Function notation and ordered pair solutions of a function are closely connected. Function notation is a way to represent a function by its name and its input value, while an ordered pair solution of a function is a pair of numbers (x, y) such that y is the output of the function when x is the input.
To evaluate a function using function notation, we simply substitute the input value into the function's expression. For example, if the function is f(x) = x^2, then to evaluate f(2), we would substitute 2 into the function's expression:
f(2) = 2^2 = 4
This means that the ordered pair solution (2, 4) is a solution of the function f(x) = x^2.
In general, any ordered pair solution of a function can be evaluated using function notation. For example, if the function is g(x) = 2x + 1, and the ordered pair solution is (3, 7), then we can evaluate g(3) as follows:
g(3) = 2(3) + 1 = 6 + 1 = 7
This confirms that the ordered pair solution (3, 7) is a solution of the function g(x) = 2x + 1.
Conversely, any function value can be represented as an ordered pair solution of the function. For example, if the function is h(x) = x^3, and the function value is 8, then we can represent this as the ordered pair solution (2, 8), since h(2) = 8.
In general, any function value can be represented as an ordered pair solution of the function by writing the input value as the first coordinate and the function value as the second coordinate.
Therefore, function notation and ordered pair solutions of a function are closely connected. Function notation is a way to represent a function and its input value, while an ordered pair solution of a function is a pair of numbers (x, y) such that y is the output of the function when x is the input. Any function value can be evaluated using function notation, and any ordered pair solution of a function can be represented as a function value.
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The following question may be like this:
What is the connection between function notation to evaluate a function at certain values and ordered pair solutions of the function?
which is greater 89.001 or 89.100
1+3+5+7+...+1003= what is the answer?
Judy got 60 marks in test 1. She got 40 marks in test 2. What are her average marks in both tests?
What is the area of a circle 3.102 cm in diameter? (note: the units will be cm2, you only need to enter the number)?
If it is 5 degrees outside and the temperature will drop 17 degrees in the next 6 hours how cold will it get?
Evaluate 37/100+3/10
round 421,906 to the nearest hundred thousand and to the nearest thousand
The expression 40x2 – 65x + 50 represents the sum of the interior angles of a regular pentagon in degrees. If the interior angles of the pentagon are equal, which expression represents the measure of two angles?
Answer:
Expression representing the measure of the two angles of the given regular polygon is 16x² - 26x + 20.
Step-by-step explanation:
Given Expression of the Sum of the all interior angles of a regular polygon
40x² - 65x + 50
We need to find expression representing the measure of the two angles.
We know that regular polygons have all side and all angles equal.
Number of side or angles in regular polygon = 5
So, when we divide given expression by 5 we get expression for an angle of the regular polygon.
[tex]\frac{40x^2-65x+50}{5}=\frac{5(8x^2-13x+10)}{5}=8x^2-13x+10[/tex]
Expression for an angle of regular pentagon = 8x² - 13x + 10
Now, For 2 angles = 2( 8x² - 13x + 10 ) = 16x² - 26x + 20
Therefore, Expression representing the measure of the two angles of the given regular polygon is 16x² - 26x + 20.
Mt. Everest, the highest elevation in Asia, is 29,028 feet above sea level. The Dead Sea, the lowest elevation, is 1,312 feet below sea level. What is the difference between these two elevations?
the average person loses about 8 x 10^1 strands of hair each day. about how many strands of hair would the average person lose in 9 days?
A college student borrow $1,500 for 3 months to pay for a semester of school. If the interest is $30.94, find the monthly payment (Round to the nearest cent.)
Answer:
Hence, the monthly payment to the nearest cent is 510.31
Step-by-step explanation:
Consider the provided information,
A college student borrow $1,500 for 3 months to pay for a semester of school.
Let us consider the monthly payment is $x.
If he pay $x for next 3 months, then the total amount student paid in 3 month is: 3x
The interest is $30.94 for 3 months.
Student pay all the borrowed money and interest in 3 months.
That means he pay $1,500 + $30.94 in 3 months while the monthly payment was 3x.
This can be written as:
[tex]3x = 1500+30.94[/tex]
[tex]3x = 1530.94[/tex]
[tex]x = \frac{1530.94}{3}[/tex]
[tex]x = 510.31[/tex]
Hence, the monthly payment to the nearest cent is 510.31
what's the area of the Square 28in• 28in
What is the volume of a frustum of a right pyramid with the area of the lower base equal to 100 square inches, the area of the upper base equal to 25 square inches, and the altitude equal to 12 inches?
A. 560 in^3
B. 700 in^3
C. 420 in^3
D. 750 in^3
Where B₁ and B₂ are the areas of the bases, the volume of the frustum is given by
... V = (1/3)(B₁ +B₂ +√(B₁B₂))h
For your dimensions, the volume is
... V = (1/3)(100 + 25 + √(100·25))·12 = (1/3)·175·12 = 700
The appropriate choice for the volume of the frustum is
... B. 700 in³
The scale on a map is ½ inch = 15 miles. How far apart are two towns that are 2 inches apart on the map? Someone help me please!
At 4:00 am the outside temperature was 28*F. By 4:00 pm that same day it rose to 38 degrees.
The temperature at 4:00 pm will be 66° F.
What are Integers?
An integer is a number with no decimal number or fractional part.
Given that;
At 4:00 am the outside temperature was 28*F. By 4:00 pm that same day it rose to 38 degrees.
Now, The temperature at 4:00 pm is calculated as;
= 28° F + 38° F
= 66° F.
Thus, The temperature at 4:00 pm will be 66° F.
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The complete question is this;
At 4:00 am, the outside temperature was 28*F. By 4:00 P.M. it rose 38 degrees. What was the temperature at 4:00 P.M. ?
-6+8(6x+2) < 7x+10
What is the answer to this inequality?
The answer choices are
A. x < 0
B. No solution
C. All numbers
D. x > 0
Jo lives on maple road her address has the digit 2 in the ones place and the digit 4 in the tens place what is jo address
a rectangular plot of ground is 10 meters longer than it is wide. its area is 10,000 square meters
What is 8.072 rounded to the nearest hundredth
The GCF of 28x^3 and 16x^2y^2
Answer:
[tex]4x^2[/tex]
Step-by-step explanation:
We are asked to find the GCF of [tex]28x^3[/tex] and [tex]16x^2y^2[/tex].
The greatest common factor of numerical part would be GCF of 28 and 16.
Factors of 28: 1, 2, 4, 7, 14, 28.
Factors of 16: 1, 2, 4, 8, 16.
The greatest common factor of 28 and 16 is 4.
The GCF of variable part:
[tex]x^3=x\cdot x\cdot x[/tex]
[tex]x^2y^2=x\cdot x\cdot y\cdot y[/tex]
The greatest common factor of [tex]x^3[/tex] and [tex]x^2y^2[/tex] is [tex]x^2[/tex].
Upon combining the GCF of numerical part and algebraic part, we will get:[tex]4x^2[/tex]
Therefore, the greatest common factor of both expressions is [tex]4x^2[/tex].
Two-thirds a number plus 4 is 7
Which is a decimal expansion of 7/22?
A.
B.
C.
D.
At a homeowners association meeting a board member can vote yes, vote no, or abstain a motion. There are three motions on which each board member must vote. Complete parts a through c
This question pertains to the voting options and procedures during a homeowners association meeting, covered under the broader subject of Social Studies in the context of High School education. It involves understanding quorum requirements and voting rules as per bylaws for decision-making on motions.
The question revolves around a homeowners association meeting where a board member has three options to participate in a vote: vote yes, vote no, or abstain from a motion. There are three motions for which each board member must decide how to vote. In such meetings, the rules outlined typically require a quorum to conduct business, the ability to make amendments to bylaws, and procedures for electing members, as seen in various articles of an organization's bylaws and rules of procedure. These rules ensure that the organization conducts its affairs in an orderly and democratic manner, often requiring a majority or unanimous consent for certain actions.
Meetings like these are essential, as they also involve critical decisions such as annual meetings, bylaw amendments, or the dissolution of the organization, each depending on the vote of the board members or the members of the organization. Membership eligibility and voting rights are typically determined by the board of directors or outlined within the bylaws. Furthermore, certain organizational procedures such as elections, member qualifications, and the transparency measures such as keeping a journal of proceedings of each meeting are often mandated.
The cost of a 12.95 pizza was shared evenly by 5 friends. How much did each person pay?
Which is the graph of f(x) = 100(0.7)x?
if alisson worked the times in the table and makes $9.32 an hour, how much was her gross pay this week
The gross pay for Alisson this week is $432.22. So option (d) is correct.
To calculate her gross pay, we first need to find the total number of hours worked during the week. We add up the hours worked each day:
1. Monday: 8:03 am to 5:13 pm = 9 hours and 10 minutes
2. Tuesday: 7:58 am to 4:49 pm = 8 hours and 51 minutes
3. Wednesday: 7:46 am to 4:41 pm = 8 hours and 55 minutes
4. Thursday: 8:32 am to 4:50 pm = 8 hours and 18 minutes
5. Friday: 7:31 am to 4:32 pm = 9 hours and 1 minute
Total hours worked = 43 hours and 15 minutes.
Since Alisson worked more than 40 hours this week, any hours beyond 40 are paid at time and a half. So, she worked 40 regular hours and 3 hours and 15 minutes of overtime.
Her regular pay = 40 hours * $9.32/hour = $372.80
Her overtime pay = 3.25 hours * ($9.32/hour * 1.5) = $59.42
Therefore, her total gross pay for the week is $372.80 + $59.42 = $432.22.
Complete Question;
If Alisson worked the times in the table and makes $9.32 an hour, how much was her gross pay this week?
8:03 am 5:13 pm
7:58 am 4:49 pm
7:46 am 4:41 pm
8:32 am 4:50 pm
7:31 am 4:32 pm
Remember that any time worked over 40 hours is paid at time and a half.
(a) $372.80
(b) $410.08
(c) $412.41
(d) $432.22
At a store clearance, a women spent less than $200 on shirts that were labeled $15 each . How many shirts did she buy? Identify the numbers that are included in the solution set .
What is the prime factorization of 15
Answer: 3 × 5
Step-by-step explanation: To find the prime factorization of 15, first create a factor tree with two branches.
Since 15 divided by 3 gives us 5, we know that and 5 are factors of 15. This means that we can write 3 and 5 at the bottom of our branches.
While 1 and 15 are also factors of 15, we don't use them in our factor tree. This because when finding a prime factorization, we only want factors other than 1 and the number itself.
Next, we circle any prime numbers in our factor tree. Since 3 and 5 are both prime numbers, we circle both 3 and 5. Since we have circles at the bottom of our branches, we are finished.
Therefore, the prime factorization of 15 is 3 × 5.
PLEASE HELP!!! Hello, I've really been struggling with trying to figure these out, can someone please help me with these?
a baker makes cakes and sells them at county fairs his initial cost was $45 to reserve a booth and $25 traveling expenses. He figures that it costs $1.75 to make each cake and he charges $6.50 per cake. Let x represent the number of cakes sold. Express the revenue R and Cost C as functions of x. Then find how many cakes will he need to sell before he will make a profit
Final answer:
The baker's revenue R can be expressed as R = x * 6.50, and the cost C can be expressed as C = 45 + 25 + (x * 1.75). To find the number of cakes he needs to sell before making a profit, we set the revenue equal to the cost and solve for x. The baker will need to sell at least 15 cakes before making a profit.
Explanation:
To express the revenue R as a function of x, we can use the equation R = x * 6.50. This is because the revenue is the number of cakes sold multiplied by the price per cake. So, every cake sold contributes $6.50 to the revenue.
To express the cost C as a function of x, we can use the equation C = 45 + 25 + (x * 1.75). The initial fixed costs of $45 for reserving a booth and $25 for traveling expenses are added to the variable costs of $1.75 per cake multiplied by the number of cakes sold.
To find the number of cakes he needs to sell before making a profit, we need to set the revenue equal to the cost and solve for x:
R = C => x * 6.50 = 45 + 25 + (x * 1.75)
Combining like terms, we get:
4.75x = 70
x = 70 / 4.75
x ≈ 14.74
Since you cannot sell a fraction of a cake, the baker will need to sell at least 15 cakes before making a profit.