The cross product of A & B (A × B) is |A| |B| Sin θ, where θ is the angle between A and B.
The vector product or cross product of two vectors, A and B, is denoted by A × B, and its resultant vector is perpendicular to the vectors A and B.
The cross product is mostly used to determine the vector, which is perpendicular to the plane surface spanned by two vectors, whereas the dot product is used to find the angle between two vectors or the length of the vector.
The cross product of two vectors, say A × B, is equal to another vector at right angles to both, and it happens in the three dimensions.
If θ is the angle between the given two vectors A and B, then the formula for the cross product of vectors is given by:
|A| |B| Sin θ
--The given question is incorrect; the correct question is
"What is the cross product of A & B?"--
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How do you spell sum in maths?.
Sum in math the sum of the series is computed using the summation formulas.
The sum of the series is computed using the summation formulas. There are many different kinds of sequences, including arithmetic and geometric sequences, and consequently, there are many different kinds of summing formulas for those different kinds of sequences.
There are also summation formulas that determine the sum of natural numbers, sum of natural number squares, sum of natural number cubes, sum of natural number evens, sum of natural number odds, etc. The list of summation formulas is provided here. Each of these formulas will be covered in detail in the section that follows.
a₁ + a₂ + a₃ +.......aₙ = Σ a
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What is the relationship of the degree of a quadratic equation to the number of its solution?.
The relationship of the degree x - [[- b+v(b2 - 4ac)V2a] = 0 describes the relationship between a quadratic equation's factors and its solutions. A quadratic equation's general equation is f(x) = ax*+ bx +. function:
A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and respectively.
expression: Terms (constants and variables) are separated by mathematical operators to form a mathematical expression. equation: Two expressions are equated using a mathematical equation. The quadratic equation f(x) = axe + bx + c is given.
The quadratic equation (ax2 + bx + c= 0) can be expressed as a product of its linear factors as (x - k)(x - h), where h, k are the quadratic equation's roots. This process is known as factoring a quadratic equation.
We may write [h] =- b + v(b2 - 4ac)y2a [K]=(-b- V(b2 - 4ac))/2a using the quadratic formula. The link between the elements of a quadratic equation and its solutions can be expressed as - x- [[-b+v(b- 4ac)y2a] =0
X=[(b' - 4AC)y2A] = 0.
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5x² + 10x + 2 in the form p(x +q)² + r,
5([tex]x^{2}[/tex] + 10/2[tex]x[/tex]) + 2
The number in the brackets is b/2a.
So:
5(x + 10/2(5))^2
5(x + 10/10)^2
5(x + 1)^2
Expand the double brackets for (x + 1)^2:
[tex]x^{2}[/tex] + [tex]x[/tex] + [tex]x[/tex] + 1
This simplifies to:
[tex]x^2[/tex] + 2[tex]x[/tex] + 1
5([tex]x^2[/tex] + 2[tex]x[/tex] + 1)
5x^2 + 10x + 5
2 - 5 = -3
5(x + 1)^2 - 3
Answer:
5(x + 1)^2 - 3
x¹10x² +9=0
Step 1. Identify the quadratic form
Let t=
We now have:
t²-10t+9=0
Step 2. Factor
Factor this and solve for t to get t
and
Step 3. Solve for
We have solved for t now we need to use this value for t
to help us solve for x. Revisit step 1 to remind you of
the relationship between t and x. Type your answers
from smallest to largest.
and +/-
x = +/-
Answer:
x = -3, -1, 1, 3.
Step-by-step explanation:
x^4 - 10x^2 + 9 = 0
Step 1
Let t = x^2
So , we have the quadratic
t^2 - 10t + 9 = 0
Step 2
Factorise:
(t - 1)(t - 9) = 0
Step 3
So, t - 1 = 0 or t - 9 = 0
t = 1, 9.
But t = x^2
So, we have x^2 = 1 or x^2 = 9
So, x = ±1, ±3.
x = -3, -1, 1, 3.
Calculate the length of the unknown side of this right angled triangle
Base: 8cm
Length: 9cm
The length of the unknown side of this right angled triangle is 12cm.
