The domain of f(x) is the set os all real numbers greater than or equal to 0 and less than or equal to 2. True of false
Answer:
True
Step-by-step explanation:
In Functions and Function Notation, we were introduced to the concepts of domain and range. In this section, we will practice determining domains and ranges for specific functions. Keep in mind that, in determining domains and ranges, we need to consider what is physically possible or meaningful in real-world examples, such as tickets sales and year in the horror movie example above. We also need to consider what is mathematically permitted. For example, we cannot include any input value that leads us to take an even root of a negative number if the domain and range consist of real numbers. Or in a function expressed as a formula, we cannot include any input value in the domain that would lead us to divide by 0.
Diagram of how a function relates two relations.
Figure 2
We can visualize the domain as a “holding area” that contains “raw materials” for a “function machine” and the range as another “holding area” for the machine’s products.
We can write the domain and range in interval notation, which uses values within brackets to describe a set of numbers. In interval notation, we use a square bracket [ when the set includes the endpoint and a parenthesis ( to indicate that the endpoint is either not included or the interval is unbounded. For example, if a person has $100 to spend, he or she would need to express the interval that is more than 0 and less than or equal to 100 and write
(
0
,
1
0
0
]
(0, 100]. We will discuss interval notation in greater detail later.
Let’s turn our attention to finding the domain of a function whose equation is provided. Oftentimes, finding the domain of such functions involves remembering three different forms. First, if the function has no denominator or an even root, consider whether the domain could be all real numbers. Second, if there is a denominator in the function’s equation, exclude values in the domain that force the denominator to be zero. Third, if there is an even root, consider excluding values that would make the radicand negative.
Before we begin, let us review the conventions of interval notation:
The smallest term from the interval is written first.
The largest term in the interval is written second, following a comma.
Parentheses, ( or ), are used to signify that an endpoint is not included, called exclusive.
Brackets, [ or ], are used to indicate that an endpoint is included, called inclusive.
The table below gives a summary of interval notation.
Summary of interval notation. Row 1, Inequality: x is greater than a. Interval notation: open parenthesis, a, infinity, close parenthesis. Row 2, Inequality: x is less than a. Interval notation: open parenthesis, negative infinity, a, close parenthesis. Row 3, Inequality x is greater than or equal to a. Interval notation: open bracket, a, infinity, close parenthesis. Row 4, Inequality: x less than or equal to a. Interval notation: open parenthesis, negative infinity, a, close bracket. Row 5, Inequality: a is less than x is less than b. Interval notation: open parenthesis, a, b, close parenthesis. Row 6, Inequality: a is less than or equal to x is less than b. Interval notation: Open bracket, a, b, close parenthesis. Row 7, Inequality: a is less than x is less than or equal to b. Interval notation: Open parenthesis, a, b, close bracket. Row 8, Inequality: a, less than or equal to x is less than or equal to b. Interval notation: open bracket, a, b, close bracket.
Brody and his brother Kael enter a race with a total of 30 runners. There will be prizes for the first three runners who cross the finish line. a) What is the probability that Brody finishes the race in the first place? Are your brother's chances of finishing the race in the first place better than Brody's? Justify your answer. b) What is the probability that Brody or Kael finish the race in the first place? c) How many ways can these 30 runners get in first, second, and third place? (NOTE: only part C asks for a permutation)
Answer:
hmm i think its answer B hope i helped :)
Step-by-step explanation:
PLEASE HELP 1) A lake near the Arctic Circle is covered by a 2-meter-thick sheet of ice during the cold winter
months. When spring arrives, the warm air gradually melts the ice, causing its thickness to
decrease at a constant rate modeled by h(t) = 2 - 0.25t, where h(t) represents the thickness of
the sheet of ice and t represents the time in weeks.
a. What is the initial value of this function?
b. What is the rate at which the ice sheet is melting?
c. How thick will the ice sheet be after 3 weeks?
Answer:
a). 2 meters
b). 0.25 meters per week
c). 1.25 meters
Step-by-step explanation:
Thickness of the ice sheet on the lake = 2 meters
Thickness decreases with a constant rate and thickness is modeled by the function,
h(t) = 2 - 0.25t [t = time or duration in weeks]
a). Initial value of this function will be it's y-intercept,
h(t) = 2 meters
b). Rate of the melting of this sheet (slope of the line) = 0.25 meter per week
c). After 3 weeks or t = 3 weeks,
h(3) = 2 - 0.25 × (3)
= 2 - 0.75
= 1.25 meters
Look at the picture below. Urgent help please!!!!
Answer:
x≅11.49 or x=2√33
Step-by-step explanation:
8^2+x^2=14^2
64+x^2=196
(subtract 64 from both sides)
x^2=132
(square root both sides)
x≅11.49
All of the following are equivalent to 3:8 = x : 32 except
8 : 3 = 32 : x
3 : x = 8 : 32
x : 8 = 3 : 32
8 : 32 = 3 : x
Answer:
8:3=32:x
Hope thos helps you
Carlo changed 800 euros into dollars for his holiday when the exchange rate was €1=$1.50. his holiday was cancelled he changed all his dollar back into euros and he received €750. find the new exchange rate
Answer:
€800 = $1200
New exchange rate =
750/1200 = 1.6
Which calculator correctly shows the quotient 6.47x10^-15/3.36x10^-29
1.92559524e+14
Step-by-step explanation:
6.47 x 10^-15 and 3.36 x 10^-29 are written in scientific notation. In this way, we have a quotient of two numbers written in scientific notation. To solve this problem, we have:
6.47/3.36 x 10^{[-15-(-29)]}=1.92559524 x 10^{(-15+29)}
Therefore 1.92559524 x 10^{14} or 1.92559524e+14
1.92559254e+ 14 is the correct value of the given expression.
What are mathematical operations?
The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.
given a number 6.47x10^-15/3.36x10^-29
Solving this given number using PEMDAS
=> 6.47x10^-15/3.36x10^-29
=> (6.47 * 10⁻¹⁵) / (3.36 * 10⁻²⁹)
=> (6.47 / 3.36) * 10⁻¹⁵ ⁺ ²⁹
=> 1.92559254 * 10¹⁴
in Scientific notation:
=> 1.92559254e+ 14
therefore, the correct value of the given expression is 1.92559254e+ 14.
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Help!!due today help as quickly plz 3 and 4
Answer and Step by Step explanation:
3. 7(1.5) + 2(4) + 3(6.5) + 5(7)
= 10.5 + 8 + 19.5 + 45
= 83 grams of salt
You look at the x-axis of the graph and that is the amount of grams of salt, and the dots represent one container. So you multiply the number of dots (containers) by the amount of grams (stated on the number line).
4. 83 x 2
= 166 grams of salt
This is because you already solved how much one of each container would be in the last question (question 3), so you would just have to multiply it my 2 to get the answer.
2. (08.01) Two lines, R and M, are represented by the following equations: Line R: 2x + 2y = 18 Line M: x + y = 9 Which statement is true about the solution to the set of equations? (4 points) It is (18, 9). It is (9, 18). There are infinitely many solutions. There is no solution.
WILL GIVE BRAINLIEST
Answer:
infinitely many solutions
Step-by-step explanation:
Given the 2 equations
2x + 2y = 18 → (1)
x + y = 9 → (2)
Equation (1) is twice (2)
Thus the equations are equal and will have infinite solutions
All identities are equations, and all equations are identities.
A. True
B. False
this is false not all equations and all equations are identities are same
Please help me I need this answer very bad (Picture Attached)
Answer:
median 2nd was the answer
Step-by-step explanation:
The vertex form of a quadratic function is f(x) = a(x - h)2 + k. What is the vertex of each function? Match the function rule with the coordinates of its vertex.
Answer:
For [tex]f(x)=6(x-5)^2-9[/tex] the vertex is: (5, -9)
For [tex]f(x)=9(x+5)^2-6[/tex] the vertex is: (-5, -6)
For [tex]f(x)=5(x-6)^2+9[/tex] the vertex is: (6, 9)
For [tex]f(x)=6(x+9)^2-5[/tex] the vertex is: (-9, -5)
For [tex]f(x)=9(x-5)^2+6[/tex] the vertex is: (5, 6)
Step-by-step explanation:
Let's identify the vertex pair [tex](x_v,y_v)[/tex] from each equation:
A) [tex]f(x)=6(x-5)^2-9[/tex] corresponds to [tex]x_v=5\,\,\,and\,\,\,y_v=-9[/tex] , that is: (5, -9)
B) [tex]f(x)=9(x+5)^2-6[/tex] corresponds to [tex]x_v=-5\,\,\,and\,\,\,y_v=-6[/tex] , that is: (-5, -6)
C) [tex]f(x)=5(x-6)^2+9[/tex] corresponds to [tex]x_v=6\,\,\,and\,\,\,y_v=9[/tex] , that is: (6, 9)
D) [tex]f(x)=6(x+9)^2-5[/tex] corresponds to [tex]x_v=-9\,\,\,and\,\,\,y_v=-5[/tex] , that is: (-9, -5)
E) [tex]f(x)=9(x-5)^2+6[/tex] corresponds to [tex]x_v=5\,\,\,and\,\,\,y_v=6[/tex] , that is: (5, 6)
What is the m < FAB?
Answer:
∠ FAB = 75°
Step-by-step explanation:
The external angle of a triangle is equal to the sum of the 2 opposite interior angles.
∠ FAB is an external angle, thus
13x - 3 = 3x + 2 + 55 = 3x + 57 ( subtract 3x from both sides )
10x - 3 = 57 ( add 3 to both sides )
10x = 60 ( divide both sides by 10 )
x = 6
Thus
∠ FAB = 13x - 3 = 13(6) - 3 = 78 - 3 = 75°
help someone please
Answer:
C) [tex]1\frac{6}{100}[/tex]
Step-by-step explanation:
Hope this helps!
A company is designing a new cylindrical water bottle. The volume of the bottle will be 149 cmcubed. The height of the water bottle is 8.7 cm. What is the radius of the water bottle? Use 3.14 for pi.
Answer:
2.33
Step-by-step explanation:
If you put the numbers into the radius formula you should end up with this number hope this helps:)
a metal pole was placed in the ground and stands 30 feet high. two strands of lights were strung down from the top of the pole, forming a 46 degree angle to the ground. which theorem would be used to prove that the two strands of lights are equal in length?
SSS
AAS
ASA
SAS
Answer:
AAS
Step-by-step explanation:
angle 46 degree rt.angle made by pole to the ground common side formed by the pole
Hope this helps!
A freight train is traveling at an average rate of 45 miles per hour. Which equation represents the situation?
Let h represent the hours traveled.
Let m represent the miles traveled.
m = 45h
h = 45m
m = 45 + h
h = 45 – m
Answer:
m=45h
Step-by-step explanation:
The independent variable here is h, the number of hours it traveled, and this determines m.
what is (3²-2³)⁶⁶ total
Answer:
1
Step-by-step explanation:
(3²-2³)⁶⁶ = (9 - 8)⁶⁶ = (1)⁶⁶ = 1
(3²-2³)⁶⁶ total is 1
To evaluate (3²-2³)⁶⁶, we will first simplify the expression we have in the bracket before carrying out the power operation
From (3²-2³)⁶⁶
(3²-2³) can be simplified as shown below
3² = 3 × 3 = 9
and
2³ = 2 × 2 × 2 = 8
∴ (3²-2³) = (9 - 8) = (1)
∴ (3²-2³)⁶⁶ becomes (1)⁶⁶
(1)⁶⁶ = 1
(NOTE: 1 raised to any power is 1)
Hence, (3²-2³)⁶⁶ total is 1
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When the determinant of the coefficient matrix of a system of equations does not equal zero, the system has _________ solution(s)?
Answer:
one solution
Step-by-step explanation:
it means when the denominator does not equal zero
HURRY, I'M BEING TIMED ON STUDY ISLAND! On Saturday, the fruit and juice bar was selling 22 glasses of fruit punch an hour. By 3 p.m., they had sold 110 glasses. If their goal was to sell more than 264 glasses of fruit punch, which inequality can be used to find h, the number of hours they must stay open to make their goal?
Answer:
I say the inequality with the greater than or equal
Step-by-step explanation:
They want to reach there goal so it’s more or equal to
Which of the following are mathematical sentences? Check all that apply.
A. 5- V
B. 2 <3
c. 4 + 3 = 7
D. G
E. 7
F. 5-d = 9
Need help
C and F
....................
Answer:
B. 2 <3 and C. 4 + 3 = 7 and F. 5-d = 9
Which expression is equivalent to
Answer:
-8
Step-by-step explanation:
Answer:
-8
Step-by-step explanation:
Debbie is making an abstract painting with two triangles. The dimensions of the painting are shown below: Two triangles share the same height of 8 inches. One triangle has a base of 6 inches and the other is 10 inches. The total area of the two triangles is _____ square inches.
The entire figure could be taken as a trapezium
A=1/2h(a+b)
h=8, a=6 and b=10
A=1/2×8(6+10)
A=4×16
A=64sq Inch
Answer:
128 or 56
Step-by-step explanation:
(8 X 10) + (6 X 6)
80 + 48 = 128
OR
No 10 eliminate it because it on the line
8 X (6 X 6) = 48 + 8 = 56
Mrs. Le has 40 markers for her art class. 20% of the markers are red. How many markers are red?
Sorry wrong question delete this awnser
The letters of the word S U M M E R were placed in a bag. What is the probability of choosing an R?
3:6
5/6
33.3%
0.16
I'm asking it again cause I got an answer that had nothing in it!
Answer:
The answer is 3:6 for above probability
In order to solve 439-165 would I need to regroup to solve? If yes in what place? Why?
Yes, you need to regroup in the ________place because
______________________.
Answer:
Yes you would need to regroup in the tens place because 3 is less than 6.
Answer:
Yes you would need to regroup in the tens place because 3 is less than 6.
Have a great day
Determine the root of the equation
f(x) = e2x- x-6 closet to the point 0.95
Leave
your answer to five decimal places
Answer:
0.97087
Step-by-step explanation:
Given the function:
[tex]f(x) = e^{2x} - x - 6[/tex]
Its first derivative is:
[tex]f'(x) = 2e^{2x} - 1[/tex]
Using Newton's method:
[tex]x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}[/tex]
and starting with the point:
[tex]x_1 = 0.95[/tex]
we get:
[tex]f(x_1) = e^{2(0.95)} - 0.95 - 6 = -0.26410[/tex]
[tex]f'(x_1) = 2e^{2(0.95)} - 1 = 12.37178[/tex]
[tex]x_2 = x_1 - \frac{f(x_1)}{f'(x_1} = 0.95 - \frac{-0.26410}{12.37178} = 0.97134[/tex]
[tex]f(x_2) = e^{2(0.97134)}- 0.97134 - 6 = 0.00608[/tex]
[tex]f'(x_2) = 2e^{2(0.97134)} - 1 = 12.95485[/tex]
[tex]x_3 = 0.97134 - \frac{0.00608}{12.95485} = 0.97087[/tex]
[tex]f(x_3) = e^{2(0.97087)} - 0.97087 - 6 = -2.6240413 \cdot 10^{-7}[/tex]
Which expression is equivalent to 4(n + 5)?
Answer:
4n+20
Step-by-step explanation:
A deck of cards contains RED cards numbered 1,2,3,4,5, BLUE cards numbered 1,2,3, and GREEN cards numbered 1,2,3,4,5,6. If a single card is picked at random, what is the probability that the card is BLUE OR has an ODD number? Provide the final answer as a fraction.
Answer:
8/15
Step-by-step explanation:
15 options and 8 odd numbers
Answer: 9/14
Step-by-step explanation:
There are 3 blue cards, 3 odd numbered red cards, and 3 odd numbered green cards. 3 + 3 + 3 = 9
Red - R1, R2, R3, R4, R5
Blue - B1, B2, B3
Green - G1, G2, G3, G4, G5, G6
= A total of 14 cards
Answer = 9/14
(This answer is verified and was the correct answer in the program)
In the figure, find m∠RST if m∠RSU = 81° and m∠UST = 18°. Answers : A) 109° B) 81° C) 99° D) 63°
Answer:
99 degrees
Step-by-step explanation:
measure angle RST= measure angle RSU+ measure angle UST
measure angle RST=81+18
measure angle RST=99 degrees
The measure angle RST is 99 degrees.
To find measure angle RST.
What is angle?In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle and corner whether constituting a projecting part or a partially enclosed space.
Given that:
SU is angle bisector of <RST. So it can divide into 2 parts.
Measure angle RST= measure angle RSU+ measure angle UST
Measure angle RST=81+18
Measure angle RST=99 degrees
So, the measure angle RST is 99 degrees.
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