An equation that combines with the given equation x + 2y = 21 to form a system of equations with the solution x = 3 and y = 9 is 4x + y = 21.
The correct answer is an option (c)
As x = 3 and y = 9 are the solution of system of equations, the required equation must be true for x = 3 and y = 9.
Given equation is: x + 2y = 21
For x = 3 and y = 9 given equation is 3.
In order to find the required equation, we substitute the values of x and y in each equation and check whether the equation is true for x = 3 and y = 9.
a. For equation, 4x + 6y = 64
LHS = 4(3) + 6(9)
LHS = 12 + 54
LHS = 66
LHS ≠ RHS
So, this is not a required equation.
b. 2x + y = 36
LHS = 2(3) + 9
LHS = 6 + 9
LHS = 15
LHS ≠ RHS
So, this is not a required equation.
c. 4x + y = 21
LHS = 4(3) + 9
LHS = 12 + 9
LHS = 21
LHS = RHS
this is the required equation.
d. -3x + 4y = 33
LHS = -3(3) + 4(9)
LHS = -9 + 36
LHS = 27
LHS ≠ RHS
So, this is not a required equation.
e. 3x + 2y = 28
LHS = 3(3) + 2(9)
LHS = 9 + 18
LHS = 27
LHS ≠ RHS
So, this is not a required equation.
Therefore, the reuired equation is 4x + y = 21
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Dr. And Mrs. Tutt are married, lives in Burleson and file a joint return. The Tutts cannot
be claimed as dependents on anyone else's tax return. Their daughter, Lavender, is 19
years old, single and a full-time student away at college. Lavender earned $4,500
during the year, but her parents provided more than half of her support. Which of the
following statements is true?
The real earning of her could be less than $2250 during the year where their parents supported more than half.
What is linear equation ?
linear equation can be defined as the equation in which the highest degree of the exponent is one.
Given
The Tutts cannot be claimed as dependents on anyone else's tax return. Their daughter, Lavender, is 19years old,
single and a full-time student away at college.
Lavender earned $4,500 during the year
The real earning of Lavender could be
as her parents supported more than half.
so,
her real earning could be less than $2250
Hence , the real earning of her could be less than $2250 .
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The length of a rectangular frame is 15 inches in the diagonal length of the frame is 17 inches what is the width of the frame in inches
The width of the frame is 8 inches.
Now, According to the question:
The length of a rectangular frame is 15 inches
The diagonal length of the frame is 17 inches.
To find the width of the frame in inches.
Let's take the width of the frame is = w
Based on the information given, it should be noted that the diagonal will be the longest side. Therefore, we'll use the Pythagoras theorem to solve the question.
This will be:
17² = 15² + w²
289 = 225 + w²
289 - 225 = w²
64 = w²
w = [tex]\sqrt{64}[/tex]
w = 8
Hence, The width of the frame is 8 inches.
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A field is in the shape of a square. The length of the field is 5x³y. What is the area of the field in terms of x and y? Write the variables in
alphabetical order. I really don’t know and I’m desperate :(
Answer:
25x^6y^2
Step-by-step explanation:
Since it is a square all sides are the same. So you multiply 5x^3y and 5x^3y together to get the area. That would get you 25x^6y^2.
The local Dairy Queen sells four
cheeseburgers and two milkshakes for $7.90.
If two milkshakes cost $0.15 than a
cheeseburger, what is the cost of a milkshake?
While two milkshakes are cheaper by $0.15 than a cheeseburger, a cheeseburger costs $1.55 and costs $.85.
what is an equation ?The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal. The three main types of linear equations are the slope-intercept form, standard form, and point-slope form. A straightforward equation shows the connection between two terms on either side of an equal sign. Additionally, simple equations incorporate one or more of the addition, subtraction, multiplication, and division arithmetic operations.
given
Let a = the cost in cents of a cheeseburger
Let b = the cost in cents of a shake
4a+2b=7 .90
2b=a+15
-a+2b=15
Subtract (2) from (1)
4a+2b=7 .90
a-2b=-15
5a=775
a=155
2b=a+15
b=170/2
b=85
While two milkshakes are cheaper by $0.15 than a cheeseburger, a cheeseburger costs $1.55 and costs $.85.