This is a question about the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. The theorem can be written as c^2 = a^2 + b^2, where c is the hypotenuse, and a and b are the other two sides.
In this case, we know that the base of the triangle is 8cm and the length is 9cm.
So we can use the formula c = √(a^2 + b^2)
c = √(8^2 + 9^2)
c = √(64 + 81)
c = √(145)
c = 12cm
Therefore, the length of the unknown side of this right angled triangle is 12cm.
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Juice wa packed in individual juice boxe of 1/2-cup each. A carton of 64 juice boxe wa hrink-wrapped and hipped to a tore. How many gallon of juice were in the hrink-wrapped carton?
The shrink-wrapped carton of 64 juice boxes contained 2 gallons of juice.
To find out how many gallons of juice were in the shrink-wrapped carton, we first need to convert the number of juice boxes to cups and then convert that amount to gallons.
Each juice box contains 1/2 cup of juice, so 64 boxes contain 64 * (1/2) = 32 cups.
There are 16 cups in 1 gallon, so to convert 32 cups to gallons, we divide 32 cups by 16 cups/gallon.
32 cups / 16 cups/gallon = 2 gallons
So, the shrink-wrapped carton of 64 juice boxes contained 2 gallons of juice.
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If the top of a hill is 532 ft. above the bottom of a hill, and it is 7 miles
between the highest and lowest points, what is the gradient between them?
(round answer to the nearest tenth)
The answer will be 76, using a gradient.
What is the gradient of the slope?
A physical feature, landform, or manmade line's grade, also known as its slope, incline, gradient, rainfall, pitch, or rise, is the tangent of that surface's angle with respect to the horizontal.Since zero denotes horizontality, it is a specific case of the slope. Increased or steeper "tilt" is indicated by a greater number.The slope is frequently determined as a ratio of "rise" to "run" or as a fraction ("rise over run"), where the run is the horizontal distance (not the slope's length), and the rise is the vertical distance.To find the gradient of the given data, horizontal as well as the vertical distance between two points in parallel is necessary to find.
The vertical distance is 532The horizontal distance is 7miles.532/7=76
Hence the answer is 76
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3 Each spinner shown is divided into equal
sections. Felix spins each spinner 30 times. He
records the number of times each section is
spun.
(5)
A
(8)
B
24
(6)
45
03
Red
(7)
(4)
Based on the results of the first 30 spins, what
is the probability that Felix will spin a green and
an F on the next spin?
Blue
(10)
Yellow
D Not here
Green
(8)
Answer:
9876567890
Step-by-step explanation:
prove that:sinA/1-cosA-1=1/cosA
Answer:
Step-by-step explanation:
To prove that sinA/(1-cosA) = 1/cosA, we will start with the left-hand side and simplify it using trigonometric identities.
sinA/(1-cosA) = sinA/(1-cosA) * (sin^2A + cos^2A) / (sin^2A + cos^2A)
= (sinAsin^2A + sinAcos^2A) / (sin^2A + cos^2A - sin^2AcosA - cos^2AcosA)
= (sinAsinAcosA + sinAcosAcosA) / (sinAcosA - cosAcosA)
= sinA/cosA / (sinA/cosA - 1)
= 1/cosA
Therefore, sinA/(1-cosA) = 1/cosA, which is true.
In the diagram below, DE ¯¯¯¯¯¯¯∥ BC¯¯¯¯¯. Elena thinks length BC¯¯¯¯¯ is 16.5 units. Lin thinks the length of BC ¯¯¯¯¯¯is 17.1 units. Who do you agree with? Why? (2 points)
Both Elena and Lin are right , in my opinion. According to Elena, length BC is 16.5 units. Lin estimates that BC is 17.1 units long.
