Find whether the following expressions are functions in the ranges they are defined.
Answers
The options that shows expressions which are functions in the ranges they are defined are;
Option A: f(x) = 2x + 5
Option B: f(x) = x² + 1
How to identify real numbers and Integers?Real numbers are defined as the combination of rational and irrational numbers, in the number system. This means that, all the arithmetic operations can be performed on real numbers and they can be represented in the number line.
Now, integers are defined as whole numbers that can be positive, negative or zero.
a) We are told that the input of real numbers must yield only real numbers. Yes this is true because any real number we put in for x in f(x) = 2x + 5 will yield an output that is also a real number.
b) We are told that the input of real numbers must yield only real numbers. Yes this is true because any real number we put in for x in f(x) = x² + 1 will yield an output that is also a real number.
c) We are told that the input of real numbers must yield only real numbers. No this is not true because if we put -1 which is a real number for x in the denominator, we will get an undefined function.
d) We are told that the input of integers must yield only integers. No this is not true because if we put 1 for x which is an integer, we will get a fraction which is not an integer.
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Related Questions
does multiplying 2 numbers together always give the first common multiple of the numbers? explain using examples
Answers
2 x 8 = 16
But the first common multiple is 8
2, 4, 6, 8, 10, 12, 14, 16…
8, 16, 24…
A quadrilateral
is a polygon with four sides. Consider
the quadrilateral and the dashed segment. What is the sum
of the measures of the four interior angles of this quadrilateral?
Draw a different quadrilateral. Can you guess the sum
of the measures of its angles? Is it possible to generalize about
the angles of a quadrilateral?
Answers
The sum of the measures of the four interior angles of a quadrilateral is always 360°
What is a quadrilateral?A quadrilateral is a closed shape and a type of polygon that has four sides, four vertices and four angles.
Given is, A quadrilateral is a polygon with four sides. Consider the quadrilateral and the dashed segment
If we draw one diagonal to quadrilateral we will get two triangles i.e. △ABC and △ACD and we know that sum of the angles of a triangle is 180°
Sum of angles of quadrilateral ABCD = sum of angles of △ABC + sum of the angles △ACD
= 180° + 180°
= 360°
If we take examples of a square or a rectangle, we know that they are also a quadrilateral and also their each angle is right angle, i.e. 90°
Therefore, the sum of their interior angles will = 90×4 = 360°
Hence, we can say that the sum of the measures of the four interior angles of a quadrilateral is always 360°
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For the rhombus below, find the measures
Answers
Angle 1 and Angle 4 are alternate internal angles, Angle 1 also equals 51.Angles 1 and 2 of the rhombus are bisector by 51 and 2, respectively.
what is rhombus ?A parallelogram has a unique variation known as a rhombus. A rhombus has opposing sides that are parallel and opposing angles that are equal. A rhombus also has equal-length sides and diagonals that are at right angles to one another. The term "rhombus" can also refer to a diamond or rhombus. A rhombus has equal opposite angles. At a 90° angle, the diagonals split in half. 180 degrees is the sum of adjacent angles.
given
There is a line that passes through the parallel line; the alternate interior angles are 3 and 39.
The alternative interior angles are similar, hence Angle 3 = 39.
Since the upper left triangle is a triangle, angles 3, 4, and the center angle all add up to 180 degrees. The angle in the middle is 90 degrees. hence, we may locate angle 4.
angle 4=51.
Since Angle 1 and Angle 4 are alternate internal angles, Angle 1 also equals 51.Angles 1 and 2 of the rhombus are bisector by 51 and 2, respectively.
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What’s is the prime factorization of |-21|
Answers
Evaluate the expression 2^x- x^22
x
−x
2
2, start superscript, x, end superscript, minus, x, squared for x=5x=5
Answers
The evaluation of the expression 2ˣ - x² when x = 5 is 7
How to evaluate the expressionFrom the question, we have the following parameters that can be used in our computation:
Expression: 2^x- x^2
Value x = 5
Rewrite the expression as
Expression: 2ˣ - x²
Substitute the known values in the above equation, so, we have the following representation
2ˣ - x² = 2⁵ - 5²
When the exponents are evaluated. we have
2ˣ - x² = 32 - 25
Evaluate the like terms in the equation
So, we have the following representation
2ˣ - x² = 7
Using the above as a guide, we have the following:
The solution is 7
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Eric added up on a number line to find 4 over 5 minus 5 over 10
Answers
Answer: 4/5 minus 5/10 can be simplified as:
(4/5) - (5/10)
It can also be re-written as
(4/5) - (1/2)
To subtract these fractions, we need a common denominator, which is 10 in this case.
So it becomes
(4/5)(2/2) - (1/2)(5/5) = 8/10 - 5/10 = 3/10
So the result of 4/5 minus 5/10 is 3/10 on a number line.
Step-by-step explanation:
1/3x-2 × 9x²-4/3x²-13x-10 - 7/x-1
Answers
Answer:
Step-by-step explanation:
Combine multiplied terms into a single fraction
one-third x minus 2 ⋅ 9 x squared plus negative 4 over 3 end fraction x squared minus 13 x minus 10 plus negative 7 over x end fraction minus 1
1 x over 3 end fraction minus 2 ⋅ 9 x squared plus negative 4 over 3 end fraction x squared minus 13 x minus 10 plus negative 7 over x end fraction minus 1
Multiply by 1
1 x over 3 end fraction minus 2 ⋅ 9 x squared plus negative 4 over 3 end fraction x squared minus 13 x minus 10 plus negative 7 over x end fraction minus 1
x over 3 end fraction minus 2 ⋅ 9 x squared plus negative 4 over 3 end fraction x squared minus 13 x minus 10 plus negative 7 over x end fraction minus 1
Multiply the numbers
x over 3 end fraction negative 2 ⋅ 9 x squared plus negative 4 over 3 end fraction x squared minus 13 x minus 10 plus negative 7 over x end fraction minus 1
x over 3 end fraction negative 18 x squared plus negative 4 over 3 end fraction x squared minus 13 x minus 10 plus negative 7 over x end fraction minus 1
Hello- some help please!! I will give you brainlist :]
Answers
Answer:
standard form
= x⁶ + 53x⁵ + 2x⁴ -2
Step-by-step explanation:
the degree is 6.
leading coefficient is 1
this is called a polynomial.
it has 4 terms
Can I get help in number 6?
Answers
Answer:
Trim A
Inches = 36
Feet = 3
Yards = 1
Trim B
Inches = 216
Feet = 18
Yards = 6
Highschool Algebra: Indicated Operation.
(-ab2)(-6ab2)(3ab)
Answers
Answer:
-18a^3b^5
Step-by-step explanation:
First do -ab^2*-6ab^2=-6a^2b^4
Then multiply that by 3ab=-18a^3b^5
Find the commission on a 1,250 sale with a commission rate of 5%.
Please help only if you know it and please explain the answer
Answers
The commission on the sale would be $62.5
To find the commission on a sale, you can use the following formula:
Commission = Sale Amount x Commission Rate
Sale Amount: the total value of the sale
Commission Rate: the percentage or decimal value of the commission rate (e.g. 5% = 0.05)
The commission on a sale can be calculated by multiplying the total sale amount by the commission rate.
In this case, the commission on a 1,250 sale with a commission rate of 5% would be:
= 1,250 x 0.05
= 62.5
So the commission on the sale would be $62.5
It's also worth noting that commission rate is given as a decimal and not a percentage. 5% is 0.05 as decimal.
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How do you know if you add or subtract in elimination?
Answers
Which expression is modeled by this set of arrows on the number line?
Answers
On solving the provided question, we can say that - here in number line we jump fron 2 to 7 as we have added +5
what is number line?A number line is a visual representation of real numbers used in introductory mathematics. It is an image of a magnitude line. On the number line, each point represents a real number, and each real number is taken to represent a point. Increments on a number line are separated by equal distances. You can only respond to the numbers on a line in the manner indicated by those numbers. How the number is utilized is determined by the question that goes with it. B: Make a point.
here,
we have +5
so 2+(+5) = 7
we will jump to 7 from 2
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The perimeter of a square room is 80 feet. How many floor tiles 1 foot square would be needed to cover the area of the room
Answers
We would require 400 square tiles, each measuring one square foot, to cover the whole surface of the square room.
If the perimeter of the room is 80 feet, we know that all four sides of the square room have the same length. To find the length of each side, we can divide the perimeter by 4: 80 feet / 4 = 20 feet.
Now that we know the length of each side of the room, we can find the area of the room by squaring that measurement: 20 feet x 20 feet = 400 square feet.
To find the number of floor tiles needed to cover the area of the room, we divide the total area of the room by the area of each tile: 400 square feet / 1 square foot/tile = 400 tiles.
So, to cover the entire area of the square room, we would need 400 square tiles of one square foot each.
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Erin is picking out some movies to rent, and he has narrowed down his selections to 5 documentaries, 5 mysteries, 5 dramas, and 7 action movies. How many different combinations of 9 movies can he rent if he wants all 5 mysteries
Answers
If he wants to rent all 7 comedies, there are 91 different combinations of 9 movies that he could do so.
How are the various combinations determined?The following formula determines how many combinations of n objects can be taken r at a time: (n,r) = C(n,r)! .
She was a master of both wit and martial arts. The art and science of education blend beautifully. He saw slam poetry as the ideal synthesis of thought, writing, and theater. The desired mix is produced by the computer system (the perfect combination of arabica and robusta).
Five documentaries make up the total.
7 comedies total are available.
Four mysteries are present.
5 horror movies are there.
A total of 14 films, excluding comedies, are available.
If he wants to rent all 7 comedies, there are a total of 9 different combinations that he can do.
1 * (14*13)/2 = 91
If he wants to rent all 7 comedies, there are 91 different combinations of 9 movies that he could do so.
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11. Manuel has two different recipes for chocolate chip
muffins. The table shows the amount of chocolate chips
needed per batch for each recipe. He has 10 cups of
chocolate chips. The equation 2b = 10 can be used to
find b, the number of batches of muffins he can make if
he uses Recipe 1. Can Manuel make 3, 4, or 5 batches if
he uses Recipe 1?
n
JID
Recipe Chocolate Chips (cups)
1
2
2
1
Answers
Answer:
Manuel can make 5 batches of muffins using Recipe 1
Step-by-step explanation:
You want to know the value of b in the equation 2b = 10, where b is the number of batches of muffins Manuel can make using recipe 1.
SolutionDivide both sides of the given equation by 2 so solve for the value of b.
(2b)/2 = (10)/2
b = 5
Manuel can make 5 batches of muffins using Recipe 1.
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Find the product using any method. (Need some help!!)
Answers
Answer:
2n^2-8n-24
Step-by-step explanation:
Uhm i just did this one with one of my classmates like 2-3 months ago so it just came to mind.
Hope this helped tho! :)
Gcf of -28, 60, and 72
Answers
Answer:
4
Step-by-step explanation:
-28 = ±2^2 x ±7
60 = ±2^2 x ±3 x±5
72 = ±2^3 x ±3^2
=> Gcf of -28, 60, 72: 2^2 = 4
Answer: 12
Step-by-step explanation:
Therefore, the highest common factor of 60 and 72 is 12.
:) I know somebody already answered but like..im answering some stuff today, hope this helped by the way!
how to solve inequations
Answers
Answer:
When solving an inequality: you can add the same quantity to each side •you can subtract the same quantity from each side you can multiply or divide each side by the same positive quantity If you multiply or divide each side by a negative quantity, the inequality symbol must be reversed.
you can add subtract multiply and divide the quantity to each side
But if you’re doing any of those with a negative quantity, the inequality symbol must be reversed
3 x -8> 29
3 x -8 < 29
Do the ratios 5/15 and 1/3 form a proportion?
Answers
Answer:
Step-by-step explanation:
We will check if 5/15 and 1/3 are in proportion or not by cross-multiplication.
5/15 = 1/3
5*3 = 15*1
15 = 15
as the left-hand side is equal to the right side. So, these fractions are in proportion.
The table below shows the number of animals at a local petting zoo.
Animal
Goats
Number
3
8:20 =
Ponies
3
Write the ratio of ponies to goats.
You may write the ratio in ANY of the three forms. Remember to REDUCE the ratio,
possible.
T
123 f() ∞*E ABC αβγ
Rabbits
8
21
7
8
O
1.
Sheep
6
a
DG
Answers
Answer: 1:1
Step-by-step explanation:
We will write a ratio of ponies to goats;
ponies : goats
3 : 3
Next, 3:3 can be simplified to 1:1. This gives us our fully reduced ratio.
In the figure, a∥e, m∥n, and m∠2 = 112°.
What is m∠6?
Enter your answer in the box
Answers
The measure of the angle ∠6 = 112°
What are parallel lines?
Parallel lines are two or more lines that are always the same distance apart and never meet, no matter how far they are extended. They are coplanar lines that do not intersect or cross each other, and they have the same direction.
As given
a∥e, m∥n, and m∠2 = 112°.
As m∥n
a is the transversal (A line that cuts across two or more (usually parallel) lines is called transverasl.)
Thus
∠ 2 = ∠3 ( Corresponding angle property )
∠3 = 112°
Also
a∥e and m are transversal.
∠ 3 = ∠6 = 112 ° ( Corresponding angle property )
Hence, the measure of the angle ∠6 = 112°
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The measure of the angle ∠6 = 112°
What are parallel lines?
Parallel lines are two or more lines that are always the same distance apart and never meet, no matter how far they are extended. They are coplanar lines that do not intersect or cross each other, and they have the same direction.
As given
a∥e, m∥n, and m∠2 = 112°.
As m∥n
a is the transversal (A line that cuts across two or more (usually parallel) lines is called a transversal.)
Thus
∠ 2 = ∠3 ( Corresponding angle property )
∠3 = 112°
Also
a∥e and m are transversal.
∠ 3 = ∠6 = 112 ° ( Corresponding angle property )
Hence, the measure of the angle ∠6 = 112°
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EX 2
QUAD ABCD is a rectangle with
diagonals that intersect at point P.
AC = 4x-13 and DP = x + 7. Find the
value of 'x'.
Answers
QUAD ABCD is a rectangular shape whose diagonals meet at point P. AC is 4x-13 and DP is x + 7.
Can you show that the quadrilateral ABCD is a parallelogram given the provided information?When one set of opposing sides in a quadrilateral are congruent and parallel, the quadrilateral is a parallelogram. ABCD is a parallelogram if — BC — AD and — BC — AD. A quadrilateral becomes a parallelogram if its diagonals are bisected by one another.
In QUAD ABCD, DP equals x + 7 and AC is 4x-13.
4x - 13 is x + 7 + x + 7
4x - 13 = 2x+14
2x-13 = 14.
hence,
The value of x is 13.5.
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For any of the vehicles listed in the table,
how many days can you rent the vehicle
before it would be less expensive to rent
for the week?
Answers
A person can rent any of the vehicles shown in the table for a minimum of two to three days before it becomes more expensive for a week.
Algebra state that it is the study of the laws and symbols of mathematics as well as the manipulation of these symbols.
The rent of the small car for a week is $250 and for a day is $100. Then,
The maximum number of days that a car could be rented is,
= 250÷100
= 2.5 days
≅ 3 days
Then, for the medium car is,
= 290÷110
= 2.7 days
≅ 3 days
For the luxury car is,
= 325÷120
= 2.7 days
≅ 3 days
For Small van is,
= 350÷150
= 2.3 days
≅ 2 days
For Large van is,
= 390÷170
= 2.2 days
≅ 2 days
We can conclude from the above calculations that a person can rent a car for 2-3 days before it becomes more expensive for a week.
The complete question is -
For any of the vehicles listed in the table, how many days can you rent the vehicle before it would be less expensive to rent for the week?
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please help solve this its for geometry
Answers
Answer:
Step-by-step explanation:
1.RS+ST=RT. so 9y+2+2y+7=15y-11
2.11y+9=15y-11
3.15y-11y=11+9
4.4y=20
finally we find the answer is y=5
Type in the missing values to complete the simplified form of the expression 4x-4+3y+ 6-2x+3y.
__ x +__ y + __
Answers
Answer:
2x+6y+2
Step-by-step explanation:
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pls help with his i dont get it at all
Answers
Answer:
D.
Step-by-step explanation:
They are parallel would be the best explanation. AB and PQ are in a sense the same segment but PQ is AB translated.
Example 2: An object is thrown upward from the top of a building, where h is the height of the object in metres and t is the time in seconds. The graph below represents the relationship between height and time.
a) What is the maximum height of the object above
the ground?
b) After how many seconds does the object reach this
maximum height?
c) From the moment the object was thrown, how much
time would it take for it to reach he ground?
d) How tall is the building?
Answers
The answers are given as 1) 165 m 2)3 seconds 3) 9 seconds 4)120 m
What is a curve in a graph?A curve is defined as a smoothly- flowing continuous line that has bent. It does not have any sharp turns. The way to identify the curve is that the line bends and changes its direction at least once. Curve of the graph is a pictorial representation of a particular function.
Given : A object is thrown from the top of the building thus by observing the graph we derive the following information
1) Maximum height = 165 m
2) The object reaches maximum height at t=3 seconds
3) The time it took to reach the ground is 9 seconds
4) The building is 120 m tall
Hence, the answers are 1) 165 m 2)3 seconds 3) 9 seconds 4)120 m
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what is 2.38 correct to 2 significant figures
Answers
Answer: 2.4
Step-by-step explanation:
we start from the right most digit, that is 8. Since 8 is greater than 5, we add 1 in the number before 8, that is 3. When we add 3 and 1 we get 4. This way, we get our answer 2.4 , which is correct to 2 significant figures.
hope that helps...
•18 POINTS• (don’t answer icebrain)
a.)
b.)
c.)
Answers
Answer: C
Step-by-step explanation:
The HL Theorem states that if the hypotenuse and leg of a right triangle are congruent to the hypotenuse and leg of another right triangle, then the two triangles are congruent.
In this case, 16 is the hypotenuse (the longest side of a right triangle) and 13 is the leg.