The recursive definition for the function f given by f(x) = 500 * (1/5)⁽ˣ⁻¹⁾, for x = 1, 2, 3 is a definition that describes how the value of f for a given x can be calculated from its inputs.
What is a recursive definition?A recursive definition of a function is when the definition of the function involves the function itself. This type of definition is used to express complex operations in a simpler form. It is an effective way to break down a complicated problem into simpler, manageable parts. It allows us to define a set of rules in terms of smaller versions of itself, which can then be worked out using a series of steps.
A recursive definition for the function f is a process by which the value of f for a given input can be defined in terms of the values of f for smaller inputs. In other words, a recursive definition for f is a definition that describes how f can be calculated from its inputs.
In this case, the recursive definition for the function f is given by:
f(x) = 500 * (1/5)⁽ˣ⁻¹⁾, for x = 1, 2, 3
This means that the value of f for a given x can be calculated by multiplying 500 (the value of f for x = 1) by 1/5 raised to the power of x-1. This is because f(1) = 500, f(2) = 100 (1/5 * 500), and f(3) = 20 (1/5 * 1/5 * 500).
This recursive definition can also be expressed in a more general form as:
f(x) = a * b⁽ˣ⁻¹⁾, for x = 1, 2, 3
Where a and b are constants. In this case, a is 500 and b is 1/5.
In conclusion, the recursive definition for the function f given by f(x) = 500 * (1/5)⁽ˣ⁻¹⁾, for x = 1, 2, 3 is a definition that describes how the value of f for a given x can be calculated from its inputs. This definition can also be expressed in the more general form of f(x) = a * b⁽ˣ⁻¹⁾, for x = 1, 2, 3.
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2. math! At 3 P.M., a dry-bulb thermometer
reading is 66°F. The wet-bulb reading is 66°F
What is the relative humidity? Explain.
When the wet-bulb reading is 66°F, the relative humidity is 100%.
What is relative humidity?
Based on the given information, the dry-bulb temperature and wet-bulb temperature are the same, which means the air is fully saturated with water vapor, and the relative humidity is 100%.
Relative humidity is the ratio of the amount of moisture in the air compared to the amount of moisture that the air can hold at a particular temperature. The wet-bulb temperature measures the lowest temperature that can be achieved by evaporating water into the air until it is fully saturated, while the dry-bulb temperature measures the actual temperature of the air.
When the wet-bulb and dry-bulb temperatures are the same, it means that the air is fully saturated and cannot hold any more moisture, resulting in a relative humidity of 100%.
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Simplify (4x3y3)(2x2y).
The simplified expression is [tex]8x^4y^4[/tex].
What is simplification?Simplifying an expression is just another way to say solving a math problem. When you simplify an expression, you're basically trying to write it in the simplest way possible. At the end, there shouldn't be any more adding, subtracting, multiplying, or dividing left to do. For example, take this expression: 4 + 6 + 5.
Here the given expression is
=> [tex](4x^3y^3)(2x.2y)[/tex]
=> [tex]4\times x^3\times y^3\times2x\times2y[/tex]
=> [tex]4\times2\times2\times x^3\times x \times y^3\times y[/tex]
=> 8[tex]\times x^{3+1}\times y^{3+1}[/tex]
=> [tex]8x^4y^4[/tex]
Hence the simplified expression is [tex]8x^4y^4[/tex].
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Answer:
Trust me I guarantee you it's correct.
Step-by-step explanation:
Last man got it wrong
D. 8x^5y^4
For which equation is x=−7
a solution?
x^2 = 14
x^2 = 49
x^3 = 21
x^3=343
The equation with a solution of -7 is x^2 = 49
How to determine the equation with a solution of -7From the question, we have the following parameters that can be used in our computation:
The list of options and x = -7
To check which equation has a solution of x = -7, we can simply substitute -7 for x in each equation and see which one is true.
For x^2 = 14: (-7)^2 = 49, which is not equal to 14For x^2 = 49: (-7)^2 = 49, which is equal to 49. For x^3 = 21: (-7)^3 = -343, which is not equal to 21For x^3 = 343: (-7)^3 = -343, which is not equal to -343Hence, the equation x^2 = 49 has x = -7 as a solution.
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Solve the given inequality and graph the solution on a number line
-x/2+3/2<5/2
Graph on number line
Fοr the inequality the sοlutiοn set is x > -2.
What is an inequality?In Algebra, an inequality is a mathematical statement that uses the inequality symbοl tο illustrate the relatiοnship between twο expressiοns. An inequality symbοl has nοn-equal expressiοns οn bοth sides. It indicates that the phrase οn the left shοuld be bigger οr smaller than the expressiοn οn the right, οr vice versa.
Tο sοlve the inequality, we can fοllοw these steps -
Subtract 3/2 frοm bοth sides -
-x/2 < 5/2 - 3/2
-x/2 < 2/2
-x/2 < 1
Multiply bοth sides by -2 (and flip the inequality since we're multiplying by a negative number) -
x > -2
The graph is drawn fοr the sοlutiοn.
The circle οn the left endpοint is nοt filled because the inequality is strict (i.e., nοt less than οr equal tο).
The arrοw οn the right endpοint is filled because the sοlutiοn set includes all values greater than -2.
Therefοre, the sοlutiοn set is all real numbers greater than -2, which can be represented οn a number line as a ray starting at -2 and mοving tοwards pοsitive infinity.
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Solve x = 6+((4x-28)^(1/2))
To solve for x, start by expanding the expression in the parentheses:
x = 6+((4x-28)1/2)
x = 6 + 2√(4x-28)
Next, subtract 6 from both sides of the equation:
2√(4x-28) = x - 6
Next, square both sides of the equation:
(2√(4x-28))2 = (x - 6)2
Then, solve for x:
(4x-28) = (x - 6)2
4x-28 = x2 - 12x + 36
x2 - 16x + 64 = 0
Solve for x by factoring:
(x-8)(x-8) = 0
x = 8
Therefore, the solution to the equation x = 6+((4x-28)1/2) is x = 8.
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−3(0.75x−2y)+6(0.5x−2y) ?
If 1760 litres of fuel is sold in 5 days, in how many days will 3872 litres be sold
It will take 11 days to sell 3872 liters of fuel at the same rate as 1760 liters sold in 5 days.
We can use the following proportion to solve the problem:
1760 liters / 5 days = 3872 liters / x days
Where x is the number of days it will take to sell 3872 liters of fuel.
We can use the unitary method to solve this problem.
Let's start by finding out how much fuel is sold in one day. To do this, we need to divide the total amount of fuel sold (1760 liters) by the number of days it was sold for (5 days):
1760 liters ÷ 5 days = 352 liters per day
Now we can use this rate to find out how many days it will take to sell 3872 liters of fuel:
3872 liters ÷ 352 liters per day = 11 days (rounded to the nearest whole number)
Therefore, it will take 11 days to sell 3872 liters of fuel at the same rate as 1760 liters sold in 5 days.
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Find the missing length indicated. Leave your answer in simplest radical form.
Answer:
x = 16
AB = 25
BC = 15
AC = 20
Step-by-step explanation:
I have marked the vertices to explain
There are three right triangles that can be seen in the picture
Δ ABC with legs BC and AC and hypotenuse AB
ΔACD with legs AD and CD and hypotenuse AC
ΔBCD with legs CD and BD and hypotenuse BC
We will using the Pythagorean formula in all three triangles:
hypotenuse² = sum of squares of legs
------------------------------------------------------------------------------------------
(1) Let's first find missing side BC
In right triangle ΔBCD ,
BC² = CD² + BD²
We have CD = 12, BD = 9
BC² = 12² + 9²
= 144 + 81
= 225
BC = √225 = 15
--------------------------------------------------------------------------------------------------
(2) Now let's focus on ΔABC
AB is the hypotenuse
AC and BC are the legs
AB² = AC² + BC²
or
AC² = AB² - BC²
Since AB = AD + BD = x + 9 and BC = 15
AC² = (x + 9)² - 15²
(x + 9)² = x² + 2 · 9 · x + 9² = x² + 18x + 81
15² = 225
AC² = x² + 18x + 81 -225
AC² = x² + 18x - 144 (1)
-----------------------------------------------------------------------------------------------
(3) Now let's turn our attention to ΔACD with legs AD and CD and hypotenuse AC
AC² = AD² + CD²
With AD = x and CD = 12,
AC² = x² + 12²
AC² = x² + 144 (2)
------------------------------------------------------------------------------------------------
Equations (1) and (2) have the same left side, AC²
So the expressions on the right side must be equal
Therefore:
x² + 18x - 144 = x² + 144
x² terms cancel out from left and right sides giving
18x - 144 = 144
Add 144 on both sides:
18x - 144 + 144 = 144 + 144
18x = 288
x = 288/18 = 16
Plugging this into equation (2) AC² = x² + 144 gives
AC² = 16² + 144
AC² = 256 + 144
AC² = 400
AC = √400
or
AC = 20
Since AB is the third unknown side and AB = x + 9 we get
AB = 16 + 9 = 25
Math part 3 question 5
The value of (f - g) (3) is 32.
What is Function?A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.
Given are two functions, f and g.
f(x) = 3x² and g(x) = x - 8
Subtraction of two functions is defined as,
(f - g) (x) = f(x) - g(x)
= 3x² - (x - 8)
= 3x² - x + 8
To find (f - g)(3), substitute 3 in place of x.
(f - g)(3) = 3(3)² - 3 + 8
= 27 - 3 + 8
= 32
Hence the value of the subtraction of functions is 32.
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How many rebounds should your team expect to have in 15 missed shots?
It is unlikely that the projected rebounds in 15 shots will actually happen.
Explain about the term probability?A probability is a scaled version of the likelihood or chance that a specific event will take place. Both percentages with values ranging from zero to one and percentages extending from 0% to 100% can be used to describe probabilities.Total shots fired equals 10.
To find that there were 15 shots total.
Consider S to be the likelihood that your team will rebound and miss a shot.
P(S) = Number of rebounds / Total Number of outcomes
P(S) = 7/15
P(S) = 0.46
Consequently, it is unlikely that the projected rebounds in 15 shots will actually happen.
Thus, it is unlikely that the projected rebounds in 15 shots will actually happen.
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The complete question is-
During a basketball game, you record the number of rebounds from missed shots for each team. How many rebounds should your team expect to have in 15 missed shots?
Picture for question is attached.
browns books are 2 for $11 and noble books are 5 for $31 who’s is cheaper
Therefore , the solution of the given problem of unitary method comes out to be Browns books are less expensive than Noble books at $5.50 each.
What is unitary method ?Take the lengths of this minute subsection and split the sum by two to complete a task using a unitary variable technique. The unit technique, in a nutshell, removes a wanted item both from the specific sets and color subsets. For instance, 40 pencils will cost Rs/kg ($1.01). It's possible that one country will have total influence over the approach taken to accomplish this. Almost every living creature has a distinctive quality. There are unanswered questions and changes (mathematics, algebra).
Here,
We must ascertain the price per book for each retailer in order to evaluate the costs of Browns and Noble books.
Two of Brown's books cost $11, so each volume costs $5.50 (11/2 = 5.50).
Five novels from Barnes & Noble cost $31, making each book $6.20 (31/5 = 6.20).
Browns books are less expensive than Noble books, which cost $6.20 per volume, at $5.50 each.
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L.8 Solve polynomial equations ZCH Solve using the quadratic formula. -9h^(2)+6h+4=0
The solutions to the given polynomial equation are x = (1 + √5)/(3) and x = (1 - √5)/(3).
To solve the given polynomial equation using the quadratic formula, we need to first identify the values of a, b, and c. In this case, a = -9, b = 6, and c = 4. The quadratic formula is given by:
x = (-b ± √(b^(2) - 4ac))/(2a)
Plugging in the values of a, b, and c into the formula, we get:
x = (-(6) ± √((6)^(2) - 4(-9)(4)))/(2(-9))
Simplifying the equation, we get:
x = (-6 ± √(36 + 144))/(-18)
x = (-6 ± √180)/(-18)
x = (-6 ± 6√5)/(-18)
x = (1 ± √5)/(3)
Therefore, the solutions to the given polynomial equation are x = (1 + √5)/(3) and x = (1 - √5)/(3).