Whose are agree this ?The remainder of the query is included in the attachment. The figure shows that ED is parallel to A B and B C is parallel to A B. In light of the Pythagoras theorem,
[tex]$\mathrm{AC}^ 2=\mathrm{AB}^ 2+\mathrm{BC}^ 2$[/tex]
[tex]$\mathrm{BC}^ 2=196-36=160$[/tex]
[tex]$\mathrm{BC}=12.649$[/tex] or [tex]$12.65$[/tex]
Both Elena and Lin are right .A visual that conveys information rather than just representing it. particularly : a diagram demonstrating the relationships and arrangements (as between parts): a dotted line drawing used in science or math .
A diagram is a picture that shows how something works, how it's organised, or how it's related to something else. Even when they go by the names "map," "chart," or "graph," several diagram kinds are still considered to be diagrams. as flowcharts, organisational charts, and mind maps. An illustration that depicts an object's component elements and their relationships to one another is called a diagram.
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Chad and Amy are married with no children, and they're filing their federal
income tax return. Chad had a gross income of $54,300 last year, while Amy had
a gross income of $50,900; they plan to use the standard deduction. They're
trying to decide whether to file their return jointly or separately, so they want to
calculate how much less they would pay in federal income taxes if they filed
jointly rather than separately.
Part 3: When filing jointly, Chad and Amy have a standard deduction of $11,400, they can claim one exemption for each of them for $3650 each, and they don’t have any addition adjustments to income. What is their taxable income?
Their taxable income $9,250.
If you were single and didn't have any dependents, what kind of filing status would you have?Single-tax-return filing status with the IRS. For unmarried individuals who are not eligible to file as the head of household, single is the default filing status.
When submitting your tax return, you must choose the single filing status if you were not married on the last day of the tax year and you are not eligible to utilize any other filing status.
The amounts for the 2022 standard deduction are as follows: Married Jointly Filing or Qualifying Widow(er) - $25,900 (an increase of $800) $19,400 (an rise of $600) for the head of the household Married Filing Separately or Single: $12,950 (an increase of $400).
An individual making $50,000 will pay $9,250, according to the exhibit that is attached.
People who make $50,000 fall into the $42,001-$100,000 category and pay $7,250 plus 25% of any amount over $42,000.
The tax burden is as follows:
= 7,250 + ( 25% x (50,000 - 42,000))
= 7,250 + (25% x 8,000)
= $9,250.
The complete question is,
Using Exhibit 11-4 as a guide, calculate the tax due on a person with a $50,000 taxable income.
$9,250 \s$10,110 \sO $15,000 \sO $12,500.
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How do you determine whether a number is rational or irrational?.
If the number can be expressed in the form of the fraction [tex]\frac{p}{q}[/tex] , then the number is called as Rational Number otherwise it is called as irrational number .
The Rational Numbers are the type of numbers that can be expressed in the form of [tex]\frac{p}{q}[/tex] , where p and q both are integers , and the denominator q should not be equal to 0 .
For Example : the numbers 5 , 2/3 , 6 are rational numbers .
The Irrational Numbers are defined as the type of real numbers which cannot be represented as simple fractions. The Irrational number cannot be expressed as a ratio .
For Example : [tex]\sqrt{2}[/tex] , [tex]\sqrt{5}[/tex] cannot be expressed as a fraction of integers , so they are irrational .
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Multiplying a trinomial by a trinomial follows the same steps as multiplying a binomial by a trinomial. Determine the degree and maximum possible number of terms for the product of these trinomials: (x2 + x + 2)(x2 – 2x + 3). Explain how you arrived at your answer.
NEED SOME HELP!
The degree and maximum possible number of terms for the product is 4 and 9 respectively
What is an algebraic expression?An algebraic expression can be described as a mathematical expression consisting of variables, factors, coefficients, terms and constants.
These algebraic expressions are also made up of arithmetic operations, such as;
AdditionSubtractionMultiplicationDIvisionBracketFloor divisionParenthesesA trinomial can be defined as an algebraic expression having three non-zero terms with more than one variable in the expression
Given the expressions;
(x² + x + 2)(x² - 2x + 3)
expand the bracket
x⁴ -2x³ + 3x² + x³ -2x² + 3x + 2x² -4x + 6
collect like terms
x⁴ -2x³ + x³ + 3x² - 2x²+ 3x - 4x + 6
Add or subtract like terms
x⁴ - x³ + x² -x + 6
Hence, the degree is 4
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You survey 72 randomly chosen students about whether they are going to attend the school play. Twelve say yes. Predict the number of students who attend the school.
