Answers
The inverse function of f(x) is [tex]\frac{x + 2}{3}[/tex] and [tex]f^{-1}(13)[/tex] = 5
What is an inverse function?
An inverse function or an anti function is defined as a function, which can reverse into another function. In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x. If the function is denoted by ‘f’ or ‘F’, then the inverse function is denoted by [tex]f^{-1}[/tex] One should not confuse (-1) with exponent or reciprocal here.
if f(x) = 3x - 2
setting y = 3x - 2 and making x the subject of the formulae,
we have
3x - 2 = y
3x = y + 2
x = [tex]\frac{y + 2}{3}[/tex]
replacing y with x and x with [tex]f^{-1}[/tex](x)
[tex]f^{-1}[/tex](x) = [tex]\frac{x + 2}{3}[/tex]
the value of [tex]f^{-1}[/tex](13) , we substitute x = 13,
[tex]f^{-1}[/tex](13) = 13 + 2 / 3
[tex]f^{-1}[/tex](13) = 15/3
[tex]f^{-1}[/tex](13) = 5
In conclusion, the inverse function is [tex]f^{-1}[/tex](x) = [tex]\frac{x + 2}{3}[/tex] and [tex]f^{-1}[/tex](13) = 5
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Related Questions
Which number line represents the solution set for the inequality 1/2 * x >= 4?.
Answers
The number line which represents the solution set for the inequality is second one.
What is number line?
In elementary mathematics, a number line may be a image of a graduated line that is visual illustration of the important numbers. each purpose of variety|variety} line is assumed to correspond to a true number, and each real to a degree.
Main body:
Start by solving for x.
-1/2x ≥ 4
Multiply each side by 2
-1x ≥ 8
then divide by -1....
but remember to flip your sign its a negative number.
x ≤ -8
hence, the second one is correct.
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If you have 675 cm? of material to make a box with a square bottom and an open top, find the largest possible volume of this box_ base edges = W height h
Answers
The largest possible volume of this box is 1687.5 cm³ with a base edge of 15 cm and a height of 7.5 cm
Let w = length of the base edge
h = height of the box
A box with a square bottom and an open top is to be made from 675 cm² of material. Hence,
675 cm² = w² + 4wh
4wh = 675 cm² - w²
h = (675 cm² - w²)/4w
The volume of the box is the product of the area of the square base and its height. Hence,
V = w²h
Substitute the expression of h to the equation of volume.
V = w²(675 cm² - w²)/4w
V = (675/4)w - (1/4)w³
To obtain the largest volume possible, the first derivative of the volume should be equal to zero.
V'(w) = 0
V = (675/4)w - (1/4)w³
675/4 - (3/4)w² = 0
Simplify and solve for the value of w.
675/4 - (3/4)w² = 0
(3/4)w² = 675/4
w² = 225
w = 15
length of the base edge = 15 cm
Solve for the value of h.
h = (675 cm² - w²)/4w
h = (675 cm² - (15)²)/4(15)
h = 7.5 cm
height of the box = 7.5 cm
Solve for the volume of the box.
V = w²h
V = (15 cm)²(7.5 cm)
V = 1687.5 cm³
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I really need help to get this done, please.
Answers
The area of sector q is [tex]\frac{\pi n^{2} }{9}[/tex]
What is a sector of a circle?A sector is said to be a part of a circle made of the arc of the circle along with its two radii. It is a portion of the circle formed by a portion of the circumference (arc) and radii of the circle at both endpoints of the arc.
The circle is divided into 9 equal parts meaning that 1/9 the area of the circle is the area of circle q
Area of circle = [tex]\pi r^{2}[/tex]
Area of sector q = [tex]\frac{\pi r^{2} }{9}[/tex]
but r = n
Area of sector q = [tex]\frac{\pi n^{2} }{9}[/tex]
In conclusion, the area of sector q is [tex]\frac{\pi n^{2} }{9}[/tex]
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Which function represents a function with direct variation?.
