Exponential function f is represented by the table. x -2 -1 0 1 2 f(x) -46 -22 -10 -4 -1 Function g is represented by the equation. Which statement correctly compares the two functions on the interval [-1, 2]? A. Both functions are increasing, but function f increases at a faster average rate. B. Only function f is increasing, but both functions are negative. C. Both functions are increasing, but function g increases at a faster average rate. D. Only function f is increasing, and only function f is negative.
Answers
Both functions are increasing, but function g increases at a faster average rate.
The correct option is (C)
What is an increasing function?If the slope of a function is continuously increasing or constant in an interval, the function is known as an increasing function.
let f(x) = [tex]ab^{x} +c[/tex] and x=0 , f(0)= -10
-10=a+c
Now,
f(x) = -33/5*[tex](\frac{1}{11} )^{x}[/tex] - 17/5
f '(x)>0
So, x is increasing function.
g(x) = -18/3*[tex](\frac{1}{11} )^{x}[/tex] +2
g'(x) =-18[tex](\frac{1}{3} )^{x}[/tex]ln(1/3)
ln 1/3<0
So, g'(x)>0
So, g(x) is an increasing function.
For any x ∈ f(x) and x ∈ g(x)
Since, g increases at a faster rate.
Hence, Both functions are increasing, but function g increases at a faster.
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Related Questions
one phone company charged 65% of its normal long-distance rate after 5 p.m. A day-rate long-distance call from Houston to Chicago costs 20 cents per minute. How much is an 11-minute call between these two cities after 5 p.m. ?
Answers
The cost of 11-minute call between these two cities after 5 p.m is: 142.
CostGiven:
Charges for long distance=65% or .65
Cost=20 cents per minutes
Number of call minutes=11 minutes
Hence:
Cost =20 cents ×11 minutes times 0.65
Cost =143 cents
Therefore the cost of 11-minute call between these two cities after 5 p.m is: 142.
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Which expressions are equivalent to the given equation. Logarithmic form
Answers
The expression that is equivalent to the given logarithm equation is log₄ 1 / 4 + log₄ x²
How to solve logarithm?log₄ (1 / 4 x²)
Using logarithm law, the logarithm can be express as follows;
using logarithm law,
Therefore, the expression that is equivalent to the given logarithm equation is as follows:
using addition law for logarithm,
log₄ (1 / 4 x²) = log₄ 1 / 4 + log₄ x²
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Which expression is the simplest form of - (4x³ + x²) + 2 (x³ − 3x²)?
OA. -2³ - 7x²
OB.
B. -2x³-5x2
O C.-6x³ - 2x²
OD. -6x³6x²
Answers
The expression which is the simplest form of; - (4x³ + x²) + 2 (x³ − 3x²) is; -2x³ -7x².
What is the simplest form of the expression?The expression given in the task content whose simplest form is to be determined is;
- (4x³ + x²) + 2 (x³ − 3x²)
Hence, upon opening up the parentheses, it follows that;
-4x³ - x² +2x³ -6x²
Upon collection and summing up of like terms; -2x³ -7x².
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A fire fighter sees a woman trapped in the building 81 feet up from the bottom floor. If the firetruck is parked 41 feet away from the bottom of the building, at what angle of elevation, to the nearest degree, shut the fire fighter extend the ladder to reach the woman?
Answers
63 Degrees
Steps:
Use the Pythagorean Theorem to find the missing side.
a^2 + b^2 = c^2
c = SQRT(a^2 + b^2)
c = SQRT(81^2 + 41^2)
c = SQRT(8242)
c = 90.785
ASIN is the inverse of sine.
Please help!
Julie wants to show that a quadrilateral with vertices J(2, 3), K(2,7), L(-2,7), M(-2,3) is a square. Using the distance formula, what should she find the length of each side to be?
8
4
3
2
Answers
Answer:
4 is the answer
Answer:
4 is the answer I believe
what is the slope of the line through the points (-2,-1) and (8,-3)
Answers
Answer:
Step-by-step explanation:
Using slope m = y_2-y_1/x_2-x_1 to find the solution slope that passes through those two-point.
Point-slope form into y-intercept form.
Answer:
For finding slope
we have the formula
m = y2 - y1/ x2 - x1
x1 = (-2)
x2. = ( 8)
y1. = (-1)
y2 =(-3)
putting the value of this in the formula we get,
m = (-3)-(-1)/8-(-2)
m = (-3+1)/8 + 2.
m = (-2)/10
m = (-1)/5.
m = (-1)/5
What's x ? find the indicated side of the right triangle
Answers
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{x = 6}[/tex]
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Given: [tex]\textsf{The image provided with 2 angles and one side}[/tex]
Find: [tex]\textsf{Solve for the unknown side of x}[/tex]
Solution: In order to determine the length of x we need to use some trigonometric functions. Using Soh Cah Toa we can see that we can either use 30 degrees or 60 degrees. We will stick to 60 and we can see that the opposite side is 3 and the hypotenuse is x meaning that we need to use sin. Plug in the values and solve for the unknown.
Plug in the values
[tex]\textsf{sin(30) = }\frac{\textsf{opposite}}{\textsf{hypotenuse}}[/tex][tex]\textsf{sin(30) = }\frac{\textsf{3}}{\textsf{x}}[/tex]Multiply both sides by x
[tex]\textsf{sin(30) * x = }\frac{\textsf{3}}{\textsf{x}}\textsf{ * x}[/tex][tex]\textsf{sin(30) * x = 3}[/tex]Divide both sides by sin(30)
[tex]\textsf{sin(30) * x}*\frac{1}{\textsf{sin(30)}}\textsf{ = 3}}*\frac{1}{\textsf{sin(30)}}[/tex][tex]\textsf{x = 3}}*\frac{1}{\textsf{sin(30)}}[/tex]Simplify
[tex]\textsf{x = 3}}*\frac{1}{\textsf{0.5}}[/tex][tex]\textsf{x = 6}[/tex]Therefore, the value of the unknown variable x is 6 units.
Which is the graph of f(x) = √x?
Answers
Look at the attached image.
a cuboid has length 18.5 cm, width 9.4 cm a height 6.2 cm. Work out the area of the cuboid
Answers
Answer:
693.76 cm²Step-by-step explanation:
a cuboid has length 18.5 cm, width 9.4 cm a height 6.2 cm. Work out the area of the cuboid
assuming you are looking for thr surface area
Surface Area of a Cuboid ·
TSA = 2 (lw + wh + hl)
2*( 18.5 * 9.4 + 9.4 * 6.2 + 6.2 * 18.5) = (remember PEMDAS)
2 * 346.88 =
693.76 cm²
3.14(a2 + ab) when a = 4 and b = 3
Answers
Step-by-step explanation:
how does the picture fit into this question ?
I guess you mean
(a² + ab)
when a = 4 and b = 3. then we simply replace the variable names by the actual values and calculate :
4² + 4×3 = 16 + 12 = 28
.
now to the picture :
i am not sure what the requested result of procedure is.
so, I am just going to simplify the expression :
(log(25) - log(4)) / (log(55) - 1/2 × log(2)
remember the rules of the logarithm :
log(a) - log(b) = log(a/b)
k × log(a) = log(a^k)
a^(1/2) = sqrt(a) (the square root of a)
I assume we are using the logarithm to the base of 10.
so, we have here
log(25/4) / log(55/sqrt(2)) =
= 0.795880017... / 1.589847692... = 0.500601423...
What is breaking probation?
Answers
Answer:
a probation violation occurs when someone who has already been sentenced for a crime breaks the terms or conditions of that probation
Which equation represents this number sentence?
Two more than one-third of a number is 8
Answers
Answer:
Step-by-step explanation:
One - third = 1/3
then:
one third of a number = a*1/3 = a/3
Then the equation that represents this sentence is:
2 + a/3 = 8
process:
a/3 = 8 - 2
a/3 = 6
a = 6*3
a = 18
Check:
2 + 18/3 = 8
2 + 6 = 8
Select the correct answer. The table represents a proportional relationship. x y 11 2 22 4 33 6 The graph represents another proportional relationship. Which equation represents the lower unit rate of these two relationships? A. B. C. D. Reset Next
Answers
The equation which represents the lower unit rate of these two relationships is y = 2x/11.
How to determine the equation?In order to determine the equation which represents the lower unit rate of these two relationships, we would find the slope of the given points.
Mathematically, the slope of a straight line can be calculated by using this formula;
[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]
Substituting the given parameters into the formula, we have;
[tex]Slope = \frac{6\;-\;4}{33\;-\;22}\\\\Slope = \frac{2}{11}[/tex]
Slope = 2/11.
From the standard equation, we have:
y = mx + c
y = 2x/11 + 0
y = 2x/11.
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f is an even function, g is an even function. a=
Answers
Answer:
a=6 it's even
Step-by-step explanation:
please mark me as brainlest
Answer:
A= 4
B= 3
i got it right.
What is the solution to the equation below? Round your answer to two
decimal places.
log2(2x-1) = 3
A. x=4
O B. x= 1/2
732
O c. x = 2/
O D. x = 5
Answers
Answer:
D. x=5
The answer is x=4.50 then it is rounded off to 5. So, the answer is 5.
Step-by-step explanation:
Find the domain of the inequality:[tex]2x-1\geq 0[/tex]
Rearrange terms to the left side of the equation:[tex]2x\geq 1[/tex]
Divide both sides of the inequality by the coefficient of the variable:
=> [tex]x\geq \frac{1}{2}[/tex]
The domain of the inequality is:[tex]x\geq \frac{1}{2}[/tex]
Convert logarithm to exponential form:[tex]2^{3}=2x-1[/tex]
Calculate the power:[tex]8=2x-1[/tex]
Rearrange terms to the left side of the equation:[tex]-2x= -8-1[/tex]
Calculate:[tex]-2x=-9[/tex]
Divide both sides of the equation by the coefficient of the variable:[tex]x=\frac{-9}{-2}[/tex]
=> [tex]x=\frac{9}{2}[/tex]
=>[tex]x=4.5\\[/tex]
Round the number: [tex]x=4.50[/tex]
Answer: [tex]x=4.50[/tex]
=> [tex]x=5[/tex]
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Answer:
x = 9/2
Step-by-step explanation:
The volume of a can of Pepsi is 0.33liter. There are 12 cans in 1 carton
What is the volume of 5 cartons of Pepsi?
Answers
Answer:
19 liters 800 milliliters
Step-by-step explanation:
0.33 * 12 * 5 = 19.8 liters
determining height from a shadow measuring 88 meter
Answers
Answer:
Height = 132 mt
Step-by-step explanation:
Shadow lengths are proportional to the height of the object.
So, multiply the length of the tree's shadow by your height.
If you are 5 feet (1.5 meters) tall, and the length of shadow is 88 meters long,
Multiply them together: 1.5 x 88 = 132 mt.
Hence, Height = 132 mt.
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A media personality argues that global temperatures are not rising, because every year an increase is reported, such as 0.09 degrees C. The difference from the previous year is less than the margin of error of about 0.13 degrees C, so that difference should be ignored. What is the best counterargument?
The difference is only 0.04, but that is still a significant change.
The margin of error is quite small compared to the change year over year, so it is a significant issue.
The change of 0.09 is not a lot and thus should be ignored.
The margin of error is larger than the increase, so we should consider it an issue of just extra information and thus can be ignored.
Answers
The best counterargument: the margin of error is quite small compared to the change year over year, so it is a significant issue.
What is Margin error?In statistics, the margin of error refers to half the confidence interval. It measures how much of a random sample does not fall within the confidence interval as the number of samples taken increases indefinitely.
As, the temperature rises by 0.09 degree.
So, the difference between margin error and increase is higher which is
= 0.13- 0.09
=0.04
Hence, The margin of error is quite small compared to the change year over year, so it is a significant issue.
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These expressions represent four numbers. The value of the median of the expressions is 12.
Answers
Answer:
Try retyping ,which expressions ..?? Maybe it didn't come out
Answer:
15
Step-by-step explanation:
Actual Question:
These expressions represent four numbers. The value of the median of the expressions is 12.
x , 2x, 6x, 11x
Work out the value of the mean of the expressions.
_____________________________________________
See the attachment for steps.
6. Divide:
6x²+7x-2/3x-1
using Long Division.
Answers
Step-by-step explanation:
3x-1) 6x^2 + 7x -2 ( 2x+3
-6x^2 -2x
+
0 + 9x -2
- 9x -3
+
1
Find the value of x for which m||n
Answers
Answer:
x = 61
Step-by-step explanation:
Alternate exterior angles must be congruent for the lines to be parallel.
3x - 43 = 2x + 18
x = 61
Find equation in slope intercept form of the line passing through the points with given coordinates (-4,-2), (-2,2)
Answers
Answer:
y = 2x + 6
Step-by-step explanation:
We are given that a line runs through the points (-4,-2) and (-2,2).
We want to write the equation of this line in slope-intercept form.
Slope-intercept form is written as y=mx+b, where m is the slope and b is the value of y at the y intercept, hence the name.
First, we need to find the slope of the line.
The slope can be found using the formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points.
Even though we have two points, let's label the values of the points to avoid confusion & mistakes.
[tex]x_1=-4\\y_1=-2\\x_2=-2\\y_2=2[/tex]
Now let's find the slope (remember: the formula has subtraction):
m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
m=[tex]\frac{2--2}{-2--4}[/tex]
This can be simplified:
m=[tex]\frac{2+2}{-2+4}[/tex]
Add the numbers together.
m=[tex]\frac{4}{2}[/tex]
Divide.
m = 2
The slope of the line is 2.
We can substitute this into the equation for m.
Here is the equation of the line so far:
y = 2x + b
We now need to find b.
As the equation passes through both (-4, -2) and (-2, 2), we can use either one of them to help solve for b.