The school is predicted to have
students.
1260
Just as 12 is to 72. 210 is to x
setup ratio, cross multiply, and solve for x:
Answer is 1260
Where is the zero of a function?.
Any alternative for the variable in a function that results in a zero answer is said to as the zero of a function.
The x-intercept(s) of the function's graph, or the real zero of a function, is where the function's graph hits the x-axis graphically.
The values of the variable in a function that allow the function to equal zero are termed the zeros of the function. The places on the x-axis where the graph crosses the x-axis are referred to as a function's zeros graphically. In other respects, we can say that the zeros of something like a function are the x-intercepts of the graph.
Finding the values of the variable that correspond to the function's zeros can be achieved by equating the function to 0. By calculating the polynomial and then equating it to 0, we can discover the zeros for polynomials.
Example:
Find the zeros of the function f(x) = ex - 1. Answer: Zero of function f(x) = ex - 1 is x = 0.
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Question: Whats 5x(8+8)3(67
Answer:
16,080
Explanation:
hope its help..... T^THow to find quotient?.
The quotient is the quantity we arrive at when dividing two numbers.
When a number is divided, the result is the quotient. The mathematical symbol (÷) stands for division, which is a technique for allocating items equally among groups. In mathematics, the quotient is the outcome of dividing an integer by any divisor. It is the quantity of times the dividend contains the divisor.
An integer or a decimal number can be the quotient.
A whole number is the quotient when a number is entirely divisible by another integer. The quotient is a decimal number when a number cannot be divided by another number entirely.
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Tom’ cell phone plan ha a monthly fee of $105, which include unlimited free text meage and phone call and 4GB of data. Each extra gigabyte of data, or part thereof, cot $12. A. Find the cot of a month in which Tom ued 7. 1GB of data b. If x repreent the number of gigabyte ued, expre the monthly charge c(x) of thi plan a a piecewie function
Total charge that Tom has to pay is $142.2, and the express function for the monthly charge is c(x) = 105 + (x -4) * 12
How to determine the monthly charge function and total charge for Tom on that month?
As per data given, monthly value given is $105 = free text + free call + 4gb and extra gigabyte x $12. Tom that use 7.1 of data will be charge as follow:
Tom charge = normal use + extra use
To charge = 105 + extra gigabyte x12
Extra gigabyte = tom use - normal use
Extra gigabyte = 7.1 - 4
Extra gigabyte = 3.1
Tom charge = 105 + 3.1 x 12
Tom charge = 105 + 37.2
Tom charge = 142.2
The expression of monthly charge, since we have already define that value is $105 = free text + free call + 4gb and extra gigabyte x $12. We can see that text is not charge and call is not charge. So the formula will be:
Monthly charge = 105 + (extra gigabyte - 4) x 12
As per question said the variable for extra gigabyte is x and monthly charge is c(x) then
c(x) = 105 + (x - 4) * 12
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the x coordinate is positive and the y coordinate is zero what is the location
If the x coordinate is positive and the y coordinate is zero, the location of the point is in positive x- axis.
What is coordinate?The position of a point or a shape in a specific space is determined by coordinates, which are numbers (a map or a graph).
Cartesian coordinates are introduced to students in Year 4 and are taught in primary school. The x axis, which is the horizontal axis, and the y axis, which is the vertical axis, are used to identify points (the vertical axis).
Coordinates are always written with two numbers separated by commas and enclosed in brackets. Coordinates are ordered pairs of numbers, where the first number represents the point on the x axis and the second, the point on the y axis.
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What is the y value of the solution to the system of equations 3x 5y 17x 4y − 13?.
The y-value of the solution to the system of equations 3x + 5y = 1 and 7x + 4y = - 13 is 2.
In the given question, we have to solve the y-value of the solution to the system of equations.
