there will be 10 cases if 300 students received the vaccine.
The fraction 5/5 is proper
A. True
B. False, this is an improper fraction. Its value is ____.
help !
the third term of an arithmetic sequence is -2 and the 8th term is -32. write a function to describe this sequence
Answer:
Step-by-step explanation:
The answer would look like (30n-44)/7
translate the image (x+7,y-19)
The translation rule (x + 7, y - 19) has the meaning given as follows:
Translation 7 units right.Translation 19 units down.What are the translation rules?The four translation rules are defined as follows:
Left a units: x -> x - a.Right a units: x -> x + a.Up a units: y -> y + a.Down a units: y -> y - a.The meaning of each translation in this problem is given as follows:
x + 7: 7 units right.y - 19: 19 units down.Missing InformationThe problem asks for the meaning of the translation (x + 7, y - 19).
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Which equation is set up correctly using the Pythagorean Theorem for the triangle below?
The equation that is set up correctly using the Pythagorean Theorem for the triangle below is 9^2 + x^2 = 15^2.
What is Pythagorean theorem?The concept that will be used here is Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
Pythagoras discovered that the square of the hypotenuse of a right-angled triangle, where one of the angles is 90 degrees, equals the sum of the squares of the other two sides:
According to theorem, the (adjacent)^2 + (opposite)^2 = (hypothenus)^2.
a^2+b^2=c^2
The 9^2 + x^2 = 15^2
Therefore, option C is correct.
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Mrs. Norris is planting a vegetable garden with tomatoes and beans. She wants to have 20 more potato plants than beat plants. She will plant 100 plants altogether. How many bean plants should she plant?
Solve using system of equations by elimination. Show your work
PLEASE help me with this question. Will name the BRAINLIEST for whoever gets it right!
The number of bean plants should she plant will be 60
t = tomato plants
b = beans
To Solve by using system of equations
Clear any fractional coefficients if there are any. Alternate the coefficients of a single variable. Select the variable you want to remove. Multiply one or both equations to make the variable's coefficients opposite.
Total plants = 100
t + b = 100 {equation 1}
20 more tomatoes than beans
t = b + 20 {equation 2}
b + 20 + b = 100
2b + 20 = 100
Finish solving for b to find a number of beans.
Then tomatoes will be b+20
Putting this in equation 1
b+20+b=100
2b+20=100
b=40
then t= b+20 {equation 2}
t=60
Hence the number of bean plants should she plant will be 60
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The scale drawing of the rectangular garden has an area of `2` ft². If Mai used a scale factor of `\frac{1}{3}`, what is the actual area of the garden?
The actual area of the garden without the scale factor is 6 square feet.
What is scale factor?The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor.
What is area?Area is the entire amount of space occupied by a flat (2-D) surface or an object's form. Depending on the size and number of sides, different forms have varying areas.
Let the original area of the garden be x.
Given that the scale factor used is 1/3, thus we have:
x (1/3) = 2
x = (2)(3)
x = 6
Hence, the actual area of the garden without the scale factor is 6 square feet.
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Select the correct answer from each drop-down menu. Consider the absolute value function f(x) = -|x + 2| + 2. The vertex of the function is a at .
The vertex of the function is at - 2
Hown to find the vertexThe vertex of the function is at the point (a, 2), where the value of x, denoted as 'a', is the x-coordinate of the vertex.
To find the value of 'a', we can use the formula for the x-coordinate of the vertex, which is -b/2a, where b and a are the coefficients of the x-squared and x terms, respectively, in the standard form of the equation (y = ax^2 + bx + c).
Since the function is already in vertex form, we can directly read the value of 'a' from the equation which is -2.
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Tank A has a capacity of 9.5 gallons. 6 1/3 gallons of the tanks water are poured out. How many gallons of water are left in the tanks
The volume of water that are left in the tank is equal to 3.2 gallons.
How to calculate the volume of a geometric figure?Mathematically, the volume of a cuboid tank is a measure of its capacity and it can be calculated by using this following formula:
Volume of a tank = L × W × H
Where:
L represents the length of a cuboid tank.W represents the width of a cuboid tank.H represents the height of a cuboid tank.In order to determine the quantity (volume) of water that are left in the tank, we would use this mathematical expression:
Volume of water left = capacity of tank A - volume of water poured
Volume of water left = 9.5 gallons - 6 1/3 gallons
Volume of water left = 9.5 gallons - 6.3 gallons
Volume of water left = 3.2 gallons.
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Parking lots A and B each charge a set fee for parking plus an hourly rate.
Hours Parked48Lot A Cost ($)19. 00/33. 00
Lot B Cost ($)20. 00/32. 00
How many more dollars does it cost per hour to park in Lot A than in Lot B? Give the answer as a decimal showing dollars and cents
It costs $0.208 more per hour to park in Lot A than in Lot B.
We know that the total parking hours = 48
Also, the cost of parking for Lot A= ($)19. 00/33. 00 and for Lot B = ($)20. 00/32. 00
To find out how many more dollars it costs per hour to park in Lot A than in Lot B, we will subtract the hourly rate of Lot B from the hourly rate of Lot A.
The hourly rate of Lot A is (33.00 - 19.00) / 48 = $0.541 (dollars and cents)
Similarly, the hourly rate of Lot B is (32.00 - 20.00) / 48 = $0.333 (dollars and cents)
So the difference in cost per hour is $0.541 - $0.333 = $0.208 (dollars and cents)
Therefore, it costs $0.208 more per hour to park in Lot A than in Lot B.
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WILL GIVE BRAINLIEST AMD GOOD AMOUNT OF POITS
PLEASE HELP
sketch the graphs of the linear inequality. :)
The graph of the linear inequality is shown below.
What is linear inequality?
A linear inequality is one that, if the equals relation were employed in place of the inequality, would result in a linear equation. The direction of the inequality is reversed when both sides are multiplied or divided by a negative integer to solve it. The solution set refers to all possible answers to an inequality.
We are given y < -x-4
In order to sketch the graph of the inequality, we need to have two points.
So, first let's put x = 0
So, we get y = -4
Now, let's put y = 0
So, we get x = -4
Thus, we get the points as (0,-4) and (-4,0)
From the points, the graph is sketched which is shown below.
Hence, the graph of the linear inequality is obtained.
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Since, there are multiple questions, so the question answered above is attached below
L
The value, V, of a computer can be modeled by the function V(t) = 1, 300(. 61), where t is the number of years since the computer was purchased.
Which function best represents the value of the computer in months?
The function that best represents the value of the computer in months is V(t) = 1,300(.61^(t/12)).Where t is the number of months since the computer was purchased
The given function V(t) = 1,300(.61), models the value of a computer in terms of the number of years since it was purchased. The value of the computer is represented by the function V(t) which is directly proportional to (0.61) raised to the power of t. Divide the t by 12, because there are 12 months in a year, to get the value in months.
As a consequence, the calculation V(t) = 1,300(.61(t/12)) displays the computer's value in terms of months from purchase. It demonstrates the decline in the value of the computer over time.
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South the inequality. The temperature of the freezer is never greater than -2°C. Yesterday the temperature was -10°C but it increased at a steady rate of 1. 5°C per hour. How long in hours and minutes did the temperature increase inside the freezer?
It took approximately 5.3 hours for the temperature inside the freezer to increase from -10°C to -2°C.
If the temperature inside the freezer increased by 1.5°C per hour, and it started at -10°C, then to reach -2°C the temperature inside the freezer would have had to increase by 8°C.
To find out how long it took for this to happen, we can use the formula:
Temperature increase/rate of increase = time
8°C / 1.5°C per hour = 5.3 hours (approx).
The temperature was exactly -10°C at the start and exactly -2°C at the end. It means that the temperature increased by 1.5°C per hour on average.
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1. An architect is drafting plans for a new supermarket. There will be a space 144 inches
long for rows of nested shopping carts. The first cart is 34 inches long and each nested
cart adds another 10 inches. The architect want to know how many shopping carts will
fit in each row.
We see the same three numbers in situations 10,34 and 144.
In the first situation, there is one shopping cart with a length of 34 and then an unknown number of carts with a length of 10. Similarly, an architect has 34 dollars saved and will save 10 each week for an unknown number of weeks. Both situations have one part of 34 and then equal parts of size 10 that add together to 144. The equation is: 34 + 10x = 144.
Since it takes 11 groups of 10 to get from 34 to 144, the value of x in these two equations is ( 144 -34) ÷ 10 = 11.
There will be 11 shopping carts in each row and it will take 11 weeks to raise the money.
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Jenny went for a drive in her new car. She drove for miles at a speed of miles per hour. For how many hours did she drive?
Answer: t = d/s
Step-by-step explanation:
Time = Distance/Speed
Substitute values in
E.g.
Jenny went for a drive in her new car. She drove for 8 miles at a speed of 4 miles per hour. For how many hours did she drive?
8/4 = 2 hours
Andrew goes to the school by bus.
The probability that the bus is late is 0.1.
If the bus is late, the probability that the Harris is late to the school is 0.8.
If the bus is not late, the probability that Andrew is late to school is 0.05.
i) Draw a tree diagram to show the above information with all the probabilities.
Answer: I am not able to create images such as tree diagrams. But I can explain to you how it could be done.
A tree diagram is a visual representation of the possible outcomes and their probabilities.
The tree diagram to show the above information would have two branches: one representing the event that the bus is late and the other representing the event that the bus is not late.
The first branch, "Bus is Late", would have a probability of 0.1 and would split into two further branches: one representing the event that Andrew is late to school (with a probability of 0.8) and the other representing the event that Andrew is not late to school (with a probability of 0.2).
The second branch, "Bus is not Late", would have a probability of 0.9 and would split into two further branches: one representing the event that Andrew is late to school (with a probability of 0.05) and the other representing the event that Andrew is not late to school (with a probability of 0.95).
This tree diagram will help you to understand the relationship between the different events and their probabilities, as well as the overall probability of Andrew being late to school.
Step-by-step explanation:
The Chess Club president brought donuts to the club meeting each week. As the club grew, more donuts were needed so that each member could have a donut. The table below shows the ratios of boxed donuts to the cost.
Donuts 2 4 B 8
Cost A 31.60 39.50 C
Determine which table has the correct values for A, B, and C.
Donuts 2 4 5 8
Cost 15.80 31.60 39.50 63.20
Donuts 2 4 6 8
Cost 7.90 31.60 39.50 63.20
Donuts 2 4 7 8
Cost 7.09 31.60 39.50 56.72
Donuts 2 4 6 8
Cost 15.80 31.60 39.50 56.72
The table that has the correct values for A, B, and C will be:
D. Donuts 2 4 6 8
Cost 15.80 31.60 39.50 56.72
How to calculate the ratio?Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).
Since we know that 4 donut cost 31.60, the.vost for 2 donut will be:
= 31.60 / 4 × 2
= 15.80
Therefore, we can see that the correct table for this is D.
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BRAINLIEST PERSON WHO GETS IT
Nyoko wrote these two questions.
Equation 1: 6x-5+2x = 4(2x-1) - 1
Equation 2: 3x +7 = bx+7
Part A
Nyoko says that Equation 1 has one solution. Do you agree with her? Explain your reasonings.
Part B
Can Nyoko find a value for b in Equation 2 so that the equation has no solutions? Explain Your REASONING!
a) The equation 1 has an infinite number of solutions, as both linear functions have the same slope and internet, hence Nyoko is incorrect.
b) Nyoko cannot find a value of b so that the equation has no solutions.
How to solve the equations?The equation 1 is given as follows:
6x - 5 + 2x = 4(2x - 1) - 1.
Combining the like terms and applying the distributive property, the simplified equations are given as follows:
8x - 5 = 8x - 4 - 1
8x - 5 = 8x - 5.
As they are linear functions with the same slope and intercept, the number of soltuions is of infinity.
The equation 2 is given as follows:
3x + 7 = bx + 7.
A system of linear equations will have zero solutions when:
The equations have the same slope.The equations have different intercepts.As they have the same intercept for this problem, it is not possible to attribute a value of b such that the equation will have no solution.
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help please 4.2 + 2.5a = 9.2
Answer: a = 2
Step-by-step explanation: 2.5 x 2 = 5 5 + 4.2 = 9.2
[tex]4.2+2.5a=9.2[/tex]
Rearrange:
[tex]2.5a+4.2=9.2[/tex]
Subtract 4.2 from both sides:
[tex]2.5a+4.2-4.2=9.2-4.2[/tex]
[tex]2.5a=5[/tex]
Divide both sides by 2.5:
[tex]\dfrac{2.5a}{2.5} =\dfrac{5}{2.5}[/tex]
[tex]\fbox{a = 2}[/tex]
Answers for this problem?
Note that the square feet of carpet that will be required for this area is: 42 Square Feet of Carpet.
This is solved using the knowledge of the area of rectangles and right-angled triangles.
What is a right-angled triangle?A right-angled triangle is a triangle in which one of the angles is 90 degrees. The total of the other two angles is 90 degrees.
Note that the area of a right-angled triangle is given as:
A = (½)×b×h square units
Where b is breath and h is height.
Note as well that the area of the rectangle is given as Lx B
To solve the above problem, we must create one more right-angled triangle beside the one already created, then solve for the areas of the respective shapes.
Now that the shape has been divided in to two Right-angled Triangles and one rectangle (See the attached) their respective dimensions are given as follows:
1) Right Angled triangled A
B = 2ft
H = 3ft
Area = 1/2 2 * 3 = 3ft
2) Right-Angled Triangle B
B = 4ft
H = 3ft
A = 1/2 * 4 * 3
A = 6ft
3) Rectangle - C
L = 11ft
B= 3ft
A = 11 * 3 = 33 Ft.
Thus total square feet of outdoor carpet required is:
3 + 6 + 33
= 42 Square Feet of Carpet.
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can someone help this thank you
Answer: slope = [tex]\frac{1}{4} x[/tex]
point on the line= (0,-4.25)
Step-by-step explanation:
[tex]y+3\\[/tex] = [tex]\frac{1}{4} (x-5)[/tex]
[tex]y=\frac{1}{4} x-\frac{5}{4} -3\\\\y= \frac{1}{4}x -3\frac{5}{4} \\\\y=\frac{1}{4}x -\frac{17}{4}[/tex]
therefore the value with the x is the gradient so the gradient (slope) is [tex]\frac{1}{4} x[/tex]
since the y-intercept is [tex]-\frac{17}{4}\\[/tex] get the simplified version in decimals which is -4.25... so the point will be (0,-4.25)
(2x-5y)+(6y+5x²)=15y
Answer:
5x² + 2x = 14y
Step-by-step explanation:
2x - 5y + 6y + 5x² = 15y
the only terms we can combine are 5y and 6y; the others are not 'like'
2x + y + 5x² = 15y
5x² + 2x = 14y
a hardware store sells toolboxes. The table shows the types of tools in each toolbox. Becca says that for every 14 tools in a toolbox, there are 2 hammers. Is Becca correct? EXPLAIN
Type l # of tools
Hammer l 2
Plies l 5
Screwdriver l 6
Wrench l 3
Becca is not correct because her probability of 2/14 is not equal to the true experimental probability of 2/16.
How to find the probability of selection?We are given the tools in the box as;
Hammer = 2 nos
Pliers = 5 nos
Screw drivers = 6 nos
Wrench = 3 nos
Thus;
Total number of tools in the box = 2 + 5 + 6 + 3
= 16
Probability of selecting a hammer = 2/16
Now, Becca says that for every 14 tools in a toolbox, there are 2 hammers. This means she is suggesting a probability of 2/14.
This is wrong because it is different from the experimental probability that we got.
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Oscar feels that in order to get a decent amount of honey there should be at least 15000 bees in the colony estimate how many months it will take oscar until he has 15000 bees
a. The function of the bee population is: [tex]f(x) = 5000 * (1.12)^x[/tex]
b. To graph the function, f(x), you can use a graphing calculator or software such as Excel or a Python library like Matplotlib.
c. It will take approximately 7.9 months for Oscar to have 15,000 bees in the colony.
The problem states that Oscar wants to own a bee colony and extract honey from the hive. He starts with a colony of 5,000 bees and the number of bees grows exponentially with a growth factor of 12% each month. To solve this problem, we can use the exponential growth formula to determine the number of bees in the colony based on the month.
The exponential growth formula is [tex]P(t) = P_0 * (1 + r)^t[/tex] where
P(t) is the population at time t[tex]P_0[/tex] is the initial populationr is the growth ratet is the number of time periods.In this case, [tex]P_0[/tex] = 5000, r = 0.12, and t = x (the number of months). So, the function of the bee population is: [tex]f(x) = 5000 * (1.12)^x[/tex]
In order to get a decent amount of honey, Oscar feels that there should be at least 15,000 bees in the colony. To estimate how many months it will take Oscar until he has 15,000 bees, we can set f(x) = 15,000 and solve for x.
By doing this, we get x = log(15000/5000) / log(1.12) ≈ 7.9 months. This means it will take approximately 7.9 months for Oscar to have 15,000 bees in the colony.
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The complete question is:
Oscar wants to own a bee colony so that he can extract honey from the hive. He starts a colony with 5,000 bees. The number of bees grows exponentially with a growth factor of 12% each month.
a. Write a function, f(x), for the bee population that can be used to determine the number of bees in the colony, based on the month, x.
b. Use technology to graph the function, f(x).
c. Oscar feels that in order to get a decent amount of honey, there should be at least 15,000 bees in the colony. Estimate how many months it will take Oscar until he has 15,000 bees.
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Trapezoid ABCD, median EF
DC=2x-1, AB=5x+1, EF=3x+2 x=
The value of EF , DC , AB are 40,14, 37 respectively.
What is trapezoid ?
Trapezoid can be defined as the 4-sided shape in which it has one of sides parallel to it .
ABCD is trapezoid with median EF
so,
DC+AB = 2EF
(2x+10) + (3x+20) = 2 * 4x
5x + 30 = 8x
8x-5x = 30
3x = 30
x = 30/3
x = 10
EF = 4x = 4*10 = 10
3x+10(x-2) = 2 (4x+10)
3x+10x-20 = 8x+20
5x = 40
x = 8
DC = 3x = 32
7(x-2) + (4x-6) = 2*3x
7x-14+4x-6 = 6x
5x = 20
x = 4
DC = (7*(4-2) ) = 14
(2x+3) + (8x+5) = 2*6x
8 = 2x
x = 4
AB = 8*4+5 = 37
Therefore, The value of EF , DC , AB are 40,14, 37 respectively.
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Substitute these values for B-A; A=7, B=2
Answer:
-5
Step-by-step explanation:
Our given equation is B-A, and we know that B = 2 and A = 7. Through what we know, we can plug in the variables' values and solve:
2 - 7 (from B-A)
= -5
Answer:
value for b-a is -5
if subsituition is only done b-a = 2-7
Step-by-step explanation:
if b=2
a=7,
b-a= 2-7
=-5
(not
1. If & D is 42, find the measurements of the following angles:
& A-
B-
& C-
4 D-42
E-
4. F-
G-
& H-
If two of the angles of an oblique triangle are equal, the Law of Sines can be used to fill in the remaining lengths or angle measurements.
How do you find the measure of an angle A and B?In the accompanying diagram, two crossing lines are shown, with the angles 1 and 3 being vertical and congruent. In addition, the angles 2 and 4 are vertical and coincide. Vertical angles are two angles that are in opposition to one another, such as D and B in the illustration above.
The sum of the subsequent angles of a ||gm is A+B=180. To view an infinite number of solutions, download the app. Estimating ratios of a particular quantity is what it is. It is created by contrasting a given quantity with the reference unit. These are used to determine something's dimensions, including length, area, perimeter, volume, and amount. Measurement There are formulas for calculating length, area, surface area, volume, circumference, density, mass, etc.
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Complete question:
Which trigonometric law can be used if two of the angles of an oblique triangle are equal?
Will the following side lengths form a right triangle?
12 ft, 16 ft, 20 ft
Answer:
The three side lengths given, 12 ft, 16 ft, and 20 ft can form a right triangle. This is because the Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, 20^2 = 12^2 + 16^2, so the sides 12 ft, 16 ft and 20 ft can form a right triangle.
Work out the area and perimeter of the shape.
Answer:
area 202.93, perimeter 62.78
Step-by-step explanation:
the triangle:
18² +14² = 520
√520 = 22.8
the curve, without further info, we'll have to assume it's 1/2 circle.
so circumference = 2πr =2 π (14/2) = 14 π = 43.96, 1/2 of it is 21.98
so perimeter of the whole thing is 18+22.8 +21.98 = 62.78
area: 1/2 circle = 1/2 π r² = 1/2 * 3.14*7² = 76.93
triangle area + 1/2 *18*14 = 126
total 202.93
Area of semi circle
πr²/2π(7)²/249π/2Area of Triangle
1/2BH1/2(18)(14)14(9)126Total area
126+49π/2202.9 m²Perimeter
7π+18+14+√18²+14²21.9+22.8+1862.7mFill in the table using this function rule.
y=2x-3
X Y
-6 ?
-3 ?
0 ?
3 ?
The table is filled considering the numeric values of the function, as follows:
x = -6, y = -15.x = -3, y = -9.x = 0, y = -3.x = 3, y = 3.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 or in the expression by the value at which we want to find the numeric value.
The numeric value in this problem is found replacing the lone instance of x by it's value, hence the numeric value at x = -6 is given as follows:
y = 2(-6) - 3
y = -12 - 3
y = -15.
The same procedure is applied for x = -3, x = 0 and x = 3.
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