How are the graphs of the functions f(x) = StartRoot 16 EndRoot Superscript x and g(x) = RootIndex 3 StartRoot 64 EndRoot Superscript xrelated?
The functions f(x) and g(x) are equivalent.
The function g(x) increases at a faster rate.
The function g(x) has a greater initial value.
The function g(x) decreases at a faster rate.
Answers
The function g(x) increases at a faster rate and has a greater initial value.
Simplify f(x).[tex]f(x) = \left(\sqrt{16}\right)^{x}[/tex][tex]f(x) =\left(\sqrt{4^{2}}\right)^{x}[/tex][tex]f(x) = \left(4\right)^{x}[/tex]Simplify g(x).[tex]g(x)=3\left(\sqrt{64}\right)^{x}[/tex][tex]g(x)=3\left(\sqrt{8^{2}}\right)^{x}[/tex][tex]g(x)=3\left(8\right)^{x}[/tex]Compare the functions f(x) and g(x).f(x) and g(x) are not equivalent as the bases of the exponents are different.We will find the initial value for both our functions (value of functions when x is 0).For x=0,[tex]f(0)=\left(4\right)^{0} = 1[/tex][tex]g(0)=3\left(8\right)^{0}=3*1=3[/tex]The initial value of g(x) is greater than the initial value of f(x).In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.With the help of a graphing tool, the two functions were plotted.The function g(x) increases at a faster rate than the function f(x)(see the attached figure).That means that the value of g(x) is greater than the value of f(x) for the same value of x.Thus,The function g(x) increases at a faster rate and has a greater initial value.To learn more about graph, visit :
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Related Questions
1=|8-2y| what’s the value of y
Answers
Answer:
y=-7/2
Step-by-step explanation:
1=|8-2y|
1=8+2y
-7=2y
2y=-7
y=-7/2
55) Lenny has $3.69 in pennies,
dimes, and quarters. The number
of pennies is three more than
the number of dimes. The number
of quarters is twice the number
of dimes. How many each coin does
he
have?
Answers
Answer:
For each coin he has 6 dimes, 12 quarters, and 9 pennies.
A rectangular garden is to be constructed so that the width is 150 ft. What are the possible values for the length of the garden if
at most 1200 ft of fencing
is to be used?
Answers
The possible values of the length of the garden is 151 ft to 450 ft. The length of the rectangle garden can vary from 151 ft to 450 ft
Given that A rectangle garden is to be constructed so that the width is 150 ft and atmost fencing can be used is 1200ft and asked to find the possible values of length of the rectangle garden.
It mean maximum value of perimeter = 1200ft
The minimum perimeter can be 2(150+151)=602ft as the length of rectangle must be greater than the bredth of rectangle
Therefore the minimum value of length of rectangle is 151 feet
The maximum perimeter is 1200ft
1200=2(150+length of rectangle)
Maximum value of the length of the rectangle=450ft
Therefore,The possible values of the length of the garden is 151 ft to 450 ft. The length of the rectangle garden can vary from 151 ft to 450 ft
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One angle in a triangle has a measure that is three times as large as the smallest angle. The measure of the
third angle is 45 degrees more than that of the smallest angle. Find the measure of the LARGEST angle.
Answer: The LARGEST angle has a measure of
Answers
Answer:
The LARGEST angle has a measure of 81°
Step-by-step explanation:
Let α be the smallest angle
β be the second angle
θ be the third angle.
• One (second) angle in a triangle has a measure that is three times as large as the smallest angle.
Then
β = 3α
• The measure of thethird angle is 45 degrees more than that of the smallest angle.
Then
θ = α + 45
• We know that the sum of the interior angles of a triangle add up to 180°
Then
α + β + θ = 180
Then
α + (3α) + (α + 45) = 180
Then
5α + 45 = 180
Then
5α = 135
Then
α = 27
_______________
β = 3α = 3 × 27 = 81
θ = α + 45 = 45 + 27 = 72
Conclusion :
The LARGEST angle has a measure of 81°
Express the following using the Roster Method.
O = {x|x∈ N and x is odd}
Answers
Step-by-step explanation:
the answer is o={3,5,79,11,13,15,17.....................}
2(2x - 5) = 3x + x - 2x What is the solution of the equation? X =
Answers
Answer:
Step-by-step explanation:
2(2x-5)=3x+x-2x
4x-10=3x+x-2x
4x-10=2x
4x-10+10=2x+10
4x=2x+10
2x=10
2/2
10/2=5
x=5
The solution to the equation 2(2x-5) = 3x + x - 2x is x = 5
Given data:
To solve the equation 2(2x - 5) = 3x + x - 2x, we will simplify and solve for x.
Step 1: Distribute the 2 to the terms inside the parentheses:
4x - 10 = 3x + x - 2x
Step 2: Combine like terms on both sides of the equation:
4x - 10 = 2x
Step 3: Subtract 2x from both sides to isolate the variable x:
4x - 2x - 10 = 0
Simplifying:
2x - 10 = 0
Step 4: Add 10 to both sides to eliminate the -10 term on the left side:
2x - 10 + 10 = 0 + 10
Simplifying:
2x = 10
Step 5: Divide both sides by 2 to solve for x:
(2x)/2 = 10/2
Simplifying:
x = 5
Hence, the solution is x = 5.
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If the groub A= {-3} then IAI equals?
Answers
The value of given set in modulus function IAI = 3.
What is termed as modulus function?A modulus function returns the magnitude of such a number regardless of its sign. It's also recognized as the absolute value function.
The modulus function, signified by |x| in mathematics, gives the modulus of such a real number x. It returns a non-negative value for x. The modulus as well as absolute value of a number too is known as the number's distance from the origin or zero.The modulus function's value is always non-negative. That unless f(x) is a modulus function, we get:
For x is positive, the value of f(x) = xFor x = 0, the value of f(x) = 0For x < 0, the value of f(x) = -xNow, as per the given question;
Groub A= {-3}
Estimate the IAI
IAI = I-3I
By the property of modulus function.
IAI = 3 (absolute value)
Therefore, the value of IAI is 3.
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(2+i)-(5-4i)
Find the difference of the following expression
Answers
Answer:
-3 + 5i
Step-by-step explanation:
We can remove the parentheses
2 + i - 5 + 4i
Collect the like terms and do the math
-3i + 5i
For runners in a race it is more desirable to have a high percentile for speed. A high percentile means a higher speed which is faster. 40% of runners ran at speeds of 7.5 miles per hour or less (slower). 60% of runners ran at speeds of 7.5 miles per hour or more (faster).
Answers
A scalar quantity, speed is defined as the size of the change in an object's or particle's location over time or the size of the change in an object's position per unit of time.
In statistics, a percentile (or centile) is a metric that expresses the value at or below which a specified percentage of observations in a collection of observations fall. The value (or score) below which 20% of the observations may be found is called the 20th percentile, for instance.
A higher percentile for speed is preferable for runners in a race. A high percentile indicates a faster, greater speed.
40% of athletes completed their runs at 7.5 mph or less (slower). 60% of athletes covered at least 7.5 miles per hour (faster).
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The temperature drops to 15 degrees below zero. What is a real world example to make 0 in this situation?
Answers
Here are the examples that combine to make zero:
Two month ago, the temperature was 15 degrees. This morning, the temperature dropped to 15 degrees below zero.
Michael has $0 in his account. He makes a purchase of $75. Later in the day, he deposits 75 in the account.
An elevator rises to the ninth floor and she then takes the elevator from the ninth floor to the ground floor.
The parking garage is located 4 floors below ground level. But, her office is 4 floors above ground level.
What are the real world examples?
In order for the examples to combine to make zero, there has to be a positive number and a negative number. A positive number is a number that is greater than zero. A negative number is a number that is less than zero.
In order for the positive and negative number to make zero, they have to be added together. Addition is determining the total value or summing two or more numbers. Addition is one of the four basic operations in mathematics.
Two month ago, the temperature was 15 degrees. This morning, the temperature dropped to 15 degrees below zero. -15 + 15 = 0
Michael has $0 in his account. He makes a purchase of $75. Later in the day, he deposits 75 in the account. - 75 + 75 = 0
An elevator rises to the ninth floor and she then takes the elevator from the ninth floor to the ground floor. + 9 - 9 = 0
The parking garage is located 4 floors below ground level. But, her office is 4 floors above ground level. = -4 + 4 = 0
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Acme Movers charges $105 plus $40 per hour to move household goods across town. Hank's Movers charges $55 per
Khour. For what lengths of time does it cost less to hire Hank's Movers?
It costs less to hire Hank's Movers for times less than
hours.
Incom
Answers
It costs less to hire Hank's Movers for times less than 7 hours.
What time would it cost less to hire Hank Movers?
The equation that can be used to represent the cost of hiring Acme movers is: $105 + $40t
The equation that can be used to represent the cost of hiring Hank's Movers : $55t
Where : t represent number of hours
The inequality sign that would be used is < less than or equal to
$55t < $105 + $40t
Combine similar terms
$55t - $40t < $105
$15t < $105
t < 105 / 15
t < 7 hours
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Somebody know what’s the endpoint and midpoint?
Answers
Answer:
The point in the middle/center of the line joining two points (also known as endpoints) is called a midpoint. Given one endpoint and a midpoint, the other midpoint can be calculated using the midpoint formula.
Step-by-step explanation:
The point in the middle/center of the line joining two points (also known as endpoints) is called a midpoint. Given one endpoint and a midpoint, the other midpoint can be calculated using the midpoint formula.
what are the two equations for 2x2−6x−9=0
Answers
Answer:
[tex]x=\frac{3\left(1+\sqrt{3}\right)}{2},\:x=\frac{3\left(1-\sqrt{3}\right)}{2}[/tex]
Step-by-step explanation:
[tex]x_{1,\:2}=\frac{-\left(-6\right)\pm \sqrt{\left(-6\right)^2-4\cdot \:2\left(-9\right)}}{2\cdot \:2} < - InsertQuadraticFormula[/tex]
[tex]x_{1,\:2}=\frac{-\left(-6\right)\pm \:6\sqrt{3}}{2\cdot \:2}[/tex]
[tex]x_1=\frac{-\left(-6\right)+6\sqrt{3}}{2\cdot \:2},\:x_2=\frac{-\left(-6\right)-6\sqrt{3}}{2\cdot \:2} < - Separate THE Solutions[/tex]
[tex]x=\frac{3\left(1+\sqrt{3}\right)}{2},\:x=\frac{3\left(1-\sqrt{3}\right)}{2}[/tex]
A toll-free consumer information line answered 105 of 120 questions in one day. What is the daily success rate of the information line?
Answers
The daily success rate of the toll-free answers is 87.5%.
What is described as a percentage?A percentage is a fraction of a whole represented as a number from zero and 100. Nothing is zero percent, everything is 100 percent, 50 per cent of everything is fifty percent, and nothing is zero percent.To calculate a percentage, divide this same portion of the total by the total and multiply by 100.Now, as per the given data;
The number of consumer information asked in one day is 120.
Total number of toll-free consumer's question answered = 105.
To find the daily success rate, determine the percentage of 105.
Let the x% of the total be 115.
Thus, x% of 120 = 105
x × 120/100 = 105
12x = 1050
x = 1050/12
x = 87.5 %
Therefore, the answer rate of the toll-free is 87.5%,
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Aisha wants to ride her bicycle 18.2 miles this week. She has already ridden 5 miles. If she rides for 4 more days, write and solve an equation which can be used to determine mm, the average number of miles she would have to ride each day to meet her goal.
Answers
The equation that could be used to determine, m, is 4m = 18.2 - 5
The average number of miles (m) is 3.3 miles to ride each day to meet her goal.
What is linear expression?
A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.
Total distance of ride Alisha wants by her bicycle (d) = 18.2 miles.
And, She has already ridden 5 miles.
She rides for 4 more days.
Now, Let the average number of miles = m
She has already ridden 5 miles.
And, She rides for 4 more days.
The number of miles she needs to ride more is
18.2 miles - 5 miles
= 13.2 miles
If m is the average number of miles she must cycle in 4 days to reach her objective,
Hence, we can formulate;
4m = 13.2
Divide both side by 4,
m = 3.3 miles
So, The equation that could be used to determine, m, is 4m = 18.2 - 5
The average number of miles is 3.3 to ride each day to meet her goal.
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find the distance between the two points in simplest radical form. (2,6) and (7,-6)
Answers
Answer:
13
Step-by-step explanation:
Use the distance formula to determine the distance between two points.
√[(x₂ - x₁)² + (y₂ - y₁)²]
Brainliest, 5 star, & thanks.
The coordinates of the vertices of △PQR are P(4, −2) , Q(6, −4) , and R(8, 0) .
The coordinates of the vertices of △P′Q′R′ are P′(−4, 3) , Q′(−6, 5) , and R′(−8, 1) .
Answers
The price of a shirt has been discounted by $20. The sale price is $25.95. What percent of the original list price is the discount?
Answers
Answer:
that's like 77% off if im reading this right
Step-by-step explanation:
Express 6 hours 28 minutes and 16 seconds in decimal form. Round your answer to two decimal places.
Answers
Answer: 6.47 hours
Step-by-step explanation:
First, you need to change your seconds into terms of minutes.
16 seconds / 60 s in a min = .266 min
Add that to your minutes:
28+.266 = 28.266 minutes
Now convert your minutes into hours
28.266 min/60 min in an hour=.47
Add that to your hours:
6+.47= 6.47 hours total
In a baseball league consisting of 13 teams, each team plays each of the other teams twice. How many games will be
played?
Answers
Answer:
156 games
Step-by-step explanation:
You want to know the total number of games when each of 13 teams plays every other team exactly twice.
GamesEach of the 13 teams will meet 12 others, for a total of 13×12 = 156 meetings.
This total counts the time team 1 meets team 2, and also the time team 2 meets team 1. In other words, this is exactly the game count we're looking for.
156 games will be played.
__
Alternate solution
Team 1 will meet teams 2 through 13, for a total of 12 games. Team 2 has already met team 1, so will need to meet teams 3 through 12 for a total of 11 games. When we count all the games for one meeting between teams, we find the count to be 12 +11 +10 +9 +... +1 = (12)(13)/2 = 78.
If the teams are to meet twice, then 2 times this number of games will be played: 2(78) = 156.
The sum of integers 1 .. n is (n)(n+1)/2.
What’s the correct answer answer asap
Answers
Answer:
The answer should be B.
Translate the quotation into symbolic form.
If you can count your money (p), you don't have a billion dollars (q). J. Paul Getty
p → q
p ∨ q
~q
q ↔ p
p ∧ q
Answers
The translated statements, in order, are:
"If you can count your money, then, you don't have a billion dollars""You can count your money or you don't have a billion dollars""You do have a billion dollars""You can count your money if and only if you don't have a billion dollars""You can count your money and you don't have a billion dollars"How to translate the symbolic form?Here we have the proposition:
p = If you can count your money.q = you don't have a billion dollars.And the symbols are:
→ = then.∨ = or~ = not↔ = if and only if ∧ = and.Then each quotation is:
p → q
"If you can count your money, then, you don't have a billion dollars"
p ∨ q
"You can count your money or you don't have a billion dollars"
~q
"You do have a billion dollars"
q ↔ p
"You can count your money if and only if you don't have a billion dollars"
p ∧ q
"You can count your money and you don't have a billion dollars"
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Answer correctly and I’ll give brainlest
Answers
Answer: division property of equality
Step-by-step explanation:
2 lines intersect. A line with points A, B, D intersects a line with points E, B, C at point B, forming 4 angles.
In the diagram, which angles are vertical angles? Select two options.
Answers
The angles that are vertical angles are:
<EBD and <ABC
<ABE and <CBD
What are Vertical Angles?When two straight lines intersect at a point, they form two pairs of angles that are directly vertically opposite each other. These pairs of angles are called the vertical angles.
Given the image below that shows two lines intersecting at point B, they form two pairs of angles that are directly vertically opposite each other, which are:
<EBD and <ABC
<ABE and <CBD
These two pairs of angles are called vertical angles.
Therefore, the angles that are vertical angles are:
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Evaluate the variable expression when a = 2 and c = −3. 2a − (c + a)2
Answers
the expression of the variable for a = 2 and c = 3. 2a − (c + a)2
2a+b^2 2a +b2
2(-3) +(-2)^2 2(-3) + (-2)
-6 +4 -6 -4
-2 -10
An expression is a set of terms combined using the operations +, -, x or ÷, for example 4 x − 3 or 5 x 2 − 3 x y + 17 . An equation is a statement with an equals sign, which states that two expressions are equal in value, for example 4 b − 2 = 6 .
Either the options are incorrect, or the problem is poorly written.
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When the chef turned the new freezer on, the temperature on the internal thermometer was 2 °C.
After breakfast had been served, the temperature had gone down by 15 °C.
What was the new temperature?
Answers
Answer: -13 °C.
Step-by-step explanation:
Form an equation in x and solve
Answers
Answer:
x+(90°-0.5x)=3x
Step-by-step explanation:
Each of the two unknown angles in the triangle is 90°-0.5x because the triangle is isosceles.
So, by the exterior angle theorem, x+(90°-0.5x)=3x.
How many subsets are there in A={x:x is letters of the alphabet}
Answers
The number of subsets formed is 67,108,864.
What is defined as the subsets?Set 1 is said to be a subset of set 2 if all of its elements are present in it. A set is a clearly defined group of numbers, alphabets, items, or any other items.
If set 1 = A,B,C and set 2 = A,B,C,D,E,F, then set 1 is a subset of set 2 because all of the elements in set 1 are also present in set 2.A subset is a subset of a larger set (another set or the same set). To symbolize a set A as a subset of a larger set B, use the set notation: A ⊆ B.The number of subsets of an n-element set is 2ⁿ.
As a result, the formula for determining the number of subsets of the a set with 'n' components is 2ⁿ.
For the given question;
A={x:x is letters of the alphabet}
Thus, the n = 26 (total letter is English alphabet).
Total subsets = 2ⁿ
Total subsets = 2²⁶ = 67,108,864.
Therefore, the total number of subsets formed by the English alphabet are 2²⁶ = 67,108,864.
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Write the mixed number 9 3/5 as an improper fraction
Answers
===========================================
Explanation:
Use the formula
a & b/c = (a*c + b)/c
So,
9 & 3/5 = (9*5+3)/5 = (45+3)/5 = 48/5
9 x 5 = 45 + 3 = 48
Your instructor makes 5 cents per minute. How much does he makes in dollars if he works for 40 hours?
Answers
Answer: $120
Step-by-step explanation:
5 * 60 (5 cents every minute with 60 minutes in a hour makes 300 cents per hour)
300 * 40 (300 cents per hour multiplied by 40 hours makes 12000 cents)
12000 / 100 (12000 cents divided by 100 since 100 cents in a dollar)
120 is the answer