The equation of the tangent line to the curve are [tex]y=x-1 , y=\frac{xe-e^{2}+8 }{e}[/tex].
It is required to find the solution.
What is a tangent ?A tangent is a line that touches the edge of a curve or circle at one point, but does not cross it. The tangent line to a curve at a point is that straight line that best approximates (or “clings to”) the curve near that point.
Given:
[tex]y=8\frac{lnx}{x} \\\\y'=8(\frac{1/x*x-lnx*1}{x^{2} } \\\\y'=\frac{1-lnx}{x^{2} }[/tex]
Now, we find the slope of the tangent by inserting the point (1,0) into the derivative.
[tex]m_{tangent}=\frac{1-ln1}{1^{2} }\\\\m_{tangent}=1-0/1\\\\m_{tangent} =1[/tex]
We can now find the equation, because we know the slope and a point (1, 0).
[tex]y-y_{1} =m(x-x_{1} )\\[/tex]
y-0=1(x-1)
y=x-1
We can now find the equation, because we know the slope and a point (e, 8/e).
[tex]y-y_{1} =m(x-x_{1} )\\\\y-8/e=1(x-e)\\\\y=\frac{xe-e^{2}+8 }{e}[/tex]
Therefore, the equation of the tangent line to the curve are [tex]y=x-1 , y=\frac{xe-e^{2}+8 }{e}[/tex].
Learn more about tangent here:
https://brainly.com/question/19064965
#SPJ4
need help like rn pls!!!
Answer:
x = 3
Step-by-step explanation:
Separate | 2 + x | = | x - 8 | into 2 possibilities
2 + x = x - 8
2 + x = -x + 8 (right side's signs are swapped)
Solve the equations:
Top equation results in no solution as the x's cancel out.
2 + x = -x + 8
2x = 6
x = 3
| 2 + 3 | = | 3 - 8 |
| 5 | = | -5 |
5 = 5
This is the correct solution.
Let's solve the problem,
→ |2 + x| = |x - 8|
→ 2 + x = -(x - 8)
→ 2 + x = -x + 8
→ x + x = 8 - 2
→ x = 6/2 = 3
Hence, the value is 3.
what equations do u insert in between these numbers to get the answer
a.5 8 3 9 =50
b.12 6 2 10=14
c.4 5 6 10=24
d.7 4 6 9 7= 16
e.4 9 6 2 =52
f.45 5 9 3 7=102
Answer:
a 5 8 3
Step-by-step explanation:
The graph shows the relationship between miles and kilometres.
a)
Convert 20 miles
to km.
b)
Convert 64 km
to miles.
By cross multiplication, we have found the following results:
a) 20 miles are equal to 32.180 kilometers.
b) 64 kilometers are equal to 39.776 miles.
How to convert a distance value into another distance unit
In this problem we must convert a given value in a unit into its equivalent quantity in another unit of same kind. We must convert miles to kilometers and viceversa by using conversion rates and cross multiplication.
First, we must convert a distance of 20 miles to kilometers by cross multiplication:
x = 20 mi × (1.609 km / 1 mi)
x = 32.180 km
Second, we must convert a distance of 64 kilometers to miles by cross multiplication:
x = 64 km × (1 mi / 1.609 km)
x = 39.776 mi
RemarkThe graph is missing, but this question can resolved by using conversion rates, that is, a mile equal 1.609 kilometers.
To learn more on conversion factors: https://brainly.com/question/13259295
#SPJ1
Answer:
here is the answer⬇️
Kind of confused with this problem, if you can’t see the image properly it says, “Find the standard form for the equation of the line which passes through the point (10,-49) and which has a y intercept of 1.”
Answer:
See below
Step-by-step explanation:
find slope between 0,1 and 10, -49
m = (-49-1) / (10-0) = -5
slope intercept form
y = mx + b
y = -5 x +1 re=arrange
5x + y = 1
Help me please translations hw
The locations of the vertices are shown below:
(- 5, 4), (- 4, 4), (- 5, 2)(- 4, 1), (- 1, 2), (0, - 1), (- 2, - 5)(2, 5), (3, 4), (1, 2)(3, - 5), (- 2, - 3), (0, - 1)What are the coordinates of the images resulting from a translation?Herein we find four representations of polygons on Cartesian plane and we must determine the coordinates of the images generated by translation, a kind of rigid transformations. Translation is described by the following operation:
P'(x, y) = P(x, y) + T(x, y)
Where:
P(x, y) - Original pointP'(x, y) - Resulting pointT(x, y) - Translation vectorCase 1 (K(x, y) = (3, - 3), X(x, y) = (4, - 3), R(x, y) = (3, - 5), T(x, y) = (- 8, 7))
K'(x, y) = (3, - 3) + (- 8, 7) = (- 5, 4)
X'(x, y) = (4, - 3) + (- 8, 7) = (- 4, 4)
R'(x, y) = (3, - 5) + (- 8, 7) = (- 5, 2)
Case 2 (E(x, y) = (0, 2), X(x, y) = (3, 3), V(x, y) = (4, 0), Z(x, y) = (2, - 4), T(x, y) = (- 4, - 1))
E'(x, y) = (0, 2) + (- 4, - 1) = (- 4, 1)
X'(x, y) = (3, 3) + (- 4, - 1) = (- 1, 2)
V'(x, y) = (4, 0) + (- 4, - 1) = (0, - 1)
Z'(x, y) = (2, - 4) + (- 4, - 1) = (- 2, - 5)
Case 3 (G(x, y) = (- 4, 5), J(x, y) = (- 3, 4), U(x, y) = (- 5, 2), T(x, y) = (6, 0))
G'(x, y) = (- 4, 5) + (6, 0) = (2, 5)
J'(x, y) = (- 3, 4) + (6, 0) = (3, 4)
U'(x, y) = (- 5, 2) + (6, 0) = (1, 2)
Case 4 (V(x, y) = (0, 0), Y(x, y) = (- 5, 2), F(x, y) = (- 3, 4), T(x, y) = (3, - 5))
V'(x, y) = (0, 0) + (3, - 5) = (3, - 5)
Y'(x, y) = (- 5, 2) + (3, - 5) = (- 2, - 3)
F'(x, y) = (- 3, 4) + (3, - 5) = (0, - 1)
To learn more on rigid transformations: https://brainly.com/question/28004150
#SPJ1
Answer:
See attachments.
Step-by-step explanation:
A translation is a type of transformation that moves a figure left, right, up or down. Every point on the original figure is translated (moved) by the same distance in the same direction.
If a figure is to be moved left, subtract the number of units it is to be moved from the x-values.If a figure is to be moved right, add the number of units it is to be moved to the x-values.If a figure is to be moved up, add the number of units it is to be moved to the y-values.If a figure is to be moved down, subtract the number of units it is to be moved from the y-values.Question 1Coordinates of the given pre-image:
K = (3, -3)R = (3, -5)X = (4, -3)Given mapping rule:
[tex](x, y) \rightarrow (x-8, y+7)[/tex]
This tells us to subtract 8 from the x-values and add 7 to the y-values.
[tex]\sf \implies K(3,-3) \rightarrow K'(3-8, -3+7)=K'(-5,4)[/tex]
[tex]\sf \implies R(3,-5) \rightarrow R'(3-8, -5+7)=R'(-5,2)[/tex]
[tex]\sf \implies X(4,-3) \rightarrow X'(4-8, -3+7)=X'(-4,4)[/tex]
Question 2Coordinates of the given pre-image:
E = (0, 1)X = (3, 3)V = (4, 0)Z = (2, -4)Given mapping rule:
[tex](x, y) \rightarrow (x-4, y-1)[/tex]
This tells us to subtract 4 from the x-values and subtract 1 from the y-values.
[tex]\sf \implies E(0,1) \rightarrow E'(0-4, 1-1)=E'(-4,0)[/tex]
[tex]\sf \implies X(3,3) \rightarrow X'(3-4, 3-1)=X'(-1,2)[/tex]
[tex]\sf \implies V(4,0) \rightarrow V'(4-4, 0-1)=V'(0,-1)[/tex]
[tex]\sf \implies Z(2,-4) \rightarrow Z'(2-4, -4-1)=Z'(-2,-5)[/tex]
Question 3Coordinates of the given pre-image:
G = (-4, 5)J = (-3, 4)U = (-5, 2)Given mapping rule:
[tex](x, y) \rightarrow (x+6, y)[/tex]
This tells us to add 6 to the x-values and the y-values remain unchanged.
[tex]\sf \implies G(-4,5) \rightarrow G'(-4+6, 5)=G'(2,5)[/tex]
[tex]\sf \implies J(-3,4) \rightarrow J'(-3+6, 4)=J'(3,4)[/tex]
[tex]\sf \implies U(-5,2) \rightarrow U'(-5+6, 2)=U'(1,2)[/tex]
Question 4Coordinates of the given pre-image:
F = (-3, 4)V = (0, 0)Y = (-5, 2)Given mapping rule:
[tex](x, y) \rightarrow (x+3, y-5)[/tex]
This tells us to add 3 to the x-values and subtract 5 from the y-values.
[tex]\sf \implies F(-3,4) \rightarrow F'( -3+3, 4-5)=F'(0,-1)[/tex]
[tex]\sf \implies V(0,0) \rightarrow V'( 0+3, 0-5)=V'(3,-5)[/tex]
[tex]\sf \implies Y(-5,2) \rightarrow Y'( -5+3, 2-5)=Y'(-2,-3)[/tex]
Learn more about transformations here:
https://brainly.com/question/28354239
can someone solve this please, thank you
Answer:KIH=18
Step-by-step explanation:
4x+3+4x+3=12x
X=1.5
4(1.5)+3=9
4(1.5)+3=9
12(1.5)=18
Solve the equation [tex]\sqrt{3x} + \sqrt{12} = \frac{x+7}{\sqrt{3} }[/tex]
i need help please step by step hurry
Answer:
Step-by-step explanation:
10 x 21 - 61
210 - 61= 149
18 x 8 + 5
144 + 5= 149
21 + 10= 31
(Don't need to right this part down)
Since the 149 is parallel or the same size on the opposite side, it should be the same answer
35. The sum of the angles of a polygon is 1620°. Calculate the number of sides that polygon has.
Answer:
11
Step-by-step explanation:
total angle of a polygon formula:
180 * (n-2) n is no. of sides
180 * (n - 2) = 1620
1620/180 = n-2
9 = n - 2
9 + 2 = n
n = 11
If everyone in a class scored 100 on a quiz, what is the standard deviation of quiz scores?
The standard deviation of quiz scores is 0.
What is the standard deviation?The standard deviation in statistics is a measure of the amount of variation or dispersion in a set of values. A low standard deviation indicates that the values of the set tend to be close to the mean (also known as the expected value), whereas a high standard deviation indicates that the values are spread out over a larger range.To find the standard deviation:
Let, the number of students = nx = 100Mean = n×x/n=xVariance = [tex]\frac{\sum(\bar{x}-x)^2}{n}[/tex]Variance = (x₁ - x)² + (x₂ - x)² + (x₃ - x)²/nV = 0Standard variance = √0Therefore, the standard deviation of quiz scores is 0.
know more about standard deviation here:
https://brainly.com/question/475676
#SPJ4
What is the area of the semicircle? Use 3.14 for pi. 22cm
hi
area of circle is π* radius²
as radius is half diameter, and as diameter is 22 , so radius is 22 /2 = 11 cm
so area is 11²π and 11² = 121 then area is 121π
as it is say to use 3.14 for pi , then 121*3.14 = 379.94
but 379.94 is the area of the whole circle , and we only have half.
so : 379.94 / 2 = 189.97
area of semi circle is 189.97
MATHMATICAL CONNECTIONS (IM2) : Write a polynomial that represents the area of the square
[see image]
Answer:
[tex]49n^2-70n+25[/tex]
Step-by-step explanation:
Since one side of the square is (7n-5), the area of the square must be [tex](7n-5)^2[/tex]. Simplifying we get [tex]49n^2-70n+25[/tex].