Answers
Functions of the form f(x)=kx represents direct variation.
The table of values that appears a constant proportion between two variables speaks to a direct variation function.
A direct variation is an equation in the form y = kx, where k is the constant of variation. Since it is in this form, the equation will pass through the origin (0, 0); this is because if we use 0 as x, y = k(0) = 0.
In the event that there's at slightest one pair of values that features a different proportion, at that point the function isn't a direct proportion. the equation applies to each corresponding value between the two variables. Functions of form f(x)=kx, where k is the constant, are as they were functions that can speak to a direct variation. T
Therefore, A direct variation is an equation in the form y = kx, where k is the constant of variation. Since it is in this form, the equation will pass through the origin (0, 0); this is because if we use 0 as x, y = k(0) = 0.
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Let z* be the common (finite) optimal value of P and D. Suppose that I is a basic infeasible solution to P whose complementary dual basic solution is feasible. Is it possible that the common objective value of this pair of primal-dual basic solutions is z*? For the linear program: Minimize{x1 : 2x1 – X220, -2x1 +3x2 2-6, x>0}, consider the basic feasible solution with a basis comprised of the columns of x1 and the slack variable in the second constraint. Give the associated complementary dual basic solution. What can you say about this pair of primal-dual basic solutions?
Answers
Pair of primal-dual basic solutions is [tex]x_1 = -3-S_1/2[/tex].
Given that
Let z* be the common (finite) optimal value of P and D.
Suppose that I is a basic infeasible solution to P whose complementary dual basic solution is feasible.
Here, for linear program, we have to
Minimize {x1 : 2x1 - x2 [tex]\geq[/tex] 0, -2x1 + 3x2 [tex]\geq[/tex] - 6}, x1 [tex]\geq[/tex] 0
Stimulate equation 1 and equation 2:
[tex]2x_1 - x_2 = 0\\\\-2x_1 + 3x_2 = -6[/tex]
Canceling [tex]-2x_2[/tex] from both the equations, we get
[tex]2x_2[/tex] = -6
= [tex]x_2[/tex] = -3
So now,
[tex]2x_1 + 3 + S_1 = 0\\\\x_1 = -3-S_1/2[/tex]
Hence the answer is pair of primal-dual basic solutions is [tex]x_1 = -3-S_1/2[/tex].
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a stiff equation is a differential equation where some numerical solution approaches are numerically stable unless you use extremely small step sizes. (T/F)
(F)alse
Answers
The given statement a stiff equation is a differential equation where some numerical solution approaches are numerically stable unless you use extremely small step sizes.is false.
What is a stiff equation
While integrating a differential equation numerically, one would expect the requisite step size to be relatively small in a region where the solution curve displays much variation and to be relatively large where the solution curve straightens out to approach a line with slope approaching to be zero. This is not always true in all the cases. In some cases in order for a numerical method to give a reliable solution to the differential system sometimes the step size is required to be at an very small level in a region where the solution curve is too smooth. The phenomenon is known as stiffness.
So, a stiff equation is a differential equation for which certain numerical methods for solving the equation are numerically unstable, unless the step size is taken to be extremely small.
Therefore, the given statement a stiff equation is a differential equation where some numerical solution approaches are numerically stable unless you use extremely small step sizes. is false.
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I will give Brainlest!
The answers will either be yes or no
Answers
The classification of the equations as direct or indirect variations are;
1) Direct Variation
2) Direct Variation
3) Indirect Variation
4) Indirect Variation
How to find direct and indirect variation?Direct variation occurs when one quantity changes and the other quantity changes as well in direct proportion. Meanwhile, Inverse variation is exactly opposite of that.
Now, let us answer the questions;
1) y = 4x + 1
This shows that y is directly proportional to x because as x is increasing, y is increasing and vice versa. Thus, it is a direct variation.
2) y = 7.5x
This shows that y is directly proportional to x because as x is increasing, y is increasing and vice versa. Thus, it is a direct variation.
3) y = (1/15)x
This shows that y is inversely proportional to x because as x is increasing, y is decreasing and vice versa. Thus, it is an indirect variation.
4) y = 6/x
This shows that y is inversely proportional to x because as x is increasing, y is decreasing and vice versa. Thus, it is an indirect variation.
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8. A table holds 4 cheese pizzas, 4 pepperoni
pizzas, and 2 supreme pizzas. How can
you write a ratio that compares part of
the pizzas to the total?
Answers
Answer: I don't know
Step-by-step explanation:
You got this pal!
What is the common ratio between successive terms in the sequence 27 9 3 1?.
Answers
What do points in this app do for me?
Answers
Answer:
to post questions.
Step-by-step explanation:
. the 49th parallel that separates the united states and canada is an example of what type of border?
Answers
The 49th parallel that separates the united states and Canada is an example of Antecedent border.
An antecedent border is one that existed before to the development of the cultural landscape and persisted even after inhabitants came in to occupy the surrounding region.A political border that existed before the area was occupied by the existing residents is known as an antecedent boundary. For instance, the colonists drew the border between the USA and Canada before they settled North America.Relict boundaries are historical boundaries that have been removed for political reasons but are still visible in the cultural environment. The majority of European borders are afterwards drawn, and we can see how well each one complies with major or minor divisions of natural and cultural areas.Thus this is the meaning Antecedent border.
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Why we Cannot construct a triangle of given sides as 5 cm 5 cm and 10 cm?.
Answers
Answer:
Because the sum of the length of any two sides of a triangle is greater than the length of the third side
Step-by-step explanation:
Why we Cannot construct a triangle of given sides as 5 cm 5 cm and 10 cm?.
5+5=10 (not possible)
What would be an appropriate way to assign digits in order to simulate flipping an unfair coin with P(H) = 0.3? *
Assign digits 1,2,3 to be a head. Assign 4 - 9 to be a tail.
Assign digits 0,1,2,3 to be a head. Assign 4 - 9 to be a tail.
Assign digits 0,1,2,3 to be a tail. Assign 4 - 9 to be a head.
Assign digits 0,1,2 to be a tail. Assign 3 - 9 to be a head.
Assign digits 0,1,2 to be a head. Assign 3 - 9 to be a tail
Answers
Assign digits 1,2,3 to be a head. Assigning 4 - 9 to be a tail would be the most appropriate way.
Option (A) is correct.
What is probability?
Probability is a branch of mathematics that deals with numerical descriptions of how likely an event is to occur or how likely a proposition is to be true. The probability of an event is a number between 0 and 1, where 0 indicates the event's impossibility and 1 indicates certainty.
There are 10 chances to flip the coin.
If we assign digits 1, 2, and 3 to be as a head and if we assign 4 - 9 as a tail,
then we can get the probability of getting head
P(H) = 3/ 10 = 0.3.
Hence, Assign digits 1,2,3 to be a head. Assigning 4 - 9 to be a tail would be the most appropriate way.
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On the planet gepil, there are 6 dibble to every 10 toy. If farmer Kent ha 50 dibble on her quet farm how many yoy are on the farm your anwer may be your eaccute to the nearet tenth
Answers
If a farmer has 50 dibbles then the number of toys would be 84.
What are ratio and proportion?
A ratio is an ordered pair of numbers a and b, denoted by the symbol a / b, where b does not equal zero. A proportion is an equation that sets two ratios equal to each other. For example, if there is one boy and three girls, the ratio could be written as 1: 3. (for every one boy there are 3 girls) One-quarter are boys, and three-quarters are girls.
For every 10 toys, there are 6 dibbles.
so for 50 dibble there will be = 10 * 50/6
= 500/6
= 83.33
≈ 84 toys
Hence, if a farmer has 50 dibbles then the number of toys would be 84.
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Is the following statement bicondional? A quadrilateral is a square if and only if it has four congruent sides and four right angles.
A) True b) False c) not enough information
Answers
The statement is true.
