The graph of the function f(x) = ex - 2x has a horizontal tangent line at x = 0.693.
To find the values of x for which the graph of the function f(x) = ex - 2x has a horizontal tangent line, we need to determine when the derivative of the function is equal to zero. A horizontal tangent line occurs when the slope of the function is zero, which corresponds to the critical points of the function.
To find the critical points, we differentiate f(x) with respect to x. The derivative of ex is ex, and the derivative of -2x is -2. Setting the derivative equal to zero, we have ex - 2 = 0.
Adding 2 to both sides, we get ex = 2. Taking the natural logarithm of both sides, we have ln(ex) = ln(2), which simplifies to x = ln(2).
Therefore, the graph of f(x) = ex - 2x has a horizontal tangent line at x = ln(2) or approximately x = 0.693. At this point, the slope of the function is zero, indicating a horizontal tangent line.
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Place the numbers 4/3 , 1/2 , 4/8 , 3/2 and 2/2 in order from least to greatest.
Answer:
1/2, 4/8, 2/2, 4/3, 3/2
Step-by-step explanation:
If you put the fractions into decimals it would easier to see which ones are greater and leasts.
4/3 = 1.333...
1/2 = 0.5
4/8 = 2/4 = 1/2 = 0.5
3/2 = 1.5
2/2 = 1
Am not sure if 1/2 go first or 4/8.
Question 3 , HELP! PLEASE!
Answer:
12mlies
Step-by-step explanation:
just add 7 + 5 and boom you have you answer
Determine the value of y, if x is 4.
PLEASE HELP
A tree is growing at a constant rate. It is recorded that at the 7th year since it was planted it was at a height of 25 feet. It was recorded again at the 10th year since it was planted and it was at a height of 31 feet. How tall was the tree when it was first planted.
Answer:
Step-by-step explanation:
h₁₀ - h₇ = 31-25 = 6 ft
The tree grew 6 ft in 3 years, or 2 ft per year.
In 7 years the tree grew 14 ft. It was 25-14 = 11 ft when planted
Find the percent change from the first value to the second.
40; 52 increase by ________.
Answer:
its increasing by 12
Step-by-step explanation:
Just count upward
20 POINTS
How do you find the interquartile range
Answer:
To find the interquartile range (IQR), first find the median (middle value) of the lower and upper half of the data. These values are quartile 1 (Q1) and quartile 3 (Q3). The IQR is the difference between Q3 and Q1.
Step-by-step explanation:
(Khan Academy)
You would first find your mean and then when you found that you would subtract you Q3 from your Q1 in order to find your IQR (Interquartile range.)
NEED ANSWERS ASAP!!! - How do you find the value of x??
Answer: Generally, the algebraic expression should be any one of the forms such as addition, subtraction, multiplication and division. To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result.
Answer:
equal the equations
(x+20)=(2x-10)
then answer the equation
Step-by-step explanation:
answer?answer?answer?answer?answer?answer?answer?
Answer:
y=6/2x-6
y=3x-6
Step-by-step explanation:
A car ride is drawn on a coordinate plane so that the first card is located at the point by (5,10) what are the coordinates of the first car after a rotation of 270° about the origin
Answer:
There are two possible solutions:
Clockwise rotation
[tex]P'(x,y) = (-10,5)[/tex]
Counterclockwise rotation
[tex]P'(x,y) = (10, -5)[/tex]
Step-by-step explanation:
There are two possible answers: (i) Clockwise rotation, (ii) Counterclockwise rotation. Vectorially speaking, rotation of point of rotation of a point about another point of reference is defined by:
[tex]P'(x,y) = O(x,y) + r_{OP}\cdot (\cos (\theta_{OP}\pm \theta'),\sin (\theta_{OP}\pm \theta'))[/tex] (1)
Where:
[tex]O(x,y)[/tex] - Point of reference.
[tex]r_{OP}[/tex] - Length of the segment OP.
[tex]\theta_{OP}[/tex] - Direction of segment OP, measured in sexagesimal degrees.
[tex]\theta '[/tex] - Angle of rotation, measured in sexagesimal degrees.
Please notice that clockiwise rotation occurs when [tex]\theta = \theta_{OP}-\theta'[/tex] and counterclockwise rotation when [tex]\theta = \theta_{OP}+\theta'[/tex]. In addition, we define length and direction of the segment below:
[tex]r_{OP} = \sqrt{(x_{P}-x_{O})^{2}+(y_{P}-y_{O})^{2}}[/tex] (1)
[tex]\theta_{OP} = \tan^{-1} \frac{y_{P}-y_{O}}{x_{P}-x_{O}}[/tex]
If we know that [tex]x_{O} = y_{O} = 0[/tex], [tex]x_{P} = 5[/tex], [tex]y_{P} = 10[/tex] and [tex]\theta' = 270^{\circ}[/tex], then the coordinates of the first car after rotation is:
[tex]r_{OP} = \sqrt{(5-0)^{2}+(10-0)^{2}}[/tex]
[tex]r_{OP} \approx 11.180[/tex]
Please notice that original point is located at first quadrant of the Cartesian plane centered at origin, then the direction of the segment OP is:
[tex]\theta_{OP} = \tan^{-1} \frac{10-0}{5-0}[/tex]
[tex]\theta_{OP} \approx 63.435^{\circ}[/tex]
The two solutions are finally presented:
Clockwise rotation
[tex]P'(x,y) = (0,0) + 11.180\cdot (\cos (-206.565^{\circ}),\sin (-206.565^{\circ}))[/tex]
[tex]P'(x,y) = (-10,5)[/tex]
Counterclockwise rotation
[tex]P'(x,y) = (0,0) + 11.180\cdot (\cos (333.435^{\circ}),\sin (333.435^{\circ}))[/tex]
[tex]P'(x,y) = (10, -5)[/tex]
the question is: The endpoints of ST are S(2,-2) and T(4,2) what are the coordinates of midpoint of ST?
