A) If the change in b results in a smaller feasible region, then the optimal objective value will either remain the same or increase.
B) If the change in b results in a larger feasible region, then the optimal objective value may remain the same or decrease.
In linear programming, the objective is to minimize or maximize an objective function subject to certain constraints. One common constraint is that the solution must be in the feasible region, which is defined by the set of all solutions that satisfy the constraints.
Recall that the constraints are given by Ax >= b, where A is a matrix of coefficients and x is a vector of variables. If we increase one component of b, say bi, then the set of solutions that satisfy the constraints will change. Specifically, any solution that previously satisfied Ax >= b may no longer satisfy the constraints, since the left-hand side of the inequality is fixed while the right-hand side has increased. In other words, the feasible region may shrink or shift in response to the change in b.
Now let's consider the effect on the optimal objective value. Recall that the objective function is given by cx, where c is a vector of coefficients. The optimal objective value is the minimum (or maximum) value of cx over all solutions in the feasible region. If we increase one component of b, then the optimal objective value may or may not change, depending on the specifics of the problem.
To see why, let's think about what happens to the feasible region. As we noted above, the feasible region may shrink or shift in response to the change in b. If the optimal solution was previously at the boundary of the feasible region, then it may no longer be feasible, and the optimal objective value will increase. On the other hand, if the optimal solution was previously in the interior of the feasible region, then it may still be feasible, and the optimal objective value will remain the same.
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Graph the following equation -3y+6x+=6
Answer:
Step-by-step explanation: Here's a step-by-step guide on how to graph the equation -3y + 6x = 6:
Isolate y: To isolate y, first subtract 6x from both sides of the equation: -3y + 6x = 6 => -3y = -6x + 6.
Divide both sides of the equation by -3: Dividing both sides of the equation by -3, we get: -3y / -3 = (-6x + 6) / -3.
Simplify the equation: On simplifying the equation, we get: y = 2x - 2.
Plot the y-intercept: The y-intercept of the equation is when x = 0. So, when x = 0, y = 2 * 0 - 2 = -2. This point is (0, -2). Plot this point on the graph.
Plot a second point: Pick a value of x and plug it into the equation to find the corresponding y value. For example, let's take x = 1. Plugging x = 1 into the equation, we get y = 2 * 1 - 2 = 0. This point is (1, 0). Plot this point on the graph.
Draw the line: Connect the two points plotted on the graph. This line represents the solution set of the equation.
That's it! You have successfully graphed the equation -3y + 6x = 6.
Answer:
Step-by-step explanation:
Arturo earns n dollars per hour. Next month he will receive a 2% raise in pay per hour. The expression n + 0.02n is one way to represent Arturo's pay per hour after the raise. Write an equivalent simplified expression that will represent his pay per hour after the raise.
Answer:
1.02n or 51/50n
Step-by-step explanation:
n + 2% raise = 1.02n and 50/51n
answers please just need help Thank you
Answer:
162π - 324 (exact) or 184.938
Step-by-step explanation:
You probably don't even need help on this one anymore, its just the same as the previous one I helped you with.
Diameter = a^2 + b^2 = c^2 = 18^2 + 18^2 = c^2
√648 = c (this is exact) so radius is √648/2
Area of square = lw = 324
Area of circle = (√648/2)^2π = (648/4)π = 162π
Area of shaded region = 162π - 324 (exact) or 184.938
A water reservoir is shaped like a rectangular solid with a base that is 40 yards by 40 yards, and a vertical height of 30 yards. At the start of a three-month period of no rain, the reservoir was completely full. At the end of this period, the height of the water was down to 5 yards. How much water was used in the three-month period?
In response to the above question, we may state that in the rectangle [tex]4,241,455[/tex] gallons [tex]= 4,570,000[/tex] Cubic feet[tex]x 7.48052[/tex] Gallons/cubic foot.
What is rectangle?In the geometry of the Euclidean plane, a rectangle is a quadrilateral having four right angles. You may also refer to it as an equiangular quadrilateral, meaning that all of its angles are equal. A straight angle could also be present in the parallelogram.
Rectangles with four evenly sized sides are called squares. Four 90-degree vertices and equal parallel sides make up a quadrilateral with the shape of a rectangle.
As a result, it's also known as an equirectangular rectangle. A rectangle is also referred to as a parallelogram, since its opposite sides are parallel and equal.