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Please help ASAP!
Solve the inequities:
k^2-7k+12. 25>0
2. 25y^2-3y+1<0
It is not possible to mix ‘greater than’ and ‘less than’ inequality signs in the same expression
Solve the inequities:
k^2-7k+12. 25>0
2. 25y^2-3y+1<0
Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
It is not possible to mix ‘greater than’ and ‘less than’ inequality signs in the same expression
So Whenever you find two conclusions which are false Just check for these two symbols . In Most of the case where two conclusions are false and these two signs are not there respectively than that statement, you can call it as Neither Nor.
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a survey was given to people who own a certain type of car. what percent of the people surveyed were completed satisfaction with the car?
The percent of the people surveyed who were completed satisfaction with the car will be 48%.
How to calculate the percentage?A percentage simply has to do with the a value or ratio which can be stated as a fraction of 100. It should be noted that when we want to we calculate a percentage of a number, we simply divide it and then multiply the value that is gotten by 100. The percentage then refers to a component per hundred. The word percentage simply means per 100 and it is represented by %.
In this case, a survey was given to people who own a certain type of car. 24 out of 50 stated that they were satisfied with the car.
The percent of the people surveyed were completed satisfaction with the car will be:
= 24 / 50 × 100
= 48%
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Complete question
A survey was given to people who own a certain type of car. 24 out of 50 stated that they were satisfied with the car. what percent of the people surveyed were completed satisfaction with the car?
Simplifying algebraic expression
Answer:
-33
Step-by-step explanation:
Given algebraic expression:
[tex]5c-9c+3[/tex]
To simplify the given algebraic expression using c = 9, substitute the given value of "c" into the expression and solve:
[tex]\implies 5(9)-9(9)+3[/tex]
[tex]\implies 45-81+3[/tex]
[tex]\implies -36+3[/tex]
[tex]\implies -33[/tex]
Answer:
[tex] \sf \: 5c - 9c + 3 = - 33[/tex]
Step-by-step explanation:
Given information,
→ 5c - 9c + 3
→ where c = 9
Let's simplify the expression,
→ 5c - 9c + 3
→ 5(9) - 9(9) + 3
→ (5 × 9) - (9 × 9) + 3
→ 45 - 81 + 3
→ 45 - 78
→ -33 => final value
Hence, the final value is -33.
Triangle ABC was translated to form A’B’C’. Which describes the transformation? Check all that apply
Translation is a rigid transformation. As such, it preserves sizes and angles. Isometric is an alternative way to say the size is preserved. Hence; B, C and E are the correct choices.
What is a triangle?A triangle is a three-sided polygon. A closed shape consisting of three straight lines and three corners. The sum of the three angles of a triangle is always 180 degrees. Triangles come in a variety of shapes and sizes and can be classified according to their angles and sides. The most common type of triangle is the right triangle, which has 90 degree angles.
Translation is the transformation that happens when we move the image without changing anything in it. Therefore, the shape, size, and orientation remain the same.
In this case the triangle ABC has been transformed to A'B'C'. This means that the triangle has been moved in one direction to form a new triangle A'B'C' without changing its size or orientation. This is an example of translation transformation.
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The complete question is follows:
Triangle ABC was translated to form A’B’C’. Which describes the transformation? Check all that apply
A. It is non rigid
B. The size is preserved
C. It is rigid
D. The angles are not preserved
E. It is isometric
Riders must be at least 42 inches tall to ride the coaster. Write an addition inequality to determine how much taller William must be to ride the coaster. Let x be the variable representing how much taller
An addition inequality to determine how much taller William must be to ride the coaster is, Height of William + x ≥ 42.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Given, Riders must be at least 42 inches tall to ride the coaster, and 'x' be the variable representing how much taller William should be.
