A quadratic function and an exponential function are graphed below. How do the decay rates of the functions compare over the interval
The exponential function decays at one-half the rate of the quadratic function.
The exponential function decays at the same rate as the quadratic function.
The exponential function decays at two-thirds the rate of the quadratic function.
The exponential function decays at three-fourths the rate of the quadratic function.
Answers
The exponential function decays at three-fourths the rate of the quadratic function.
The given inequality is -2≤x≤0.
We need to determine how do the decay rates of the functions compare over the interval.
What is the quadratic function?A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of the second degree.
We calculate the average slope of each graph in the indicated interval, the slope can be calculated as [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex].
Now, for the exponential function:
[tex]m_{c} =\frac{4-1}{-2-0} =\frac{3}{-2}[/tex]
For the quadratic function:
[tex]m_{q} =\frac{4-0}{-2-0} =\frac{4}{-2}=-2[/tex]
Now, the ratio of both average slopes is[tex]\frac{m_{c} }{m_{q}} =\frac{\frac{3}{-2} }{-2} =\frac{3}{4}[/tex].
Therefore, the exponential function decays at three-fourths the rate of the quadratic function.
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Related Questions
If f(x)=x+2 and g(x)=x2+1 find:a. f(g(x)) b. g(f(x))
Answers
Answer:
Step-by-step explanation:
Answer:
x² + 3 and x² + 4x + 5
Step-by-step explanation:
(a)
to find f(g(x)) substitute x = g(x) into f(x)
f(g(x))
= f(x² + 1)
= x² + 1 + 2
= x² + 3
(b)
to find g(f(x)) substitute x = f(x) into g(x)
g(f(x))
= g(x + 2)
= (x + 2)² + 1 ← expand factor using FOIL
= x² + 4x + 4 + 1
= x² + 4x + 5
Prove: An odd number squared is
an odd number.
(2n + 1)² = [?]n² + [ ]n +
=
[](2n² + 2n) + [ ]
= an odd
Answers
Considering the result of the expression of the square of the sum, 2(2n² + 2) is always an even number, then when 1 is added it will always be an odd number.
What is the square of the sum notable product?It is given as follows:
(a + b)² = a² + 2ab + b².
In this problem, the expression is:
(2n + 1)² = (2n)² + 2(2n)(1) + 1²
= 4n² + 4n + 1
= 2(2n² + 2) + 1
The term 2(2n² + 2) will always be even(multiplication by 2), and when 1 is added to an even number it will always be odd, hence it is proved that an odd number squared is an odd number.
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What are the solutions to the quadratic equation below?
x²-2x-168 =0
Answers
Answer:
x= 14, –12
Step-by-step explanation:
The given question might make you believe that it's difficult due to it's frightening digit (168) but in fact in you use the following methods, it's going to be a pieces of cake.
the delta formula:
Δ=b²–4ac===> (–2)²–4(1)(–168)=676
[tex]x 1 = \frac{ - ( - 2) + \sqrt{676} }{2} = 14 [/tex]
[tex]x2 = \frac{ - ( - 2) - \sqrt{676} }{2} = - 12[/tex]
well this can be on of the methods and the other one is
The full square formula:
[tex]x ^{2} - 2x - 168 = 0 \\ {x}^{2} - 2x = 168[/tex]
[/tex]
now what you need to do is to put this on both side of the equation (½b)²=1
[tex] {x}^{2} - 2x + 1 = 168 + 1 \\ {(x - 1)}^{2} = 169 \\ x - 1 = 13 = = > x = 14 \\ x - 1 = - 13 = = = > x = - 12[/tex]
A $1,000.00 bond at 85 1/4 % pays 6.8 % annual interest. Calculate cost of bond.
Answers
Based on the par value of the bond and the percentage it was issued at, the cost of the bond is $852.50.
What is the cost of the bond?The current cost of the bond is the present value of the bond's cashflows and its par value.