PLEASE HELP ASAPPP !!! WILL GIVE BRAINLIEST AND 5 STAR RATING
In mapping diagram D, what is the range?
The range of the relation that is represented in the mapping shown in the diagram attached below is: {3, 5, 11, 21}.
What is the range of a Relation?If we are given a mapping that represents a relation, the input values (x-values) make up the domain of the relation while the output values (y-values) make up the range of the relation.
In the mapping shown in the diagram attached below, we have the following:
The domain of the relation is: {-1, 0, 1, 2, 3}
The range of the relation is: {3, 5, 11, 21}
Thus, we can conclude that, the range of the relation that is represented in the mapping shown in the diagram attached below is: {3, 5, 11, 21}.
Learn more about the range of a mapping on:
https://brainly.com/question/7382340
#SPJ1
What is a major area of jurisdiction for local law enforcement agencies
Answer:
Patrolling Communities.
Step-by-step explanation:
Bit much for this lol
A student increased in height from 1.52m to 1.68m, calculate the percentage increase (show your working)
The percentage increase in the student's height is 10.52%.
Here we are given that a student's height increases from 1.52m to 1.68m.
Thus, the absolute increase in the student's height will be-
1.68 - 1.52 = 0.16 meters.
Now, we need to find the percentage increase in the student's height.
The formula for calculating percentage increase is given by-
Percentage increase = change in value/ initial value * 100
Here, the change in value is 0.16 meters and the initial value is 1.52 meters.
Thus, percentage increase in height = 0.16 / 1.52 *100
= 1600/ 152
= 400/ 38
= 200/ 19
= 10.52%
Thus, the increase in the student's height is 10.52%.
Learn more about percentage change here-
https://brainly.in/question/19592355
#SPJ9
please help me im begging ANYONE
Answer:
B
Step-by-step explanation:
Answer B is the result of simplifying
(8.41 x 10^-5) - (7.9 x 10^-6)
Answer:
7.62×10^-5
Step-by-step explanation:
Answer: 0.000076
Step-by-step explanation:
8.41(10^-5) - 7.9(10^10-6)
= 8.41 (1/100000) - 7.9(10^-6)
= 0.000084 - 7.9(10^-6)
= 0.000084 - 7.9(1/000000)
= 0.000084 - 0.000008
= 0.000076
ugfgvthgrfbuyjhdvyrdhsdgfbythdfgjhmhjilk.l
Answer:
yo same
Step-by-step explanation:
ur lookin pretty shreksy
If the sum of squares for a sample containing 101 items equals 500, what is the standard deviation? 5.00 4.95 2.24 2.22
The standard deviation is 2.24 if the sum of squares for a sample containing 101 items equals 500 option (C) is correct.
What is the standard deviation?It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.
[tex]\rm SD = \sqrt{\dfrac{ \sum (x_i-X)^2}{n-1}[/tex]
SD is the standard deviation
xi is each value from the data set
X is the mean of the data set
n is the number of observations in the data set.
∑(x(i) - X)² = 500
n = 101
SD = √(500/101-1)
SD = √5
SD = 2.236 ≈ 2.24
Thus, the standard deviation is 2.24 if the sum of squares for a sample containing 101 items equals 500 option (C) is correct.