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What is the value of the variable if
the trinomial 3x^2-x+1 and the trinomial 2x^2+5x-4 have the same value?
Answer:
x = 1 or 5
Step-by-step explanation:
You want the value(s) of x that make 3x^2-x+1 and 2x^2+5x-4 have the same value.
EquationEquating their values, we have ...
3x² -x +1 = 2x² +5x -4
x² -6x +5 = 0 . . . . . . . . . subtract (2x²+5x-4)
(x -5)(x -1) = 0 . . . . . . . factor
x = 1 or x = 5 . . . . . . values of x that make the factors zero
The two trinomials will have the same value for x=1 and for x=5.
__
Additional comment
The attached graph shows the points where the trinomials have the same value.
What is the equation of the line that passes through the point ( − 4 , − 3 ) and has a slope of − 43?
Answer:
y = -43x - 175
Step-by-step explanation:
Slope-intercept form is y = mx + b
m = -43
x = -4
y = -3
-3 = -43(-4) + b
b + 172 = -3
b = -3 - 172 = -175
=> y = -43x - 175
What is the slope of a line, in the standard (x,y) coordinate plane, that is parallel to x+5y=9 ?
Answer:-15
Step-by-step explanation:
>If √x-3a+√x-3b=√x-3c then prove that x=(a+b+c) ±2√a² + b² + c²-ab-bc-ca
Answer: See the Picture.
Step-by-step explanation:
Please follow this account
List the symmetries of the given function, if there are any. Otherwise, state "No symmetry". f(x)=-3x^(2)+4
The given function, f(x)=-3x^(2)+4, has three types of symmetry: 1. Symmetry with respect to the y-axis (even symmetry).
2. Symmetry with respect to the x-axis (odd symmetry). 3. Symmetry with respect to the origin (rotational symmetry)
To check for symmetry with respect to the y-axis, we can substitute (-x) for x in the function and see if it is equal to the original function.
f(-x)=-3(-x)^(2)+4=-3x^(2)+4
Since f(-x)=f(x), the function is symmetric with respect to the y-axis.
To check for symmetry with respect to the x-axis, we can substitute (-y) for y in the function and see if it is equal to the original function.
-3x^(2)+4=-y
y=-3x^(2)-4
Since this is not equal to the original function, the function is not symmetric with respect to the x-axis.
To check for symmetry with respect to the origin, we can substitute (-x) for x and (-y) for y in the function and see if it is equal to the original function.
-3(-x)^(2)+4=-y
y=-3x^(2)-4
Since this is not equal to the original function, the function is not symmetric with respect to the origin.
Therefore, the given function f(x)=-3x^(2)+4 has symmetry with respect to the y-axis, but does not have symmetry with respect to the x-axis or the origin.
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need to find the volume in both terms of π and the nearest tenth
Answer: why do u need help again? this is easy boy
Step-by-step explanation:
5(y+25)=−13
y = ??
Please answer this if you can!!
Answer:
y = - 125/18
Step-by-step explanation:
okay so here what i got when i was doing the equation
5 ( y + 25) = - 13y
5 y + 125 = - 13y
then you subtract 125 from both sides
subtract the numbers
and my solution was y = - 125 / 18 trust me!
Hope that helped
Rewrite the set U by listing its elements. Make sure to use the appropriate set notation. U={z|z is an integer and -3<=z<=-1}
The answer of set U by listing its elements is {-3, -2, -1}
To rewrite the set U by listing its elements, we need to identify the integers that fall within the given range of -3<=z<=-1.
The appropriate set notation for listing the elements of a set is {element1, element2, element3, ...}.
So, the integers that fall within the given range are -3, -2, and -1.
Therefore, we can rewrite the set U as:
U = {-3, -2, -1}
This is the answer in the appropriate set notation, listing the elements of the set U.