Volume of rectangular solid is L × W × H
[tex]50 × 30 × 20 = 30000[/tex] cubic yards
[tex]50 × 30 × 6 = 9000[/tex]cubic yards
[tex]30000–9000 = 21000[/tex]cubic yards
This needs to be converted to gallons of water. We are given the conversion factor between a gallon of water and cubic feet, therefore even though we have cubic yards rather than cubic feet, we must first convert the [tex]21,000[/tex] Cubic yards to cubic feet.
A cubic yard has a volume of 27 cubic feet.27 cubic feet per cubic yard times [tex]21,000[/tex]cubic yards equals 567,000 cubic feet.
7.48052 gallons make up 1 cubic foot.
Therefore, 4,241,455 gallons are equal to 567000 cubic feet times 7.48052 gallons/cubic foot.
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Find the area of the figure. Round to the nearest tenth, if necessary.
Simplify.
(-32)^-9/5
Answer: undefined
Step-by-step explanation: can’t raise a negative number to a integer exponent
Figure ABCD is a kite.
Find the value of x.
A
X =
= [?]
14x - 22
H
B
C
The value of x is equal to 8, in the equation 14x -22.
What is equation?An equation is a mathematical statement consisting of two expressions joined by an equal sign.
Solution:
The diagonals of the dragon intersect at right angles. This gives a solvable relationship for x.
setting the displayed dimensions correspond to 90° angular dimensions.
14x -22 = 90
You can solve this two-level linear equation in the usual way.
14x = 112. . . . . . Step 1, add the reciprocal of the constant to get just x
x = 112/14 = 8 . . . Step 2, divide by the factor of x
Hence, the value of x is 8.
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A bag of garden soil weighs 40 pounds and holds 5 cubic feet. Find the weight of 15 bags in kilograms and the volume of 15 bags in cubic yards.
75
Step-by-step explanation:
I think this is the answer I'm not sure I hope this helps
A bag contains 2 gold marbles, 7 silver marbles, and 29 black marbles. The rules of the game are as follows: you randomly select one marble from the bag. If it is gold, you win $4, if it is silver, you win $2. If it costs $1 to play, what is your expected profit or loss of you play this game?
Total number of marbles is 5 + 7 + 29 = 41.
Your expected profit or loss of you play this game $0.17 loss?
The given parameters are
2 gold marbles,
7 silver marbles,
and 29 black marbles
Also you win $4, if it is silver, you win $2. If it costs $1 to play
Event P(Event) Net Winnings P(Event) * Net Winnings
Gold 5/41 4 - 1 = 3 15/41
Silver 7/41 2 - 1 = 1 7/41
Black 29/41 -1 -29/41
sum -7/41 = $0.17 loss
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BRAINLIEST
QUICKLY HELPP
Answer:
BEF
What is an angle?An angle is a measure of a turn, measured in degrees or °. Angles are made up of two rays, making the sides of the angle.
What types of angles are there?There are right angles (exactly 90 degrees), acute angles (less than 90 degrees), obtuse angles (more than 90 degrees), and reflex angles (more than 180 degrees).
Looking at the following answers provided, we can see that BEF is a proper angle, because it is made up of two rays in the proper order.
KGH on the other hand, is not. KGH would be a proper angle if it was in the correct order (GHK or KHG), but because it is not in the right order, it is not a proper angle. LEA is not a proper angle either. We know that an angle is made up of two rays, but LEA isn't, and it's the same with ADE.
Answer:
BEF and ADE
Step-by-step explanation:
These points when connected make and angle. The others do not as they sinply dont make sense or have the points in a way that makes the whole statement false.
The fish in a hatchery tank have mean length = 9.7 inches, with standard deviation = 1.2 inches. If a random sample of 40 fish is taken from the tank, what is the probability that their average length is less than 10 inches?
The probability that the average length of a random sample of 40 fish is less than 10 inches is 0.8869 or 88.69%.
What is probability ?
Probability is a metric used to determine how likely an event or result is to occur. It is a number between 0 and 1, where 0 denotes an improbable event and 1 denotes a certain event.
A group of potential possibilities is referred to as an event in probability theory. By dividing the number of positive possibilities by the total number of possible outcomes, the probability of an event happening is determined.
The fish in the hatchery tank are distributed in length according to a normal distribution, with a mean length of 9.7 inches and a standard deviation of 1.2 inches.
With a mean that is equal to the population mean and a standard deviation that is equal to the population standard deviation divided by the square root of the sample size, the distribution of the sample means will also follow a normal distribution.
The formula to calculate the z-score for the sample mean is:
z = (x - μ) / (σ /[tex]\sqrt{n}[/tex] )
where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.
In this case, we want to find the probability that the sample mean is less than 10 inches. So we need to calculate the z-score for a sample mean of 10 inches:
z = (10 - 9.7) / (1.2 /[tex]\sqrt{40}[/tex]) = 1.21
Using a standard normal distribution table or calculator, we can find that the probability of getting a z-score less than 1.21 is approximately 0.8869. This means that there is an 88.69% chance of getting a sample mean less than 10 inches.
Therefore, the probability that the average length of a random sample of 40 fish is less than 10 inches is 0.8869 or 88.69%.
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PLEASE HELP!!
i think it wants it in the form of
m = y2-y1
——————
x2-x1
but i could be wrong please please please help if you can it’s greatly appreciated
a) Two different ways.
x = ln(32)/ln(2)
2^x = 2^5
b) Only the natural logarithm way can be used.
c) x = 3.58
How to solve the equation?We want to solve:
2^x = 32
in two ways.
The first way is trivial, apply the natural logarithm to both sides:
ln(2^x) = ln(32)
x = ln(32)/ln(2)
The second way is the next one:
2^x = 32
The right number can be written as:
4*8 = 32
Now we can factorize the left side:
4*8 = (2*2)*(2*2*2) = 2^5
Replacing that we get:
2^x = 2^5
So we know that x = 5.
b) The second way can't be used to solve:
2^x = 12
Because 12 has a factor different than 2.
c) Using the natural logarithm way:
x = ln(12)/ln(2) = 3.58
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19. The mass of a radioactive element is 35
milligrams. The mass of the element decreases by
12.9% every year.
a. Write a function that represents this situation.
b. Predict the mass of the element in 4 years. Round
your answer to the nearest tenth.
c. Will the mass of the radioactive element ever be 0
milligrams? Explain.
a) The function that represents this situation is,
⇒ y = 35 (1 - 12.9%)ⁿ
Where, 'n' is number of years and 'y' is mass of element.
b) For 4 years, the mass of the element is, 19.95 milligrams
c) No, the mass of the radioactive element will never be 0 milligrams.
What is expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Now,
The function that represents this situation is,
⇒ y = 35 (1 - 12.9%)ⁿ
Where, 'n' is number of years and 'y' is mass of element.
Now, For 4 years, the mass of the element is,
⇒ y = 35 (1 - 12.9%)ⁿ
⇒ y = 35 (1 - 12.9%)⁴
⇒ y = 35 (1 - 0.129)⁴
⇒ y = 35 (0.87)⁴
⇒ y = 35 × 0.57
⇒ y = 19.95 milligrams
No, the mass of the radioactive element will never be 0 milligrams.
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Help me with this question…..
Answer:
In order from least to greatest, the numbers would be organized as such: [tex]\frac{2}{3}[/tex] , [tex]\sqrt{5}[/tex] , [tex]\frac{5}{2}[/tex] , [tex]\pi[/tex]. So C is the correct answer.
Step-by-step explanation:
At first glance, these numbers are not the simple whole and decimal numbers one might be used to. However, we can find their approximate values and order them correspondingly. [tex]\frac{2}{3}[/tex] is a fraction that is less than one, so on a number line it would be between 0 and 1, making it the smallest number out of the four. [tex]\sqrt{5}[/tex] and [tex]\frac{5}{2}[/tex] are both between 2 and 3, but [tex]\sqrt{5}[/tex] is approximately equal to 2.24, while [tex]\frac{5}{2}[/tex] is equal to 2.5. Therefore, we can conclude that [tex]\frac{5}{2}[/tex] is greater than [tex]\sqrt{5}[/tex]. Lastly, [tex]\pi[/tex] is a constant number that is the ratio of a circle's circumference to its diameter that equals approximately 3.14, so we can conclude that [tex]\pi[/tex] is the greatest number out of the four.
Now that we have the four numbers in an easier and visually more clear way to find their exact values, we know that the order of these numbers from least to greatest would be choice C: [tex]\frac{2}{3}[/tex] , [tex]\sqrt{5}[/tex] , [tex]\frac{5}{2}[/tex] , [tex]\pi[/tex] .
Have a great day! Feel free to let me know if you have any more questions :)
5. Annette bought 8 dozen eggs from Mr. Joseph's Farm Store for $2,800.00. What was the price per dozen?
In a casee whereby Annette bought 8 dozen eggs from Mr. Joseph's Farm Store for $2,800.00 the price per dozen is $350 per dozen
How can the price per dozen be calculated?The concept that will be use here is division. Multiplication is the opposite of division. If 3 groups of 4 add up to 12, then 12 divided into 3 groups of equal size results in 4 in each group. Creating equal groups or determining how many people are in each group after a fair distribution is the basic objective of division.
The total dozen = 8 dozen eggs
The total price of the 8 dozen eggs $2,800.00
The price per dozen = $2,800.00/ 8 dozen
=$350 per dozen
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Complete the Recursive formula.
Answer:
[tex]-13[/tex]
Step-by-step explanation:
The common difference of the arithmetic sequence is [tex]-13[/tex].
Raul tried to evaluate an expression step by step. \qquad\begin{aligned} &3 -(-5) - 7\\\\ \\ =&3+5-7&\green{\text{Step } 1}\\\\ \\ =&3+2&\blue{\text{Step } 2}\\\\ \\ =&5&\purple{\text{Step } 3} \\\\ \end{aligned} = = = 3−(−5)−7 3+5−7 3+2 5 Step 1 Step 2 Step 3
Raul made a mistake in evaluating the expression 3 - (-5) - 7 in B) Step 2 by not following PEMDAS.
What is PEMDAS?PEMDAS means Parentheses, Exponents, Multiplication and Division, Addition and Subtraction from left to right.
PEMDAS refers to the correct order for evaluating mathematical expressions.
The expression 3 - (-5) - 7 should be evaluated as follows:
3 - (-5) - 7
= 3 + 5 - 7
= 8 - 7
= 1
Thus, if Raul did not make a mistake in Step 2, he would have valued the expression as 1.
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Complete Question:Raul tried to evaluate an expression step by step.
3 - (-5) - 7
Step 1: 3 + 5 - 7
Step 2: 3 + 2
Step 3: 5
Find Raul's mistake.
Answer Options:A) Step 1
B) Step 2
C) Step 3
D) Raul did not make a mistake.
A right rectangular prism has a square base with sides 1/2 in. Long. The volume of the prism is 3/8 in to the third power. What is the prism?
Answer:
If the base of the right rectangular prism is a square with sides that are 1/2 inch long, then the area of the base is (1/2)^2 = 1/4 square inches.
Since the volume of the prism is given as 3/8 cubic inches, we can use the formula for volume of a right rectangular prism (V = Bh) to solve for the height of the prism:
V = Bh
3/8 = (1/4)h
Multiplying both sides by 4, we get:
3 = h
So the height of the prism is 3 inches.
Therefore, the right rectangular prism has a square base with sides 1/2 inch long and a height of 3 inches, making it a 1/2 x 1/2 x 3 inch rectangular prism.
Construction each spatial figures
Blue pyramid
Black cown
Yellow cube
Green rectangular prism
Red silendar
Violet sphere
A pyramid is a three-dimensional geometric shape that has a polygonal base and triangular faces that meet at a common point. The height of a pyramid is the perpendicular distance from the base to the apex.
How to explain the shapesA cube is a three-dimensional shape that has six square faces of equal size. All angles of a cube are right angles, and all edges have the same length. The volume of a cube is given by the formula V = s³ where s is the length of one edge.
A rectangular prism is a three-dimensional shape that has six rectangular faces. The opposite faces are congruent and parallel, and all angles are right angles. The volume of a rectangular prism is given by the formula V = lwh, where l, w, and h are the lengths of the three perpendicular edges.
A sphere is a three-dimensional shape that is perfectly round and has no edges or corners. It is defined as the set of all points in three-dimensional space that are equidistant from a given point called the center. The volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius of the sphere.
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A
B
C
D
Pick a letter
Answer: D
Step-by-step explanation:
1 in.=1488 milesx5=7440 miles.
Area= pi x r^2
=pi x (7440)^2 or option D.
Hope this helps :)
Evaluate the limit limx approches 0 x square+ x over x
Step-by-step explanation:
If we use direct substitution, we will get
[tex] \frac{0}{0} [/tex]
Which is intermediate from so we must use.algebraic manipulation
Let's divide everything by x
We would get
[tex] \frac{x + 1}{1} [/tex]
So the limit as x approaches 0 is
[tex]1[/tex]
Proof using a graph:
As x gets close and closer to 0, f(x) approaches 1. Limits does not care about discontinuity, only what the function gets closer to.
Trigonometry question
The value of sin(tetha/2) is ±√½(1-8/√113)
What are half angles?In trigonometry, the half-angle formula is used to determine the exact values of the trigonometric ratios of angles such as 15° (half of the standard angle 30°), 22.5° (half of the standard angle 45°), and so on. If θ is an angle, then the half angle is represented by θ/2.
if tan(tetha) = 7/8
this means that 7 is the opposite and 8 is the adjacent
hyp² = opp² +adj²
hyp² = 49+64
hyp = √113
sin(tetha/2) = ±√1-cos(tetha))/2
= ±√1-(8/√113))/2
therefore the value is sin(tetha)/2
= ±√1-(8/√113))/2 or ±√½(1-8/√113)
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While on a camping trip with his friends, Finn made a pot of stew over the campfire. He
divided it equally among their 6 bowls. Each bowl had more than 2.5 cups of stew.
Let x represent how much stew Finn made. Which inequality describes the problem?
≥2.5
>2.5
Solve the inequality. Then, complete the sentence to describe the solution.
Finn made more than
cups of stew.
Submit
The inequality which describes the problem about the pot of stew Finn made is x/6 > 2.5
Which inequality describes the problem?Number of bowls= 6
Quantity of stew in each bowl > 2.5
Quantity of stew Finn made = x
The inequality
Quantity of stew Finn made / Number of bowls > Quantity of stew in each bowl
x/6 > 2.5
Therefore, x divided by 6 greater than 2.5 is the inequality which describes the situation.
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SAQ-18. The firm provides the following information: Annual requirement Cost per unit ........ Rent, tax, and insurance Insurance per order...... Required: a. EOQ ..... Rs. 20 Rs. 2 per unit ..Rs. 200 ...............100,000 units Carrying cost per unit per year ...........10% of unit price Cost per order...... ...........Rs. 300 b. Total Cost of EOQ c. Number of order
Note that the Economic Order Quantity is given as approximately 4,472.13 Units.
Economic Order Quantity, also known as Economic Purchasing Quantity, is the order quantity in inventory management that minimizes overall holding costs and ordering expenses. It is one of the most ancient traditional production scheduling models.
EOQ = √[(2 * AR* OC)/CC]
Were AR = Annual Requirement = 100,000 units
OC = Ordering Cost = Rs 20 per unit
CC = Carrying Cost = 10% of Per Unit Cost
Per Unit Cost = Rs. 2
Thus,
EOQ = √[(2 * 100,000* 20)/10% * 2]
EOQ = √[(4000000)/0.2]
EOQ = √20000000
EOQ = 4472.135955
EOQ [tex]\approx[/tex] 4,472.13 Units.
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Rick was given 2 new gaming consoles for his birthday, one from each set of grandparents. He wants to return one of the consoles and use the store credit to buy new video games. He will receive $299 in store credit, and each video game costs $60. You can use a function to describe the amount of store credit he will have left after purchasing x video games. Write an equation for the function. If it is linear, write it in the form f(x)=mx+b. If it is exponential, write it in the form f(x)=a(b)x. f(x)=
don't spam ;-;
The linear function for the amount of store credit he will have left after purchasing x video games is given as follows:
f(x) = 299 - 60x.
How to obtain alinear function?
The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the rate of change.The intercept b represents the value of y when x = 0.The parameters for this problem are given as follows:
b = 299, which is the initial credit that he has.m = -60, as for each videogame purchased, the amount of credit decays by $60.Hence the function is given as follows:
f(x) = 299 - 60x.
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A boat has a top speed of 26 knots and a displacement of approximately 81000 tons. (1 knot= 1 nautical mile per hour; 1 metric ton =1000 kilograms)
Express the top speed in miles per hour and the displacement in metric tonnes.