3x + 5y = 1..................(1)
7x + 4y = -13...............(2)
Multiply equation 1 by 4 and equation 2 by 5, we get
12x + 20y = 4................(3)
35x + 20y = -65................(4)
Subtract equation 4 by 3, we get
23x = -69
Divide by 23 on both side, we get
x = -3
Now putting the value of x in the equation 1, we get
3(-3) + 5y = 1
-9 + 5y = 1
Add 9 on both side, we get
5y = 10
Divide by 5 on both side, we get
y = 2
Hence, the y-value of the solution to the system of equations 3x + 5y = 1 and 7x + 4y = - 13 is 2.
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The complete question is:
What is the y-value of the solution to the system of equations?
3x + 5y = 1; 7x + 4y = - 13
If you wanted to buy a 75 inch tv for your living room and the width is 43.25 inches, what is the height
The height of the TV would be 61.27 inches.
What is Pythagoras theorem?
The hypotenuse's square length is equal to the sum of the squares of the lengths of the other two sides of the right-angled triangle, according to the Pythagorean theorem, commonly known as the Pythagoras theorem.
Here, The 75 inches represents the length of diagonal of the TV because the length of TV is always measured diagonally. So, the diagonal's length is 75 inches.
We've width as 43.25 inches.
Since TV is of the shape of rectangle, we can calculate the height by applying Pythagoras theorem.
So, we've hypotenuse² = (side 1)² + (side 2)²
It can be written as,
diagonal² = height² + width²
(75)² = height² + (43.25)²
height² = (75)² - (43.25)²
= 5625 - 1870.5625
= 3754.4375
height = √3754.4375 = 61.27 inches.
Hence, height will be 61.27 inches.
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What method of solving quadratic equations must be used in order to derive the quadratic formula?.
By utilizing the Quadratic Equations' formula for the roots, we can solve the most complex quadratic equations.
For example,
if (ax2+bx+c) = 0,then the equation's roots
x =[—b+ —(b^2-4ac)^1/2] / 2aNow
x^2+5x+6=0a=1 b= 5 c=6x=[ --5+ — (25-4×1×6)^1/2 ] /2x1 =( --5+1)/2 =4/2=-2X2 =[ --5-1] /2 = -3The equation's roots are -2 and —3.
The polynomial equations of degree two in one variable of type f(x) = ax2 + bx + c = 0 and with a, b, c, and R R and a 0 are known as quadratic equations. It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" for the absolute term of f. (x).
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Which of the following are solutions to x < 12?
l. x = -4
II. x = 0
III. x = 12
IV. x = 13
Answer:
I. x = -4 and II. x = 12
Step-by-step explanation:
For this problem, you would simply need to plug in the values and see if the inequality is true, and if it is, it is a solution, so let's go through the options.
Plugging in x = -4 gives us: -4 < 12 which is true since negative four is less than positive twelve, so this is a solution.
Plugging in x = 0 gives us: 0 < 12 which is true since zero is less than twelve, so this is a solution.
Plugging in x = 12 gives us: 12 < 12 which is false since twelve is not less than twelve but is rather equal to it. if the less than symbol had a line under it, it would also include values equal to it in which case x = 12 would be a solution but since it doesn't, this is not a solution.
Plugging in x = 13 gives us: 13 < 12 which is false since thirteen is not less than twelve but is rather greater than it, so this is not a solution.
Carrie’ head i full of curler. There are 16 in all. One-fourth of the curler are pink. There are twice a many green curler a pink one. The ret are oda can. How many can are on Carrie’ head?
Carrie average has a head full of 16 curlers, with 4 of them being pink, 8 of them being green, and the remaining 12 being can curlers.
1. There are 16 total curlers on Carrie's head
2. One-fourth of the curlers are pink, so that is 16 ÷ 4 = 4 pink curlers
3. There are twice as many green curlers as pink ones, so that is 4 x 2 = 8 green curlers
4. The remaining 12 curlers are can curlers, so there are 12 can curlers on Carrie's head
Carrie has a head full of 16 curlers in total. One-fourth of the curlers are pink, so we can divide 16 by 4 to get 4 pink curlers. There are twice as many green curlers as pink ones, so we can multiply 4 by 2 to get 8 green curlers. This leaves 12 curlers, which must be can curlers. Therefore, there are 12 can curlers on Carrie's head. We can use basic mathematics to break down the problem into smaller pieces and calculate the number of each type of curler on her head.