Answer:
(3,0)
Step-by-step explanation:
If you use a graphing calculator and connect the two points then you would get (3,0) :))
the sum of the three terms consecutive terms of an ap is -6 and the product is 64, find the terms. using a, a + d, a + 2d
Answer:
-8, -2 and 4
Step-by-step explanation:
Let the terms of the AP be a-d, a and a+d
If the sum is 6, then;
a-d+a+a+d = -6
3a = -6
a = -6/3
a = -2
Hence the first term is 6
If the product is 64
(a-d)(a)(a+d) = 64
-2(a²-d²) = 64
-2(4-d²) = 64
4-d² = -64/2
4-d² = -32
-d² = -32-4
-d² = -36
d² = 36
d = 6 or -6
The first term is a-d = -2-6 = -8
second term is a = -2
third term is a+d = -2+6 = 4
Hence the required AP is -8, -2 and 4
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. Yvonne put $4,000 in a savings account. At the end of 3 years, the account had earned $960 in simple interest. a. How much does she have in her account at the end of 3 years?b. At what annual simple interest rate did the account grow? C. How many more dollars would she have in her account if the interest rate were 1% greater?
Solution :
The amount invested by Yvonne = $ 4,000
Time of investment = 3 years
The simple interest earned by Yvonne in 3 years = $ 960
a). Therefore, the amount Yvonne earned by the end of three years is
= principal + interest earned
= 4,000 + 960
= $ 4,960
b). The formula for simple interest(S.I.) is given by :
[tex]$S.I. =\frac{P.T.R}{100}$[/tex]
or [tex]$R = \frac{SI \times 100}{P.T}$[/tex]
[tex]$ = \frac{960 \times 100}{4000 \times 3}$[/tex]
= 8%
c). Now if the interest rate is 1% greater, i.e. R = (8+1) = 9%
∴ [tex]$SI =\frac{P.T.R}{100}$[/tex]
[tex]$SI =\frac{4000 \times 3 \times 9}{100}$[/tex]
SI = $1,080
Therefore, the amount at the end of 3 years with 9% rate of interest will be
= 4000 + 1080
= $ 5080
Thus, Yvonne will have 5080 - 4960 = $ 120 money more in her account if the rate of interest was 1% greater.
Part A
In "The Case for Shelter Animals," what does the author explain about the cost of becoming a pet owner?
Adoption costs more money than buying a pet.
Pet stores are more expensive than breeders.
It is more expensive to buy a pet than it is to adopt.
Cats are less expensive than dogs.
Question 2
Part B
Which evidence from the text best supports the answer to Part A?
"So those who buy from pet stores and breeders can expect to pay those fees on top of already-high purchase costs."
"The guide states that adopting a dog or a cat from a shelter usually costs between $50 and $500."
"Meanwhile, an animal from a pet store typically costs at least $1,000. Breeders are even more expensive."
"One reason that adopting pets from shelters is the logical choice is that shelter animals are less expensive than those bought from pet stores or breeders."
Answer:
part a, c part b, d
Step-by-step explanation: i just took the test for k12
Statement 1 is incorrect.
Statement 2 is incorrect.
Statement 3 is correct.
Statement 4 is incorrect.
What is the adoption cost?Adoption cost in the given problem is the money spent in maintenance, feeding, and other expenses in order to adopt a pet.
"Adoption costs more money than buying a pet" is an incorrect statement because if we extract the conclusion combinedly from statements 2 and 3, it is clear that adoption cost is in the range of $50 and $500 in the case of a shelter animal while an animal from a pet store typically costs at least $1,000.
"Pet stores are more expensive than breeders", this is an incorrect statement because in the third paragraph it is mentioned that "an animal from a pet store typically costs at least $1,000. Breeders are even more expensive."
"It is more expensive to buy a pet than it is to adopt" is a correct statement because in the fourth paragraph it is mentioned that "adopting pets from shelters is the logical choice because shelter animals are less expensive than those bought from pet stores or breeders."
"Cats are more expensive than dogs" is an incorrect statement because in the second paragraph it s mentioned, "adopting a dog or a cat from a shelter usually costs between $50 and $500." There has not been discussed anything about the individual adoption costs for each.
Therefore, Statement 1 is incorrect.
Statement 2 is incorrect.
Statement 3 is correct.
Statement 4 is incorrect.
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What is the x-value of the solution to the system of equations?
5x + 4y =8
2x -3y = 17
-3
O -2
O 4
O5
Answer:
-234
Step-by-step explanation:
5x + 4y =8 2x -3y = 17 -3 O -2 O 4 O5=234
Evaluate the expression
27²
⁻⁻⁻⁻
27^4/3
Answer:
The answer is 9
Step-by-step explanation:
27^2 =729
729/27^4/3
50 apples cost $25. How much would 75 apples cost?
Answer:
[see below]
Step-by-step explanation:
50 apples cost 25 dollars.
25/50 = 0.5
Each apple cost half a dollar.
0.5 * 75 = 37.50
75 apples should cost $37.50.
Hope this helps.
PLEASE SOLVE! Also how do you properly solve them ( please include steps)
Solve the equation for x:
2(8x – 16) = 48
Answer:
The answer would be 5
Step-by-step explanation: Plz mark brianliest
Find the value of X.
Answer:
3X+ 2X =180
5X = 180
X,/ 180/5
X = 36
Solve the inequality and enter your solution as an inequality in the box below, using "" for 2 if necessary. -5(4x + 7)
Answer:
I simplified it to -20x - 35
Step-by-step explanation:
-5 times 4x is -20x, -5 times 7 is -35.
Two ships leave Liverpool at the same time one travel north- west at an average speed of 10.5 km/h while the other travels at an average speed of 14km/h in a bearing of 280
Answer:
нечего не понятно но очень интересно да, очень
Find the area of the shaded (gray) region.
15 points
Answer:
36 cm
Step-by-step explanation:
In class 10 out of 25 students ride the bus.what percent of students ride the bus?
Answer:
40%
Step-by-step explanation:
it's easiest to get a percentage from 100, multiplying 25 by 4 gives you 100 so if you do that then multiply 10 by four to make the equation even that will give you the answer
Which statement(s) about the line
below are true? Select all that apply.
A The x-intercept is -8.
B The line has a positive slope.
C The y-intercept is 4.
D The line has a negative slope.
Answer: A, B, and C.
Step-by-step explanation: The answers you have selected in the picture are correct.
These are the actual claims made regarding the line:
The x-intercept is at - 8 because y = 0 when x = -8.
The line is growing and has a positive slope.
As soon as x = 0 and y = 4, the y-intercept is at 4.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and the equation of a line in slope-intercept form is
y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
The true statements about the line are,
The x-intercept is at - 8, as when x = - 8 y = 0.
The line has a positive slope as it is increasing.
The y-intercept is at 4 as when x = 0 y = 4.
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The figure shows two lines cut by transversal.wich statement correctly explains why the two lines are parallel
Answer:
D
Step-by-step explanation:
This is because the angle are corresponding which mean they are on the same side and are the same number
Hope this Helped
Diego drank 0.162 liters of water from a 1-liter bottle. How much water is left in the bottle?
4. Calculate the mean of the data set {22, 34, 37, 23, 45, 21, 29, 37}. Round to the nearest tenth.
37
31.0
35.4
31.5
Answer:
31.0
Step-by-step explanation:
The mean of a given set of data is the ratio of the sum of the data to the number of units that make up the data set. It is also called the average of the data set.
Given the data set {22, 34, 37, 23, 45, 21, 29, 37}. There are 8 numbers in the set. The total of these numbers
= 22 + 34 + 37 + 23 + 45 + 21 + 29 + 37
= 248
The mean = 248/8
= 31
Janna works at a lab with a huge circular particle accelerator. It has a radius of 4 kilometers. What is the accelerator's diameter?
Step-by-step explanation:
since it is a circle the diameter is two times larger than radius.So 4×2=8km
DEF is a right angled triangle calculate the length of EF correct to 3 sigificant figures
Answer:
[tex]\displaystyle EF \approx 15.9[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightEquality Properties
Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of EqualityTrigonometry
[Right Triangles Only] SOHCAHTOA[Right Triangles Only] cosθ = adjacent over hypotenuseStep-by-step explanation:
Step 1: Define
Angle θ = 28°
Adjacent Leg = EF = x
Hypotenuse = DF = 18
Step 2: Solve for x
Substitute in variables [Cosine]: [tex]\displaystyle cos28^\circ = \frac{x}{18}[/tex][Multiplication Property of Equality] Multiply 18 on both sides: [tex]\displaystyle 18cos28^\circ = x[/tex]Evaluate trig: [tex]\displaystyle 18(0.882948) = x[/tex]Multiply: [tex]\displaystyle 15.8931 = x[/tex]Rewrite: [tex]\displaystyle EF = 15.8931[/tex]Round: [tex]\displaystyle EF \approx 15.9[/tex]Find the distance between the two points. Leave
your answer exact. (-8, 10) and (-6, 7)
A. V13
B. 3.6
C. V169
D. 13
Answer:
A. V13
Step-by-step explanation: