Determine the end behavior of each function.
(a)
p(x) = a(x + b)5(x − c)3
, where a, b, and c are constants and
a < 0
.
p(x) → as x → −∞
p(x) → as x → ∞
(b)
f(x) =
9x2 − 11x + 2
8x2 − 6
f(x) → as x → −∞
f(x) → as x → ∞
(c)
g(x) = 9 + e−6x
g(x) → as x → −∞
g(x) → as x → ∞
Step-by-step explanation:
(a)
a, b, c are constants and play no role with their value when it goes relative to enormous numbers and to infinity.
but the sign is important.
a < 0, so, it will stay < 0 for all eternity/infinity.
(x + b)⁵ for x going to infinity, this goes to infinity.
for x going to -infinity, this also goes to -infinity (the exponent 5 is odd, so a negative value put to an odd power will create a negative result value).
(x - c)³ for x going to infinity, this goes to infinity.
for x going to -infinity, this also goes to -infinity (for the same reasons - 3 is an odd number).
x going to -infinity,
p(x) = -×-infinity×-infinity = -infinity
x going to infinity,
p(x) = -×infinity×infinity = -infinity
(b)
the x² terms drown out all other terms with lower x exponent (so, incl. -11x or any constants).
what remains for very, very large x is
9x²/8x² = 9/8 = 1.125
since we have x² terms, it does not matter, if x is positive or negative, the result is always positive.
so, x going to infinity or to -infinity, p(x) is the same again :
p(x) = 9/8 = 1.125
(c)
finally, we have a different result for x going to -infinity or to infinity.
x going to -infinity :
the exponent of e is then -6×-infinity = infinity. and e to the power of infinity is infinity.
p(x) = 9 + infinity = infinity
x going to infinity :
the exponent of e is then -6×infinity = -infinity. and e to the power of -infinity is 1/e to the power of infinity.
and that is 1/infinity. the limit for that is 0.
p(x) = 9 + 0 = 9
If w = 18, what is the value of 3w − 11?
A: 307
B: 65
C:43
D: 10
Answer: 43 ==> C
Step-by-step explanation:
3w − 11=
3(18)-11=
54-11=43 ==> C
Answer:
c, 43
Step-by-step explanation:
3 times 18, minus 11
Hey beinggreat78, the ones with a large amount of points are for u and they also mention your name so its easier to spot them (not that i dont want u to answer all the questions)
Answer:
C.
Step-by-step explanation:
[tex]3 \div 10 = 0.3 < 0.4[/tex]
Answer:
C
Step-by-step explanation:
All work and the answer is provided in the attached screenshot! :)
Evaluate the expression.
-2/3(1.5÷0.25÷5/4)-5/6
The value of the given expression is -121/ 30.
PEMDAS stands for parentheses, exponents, multiplication, division, addition, then subtraction. It is basically the rule of the order in which a mathematical expression must be solved.
Here, we are given an expression- -2/3 (1.5 ÷ 0.25 ÷ 5/4) -5/6
It can be written as -2/3 (15/10 ÷ 25/ 100 ÷ 5/4) -5/6
= -2/3 (3/2 ÷ 1/4 ÷ 5/4) -5/6
As per the rules of PEMDAS, we first deal with the terms inside the bracket-
(3/2 ÷ 1/4 ÷ 5/4) = (3/2 × 4 × 4/5)
= (3 × 2 × 4/5)
= 24/5
Thus, the expression becomes-
-2/3 (24/5) -5/6
= -48/ 15 - 5/6
LCM of 15 and 6 is 60
⇒ -(48 × 4)/ 60 - (5 × 10)/ 60
-192/ 60 - 50/ 60
= (-192 - 50)/ 60
= -242/ 60
= -121/ 30
Thus, the value of the given expression is -121/ 30.
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Is 7 hundreds + 4 thousands + 27 ones greater than, less than or equal to 6 thousands + 4 hundreds? *
Answer:
6 thousands + 4 hundreds
4727>6400
Step-by-step explanation:
4727<6400
Home Depot entered fiscal 2017 with a total capitalization of $21,904 million. In 2017, debt investors received interest income of $877 million. Net income to shareholders was $8,654 million. (Assume a tax rate of 21%.)
Calculate the economic value added assuming its cost of capital is 10%. (Do not round intermediate calculations. Enter your answer in millions rounded to 2 decimal places.)
The economic value added (EVA) for Home Depot in the fiscal year, 2017, is $6,463.60 million.
What is the economic value added?Economic value added (EVA) measures a company's financial performance or economic profit.
EVA is based on the residual wealth of the company for the fiscal year. It measures the value a company generates from its invested funds at the cost of capital.
EVA is calculated by deducting the cost of capital from the operating profit after tax (NOPAT).
Data and Calculations:2017 total capitalization = $21,904 million
2017 interest paid to debt investors = $877 million
Net income to shareholders = $8,654 million
Corporate tax rate = 21%
Profit before taxes = $10,954 million ($8,654/ 1 - 0.21)
Cost of capital = 10%
= $2,190.4 million ($21,904 x 10%)
EVA = NOPAT - (Invested Capital * WACC)
= $8,654 million - $2,190.4 million
= $6,463.60 million.
Thus, the economic value added (EVA) for Home Depot in the fiscal year, 2017, is $6,463.60 million.
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Refer to the diagram to the right.
a. Write an equation for the diagram to the right.
b. Find the sum.
C.
d.
Describe the sum in terms of the distance from the first addend. Explain.
What integers do the arrows represent?
0
TTTTTTTT
Answer:
Where is the diagram?
Step-by-step explanation:
Triangle p has b en rotated onto triangle Q
How many degrees anticlockwise has triangle P been rotated?
How many degrees clockwise has triangle P been rotated?
a. triangle P been rotated by 90 degree in anticlockwise direction
b. triangle P been rotated by 270 degree in clockwise direction
What is angle of rotation ?
In mathematics, the angle of rotation is a measurement of the amount, of namely angle, that a figure is rotated about a fixed point, often the center of a circle.
a. if we rotate the triangle P at 90 degree, from point O at anticlockwise direction, we get triangle Q
b. if we rotate triangle P at 270 degree from point O at clockwise direction, we get triangle Q
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Write a rule for the relation shown in the table.
X: 1, 2, 3, 4
Y: 10, 12, 14, 16
Of the following fractions which one is the largest 9/19 , 5/11 ,7/15
Answer: 9/19
Step-by-step explanation:
9/19=0.4737
5/11=0.4545
7/15=0.4666
9/19 has the largest decimal making it largest.
What geométric symbol would be represented by a baseball bat
Answer: i think the overall shape of a baseball bat would be more rectangular
Step-by-step explanation:
reason for thinking so: because a baseball bat depending on size, would normally fit into a rectangular box
Round 782,317.772 to the nearest whole number.
Nearest whole number will be 782318.
Nearest ones whole number is the first digit before the decimal point of a number.
For example nearest ones of 9.6 is equal to 10.
If the tenth digit (first number before decimal point) of the number is greater than or equal to 5 we round up and add 1 to ones of number, If the tenth digit of the number is less than 5 we remove the decimal part. Example:
124.6
The first number of right of decimal point is 6
6 is greater than 5, so we add 1.
Result = 125
Now given number is 782317.772
since the first digit after decimal is 7 which is greater than 5 thus the nearest whole number will be 782318.
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To make five cups of lemonade you mix three cups of water with two cups of lemon
juice. If there are sixteen cups in a gallon, how many cups of lemon juice are needed to
make ten gallons of lemonade?
A: 16
B: 32
C: 40
D: 48
E: 64
(I know the answer is E but I don't know how to get it)
At end of the first half of a football game, Nathan had carried the ball for 50.5 yards. By the end of the game, he carried the ball for a total of 75 yards. Find the percent of increase in the number of yards he carried. Round to the nearest whole tenth if necessary
The percent increase in the number of yards is 32.7%
How to calculate the percent increase ?At the end of the football game, Nathan carried the ball for 50.5 yards
At the end of the game, the ball was carried for a total of 75 yards
The percent increase in the number of yards can be calculated dividing the percentage change by the original value and multiplying by 100
= 75 - 50.5/75 × 100
= 24.5/75 × 100
= 0.3266 × 100
= 32.66
= 32.7%
Hence the percent increase in the number of yards is 32.7%
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The sum of first five prime numbers is
PLEASE HELP URGENT
Find the value of the variables. Then find the measure of each angle in the diagram.
The value in fig 4 x = 18.7 and γ = 12.72 . The value in fig 5 x = 10 and γ = 40 .
In figure 4 .
Solving linear equation in two variable
10 γ + 4 x - 22 = 180
3 γ + 11 + 7 x + 4 = 180
10 γ + 4 x = 202 ... eq 1
3 γ + 7 x = 169 ... eq 2
mult. ... eq 1 by - 3 and ... eq 2 by 10 .
- 30 γ - 12 x = - 606
30 γ + 70 x = 1690
Adding above 2 eqns
58 x = 1084
x = 18.7
γ = 12.72
Measurement of angles : 127.2 degrees , 52.8 degrees 134.9 degrees , 49.16 degrees .
In fig . 5
4 x + 13 x + 10 = 180
17 x = 170
x = 10
2 ( γ + 25 ) + 2 γ - 30 = 180
4 γ + 20 = 180
4 γ = 160
γ = 40
Measurement of angles are 130 degrees , 50 degrees , 130 degrees , 50 degrees .
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36x+9 equals what
big blak vjndjgd
We can conclude that the equation 36x + 9 equals -1/4.
What exactly is an equation?An equation, in its most basic form, is a mathematical statement demonstrating that two mathematical expressions are equal.3x + 5 = 14, for example, is an equation in which the expressions 3x + 5 and 14 are separated by a 'equal' sign.So,
36x + 936x + 9 = 036x = -9x = -9/36x = -1/4Therefore, we can conclude that the equation 36x + 9 equals -1/4.
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What’s the domain and range of y = |x4|
Domain: (-∞,∞) {x,x∈R }
Range: [0,∞)
Solution :
The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.
Interval Notation
Interval notation is a method to represent an interval on a number line. In other words, it is a way of writing subsets of the real number line. An interval comprises the numbers lying between two specific given numbers. For example, the set of numbers x satisfying 0 ≤ x ≤ 5 is an interval that contains 0, 5, and all numbers between 0 and 5.
Different Types Of Intervals
Intervals can be classified based on the numbers the set comprises. Some sets include the endpoints specified in the notation, while some might partially or not include the endpoints. In general, there are three types of intervals given as,
Open Interval
Closed Interval
Half-Open Interval
Let us understand the interval notation and different types of intervals in detail using solved examples.
Interval Notation:
y = |x4|
(−∞,∞)
Set-Builder Notation:
{x|x∈R}
The range is the set of all valid
y
values. Use the graph to find the range.
Interval Notation:
[0,∞)
Set-Builder Notation:
{y|y≥0}
Determine the domain and range.
Domain:
(−∞,∞),{x|x∈R}
Range:
[0,∞) , {y|y≥0}
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A friend comes to visit and mentions the temperature in their hometown is currently 25 degrees
Celsius. What is this in Fahrenheit? (Write your answer as a whole number.)
Answer:
77
Step-by-step explanation:
Mate m.1 is so hard help me pls someone
x[tex]x^{2}+ 10x =11[/tex]
Answer:
For this problem, x has multiple values, so we will solve for both.
Step-by-step explanation:
[tex]x^2+10x-11=11-11\\x^2+10x-11=0\\[/tex]
Quadratic rule
[tex]x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]\mathrm{For\:} a=1,\:b=10,\:c=-11[/tex]
[tex]x_{1,\:2}=\frac{-10\pm \sqrt{10^2-4\cdot \:1\cdot \left(-11\right)}}{2\cdot \:1}[/tex]
Dealing with radicals
[tex]\sqrt{10^2-4\cdot \:1\cdot \left(-11\right)}\\=\sqrt{10^2+4\cdot \:1\cdot \:11}\\=\sqrt{10^2+44}\\=\sqrt{100+44}\\=\sqrt{144}\\=\sqrt{12^2}\\=12\\[/tex]
Multi-solution expression
[tex]x_1=\frac{-10+12}{2\cdot \:1},\:x_2=\frac{-10-12}{2\cdot \:1}[/tex]
Solve for x₁
[tex]\frac{-10+12}{2\cdot \:1}\\=\frac{2}{2\cdot \:1}\\=\frac{2}{2}\\=1[/tex]
Solve for x₂
[tex]\frac{-10-12}{2\cdot \:1}\\=\frac{-22}{2\cdot \:1}\\=\frac{-22}{2}\\= -\frac{22}{2}\\= -11[/tex]
Thus, x has 2 values for 2 different numbers:
x₁ = 1
x₂ = -11
➲ Hope this helps!
please refer to the image
Can someone please help me I will mark u brilliant
Answer:
M would be at (0,-2)
Step-by-step explanation:
The question asks you to rotate the image 180 degrees clockwise. Clockwise means towards the right, such as how a clock moves. Each axis is 90 degrees, so by moving it twice would land at (0,-2).
A horizontal line (such as the x-axis) is 180 degrees, so by mirroring the point, you would see the point is at (0,-2).
b. A lap pool has a length of 27 yards, a width of 23 yards, and a depth of 5 yards. Find the pool's surface area (the water surface) and the total volume of water that the pool holds.
The volume is 3105 and the surface area is 1742
What is the volume of and what is the surface area?The given parameters are
Length = 27 yards
Width = 23 yards
Height = 5 yards
The volume is
Volume = Length * width * height
So, we have
Volume = 27 * 23 * 5
Evaluate
Volume = 3105
The surface area is
A =2 *(LW + LH + WHW)
So, we have
A = 2 * (27 * 23 + 27 * 5 + 23 * 5)
Evaluate
A = 1742
Hence, the volume is 3105 and the surface area is 1742
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There are 50 minutes left before the event begins. You have 20 balloons to inflate before the event. How much time can you spend inflating each one equally?
Answer: 24 seconds
Step-by-step explanation:
20/50=0.4
0.4*60=24
(-5.2)(-7.8) what is it
Answer:
40.56
Step-by-step explanation:
:)
Helps solve Application
The percentage of 0 - 17 in 2015 is 23.97% and the percentage is decreasing by 0.048% in 2015
The percentage of 0 - 17 in 2015The equation of the function is given as
P(x) = 26x^-0.03
In 2015, x = 15
Substitute x = 15 in the equation P(x) = 26x^-0.03
P(15) = 26 * 15^-0.03
Evaluate the expression
P(15) = 23.97
Hence, the percentage of 0 - 17 in 2015 is 23.97%
How fast is the percentage decreasing in 2015The equation of the function is given as
P(x) = 26x^-0.03
Differentiate the function
P'(x) = -0.03 * 26x^-1.03
In 2015, x = 15
Substitute x = 15 in the equation
P'(15) = -0.03 * 26 * 15^-1.03
Evaluate
P'(15) = -0.048
Hence, the percentage is decreasing by 0.048% in 2015
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PLEASE PLEASE HELP!!!
Answer:
Step 1: 1605 - 75 = 1530
Step 2: 1530 / 255 = 6
Step-by-step explanation:
20 chocolates in a box, 2 are coconut cream, what is the probability that after eating two chocolates in a row that they are not coconut cream
Answer:
18/20 * 17/19 ≈ 0.805263158
Step-by-step explanation:
18/20 for the first chocolate not to be coco cream
then, the number of non-coco ones is lowered by 1 and the number of total too, so
17/19 for the second chocolate not to be coco cream
The chance that neither of the 2 chocolates is coconut cream is 18/20*17/19 ≈ 0.805263158
what is the answer to 0.25 x 2.6 this is for hw