Therefore, Height of William + x ≥ 42 is an inequality that may be used to calculate how much taller William has to be in order to ride the coaster.
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A coat hanger has four knobs, and each knob can be painted any color. If six different colors of paint are available, how many ways can the knobs be painted
If six different colors of paint are available, 360 ways can the knobs be painted.
how many ways can the knobs be painted?A coat hanger has four knobs, and each knob can be painted any color. If six different colors of paint are available,
When examining permutations and combinations, we use factorials. Permutations tell us how many different ways we can arrange things if their order matters. Combinations tells us how many ways we can choose k item from n items if their order does not matter.
coat hanger has four knobs
6! / 4! ( 4!)
6 * 5 * 4* 3 / 4 * 3 * 2* 1 (4 * 3 * 2 * 1)
= 30 * 1 2
=360
360 ways can the knobs be painted.
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Angle of depression: A person standing on the top of the Petronas Tower I looks out
across the city and pinpoints her residence. If the angle of depression from the person's
eyes to her home is 5°, how far away (in feet and in miles) is the residence?
Identify the inverse function of f(x)=√x - 2 + 3.
A) f-¹(x) = (x + 2)² - 3
B) f-1(x) = (x - 3)² + 2
C) f-¹(x) = √x + 2 - 3
D) ƒ-1(x) = √x + 3 − 2
Questi
The inverse of the function f(x) =√x - 2 + 3 is (x - 3)² + 2 so, option B is correct.
What is the function?An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable (the dependent variable). In mathematics and the sciences, functions are fundamental for constructing physical relationships.
Given:
f(x)=√x - 2 + 3.
The inverse function can be found as shown below,
f⁻(x) = √(y - 2) + 3 (Replace x by y)
x = √(y - 2) + 3
solve the equation as shown below,
x - 3 = √(y - 2)
Squaring both sides,
(x - 3)² = [√(y - 2)]²
x² + 9 - 6x = y - 2
x² + 9 - 6x + 2 = y
y = x² - 6x + 11 or y = (x - 3)² + 2
Thus, the inverse of the function is (x - 3)² + 2.
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Fractions
Malik and his friends ate 1.
1
--
4
pepperoni pizzas, 2 cheese pizzas, and
2
--
3
of a vegetarian pizza.
a) How many pizzas did they eat?
b) How many more cheese pizzas than
vegetarian pizzas did they eat?
a) The total amount of pizzas that they ate is given as follows: 2.92 pizzas.
b) The difference between the number of cheese pizzas and the number of vegetarian pizzas is given as follows: 4/3, which is the amount that they ate more of cheese pizzas than vegetarian pizzas.
How to obtain the amounts?The fractions relative to the amount of each type of pizza eaten are given as follows:
Pepperoni pizza: 1/4.Cheese pizza: 2.Vegetarian pizza: 2/3.The total amount of pizzas eaten is given by the addition of these fractions, hence:
1/4 + 2 + 2/3 = 3/12 + 24/12 + 8/12
(as the least common factor between 4, 1 and 3 is of 12).
3/12 + 24/12 + 8/12 = (3 + 24 + 8)/12
(3 + 24 + 8)/12 = 35/12
2.92 pizzas.
The difference between the number of cheese pizzas and the number of vegetarian pizzas is obtained as follows:
2 - 2/3 = 6/3 - 2/3 = 4/3.
(as the least common factor of 1 and 3 is of 3).
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What is the coefficient of XY in the expression *?
The numerical coefficient of xy in the given expression -7xy is -7.
The numerical coefficient of an expression is a number that is multiplied by a variable or a product of variables. The coefficient is the number that appears in front of a variable or a product of variables. In the case of a constant term, the coefficient is the constant itself.