The quadrilateral is a square if and only if it has four congruent sides and four right angles.
Quadrilateral:
A closed quadrilateral has four sides, four vertices, and four angles. It is a type of polygon. In order to create it, four non-collinear points are joined. Quadrilaterals always have a total interior angle of 360 degrees. The Latin words quadra, which means four, and latus, which means sides, are combined to form the English word quadrilateral. A quadrilateral does not necessarily have to have equal lengths on each of its four sides. As a result, depending on the sides and angles, we can have different types of quadrilaterals.
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The number of newspapers sold decreases exponentially by x% each year.
Over a period of 21 years the number of newspapers sold decreases from 1763 000 to 58000.
Calculate the value of x.
Answers
In the exponential decrease function, the rate of decline is approximately 17.7%
Exponential FunctionAn exponential function is a Mathematical function in the form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e, which is approximately equal to 2.71828. An exponential curve grows, or decay depends on the exponential function. Any quantity that grows or decays by a fixed per cent at regular intervals should possess either exponential growth or exponential decay.
In this problem, we can write an exponential function as
58000 = 1763000(1 + x)⁻²¹
Solving for x
x = 0.1765
Converting this into percentage;
x = 0.1765 * 100 = 17.7%
The rate is 17.7%
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TRUE/FALSE return values are type-specific in php functions (a function only returns a value of a specified data type.)
Answers
Return values are type-specific in php functions The answer is False.
What is php function?
A PHP function is a piece of code that is very reusable. It can accept an argument list as input and return a value. Inbuilt functions in PHP number in the thousands.
You can develop your own functions in addition to the built-in PHP functions.
A function is a collection of statements that a programme can use repeatedly.
When a page loads, a function won't start running immediately.
A call to a function will cause the function to run.
In this a function only returns a value of a specified data type.
Hence, the given statement return values are type-specific in php functions is FALSE
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a new restaurant is interested in determining the best time-temperature combination for roasting a five-pound cut of lamb. the times to be tested are 45 minutes, 60 minutes, and 90 minutes at temperatures of 350 degrees fahrenheit and 425 degrees fahrenheit for each time, with the exception of the 90 minute - 425 degree combination. that combination is being eliminated because it will overcook the lamb, which leaves five combinations remaining. from 10 identical cuts of lamb, 2 are randomly selected to roast using each of the time-temperature combinations in the same oven. the quality of the finished product is evaluated for each roast. which of the following is true?
The explanatory variable is the quality of the finished lamb.
If the experiment is repeated, identical results will be expected.
The two cuts that are being roasted for each time-temperature combination are an example of replication.
There should be a control group (i.e. a group in which no treatment is given).
The response variable is the roasting temperature for the lamb.
Answers
The two cuts that are being roasted for each time-temperature combination are an example of replication.
Given,
In the question:
The best time-temperature combination for roasting a five-pound cut of lamb. the times to be tested are 45 minutes, 60 minutes, and 90 minutes at temperatures of 350 degrees Fahrenheit and 425 degrees Fahrenheit for each time, with the exception of the 90 minute - 425 degree combination.
Now, According to the question:
In the question it is given that From 10 identical cuts of lamb, 2 are randomly selected to roast using each of the time-temperature combinations in the same oven. Here it is an act of copying the exact shape size of the lamb in all cuts, which is nothing but replication. Moreover, this replication can help in proper comparison.
which of the following is true?
Hence, The two cuts that are being roasted for each time-temperature combination are an example of replication.
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Can you help me find the radius of the circle?
Answers
Answer:
r=4
Step-by-step explanation:
The radius is equal to half of the diameter. The diameter in this problem is 8 units; half of 8 is 4.
Answer:
The radius would be 4.
Step-by-step explanation:
The radius is always half of the diameter, which would be all the way around the circle. The radius would be halfway around the circle.