(1 knot=1 nautical mile per hour; 1 metric tonne=1000 kilograms)
On solving the provided question we can say that 2 decimal places =29.92 miles per hour
what is decimal?Integer and non-integer numbers are often expressed using the decimal numeral system. The Hindu-Arabic numeral system has been expanded to include non-integer values. Decimal notation is the name for the method used to represent numbers in the decimal system. A decimal is a number with a whole and a fractional component. Decimal numbers, which are in between integers, are used to express the numerical value of full and partially whole amounts. A decimal point separates the complete number and the fractional portion of a decimal number. The dot between the whole number and the fractions is known as the decimal point. A decimal number is, for instance, 25.5. In this instance, 25 is the entire number, while 5 is the
top speed is 26 knots,
1 knot = 1.15078 miles per hour
26 knots = 26 * 1.15078
= 29.92028 miles per hour
2 decimal places
=29.92 miles per hour
boat has a displacement of 96000 tons
1 ton = 0.907185 metric tonnes
96000 tons = 0.907185 * 96000
= 87,089.76 metric tonnes
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You paid $29.75 in tax when you bought a $350 bike. What is the percent tax?
The percent tax you paid when you bought the bike is approximately 8.493%.
What is percentage ?
Percentage can be defined as the product of ratio of given value, total value and hundred.
given ,
You paid $29.75 in tax when you bought a $350 bike
To find the percent tax, we can divide the amount of tax by the total cost (including tax) and multiply by 100 to express the result as a percentage.
tax = 29.75
total = 350
percent tax = (tax / total) * 100
So the percent tax would be
percent tax = (29.75 / 350) * 100
= 8.493%
Therefore, The percent tax you paid when you bought the bike is approximately 8.493%.
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Part B
Landon thinks that the answer is
12 guests. He says, "10+ 4 = 14, and
14 rounds to 10. Then 10 X 12=120."
Do you agree with his reasoning? Explain
why or why not.
The number of guests that shared one platter is 10.
How to solve thisA. Since 3 people bring a total of 4 platters each, there are a total of 3 x 4 = 12 platters.
If the 120 guests share the platters equally, then each platter is shared by 120/12 = 10 guests. Therefore, 10 guests share 1 platter.
B. Landon's reasoning is incorrect.
While it is true that 3 people bring 4 platters each, the total number of platters is 3 x 4 = 12, not 7.
Therefore, 7 guests cannot be the correct answer. The correct answer is 10 guests share 1 platter, as explained in part A.
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Three people each bring 4 platters of food to a family reunion. The 120 guests all share the platters equally. A. How many guests share 1 platter? Explain your answer. 3.AR.1.2 B. Landon thinks that the answer is 7 guests. He says, " 3+4=7, and 7 rounds to 10 . Then 10×12=120." Do you agree with his reasoning
Hannah has to make 168 gallons of punch for a big party. The punch is made of soda and fruit drink. The cost of the soda is $1.57 per gallon and the cost of the fruit drink is $2.41 per gallon. Hannah's budget requires that the punch cost $1.66 per gallon. How many gallons of soda and how many gallons of fruit drink does she need?
Gallons of soda =
Gallons of fruit punch =
The number of gallons of fruit drink is 118 gallons and the number of gallons of soda is 150 gallons.
How much fruit drink and soda does he need?The system of equations that represents the question is:
f + s = 168 equation 1
2.41f + 1.57s = (1.66 x 168)
2.41f + 1.57s = 278.88 equation 2
Where:
f = number of gallons of fruit drink s = number of gallons of sodaThe elimination method would be used to determine the required values
Multiply equation 1 by 2.41
2.41f + 2.41s = 404.88 equation 3
Subtract equation 2 from equation 3
126 = 0.84s
s = 126 / 0.84
s = 150
Substitute for s in equation 1
f + 150 = 168
f = 168 - 150
f - 118 gallons
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nellie is analyzing a quadratic function f(x) and a linear function g(x). will they intersect?
Yes, at positive x-coordinates
Yes, at negative x-coordinates
Yes, at negative and positive x-coordinates
No, they will not intersect
Yes, It intersect at positive x-coordinates.
What is Equation of line?The equation of line in point-slope form which passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, Slope (m) = (y₂ - y₁) / (x₂ - x₁)
Given that;
The function f (x) is defined in graph.
Now, The function g (x) is defined as,
⇒ y - 5 = (10 - 5) / (2 - 1) (x - 1)
⇒ y - 5 = 5 (x - 1)
⇒ y - 5 = 5x - 5
⇒ y = 5x
Clearly, By the graph of functions f (x) and g (x), both intersect at positive x - coordinate.
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