For example, in the expression 3[tex]x^2[/tex] + 4x - 5, the numerical coefficient of [tex]x^2[/tex] is 3, the numerical coefficient of x is 4, and the numerical coefficient of the constant term -5 is -5.
Here, in the expression -7xy, the numerical coefficient of xy is -7.
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The complete question is -
What is the coefficient of XY in the expression - 7xyz?
In right triangle abc, altitude cd with length h is drawn to its hypotenuse. we also know ad = 12 and db = 3.
The value of h is 6.
Now, According to the question:
In right triangle, ABC
Given data:
AD = 12 and DB = 3
The equivalent ratio of the triangles is:
h : 12 = 3 : h
Express as fractions
[tex]\frac{h}{12} =\frac{3}{h}[/tex]
Cross Multiply:
[tex]h^2[/tex] = 36
Take positive square roots of both sides
h = 6
Hence, the value of h is 6.
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Think about all the models and strategies you have discussed today. Describe how one of them helped you better understand how to find the slope of a line.
Answer:
I could find the slope of a line by looking at the gradient of a graph that the line creates. If the line is linear, then the gradient will be a constant value, which I can use to find the value of the slope. If the line is not linear, then I can use a derivative to find the slope at a given point. However, if the line is concave or concave up, then I will need to take the second derivative of the equation to determine which point on the line is closest to the point that I'm trying to calculate.
Step-by-step explanation:
A high school student working part time as a shelf stocker had a gross income of $6675 last year. If his federal tax rate was %10 and his state tax was 3% what was the amount withheld from his Pat last year in federal tax, state tax, and FICA combined?
A. 867. 75
B. 667. 50
C. 200. 25
D. 1378. 39
The total amount withheld from the student's pay last year in federal tax, state tax, and FICA is $667.50 + $201.25 = $868.75
What is percentage?Percentage is a way of expressing a number as a fraction of 100. It is often denoted using the symbol "%" (percent sign). Percentages are used to express how much of something there is in relation to the whole. For example, if a student answers 80% of the questions correctly on a test, it means they answered 80 out of 100 questions correctly.
What is tax?A tax is a financial charge imposed by a government on individuals, businesses, or other entities to raise revenue for government spending. Taxes are typically based on a percentage of income or sales, and can be levied on various forms of income, including wages, salaries, and profits. The purpose of taxation is to fund government programs and services, such as roads, schools, and national defense. Taxes can also be used to redistribute wealth and influence economic behavior.
The amount withheld from the student's pay last year in federal tax is $6675 x 0.1 = $667.50
The amount withheld from the student's pay last year in state tax is $6675 x 0.03 = $201.25
The total amount withheld from the student's pay last year in federal tax, state tax, and FICA is $667.50 + $201.25 = $868.75
So the answer is A. 867.75
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Alex is planning to surround his pool ABCD with a single line of tiles. How many units of tile will he need to surround his pool
The number of units that tile will he need to surround his pool is 19.82units.
this question is of quadratic equation ,
The number of units of tile simply refers to the perimeter.
So, we need to find all the sides of the rectangle.
Now, we have,
AB = 4.24 units
BD = 7.07 units.
So, we can find AD using pythagoras theorem.
So,
(AD)² + 4.24² = 7.07²
(AD)² + 17.978 = 49.985
(AD)² = 49.985 - 17.978
AD = √32.007
AD = 5.66 units
AD = BC = 5.66 units
Likewise, AB = DC = 4.24 units
Thus,
perimeter = 2(5.66) + 2(4.24) = 19.8 units.
The number of units that tile will he need to surround his pool is 19.82units.
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The radii of two concentric circles are in the ratio 3:5. If the length of the chord of the larger circle that is tangent to the smaller circle is 40 cm, complete the following statements:
The length of the chord of the larger circle can be found by taking the square root [tex](5r)^2 - (2r)^2[/tex] which is equal to r√21, where r is the radius of the smaller circle.
The given problem states that there are two concentric circles with radii in the ratio of 3:5. This means that the radius of the smaller circle is 3r and the radius of the larger circle is 5r. The distance between the center of these two circles is 2r.