Taking (-4, -2) for instance:
Substitute -4 as x and -2 as y in the equation we have.
-2 = 2(-4) + b
Multiply.
-2 = -8 + b
Add 8 to both sides.
6 = b
Substitute 6 as b into the equation.
y = 2x + 6
Topic: finding the equation of the line (slope-intercept form)
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Divide.
74.48 ÷ 7.6
Enter your answer as a decimal in the box.
Answers
(3/7 * (- 5/8)) + (1/3 * 5/6) + |- 1/2 - 1/5|
Answers
Answer:
Exact Form:
1789/2520
Decimal Form:
0.70992063
You are choosing between two different cell phone plans. The first plan charges a rate of
21 cents per minute. The second plan charges a monthly fee of $44.95 plus 11 cents per
minute. How many minutes would you have to use in a month in order for the second
plan to be preferable?
Answers
Answer:
at least 450 minutes
Step-by-step explanation:
Find an expression for the cost of each plan as a function of the number of minutes. Set the expressions equal to each other, and solve for the number of minutes.
Let x = number of minutes.
First plan:
cost (in dollars) = 0.21x
Second plan:
cost (in dollars) = 0.11x + 44.95
Set the expressions equal:
0.21x = 0.11x + 44.95
Subtract 0.11x from both sides.
0.1x = 44.95
Divide both sides by 0.1
x = 44.95/0.1
x = 449.5
Since you cannot have a fraction of a minute, the answer is 450 minutes.
Write an explicit rule to represent the sequence:
20, 24, 28, 32, 36,...
a) f(n)=4n+20
b) f(n)=4n+16
c) f(n)=4n+24
d) f(n)=4n+12
Answers
Answer:
b)f(n)=4n+16
Step-by-step explanation:
if n=1
substitute 1 for n in the equation
f(1)=4(1)+16
=4+16
=20
f(2)=4(2)+16
=8+16
=24
And so on
Help I have no idea to do this!! I’m stuck!
Answers
Answer: 7
Step-by-step explanation:
[tex]A \cap C[/tex] denotes the intersection of A and C, or in other words, how many elements are shared between them.
The number of elements is 2 + 5 = 7
hope that helps !
URGENT + 20 Points! The regression equation for water being poured into a large, cone-shaped cistern is In(volume) = -1.327 +2.993 In(Time). What is the predicted volume for a time of 12 seconds?
- There is a line above "(volume)"
1.810 cm3
6.110 cm3
34.589 cm3
450.485 cm3
Answers
The predicted volume for a time of 12 seconds of the large, cone-shaped cistern is; V = 450.485 cm³
How to Solve Regression Equations?We are given the regression equation;
In V = -1.327 + 2.993 In T
Where;
V is volume
T is time
At T = 12, we have;
In V = -1.327 + 2.993 In 12
In V = -1.327 + 7.4373
In V = 6.1103
V = e^(6.1103)
V = 450.485 cm³
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The domain of (fg)(x) consists of the numbers x that are in the domains of both f and g.
Answers
The statement "The domain of (fg)(x) consists of the numbers x that are in the domains of both f and g" is FALSE.
Domain is the values of x in the function represented by y=f(x), for which y exists.
THe given statement is "The domain of (fg)(x) consists of the numbers x that are in the domains of both f and g".
Now we assume the [tex]g(x)=x+2[/tex] and [tex]f(x)=\frac{1}{x-6}[/tex]
So here since g(x) is a polynomial function so it exists for all real x.
[tex]f(x)=\frac{1}{x-6}[/tex] does not exists when [tex]x=6[/tex], so the domain of f(x) is given by all real x except 6.
Now,
[tex](fg)(x)=f(g(x))=f(x+2)=\frac{1}{(x+2)-6}=\frac{1}{x-4}[/tex]
So now (fg)(x) does not exists when x=4, the domain of (fg)(x) consists of all real value of x except 4.
But domain of both f(x) and g(x) consists of the value x=4.
Hence the statement is not TRUE universarily.
Thus the given statement about the composition of function is FALSE.
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Plss helppppppppppppppp
Answers
Answer: [tex]-\frac{3}{2} \leq x < 5[/tex]
Step-by-step explanation:
We can split this into two inequalities, namely [tex]2x-3 < x+2[/tex] and [tex]x+2 \leq 3x+5[/tex].
Solving the first inequality,
[tex]2x-3 < x+2\\\\x-3 < 2\\\\x < 5[/tex]
Solving the second inequality,
[tex]x+2 \leq 3x+5\\\\2 \leq 2x+5\\\\-3 \leq 2x\\\\-\frac{3}{2} \leq x[/tex]
So, the solution is [tex]-\frac{3}{2} \leq x < 5[/tex]