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Is f x )= 2x 3 a one-to-one function?.
Yes, the function f(x)=2x-3 is a one-to-one function.
The Inverse of a Function:
The inverse of a function can be computed if the function can be proven to be one-to-one. Take the one-to-one function and compute its inverse by interchanging x and y in the expression and solving for y.
Graphically, then, the graphs of the function and its inverse are the reflections of each other about the line y=x.
Use the definition to test the one-to-one of f.
Let x and x be the elements in the domain off and assume f(x₁)=f(x₂)
2x₁-3=2x₂-3
2x₁=2x₂
x₁=x₂
since f(x₁)=f(x₂) implied x the function f is one-to-one.
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Angel check out 12 library book and Inola check out 1/3 le than that. How many doe Inola check out?
Angel check out 12 library book and Inola check out 1/3 then Inola checks out 8 books.
What is algebraic equation ?
An algebraic equation is a mathematical statement that uses mathematical symbols (such as numbers, variables and mathematical operations) to express the equality of two expressions. It is used to represent mathematical relationships and to find solutions to problems. The most common operations used in algebraic equations are addition, subtraction, multiplication, and division.
Let x be the number of books that Inola check out
We know that:
Angel checks out 12 books
Inola checks out 1/3 less than Angel
We can set up the equation:
x = 12 - (1/3*12)
x = 12 - 4
x = 8
So, Angel check out 12 library book and Inola check out 1/3 then Inola checks out 8 books.
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Angel checks out 12 books
Inola checks out 1/3 less than Angel
We can set up the equation:
x = 12 - (1/3*12)
x = 12 - 4
x = 8
f divided by -7 = -8
Answer:f=56 I hope this helps
Step-by-step explanation:
f divide (-7) =-8
Dividing a positive and a negative equals a negative: (+) divided sign (-) =( -) and then
Write the division as a fraction
-1/7f=-8
Multiply both sides of the equation by -7
f=56
Answer:
f = 56
Step-by-step explanation:
Given statement,
→ f divided by -7 is -8.
Forming the equation,
→ f/-7 = -8
Now the value of f will be,
→ f/-7 = -8
→ f = -8 × -7
→ f = 8 × 7
→ [ f = 56 ]
Hence, the value of f is 56.
count the unit squares to find the area of this plane figure.
Five rows of squares. Each row has 3 squares.
Answer:
you take rows multiplied by row
such that 5rows × 3 rows = 15 squares in total
How many solutions does Y =- 2x 3 have?.
The equation, Y = - 2x + 3 has infinitely many solutions.
Here we are given the equation y = 2x + 3. Now since this equation has 2 variables, it can be easily plotted on a graph. After plotting this equation, we can see that it makes a never-ending line, hence, this equation will have infinitely many solutions.
For any equation to have a solution, there must be an intersecting point or a common value for x or y.
Here for every value of x, we get a different value of y, which can be easily seen in the graph.
Furthermore, when an equation has 2 variables, there must be at least 2 equations for the system to have a unique solution, hence the given equation has infinitely many solutions.
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Correct Question
How many solutions does Y = - 2x + 3 have?
Determine if this data is an example
of a function.
(36, 6); (18, 5); (0, 4); (-18, 3)
The data 36, 6); (18, 5); (0, 4); (-18, 3) is an example of a function.
What is a function?A relation is a function if it has only One y-value for each x-value.
We have to check whether the data (36, 6); (18, 5); (0, 4); (-18, 3)
is an example of function.
The ordered pairs are thirty six comma six comma eighteen comma five comma zero comma four comma minus eighteen comma three.
As we observe there is only one y value for each x value.
and the x values are not repeated.
Hence, the data 36, 6); (18, 5); (0, 4); (-18, 3) is an example of a function.
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