So looking at the graph, we can see that the circle surrounds the origin (0) 4 spots to the left and 4 spots to the right. This represents the diameter which is 8 and this can be found by adding the two directions (4 + 4) which gets you 8 as a sum. Now knowing this, we simply divide 8 by 2 and we get the radius which is 4.
Therefore, the answer is 4.
Find the equation of the line
Answers
The linear equation on the given graph can be written as:
y = (-1/4)*x - 6
How to find the equation of the line?The general linear equation is written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
On the graph we can see that the line intercepts the y-axis at y = -6, then the value of b is -6, so we can write:
y = a*x - 6
To find the value of the slope we can use another point on the graph, we can see that the line passes through (-8, -4)
Replacing these values we get:
-4 = a*-8 - 6
-4 + 6 = -8a
2/-8 = a
-1/4 = a
The linear equation is:
y = (-1/4)*x - 6
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8.
Two airport shuttle trains leave the
main station at the same time, Shuttle
A returns to the station every 8 minutes.
Shuttle B returns to the station
every
10 minutes. In how many minutes
will Shuttles A and B leave the station
together for the second time?
Answers
Shuttles A and B leave the station together for the second time in 40 minutes.
What is LCM?The smallest number that can be divided by both numbers is known as the least common multiple (LCM) of two numbers
Given that, the two trains leave the station at the same time, but shuttle A returns every 8 minutes while shuttle B returns every 10 minutes.
To find the time when both trains will leave the station together for the second time, find the LCM of 8 and 10.
The LCM of 8 and 10 is 40.
Hence, Shuttles A and B leave the station together for the second time in 40 minutes.
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The two triangles are similar, solve for x.
Answers
There are two triangles and both of them are similar, then the value of x will be equal to 4.5.
What is an expression?Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both. A mathematical operation such as reduction, addition, multiplication, or division is used to integrate terms into an expression.
As per the given diagram shown in the question,
Δ JKL is similar to Δ ABC.
Then,
10x + 9 = 54
Solve the equation for x,
10x = 54 - 9
10x = 45
x = 45/10
x = 4.5
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15 ft
10 ft
20 ft
Find the area of the trapezoid
Answers
[tex]\textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h~~=height\\ a,b=\stackrel{parallel~sides}{bases~\hfill }\\[-0.5em] \hrulefill\\ a=15\\ b=20\\ h=10 \end{cases}\implies A=\cfrac{10(15+20)}{2}\implies A=175~ft^2[/tex]
the difference between the squares of two numbers is 10. the difference between the two numbers is 2. what is their sum?
Answers
If the difference between the squares of two numbers is 10 and the difference between the two numbers is 2, their sum would be 5.
How to solve an equation?An equation is an expression that can be used to show the relationship between variables and numbers.
Let a and b represent the two numbers.
The difference between the squares of two numbers is 10. Hence:
a² - b² = 10
(a - b)(a + b) = 10 (1)
The difference between the two numbers is 2, hence:
a - b = 2
Substituting:
(a - b)(a + b) = 10
2(a + b) = 10
(a + b) = 5
Their sum is 5.
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Jessica is photographing birds. She tilts her camera so that it first forms a 34° angle with the ground. She then tilts it up some more so that it forms a 63° angle with the ground.
How many degrees does she tilt the camera from its first position to its second position?
Answers
The photographing of Jessica as depicted shows adjacent angles and the angle she tilt the camera from its first position to its second position is 29 degrees
What are adjacent angles?When two angles have a similar vertex and side, they are referred to as adjacent angles.