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A population of bacteria is decaying.
The number of bacteria after h hours is given by the expression 350(1 - 0.3)
Which statement is true?
A)Each hour, the population decreases by 3%
B)Each hour, the population increase by 3 bacteria.
c) The hourly decay rate for the population is 30%
D)The initial population of bacteria is 245.
Answer:
D
Step-by-step explanation:
As an engineer, you are responsible for building a road
across a very steep slope. What factors would you consider
when building your road and how would you address them
to ensure the road is safe? Explain
The factors which would be considered while constructing a road for a steep slope are the terrain of the area, the estimated daily traffic, minimum and maximum sight distance, and the design speed.
Constructing roads on a steep slope is a challenge for every civil engineer. It is because such slopes which are possibly found in hilly areas have less access to main land from where the resources/ material for construction are to be transported and also need specific calculations to estimate maximum durability of the roads and also prevent accidents which might occur due to steep slopes.
Hence, an engineer has to keep in mind several factors which can help to reduce the accident cases, provide road safety and better connectivity with major areas. It is essential that roadway engineers design roads that allow drivers to travel at the right speed. Topography determines the terrain, the different gradient and the construction cost. Every roadway should be built with illuminated raised pavement markings for facilitating safe travel during the night.
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Question of the Day: ACT Math Find the mode of the following set of numbers. 2,5,6,8,9,11,15
The mode of the set {2, 5, 6, 8, 9, 11, 15} is the number that appears most frequently in the set. In this case, all of the numbers appear only once, so there is no mode.
The mode of a set of numbers is the value that appears most frequently in the set. To find the mode of the set {2, 5, 6, 8, 9, 11, 15}, we need to count how many times each number appears and then determine which number appears most frequently.
From the set, we can see that no number appears more than once. Therefore, there is no single number that appears most frequently and we cannot determine a mode for this set.
In some cases, a set of numbers may have multiple modes if two or more numbers appear with the same frequency. For example, the set {1, 2, 2, 3, 3, 3, 4, 5, 5} has two modes, 2 and 3, since both of these numbers appear three times in the set.
However, in the case of the set {2, 5, 6, 8, 9, 11, 15}, there are no repeating numbers, so there is no mode.
In conclusion, the mode of the set {2, 5, 6, 8, 9, 11, 15} is undefined as there are no repeating numbers in the set.
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The total surface area of a spherical segment is (7) times greater than the surface area of the sphere inscribed in it. Determine the altitude of the segment. if the radius of its spherical surface is equal to R.
To find the altitude of the spherical segment, we need to use the formula for the total surface area of a spherical segment, which is given by:
A = 2πR(r + h), where R is the radius of the spherical surface, r is the radius of the base, and h is the height of the segment.
We are given that the total surface area of the spherical segment is 7 times greater than the surface area of the sphere inscribed in it, which means that:
7(4πR^2) = 2πR(r + h)
Simplifying this equation gives us:
14R = r + h
We are also given that the radius of the spherical surface is equal to R, which means that r = R. Substituting this into the equation gives us:
14R = R + h
Solving for h, we get:
h = 14R - R
h = 13R
Therefore, the altitude of the spherical segment is 13R.
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You need to spend exactly $1 and buy 40 stamps. There are 3
kinds of stamps that cost 1, 4, and 12 cents respectively. How many
stamps do you need to buy of each kind (if you have at least one of
each
You need to buy 1 stamp that costs 12 cents, 3 stamps that cost 4 cents each, and 8 stamps that cost 1 cent each, to have a total of 40 stamps and spend exactly $1.
The reasoning is as follows:
If you were to buy only 1 cent stamps, you would need to purchase 100 of them to spend $1, which would exceed the required 40 stamps. On the other hand, if you were to buy only 12 cent stamps, you would only be able to purchase 8 stamps, which would fall short of the required 40 stamps. Therefore, a combination of all three types of stamps is necessary.
Starting with the most expensive stamp, one 12 cent stamp leaves you with 88 cents. Then, 3 stamps of 4 cents each will cost you 12 cents, leaving you with 76 cents. Finally, 8 stamps of 1 cent each will cost you 8 cents, which adds up to $1 and gives you a total of 40 stamps.
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A rectangular prism has a volume of 109.86 cubic centimeters. The width of the prism is 13.2 cm. The height of the prism is 4.1 cm. What is the length of the rectangular prism? Show work.
A. 0.5 cm
B. 2.1 cm
C. 2.03 cm
D. 6.4 cm
The length of the rectangular box will be 2.03 cm. Then the correct option is C.
What is the volume of the rectangular prism?Let the prism with a length of L, a width of W, and a height of H. Then the volume of the prism is given as,
V = L x W x H
The volume of a rectangular box is 109.86 cubic centimeters. The prism's breadth is 13.2 cm. The prism stands 4.1 cm tall.
The length of the rectangular prism is given as,
109.86 = L x 13.2 x 4.1
109.86 = 54.12L
L = 109.86 / 54.12
L = 2.03 cm
The length of the rectangular box will be 2.03 cm. Then the correct option is C.
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Ross has a rectangular garden in his backyard. He measures one side of the garden as 30 feet and diagonal as 33 feet. What is the length of the other side of his garden? Round to the nearest tenth of a foot.
Therefore, the length of the other side of Ross's garden is approximately 13.7 feet.
What is rectangle?A rectangle is a four-sided flat shape with four right angles (90-degree angles) between opposite sides. It is a type of quadrilateral, which means it has four sides. In a rectangle, the opposite sides are equal in length and parallel to each other, which makes it different from a square, where all sides are equal in length. The area of a rectangle can be found by multiplying the length by the width, and the perimeter can be found by adding up the lengths of all four sides.
Here,
Let the length of the other side of the garden be x feet.
Using the Pythagorean theorem, we have:
x² + 30² = 33²
Simplifying the equation:
x² = 33² - 30² = 1089 - 900
= 189
Taking the square root of both sides:
x = √189 ≈ 13.7 feet
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The cost of a hotel room is $50 per night plus a one-time fee of $10 for cleaning. For how many nights can the hotel room be booked if the total cost can be a maximum of $410? Write an inequality to represent the situation. Use x to represent the number of nights
Answer:
410=50x+10
Step-by-step explanation:
your total is 410 so to get there you have to know the number of nights which is x. the 10 is a one time fee so you only need that once and not per night.
HELP ASAP
Use the square below
N
K
Find the mZOKL
Find the m/MOL
M
L
For the given square, m∠OKL=45° and m∠MOL=90°.
What is a Square?A square is a regular quadrilateral in Euclidean mathematics because it has four equal sides and four equal angles (right angles, 90-degree angles). It can also be explained as a rectangle with two adjacent sides that are of identical length. It is the only regular polygon whose diagonals are all the same length and whose internal, central, and exterior angles are all equal (90°).
What are Angle Bisectors?In mathematics, an angle bisector is a line that divides an angle into two equal angles. The term "bisector" refers to a device that divides an object or a shape into two equal sections. An angle bisector is a beam that divides an angle into two identical segments of the same length.
Angle bisector points are equally spaced from both angle lines.
Any angle, including acute, obtuse, and right angles, can have an angle bisector traced to it.
In the given square,
The diagonals NL and KM are angle bisectors of ∠K, ∠L, ∠M and ∠N.
Therefore, ∠OKL= 90/2
∠OKL=45°
We know that, in a square, diagonals are equal and bisect each other at right angles.
Therefore, ∠MOL=90°
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help me if u can thanks
The graph of the function y=3x+1 is shown.
How to know if a point lies in the graph of a function?All the points (and only those points) which lie on the graph of the function satisfy its equation.
Thus, if a point lies on the graph of a function, then it must also satisfy the function.
We are given that;
The function is y=3x+1
Now,
When x = 0, y = 3(0) + 1 = 1, so one point on the function is (0, 1).
When x = 1, y = 3(1) + 1 = 4, so another point on the function is (1, 4).
When x = -1, y = 3(-1) + 1 = -2, so a third point on the function is (-1, -2).
Therefore, the graph will be given the attachment
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