Also, it is given that the length of the chord of the larger circle that is tangent to the smaller circle is 40 cm. Using this information, we can find the length of the chord of the larger circle by using the Pythagorean theorem.
The length of the chord of the larger circle is found by taking the square root of [tex](the radius of the larger circle)^2[/tex] - [tex](the distance between the two centers)^2[/tex] which is √21[tex]r^2[/tex]= r√21.
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How do you find the sides of a triangle with only the angles?
The Sides of triangle when only the angles of triangles are given can be found by using the Law Of Sines .
What is Law Of Sines ?
The Law Of Sines states that the ratio of sides of a triangle and their respective Sine angles are equivalent to each other. The other names by which the law of sines is known are Sine Law, Sine Rule and Sine Formula.
The Sine Law is used to find unknown side of an oblique triangle. The oblique triangle is defined as a triangle that is not a right triangle.
Let a , b and c be the sides of a triangle ABC , and A , B and C be the angles .
So , by Sine Law : [tex]\frac{a}{SinA}=\frac{b}{SinB}=\frac{c}{SinC}[/tex] ;
Therefore , The Law Of Sines help in finding the sides of triangle that has only angles .
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What is the coefficient of y² in the expression 3y² 4x *?
The coeficient of y² in the expression is the number 3
What is an algebraic expression?
An algebraic expression is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.
In the given expression we have the following:
3y² + 4x
As we are asked for the coefficient of the variable "y" then we must take the number that is just before the letter which in this case is the number 3.
3 is the coefficient of y²
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A piggy bank contains 22 dimes, 7 nickels and 15 quarters. This morning you removed 8 dimes and 3 nickels. Which expression correctly shows the amount remaining in the piggy bank?
The expression that correctly shows the amount remaining in the piggy bank will be; 22d + 7n + 15q - (8d + 3n) = $4.85
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
We are given that piggy bank contains 22 dimes, 7 nickels and 15 quarters. This morning you removed 8 dimes and 3 nickels.
LEt consider
→ dimes = d
→ nickels = n
→ quarters = q
Now the expression will be;
22 dimes + 7 nickels + 15 quarters - 8 dimes - 3 nickels
22d + 7n + 15q - 8d - 3n = $4.85
22d + 7n + 15q - (8d + 3n) = $4.85
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Work out the size of angle x
Answer:
x = 13
Step-by-step explanation:
There is more than one 98-degree angle since they are all corresponding interior angles.
The supplementary angle to the 98-degree angle next to the triangle is:
180 - 98 = 82 degrees
In addition, another angle inside the triangle is an 85-degree angle. This is because this 85-degree angle is opposite adjacent to the other 85-degree angle.
Hence, the angles inside the triangle are: x, 85, and 82
x + 85 + 82 = 180 ==> Triangles add up to 180 degrees
x + 167 = 180 ==> simplify
x = 13 degrees ==> subtract 167 on both sides
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35x+60y>(or equal to)7,000
Solve for x and y
For this question u have to assume value of either x or y
For example
to find the value of x
side calculation (7000/35 = 200)
let x = 200
then 35(200) +60y = 7000
7000 + 60y = 7000
60y = 7000-7000
so y = 0
so value of x should be greater than or equal to 200
x >(or equal to) 200
to find the value of y
side calculation ( 7000/60 = 116.67)
let y = 116.67
then 35x + 60(116.67) = 7000
35x + 7000 = 7000
35x = 7000-7000
35x=0
so x = 0
so the value of y should be greater than or equal to 116.67
y >( or equal to 116.67)
That, given an array a of n integers, returns the smallest positive integer (greater than 0) that does not occur in a. For example, given a = [1, 3, 6, 4, 1, 2], the function should return 5
There is one way to implement a function in Python that takes in an array of integers and returns the smallest positive integer that does not occur in the array.
def smallest_missing_positive(a):
#Create a set to store the unique elements in the array
unique_set = set(a)
#Iterate through the positive integers starting from 1
for i in range(1, len(a) + 2):
#If the current integer is not in the set, return it
if i not in unique_set:
return i
This function first converts the input array into a set, which removes any duplicate elements. It then iterates through the positive integers starting from 1 up to the length of the array plus 2. For each integer, it checks whether it is in the set of unique elements from the input array. If it is not, the function returns that integer as it is the smallest positive integer that does not occur in the array.