The vertex of an angle is the point at which the rays that make up its sides come to an end. Adjacent angles have same vertex and side, they can be a complimentary angle or supplemental angle but in this case the sum is 63 degrees. This is to say that
? + 34 = 63
? = 63 - 34
? = 29
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write code to assign x and y coordinates to currcoord, and store currcoord in locations. input first receives an x value, then a y value. input example: 12 32 88 2 -1 -1
Answers
It will be feasible to create a coordinate code that looks like this using the knowledge of the Python computational language:
Writing coordinate code in python:
def __init__(self, x, y):
self.x = x
self.y = y
def getX(self):
directly
return self.x
def getY(self):
return self.y
def __str__(self):
return '<' + str(self.getX()) + ',' + str(self.getY()) + '>'
class Coordinate(object):
def __init__(self,x,y):
self.x = x
self.y = y
def getX(self):
return self.x
def getY(self):
return self.y
def __str__(self):
return '<' + str(self.getX()) + ',' + str(self.getY()) + '>'
def __eq__(self, other):
if other.x == self.x and other.y == self.y:
return True
else:
return False
def __repr__(self):
return "Coordinate"+ str((self.x, self.y))
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1. -6 - 8(x - 5)= algebric expression'
2. x + 8 + 6x=
Answers
Answer:
I'm not sure if this is what you want to be solved.
[tex]-6-8(x-5)=-6-8x+40=34-8x[/tex][tex]x+8+6x=7x+8[/tex]Context and sensory clues aid one in deciding whether or not something occurred. this is called __________. a. reality monitoring b. source monitoring c. misinformation effect d. source-monitoring error
Answers
Option-A is correct that is reality monitoring. One can determine whether or not something happened with the use of context and sensory evidence. This is referred to as reality monitoring.
Given that,
One can determine whether or not something happened with the use of context and sensory evidence. This is referred to as----
We have to fill the blank.
We know that
What is sensory context?sensory environment The auditory system adjusts to continuing, presumably irrelevant regularities in the acoustic environment in order to improve reactions to unexpected and possibly significant sounds, according to a prevalent theory in studies of sensory context.
We get,
The capacity to discern internally created information from external reality is known as reality monitoring.
Therefore, Option-A is correct that is reality monitoring. One can determine whether or not something happened with the use of context and sensory evidence. This is referred to as reality monitoring.
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all of these are factors that influence whether an infant will show stranger wariness except .
Answers
All of the aforementioned are factors that influence whether an infant will show stranger wariness except: A. the infant's ability to regulate emotion.
What is stranger wariness?In Psychology, stranger wariness is sometimes referred to as stranger anxiety or stranger fear and it can be defined as any form of distress and apprehension that is typically experienced by infants (young children or babies) when they are around or within the proximity of individuals who are strange (unfamiliar) to them.
This ultimately implies that, stranger wariness simply refers to a form of distress and apprehension which an infant (young child or baby) experiences when exposed to strangers.
In this context, we can reasonably infer and logically deduce that the ability of an infant (young child or baby) to regulate emotion is not a factor that would influence whether an infant shows stranger wariness.
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Complete Question:
All of these are factors that influence whether an infant will show stranger wariness EXCEPT ______.
A. the infant's ability to regulate emotion
B. the overall temperament of the infant
C. the past experience of the infant
D. the situation in which the infant meets the stranger
Cooper and his children went into a grocery store and he bought $6 worth of apples and bananas. Each apple costs $1 and each banana costs $0.50. He bought a total of 10 apples and bananas altogether. Determine the number of apples, x, and the number of bananas, y, that Cooper bought.
Answers
Cooper bought 2 apples and 8 bananas.
An algebraic expression is the combination of numbers and variables in expressing and solving a particular mathematical question. An equation is the equality of expressions.
Let x = number of apples
y = number of bananas
If he bought a total of 10 apples and bananas altogether, then
x + y = 10
Rearranging, x = 10 - y (equation 1)
If each apple costs $1 and each banana costs $0.50, then the total cost of the apples and bananas he bought is $1x and $0.50y, respectively.
If he bought $6 worth of apples and bananas, then the total cost of the fruits is equal to $6.
$1x + $0.50y = $6
x + 0.5y = 6
Substitute equation 1 and solve for y.
x + 0.5y = 6
10 - y + 0.5y = 6
4 = 0.5y
y = 8
number of bananas = 8
Substitute the value of y to equation 1 and solve for x.
x = 10 - y
x = 10 - 8
x = 2
number of apples = 2
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