This is taken into account when the bond is issued at a certain percentage which in this case is 85 ¹/₄%.
The cost of the bond is:
= 1,000 x 85 ¹/₄%
= $852.50
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Simplify this expression:
12a−8−5a+12
Answers
12a - 8 -5a + 12
arranging like terms
12a - 5a - 8 + 12
a ( 12-5) - 8 - 12
a(7) - 4(2 - 3)
a(7) -4(-1)
a(7) + 4
7a + 4
simplifing the expressions
Answer:
12a-5a-8+12
=(12-5)a+4
=7a+4
What is the value of x in the figure below? In this diagram, AABD ~ ACAD.
Answers
The value of x in the right angle triangle is 45 / 4 units
How to find the side of a right triangle?AB² = 20² - 15²
AB = √400 - 225
AB = √175
AB = √175 units
Hence, using similarity ratio,
x / 15 = 15 / 20
cross multiply
20x = 225
x = 225 / 20
x = 45 / 4
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HELP ASAP!!!
At which values of x does the graph of the function F(x) have a vertical asymptote? Check all that apply. x = -8 x = 4 x = 3 x = -3 x = 8 x = -4
Answers
Answer:
A,E
Step-by-step explanation:
Answer:
x = 3
x = -8
Step-by-step explanation:
Please help me answer this question
Answers
Answer:
Z = sin(xy)
[tex]\frac{1}{y} \times \frac{\partial Z}{\partial x} =\cos \left( xy\right) =\frac{1}{x} \times \frac{\partial Z}{\partial y}[/tex]
I need all of these please
Answers
Answer:
second answer is 120
firsr answer is 25
1) (625/5) * 0.2
= (625/5) * 0.2
= 125 * 0.2
=> 25
2) 83 + (-85)
= 83 + (-85)
= 83 + -85
=> -2
3) 150/-5 * (-4)
= 150/-5 * (-4)
= -30 * -4
=> 120
4) (-34) + (-255)
= (-34) + (-255)
= -34 + -255
=> -289
5) 80 - (-22)
= 80 - (-22)
= 80 + 22
=> 102
6) 28 - (-65)
= 28 - (-65)
= 28 + 65
=> 93
7) -555/-5 * (-6)
= -555/-5 * (-6)
= 111 * -6
=> -666
8) 28 - (-26)
= 28 - (-26)
= 28 + 26
=> 54
9) -3 * 5
= -3 * 5
= -(3 * 5)
=> -15
10) [-19 - (-20) - (-34)] / (-6)
= [-19 - (-20) - (-34)] / (-6)
= [-19 + 20 + 34] / (-6)
= [1 + 34] / -6
= 35/-6
=> 5.83
11) -424/4
= -424/4
=> -106
12) [-18 - (-66) - 22] * 2
= [-18 - (-66) - 22] * 2
= [-18 + 66 - 22] * 2
= 26 * 2
=> 52
13) 19 - 23
= 19 - 23
=> -4
14) -61 - (-21)
= -61 - (-21)
= -61 + 21
=> -40
15) (-72/9) + (-64/8) + (-44/11)
= (-72/9) + (-64/8) + (-44/11)
= -8 + -8 + -4
= -16 + -4
=> -20
16) (16 - 21 + 34) / (-8)
= (16 - 21 + 34) / (-8)
= (29) / (-8)
= 29/-8
=> 3.625
The graph of a function is shown on the coordinate plane below.
Between which two values of x is the function nonlinear and increasing?
A -5 and -3
B -3 and 1
C 1 and 4
D 4 and 6
Answers
The answer to this question is choice B
5
The recursive formula for a geometric sequence is given below. What is the third term in the sequence?
f(1) = 2
f(n) = 3f(n − 1)
-
OA. 18
OB. 54
OC. 162
OD. 12
Reset
Submit
Answers
f(2) = 3f(1) = 3(2) = 6
f(3) = 3f(2) = 3(6) = 18 (A)
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[tex] \: \: [/tex]
A. 18[tex] \: \: [/tex]
[tex]\Large{ \boxed{ \tt{ \blue{S}}}}\Large{ \boxed{ \tt{ \pink{O}}}}\Large{ \boxed{ \tt{ \green{L}}}}\Large{ \boxed{ \tt{ \purple{U}}}}\Large{ \boxed{ \tt{ \red{T}}}}\Large{ \boxed{ \tt{ \pink{I}}}}\Large{ \boxed{ \tt{ \blue{O}}}}\Large{ \boxed{ \tt{ \pink{N}}}}[/tex]
[tex] \: \: [/tex]
[tex] \mathtt{f(1) = 2}[/tex][tex] \tt{f(2) \: = \: 3f \: (1) \: = \: 3(2) \: = \: 6}[/tex][tex] \tt{f(3) \: = \: 3f(2) \: = \: 3(6) \: = \: 18}[/tex][tex]\color{pink}─────────────────────────────────────[/tex]
keep learning
the data below shows the number of workers employed in the various section s of each a construction company in the Lagos
Carpenter 24
plumber 12
labourers 27
plasterers 15
painters 9
Messengers 3
bricklayers 18
if the Worker is retrenched, what is the probability that he is a plumber or a plasterer?
Answers
If the Worker is retrenched, the probability that he is a plumber or a plasterer will be 0.0152.
What is probability?The chances of an event occurring are defined by probability. Probability has several uses in games, in business to create probability-based forecasts,
The probability that the employee is a plumber;
[tex]\rm P(plumber)= \frac{No \ of \ plumber}{Total \ number \ of \ employ} \\\\ P(plumber)=\frac{12}{108} \\\\\ P(plumber)= 0.11[/tex]
The probability that the employee is a plasterer;
[tex]\rm P(plasterers )= \frac{No \ of \ plasterers }{Total \ number \ of \ employ} \\\\ P(plasterers )=\frac{15}{108} \\\\\ P(plasterers )= 0.13[/tex]
The probability that he is a plumber or a plasterer:
P = 0.13 × 0.11
P= 0.0152
Hence, if the worker is retrenched, the probability that he is a plumber or a plasterer will be 0.0152.
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Maria expanded the following square as follows: (x+3)² =x²+9, is this correct?
Answers
Answer:
x² + 6x + 9
Explanation:
[tex]\sf = \left(x+3\right)^2[/tex]
Use perfect square formula: (a + b)² = a² + 2ab + b²
[tex]= \sf x^2 + 2(x) (3) + 3^2[/tex]
simplify the following
[tex]= \sf x^2 + 6x +9[/tex]
Hence Maria is not correct. The correct answer is x² + 6x + 9.
PLEASEEEEEEE PLEASEEEEEE HELPPPPPP ASAPPPP
Find the measure of angle A in degrees.
Answers
Answer:
Angles are 45, 45 and 90 degrees because
AB and BC are congruent so that means the angles eating the sides are also congruent.
So to find the congruent angles:
180-90=90/2=45 degrees
To find AC:
a²+b²=c²
x²+x²=h²
√18=√c²
3√2=c
(I don't know why it says 3√3, but I think the q is wrong)
Hope it helps!
Answer:
45 degrees
Step-by-step explanation:
This is a special right triangle with these lengths. Which leads us to find the angles of 45, 45, 90 and B is 90 so A and C are 45 degrees.
2) Sarah takes a small business loan for
$25,000. The term for repayment is 60
months and the interest rate is 5.75%.
formula,
Use the loan amortization
what is the estimated monthly
payment?
Answers
Using it's formula, it is found that the estimate monthly payment is of $480.42.
What is the monthly payment formula?It is given by:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
In which:
P is the initial amount.r is the interest rate.n is the number of payments.The parameters are given as follows:
P = 25000, n = 60, r = 0.0575.
Hence:
r/12 = 0.0575/12 = 0.00479167.
Hence the payment will be of:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
[tex]A = 25000(0.00479167)\frac{(1+0.00479167)^{60}}{(1+0.00479167)^{60}-1}[/tex]
A = 480.42.
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The square of the difference between a number and 7 is 81 . Find the number(s).
Answers
Answer:
16 or -2
Step-by-step explanation:
Let the number be x.
Difference between the number and 7
= x -7 or 7-x
The square of the difference between x and 7
= (x -7)²
(x -7)²= 81
Square root both sides:
[tex]x - 7= \pm \sqrt{81} [/tex]
[tex]x - 7 = \pm9[/tex]
Add 7 to both sides:
[tex]x = 7\pm9[/tex]
x= 16 or x= -2
Thus, the number could either be 16 or -2.
If x=3 y=4 z=6 then 4x+8yz+3y equals
Answers
Answer:
216
Step-by-step explanation:
4x+8yz+3y
Let x=3 y=4 z=6
Substitute the values into the expression
4(3)+8(4)(6)+3(4)
Multiply first
12+192+12
Then add
216
Samantha opened a savings account and deposited $8192. The account earns 10% in interest annually. She makes no further deposits and does not withdraw any money. In t years, she has $25,710 in this account. Write an equation in terms of t that models the situation.
Answers
The equation in terms of t that models the situation is given by
[tex]8192(1+\frac{0.01}{12} )^{12t} = 25710[/tex].
We know that the interest on a loan or deposit that is accrued on both the initial principal and the total interest from prior periods is known as compound interest and it can be calculated as
[tex]A = P(1+\frac{r}{n})^{nt}[/tex],
where P is the initial principal, r is the rate of interest, n is the number of times interest was charged for each time period, t is the amount of time that has passed and A is the final amount.
Here, P = 8192, r = 10% = 10/100 = 0.01, n = 12 and A = 25,710
So, we can write
[tex]8192(1+\frac{0.01}{12} )^{12t} = 25710[/tex]
Therefore the required equation is
[tex]8192(1+\frac{0.01}{12} )^{12t} = 25710[/tex]
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Factor the following expression. x² - 10x +9 2 Factor the following expression . x² - 10x +9 2
Answers
Answer:
x² - 10x + 9 = (x-9)(x-1)
the factored expression would be (x-9)(x-1)
8
Diameter;
Radius:
B
(a) Find the perimeter of the square
(b) Find the area of the square Area =
(c) Find the circumference of the circle C = 2πr
(d) Find the area of the circle. Area = πr²
(e) Find the area of the region between the square and the circle
Answers
answer: A: 16
B: 16
C: 12.57
D: 12.57
E: 3.43 (do area of square-area of circle 16-12.57
file attached belowfile attached below
Answers
explanation: im not sure what youre asking
Find the product write your answer in exponential form 7^-1•7^-7
Answers
Answer:
1/5764801
Step-by-step explanation:
7^-1 × 7^-7
= 1/7(7^-7)
= 1/7(1/823543)
= 1/5764801
paul asked to order snacks for an office meeting of 180 people. she decides to order desert squares which come in boxes of 24. she estimates she will need 3.5 snacks per person. how many boxes should she buy?
Answers
Answer:
27 boxses
Step-by-step explanation:
calculations is shown in the picture
Use the Factor Theorem to determine whether x−1 is a factor of 4x^3−6x^2+2x+1.
Answers
? Question
Select the graph of the transformation.
The graph f(x)=√√ is transformed to form
shows g(x).
Answers
Answer: The vertex of the graph of [tex]y=x^2[/tex] is shifted to the right 4 units and up 3 units.
Write and solve an inequality that means a number plus four is greater than or equal to twelve.
Answers
Answer:
[tex]x+4\geq 12[/tex]
Step-by-step explanation:
x - a number
x+4 - a number plus 4
x+4[tex]\geq[/tex] - a number plus 4 is greater than or equal to
x+4[tex]\geq[/tex]12 - a number plus 4 is greater than or equal to twelve
Answer:
Inequality: x + 4 ≥ 12
Solution: x ≥ 8
Step-by-step explanation:
Plus: "+" → to add something to something else
Greater than or equal to: "≥" → the expression on the left side of the inequality sign is greater than the expression on the right side of the sign.
Let x be the unknown number.
A number plus four is greater than or equal to twelve:
x + 4 ≥ 12
To solve the found inequality, subtract 4 from both sides:
⇒ x + 4 - 4 ≥ 12 - 4
⇒ x ≥ 8
Therefore, the solution to the inequality is x ≥ 8. The unknown number x can be any real number equal to or greater than 8.
HELP! ASAP!
A box without a top is to be made from a rectangular piece of cardboard, with dimensions 4 in. by 8 in., by cutting out square corners with side length x and folding up the sides.
(a) Write an equation for the volume V of the box in terms of x.
(b) Use technology to estimate the value of x, to the nearest tenth, that gives the greatest volume. Explain your process.
Answers
Step-by-step explanation:
Part A:
So the height is going to be x when you fold the sides up. So that's one part of the volume but for the width it was going to be 4 but since two corners were cut out with the length x the new width is going to be (4-2x). The same thing applies for the length which should be 8 inches but since two corners were removed with the length x it's now (8-2x)
v = x(4-2x)(8-2x)
Part B:
The volume can be graphed although there must be a domain restriction since the height, width, or length cannot be negative. So let's look at each part of the equation
so for the x in front it must be greater than 0 to make sense
for the (4-2x), the x must be less than 2 or else the width is negative.
for the (8-2x) the x must be less than 4 or else the length is negative
so the domain is going to be restricted to 0 < x < 2 so all the dimensions are greater than 0
By using a graphing calculator you can see the maximum of the given equation with the domain restrictions is 0.845 which gives a volume of 12.317
Complete the following table using the equation: y = -2x²
Answers
The parabola is a downward parabola which is passing through origin and leading coefficient of the negative 2.
What is the parabola?It's the locus of a moving point that keeps the same distance between a stationary point and a specified line. The focus is a non-movable point, while the directrix is a non-movable line.
The equation of a quadratic function, of vertex (h, k), is given by:
y = a(x – h)² + k
where a is the leading coefficient.
The equation of the parabola will be
y = -x²
The given parabola is a downward parabola which is passing through origin and leading coefficient of the negative 2.
The graph of the function is given below.
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Solve the linear programming problem.
Minimize and maximize
P = 10x + 5y
Subject to
2x+3y 230
2x+y ≤ 26
-2x+3y ≤ 30
x, y 20
Answers
The minimized value is 50 and the maximized value is 130
How to minimize and maximize the function?The objective function is:
P = 10x + 5y
Subject to
2x+3y ≤30
2x+y ≤ 26
-2x+3y ≤ 30
x, y >0
Next, we plot the graph of the constraints (see attachment)
From the graph, the vertices of the feasible regions are:
(0, 10),(12, 2) and (6,14)
Substitute these values in P = 10x + 5y
P = 10(0) + 5(10) = 50
P = 10(12) + 5(2) = 130
P = 10(6) + 5(14) = 130
Hence, the minimized value is 50 and the maximized value is 130
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Given the coordinate T(8, -4), find the location of T after a dilation using a scale factor of 0.4.
Answers
The new coordinate will be T'(3.2 , -1.6) .
What is the meaning of Dilation ?Dilation is the transformation that changes the size of the object without changing its shape .
If a coordinate point is (x,y) and a dilation of scale factor f is applied then the new coordinates will be (fx ,fy)
The coordinate given in the question is T(8, -4)
The scale factor is 0.4
The new coordinate is
T'( 0.4 * 8 , 0.4 * (-4))
T'(3.2 , -1.6)
Therefore the new coordinate will be T'(3.2 , -1.6)
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