For example, when the function is called with the input array [1, 3, 6, 4, 1, 2], it will return 5 as it is the first missing positive number.
You can also use a set and difference() method of set to check the missing elements from 1 to maximum element of array+1 and find the missing first one, this method is more efficient than the above one when the array is large.
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Can anyone me help PLEASE
Answer: (0, 1), (2,3), (x,x), (-5,x) (I put x's in for the missing numbers)
Step-by-step explanation: Hope this helps!!
Here is the graph:
Solve (x – 3)2 = 49. Select the values of x. –46 -4 10 52
Answer: 27.5
Step-by-step explanation:
[tex](x-3)2 = 49\\x-3 = \frac{49}{2} \\x-3 = 24.5\\x = 24.5 + 3\\x = 27.5[/tex]
Erin has 4 cards, one with the letter A, one with the letter B, one with the letter C, and one with the letter D. She places the cards in a row in random order. What is the probability that either the words BAD or CAB will appear as part of the row? Enter your answer as a percent, to the nearest tenth of a percent, like this: 42.5%
The probability that either the words BAD or CAB will appear as part of the row is 16.7%
How to determine the probability that either the words BAD or CAB?We have 4 places where we can put the cards.
Let's count the number of possible outcomes for each place.
In the first place, we can put one of 4 cards.
In the second place, we can put one of 3 cards (because one card was taken in the first place).
In the third place, we can put one of 2 cards
In the last place, we can put one of one cards.
The total number of different combinations is the product between the number of options for each place, then we have:
4×3×2×1 = 24
Now we need to count the number of combinations such that the words BAD or CAB appear. We have:
BADC
CBAD
CABD
DCAB
That is 4 out of 24.
Thus, the probability that either the words BAD or CAB will appear as part of the row will be:
P(BAD or CAB) = 4/24 = 16.7%
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The probability is 16.7%
Why is y 4 a horizontal line?
The graph of the equation y=4 is a horizontal line. It is function since each x is mapped to one y or each element of the domain is mapped to only one element of the range. It also passes the vertical line test.
Now, According to the question:
Let's know:
What is Horizontal lines?
If we are given the equation of y equal to a number, our graph will be a horizontal line. Is this equation a function? The answer would be yes since it passes the vertical line test. The vertical line test tells us if we draw a vertical line through any point of the graph and it goes through only one point at each line, then it is a function. If it passes through more than one point, it does not. The slope of a horizontal line is zero.
The equation is y = 4.
The graph of the equation y=4 is a horizontal line. It is function since each x is mapped to one y or each element of the domain is mapped to only one element of the range. It also passes the vertical line test.
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Which fraction is equivalent to fraction with numerator 6 and denominator negative 8 ? (5 points)
fraction with numerator negative 8 and denominator 6
fraction with numerator negative 6 and denominator 8
fraction with numerator negative 6 and denominator negative 8
fraction with numerator 8 and denominator 6
Answer:
A fraction is a mathematical expression that represents the division of two numbers, called the numerator and the denominator. The numerator represents the number of parts being considered, while the denominator represents the number of parts in the whole. A fraction with a numerator of 6 and a denominator of negative 8 can be simplified to -3/4. To find an equivalent fraction, we can multiply or divide both the numerator and denominator by the same number without changing the value of the fraction. In this case, the fraction with a numerator of negative 8 and a denominator of 6 is equivalent to -4/3.
Step-by-step explanation: