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
you have earned $151.00 with coins that are $2.00 and $5.00. How many coins of each will you have if you have a total of 47 coins?
Answers
The coins are 19 and 28 each
How to calculate the number of coins ?Let x represent the first coin and let y represent the second coin
x + y= 47.....equation 1
2x + 5y= 151.......equation 2
From equation 1
x + y= 47
x= 47-y
Substitute 47-y for x in equation 2
2(47-y) + 5y= 151
94 - 2y + 5y= 151
collect the like terms
94 + 3y = 151
3y= 151 - 94
3y= 57
y= 57/3
y= 19
Substitute 19 for y in equation 1
x + y = 47
x + 19 = 47
x= 47-19
x= 28
Hence the coins are 19 and 28 each
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the sum of eleven and ten times a number is 1. What is the number?
Answers
Answer:
the number is -1
Step-by-step explanation:
11 + 10x = 1 Subtract 11 from both sides
10x = -10 Divide both sides by 10
x = -1
Check:
11 + (10 x -1) = 1
11 + (-10) = 1
-1
The value of a phone when it was purchased was $500. It loses 1/5 of its value a year. What is the value of the phone after 1 year, 2 years, and 3 years?
Answers
Answer:
$200
Step-by-step explanation:
1/5 of 500 is 100 because 5 100s equal 500. so 3 years is 300. 500-300=200
Most new jobs in the United States will be in the _____. a. manufacturing industries b. goods-producing industries c. service-producing industries d. agriculture-producing industries Please select the best answer from the choices provided A B C D
Answers
Answer:
C - service producing industries.
Step-by-step explanation:
Brainliest pls, thank you
Answer:
Option C
Step-by-step explanation:
I took this already
is it correct ?
the question is :
(2/5 ÷ 3/8) ÷ (-3/5)
solution : =
2/5 × 8/3 = 16/15. 16/15 × -3/5 = -39 / 80
if its not correct please tell how to do it.
Answers
Answer:
Step-by-step explanation:
It is correct till 16/15
But after that it is 16/15 × 5/-3 = 80/-45
simplify it to 16/-9
i need help asap. plsss give me the right answer
Answers
Answer:
x < 3
Step-by-step explain: I used quizlet
Write an inequality and then solve.
9. A freight elevator can safely hold no more
than 2200 pounds. An elevator operator must
take 60-pound boxes to a storage area. If the
operator weighs 155 pounds, how many boxes
can be safely moved at one time?
Answers
Let the number of boxes be x.
The total weight of the boxes is 60x.
Adding the operator, the total weight is 60x+155, which is no more than 2200.
[tex]60x+155 \leq 2200 \\ \\ 60x \leq 2045 \\ \\ x \leq 34.08333... \\ \\ \lfloor x \rfloor =\boxed{34}[/tex]
order of operations MC
Joshua purchased a game card for the arcade for a total of $15. He played two basketball hoop games for $2.75 each and three rounds of air hockey for $1.25 each. How much did he have left on the game card?
Answers
Answer: $5.75
Step-by-step explanation: 2.75 x 2 = 5.5 1.25 x 3 = 2.75 2.75 + 5.5 = 9.25 $15 - $9.25 = $5.75
Give the equation of the line with a slope of - 5/7 and a y intercept of 5
Answers
Answer:
[tex]y=-\frac{5}{7}x+5[/tex]
Step-by-step explanation:
The equation of a line can be written in the form of y= mx +c, where m is the slope and c is the y-intercept. This is also known as the slope-intercept form.
Identify the value of the slope, m:
Given that the slope is [tex]-\frac{5}{7}[/tex], m= [tex]-\frac{5}{7}[/tex].
Substituting the value of m into the equation:
[tex]y=-\frac{5}{7} x+c[/tex]
Identify the value of the y-intercept:
Given that the y-intercept is 5, c= 5.
Substitute c= 5:
[tex]\bf{y=-\frac{5}{7}x+5}[/tex]
Thus, the equation of the line is [tex]\bf{y=-\frac{5}{7} x+5}[/tex].
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Write an equation of the form y=a sin b x or y=a cos b x to describe the graph below.
Answers
Greetings from Brasil...
In a trigonometric function of Cosine, we have:
F(X) = ±A ± B.COS(MX + N)where
A = move the graph up or down
B = change the amplitude
M = change period
N = move the graph left or right without distorting it
According to the statement, we don't have A and N, so
F(X) = ± B.COS(MX)
According to the graph presented, we have:
B = amplitude = 2.5 = 5/2
period = π
detail that
Period = 2π/M
π = 2π/M ⇒ M = 2
As B = 5/2 and M = 2, then
F(X) = (5/2)COS(2X)(I used the cosine function, because in X = 0 Y will have a non-zero value, as we can see in the graph)
Translate this phrase into an algebraic expression.
The sum of 17 and twice Matt's score
Use the variable m to represent Matt's score.
Answers
Answer:
17 + 2 x m
Step-by-step explanation:
sum is to add and twice is to multiply by 2
Suppose you just won the state lottery, and you have a choice between receiving $4,500,000 today or a 20-year annuity of $250,000, with the first payment coming one year from today. What rate of return is built into the annuity? Disregard taxes
Answers
A 1.03% rate of return is built into the annuity.
First optionTo receive a single payment today of $4,500,000Second optionTo receive an annual payment of $250,000.Term is equal to 20 years.Let the rate of return be x%.A series of payments paid at regular intervals is known as an annuity. Regular savings account deposits, mortgage payments, insurance premiums, and pension payments are all examples of annuities. The periodicity of payment dates allows for the classification of annuities.At this rate, the present value of the annuity is $4,500,000.The present value of the first option equals the present value of the second option. $4,500,000 = $250,000[1/x + 1/x² + … + 1/x^20]Upon solving, we get approximately x is 1.03%.To learn more about annuity, visit :
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The depth of a local river averages 20 ft, which is represented as |−20|. In January, it measured 6 ft deep, or |−6|, and in July, it was 22 ft, or |−22|. What is the difference between depths in January and July?
Answers
The computation shows that the difference in depth is 16 feet
How to calculate the value?From the information, in January, it measured 6 ft deep, or |−6|, and in July, it was -22.
Therefore the difference between the depth will be:
= -6 - (-22)
= -6 + 22
= 16
Therefore, the difference in depth is 16 feet
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Identify the slope of the line. Interpret the slope in the context of this problem. Y=-2.3332x+123.98
Answers
Answer:
Slope = 2.3332
Interpretation: As increases by 1 unit, y increases by 2.332 units
Step-by-step explanation:
Equation of a line in slope-intercept form is
y = mx + b
where m = slope and b = y-intercept
Comparing y=-2.3332x+123.98 to the standard equation form we get
m = 2.3332
b = 123.98
Slope is rise/run
It tells you the change in y-value for a unit change in x-value
Here 2.332 can be interpreted to mean that as x changes by +1 value, y changes by + 2.332
A game of Blackjack or “21” is played with a regular deck of cards. The aim of the game is to have cards that add up to 21. The cards are not replaced to the deck once they have been drawn. If you draw two cards in a row, what is the probability of getting 21, when first card you get is an ace and the second card is a queen?
Answers
The probability of getting 21, when first card is an ace and the second card is a queen = 0.024133.
The term blackjack means that you get a value of 21 with only two cards.
Number of cards in a deck of cards = 52
There are 4 types of cards in a deck of cards - spades, clubs, hearts, and diamonds, out of which spades and clubs are black in colour.
Given that first card is Ace and second one is a Queen.
Odds of getting an Ace are 4/52, odds of the next being Queen is 16/51.
P(blackjack)=4×16/(52/2).
where P is used for probability .
Probability: Probability is simply how likely something is to happen. Whenever we are unsure about the outcome of an event, we can talk about the probabilities of certain outcomes. The analysis of events governed by probability is called statistics.
Probability of getting an ace followed by a queen card: 4/52 * 16/51 = 0.024133.
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If you have only $50, can you afford to buy a pair of shoes marked $69.99?
Answers
What is the summative product of B4=MY when B=M to the 2nd power times the Y? Explain how you got the answer.
Answers
The summative product of B⁴ + [tex]M^{y}[/tex] is; [tex]M^{8y} + M^{y}[/tex]
How to use Laws of Exponents?We are given the equation as;
B⁴ + [tex]M^{y}[/tex]
Now, we are further told that;
B = [tex]M^{2y}[/tex]
Thus, we have our original expression as;
[tex](M^{2y})^{4}[/tex] = [tex]M^{y}[/tex]
According to laws of exponents, we know that;
When multiplying like bases, the same bases are kept and we add the exponents. When raising a base with a power to another power, retain the base the same and multiply the exponents. When dividing like bases, keep the base the same and subtract the denominator exponent from the numerator exponent.Thus; (x²)³ = x²*³ = x⁶
Applying that to our expression means we now have;
[tex]M^{8y} + M^{y}[/tex]
Thus, the summative product of B⁴ + [tex]M^{y}[/tex] is; [tex]M^{8y} + M^{y}[/tex]
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Answer:
wtfStep-by-step explanation:
if you are given a number x and you subtract a number from it. under what circumstance will the answer be negative
Answers
the number x, you must deduct another number from it , conditions will the response be unfavorable,
This is a Tutor Verified Response.
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In an expression, a positive number is subtracted from two other integers. If the value of the negative number is higher than that of the positive number, then the expression's value will be considered negative. Additionally, according to the fundamental rule of integers, the number's sign-bearer must always have a higher value.
For instance,
1. 2 - 3 = -1
2. 10 + (- 8) + (- 11) = -9
3. -6 + 3 = -3
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Jessica is putting money into a checking account. Let y represent the total amount of money in the account (in dollars). Let x represent the number of weeks Jessica has been adding money. Suppose that x and y are related by the equation =+55030xy.
Answers
After differentiating, the amount when x=0 yields starting amount,
300 dollars.
What is diffrentiation?
A technique for determining a function's derivative is differentiation.A technique for determining a function's derivative is differentiation. Mathematicians use a procedure called differentiation to determine a function's instantaneous rate of variation based on a particular variables. The most typical illustration is velocity, which is the rate at which a distance changes in relation to time.In mathematics, differentiation is used to determine change rates.Differentiating the given equation with respect to x,
Given equation,
y= 55x+ 300
[tex]\frac{dy}{dx} =\frac{d(55x+300)}{dx} = 55+0 =$55[/tex] dollars.
The amount when x=0 yields starting amount,
y=55(0)+300=300
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OC
Question B
Jim and Wendy Scott's home lot is illustrated here.
The Scotts which to hire a lawn service to cut their
lawn. M&M Lawn Service charges $0.03 per square
yard of lawn. How much will it cost for the Scotts to
have their lawn cut?
K
24
ft
Pool
$6,480
17
-200 ft-
mbell 40 ft
Patio
Shed
10 ft
Drive 30 ft
10 ft
10 ft
House-50 ft-25 ft 100 ft
8 ft
Answers
$ 58.392 will it cost for the area of Scotts to have their lawn cut.
What does area in math mean?
Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies. Consider your square as being composed of smaller unit squares.Area of pool = πr² = π(12)²= 452.4 ft²
area of house = 25 × 50 = 1250 ft²
area of ratio = 40 × 10 = 400 ft²
area of drive = 30 × 10 = 300 ft²
area of shed = 10 × 8 = 80 ft²²
total are all combined for above will be = 2482.4 ft²
total area of plot = 200 × 100 = 20000 ft²
lawn area = 20000 - 2482.4 = 17517.6 ft²
on converting ft² into yard²
lawn area = 17517.6 ft² = 1946.4 yard²
cost of each yard² = $0.03
then total cost = 1946.4 × $0.03
= $ 58.392
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A perpendicular bisector of DC is AB and a perpendicular bisector of AB is DC. the intersection of AB and DC is at E. Which equation is true?
EB =CD
AE= DE
DE = CE
CD= CE
AB=CD
Answers
Answer: DE = CE
Step-by-step explanation: AB is a continuous line so the distance from A to E could be different than the distance from D to E.
DE = CE is true.
A perpendicular bisector is a line that divides another line into two equal parts and is also perpendicular to it.
Here, we are given that AB is the perpendicular bisector of DC and DC is a perpendicular bisector of AB.
This means that AB and DC are the perpendicular bisectors of each other at the point of intersection, that is, E.
Now, since AB bisects DC at point E
⇒ DE = CE
and similarly, DC bisects AB
⇒ AE = BE
Apart from these two equalities, we cannot infer anything else from the given information.
Thus, out of the given options, we can see that only option 3, that is, DE = CE is true.
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2/9=?/18=?/27 help pleace thank u so much
Answers
Answer:Not there yet
Step-by-step explanation: Think about it your close 2/9 = nothing why do numbers determine our grades so don't answer if anything flunk out of school
What is the value of c in the equation below?
Answers
Answer:
1/4
Step-by-step explanation:
[tex]x^y \ctimes x^z = x^{y + z}[/tex]
[tex]2^{-4} \cdot 2^2 = 2^{-4 + 2} = 2^{-2} = \frac{1}{2^2} = \frac{1}{4}[/tex]
Complete the table with the number of sit-ups you need to do on Sunday so that the mean number of sit-ups per day is 80.
Monday: 100
Tuesday: 80
Wednesday: 60
Thursday: 70
Friday: 90
Saturday: 100
Sunday: X
If correct you get brainliest!
Answers
4x 2x - 2 = 2x
What does “X” equal?
Answers
Answer: x=0.5
Step-by-step explanation:
4x+2x - 2 = 2x
6x-2=2x
6x=2x+2
4x=2
x=0.5
1 foot = 0.305 meters to convert 20 meters into feet.
20 meters = feet
Answers
20 meters equal to 65.6168 feet by unit conversion.
What is unit conversion?
The process of translating measurements of a given quantity between different units, frequently using mathematical conversion factors that change the measurement of the quantity without changing its effects, is known as unit conversion.The specific circumstances or the desired result dictate the conversion process. This may be governed by regulation, contract, set of technical requirements, or other publicly available standards.Certain measurements must be accurately converted from one system to another without compromising the accuracy of both the original measurement.Each conversion factor is chosen based on the relationship here between particular pair of original units and a particular pair of target units.Using the given information about unit conversion, that,
1 foot = 0.305 meters
1 meter= (1/0.305) feet
20 meters = (1/0.305)*20 = 65.6168 feet
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SOMEONE HELP ME ON THIS SIMPLE QUESTION
Answers
Step-by-step explanation:
1. 10+m= -9 ANSWER: M= -19
subtract 10 from both sides (m=−9−10)
Subtract 10 from −9 to get −19.
2. -12x= 60 ANSWER: X= -5
Divided both sides by negative 12 (x= 60 over -12)
Divide 60 by −12 to get −5.
3. v/20 = 7 ANSWER: V= 140
Multiply both sides by 20 (v=7×20)
Multiply 7 and 20 to get 140.
(Hopefully this helps)
Wha is a risk of having a YOLO mindset when making financial
decision
Answers
Answer:
You either lose everything or gain everything (losing is more probable :) )
Step-by-step explanation:
Which number has a 6 that is 1/10 the value of the 6 in 527.6?
A. 1432.986
B. 982.46
C. 54.6
D. 36
Answers
The number that has a 6 that is 1/10 the value of the 6 in 527.6 is B. 982.46.
How to illustrate the information?It should be noted that we are to simply find the place value of the numbers.
In 527.6, the place value is 1/10.
On the other hand, in 982.46, the place value is 1/100.
Therefore, the number that has a 6 that is 1/10 the value of the 6 in 527.6 is 982.46.
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The average age of 8 men, 7 women and 1 boy is 45 years, that of 8 men being 48 years and of 7 women
being 46 years, determine the age of the boy.
Answers
The age of the boy is 14 years.
Given average age of 8 men, 7 women and 1 boy is 45 years.
Averages are used to condense a vast number of data points into a single value. It is a visual depiction of all the data set's available numbers. By adding up all the data values and dividing them by the total number of data points, the average is calculated.
age of 8 men is 48 years.
age of 7 women is 46 years.
age of the boy is = ?
= (45 ×16 ₋ 48 × 8 ₋ 7 × 46)
= (720 ₋ 324 ₋ 322)
= 14 years.
Hence the age of the boy is 14 years.
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