Learn more about the standard deviation here:
brainly.com/question/12402189
#SPJ4
in algebra 1 how do you find 81% of 32
X
1
y=ax²+bx+c 1.75
B
2
6
3
11.75
4
19
5
27.75
Answer:
ydiyetd5dtd7rowo47do7tso47syjfzj4tsuryusu6eaitddtsie6i64so7rso6ro6zoyds7orsoslu4sp
HELP ME PLEASE....I HATE ALGEBRA Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Quadrilateral ABCD is transformed to create A′B′C′D′. Match the coordinates of A′ with the transformations that create it. (2, 4) (2, 1) (6, 12) (4, -5) (-2, 4) (2, -4) (6, -12) (-4, 5) Quadrilateral ABCD is reflected over the x-axis. arrowRight Quadrilateral ABCD is translated 2 units right and 1 unit down. arrowRight Quadrilateral ABCD is dilated about the origin by a scale factor of 3. arrowRight Quadrilateral ABCD is rotated 180° clockwise about the origin. arrowRight
Quadilateral ABCD is reflected over the x-axis. ---> (2, -4)
ABCD is translated 2 units right and 1 unit down. ---> (4, -5)
ABCD is dilated about the origin by a scale factor of 3. ---> (6, 12)
ABCD is rotated 180° clockwise about the origin. ---> (-2, 4)
What exactly is a quadrilateral?Four sides, four vertices, and four angles make up a quadrilateral, which is a two-dimensional shape. Concave and convex are the two most common forms. Additionally, there are numerous subgroups of convex quadrilaterals, including trapezoids, parallelograms, rectangles, rhombus, and squares.
Which of these seven quadrilateral types are they?quadrilaterals come in a variety of forms.
Trapezium.
Parallelogram.
Rectangle.
Rhombus.
Square.
Kite.
To know more about Quadrilateral visit:
https://brainly.com/question/29934291
#SPJ1
solve for h pleas
A=1/2bh
h = 2A/b
An equation is a group of expressions formed by using arithmetic operations, along with an equality sign.
Here, we are given an equation, A = 1/2bh
As we are not given any values for any of the variables, we can find the value of h in terms of A and b only.
To do this, we keep h on one side and take all the other terms to the other side of the equation.
A = 1/2bh
Multiplying both sides by 2,
⇒ 2A = 2/2bh
2A = bh
now, dividing both sides by b,
2A/ b = bh/b
2A/b = h
h = 2A/b
Thus, the value of h is 2A/b
Learn more about equations here-
https://brainly.com/question/15602982
#SPJ9
which expression is equivalent to (3x+2)(3x-5)?
A. 6x - 3
B. 9x^2 - 10
C. 9x^2 - 3x - 10
D. 9x^2 - 9 - 10
Answer: 9x^2-9x-10 ==> D
Step-by-step explanation:
(3x+2)(3x-5)=
3x*3x + (-5)(3x) + 2*3x + (-5)(2)=
9x^2 - 5(3x) + 6x - 5(2)=
9x^2-15x+6x-10=
9x^2-15x+6x-10= 9x^2-9x-10 ==> D
=================================================
Explanation:
Let's make
y = 3x+2
So we can replace the (3x+2) with y
We go from (3x+2)(3x-5) to y(3x-5)
Distribute that y term through
y(3x-5)
y(3x) + y(-5)
3xy - 5y
Then plug in y = 3x+2 and distribute two more times
3xy - 5y
3x( y ) - 5( y )
3x( 3x+2 ) - 5( 3x+2 )
3x(3x) + 3x(2) - 5(3x) - 5(2)
9x^2 + 6x - 15x - 10
9x^2 - 9x - 10
which seems to point to choice D assuming the -9 in the middle is supposed to be -9x
------------------
Side note: Alternative methods are the FOIL rule and the box method.
176.912 round off to the closest integer.
help asap!!
Answer:
177
Step-by-step explanation:
In order to round 176.912 to the nearest integer firstly look at the first digit after the decimal point also known as the tenth digit.If the digit in the tenth place is >=5 we will round up and if it is < 5 we will round down keeping the ones place the same and truncating the decimal points.Since the tenth digit 9 is >= 5 we will round up i.e. ( ones place digit + 1 ) and the remaining all digits next to the decimal point are removed.Therefore, the number 176.912 rounded to the nearest integer value is 177 .All Done! Please mark as Brainliest :)
Answer:
177
Step-by-step explanation:
The tenth is 9 which means you round up so the correct answer is 177.
Hope It Helps Sorry If I'm Wrong
What is 6+42 for gcf
Answer:
48
Step-by-step explanation:
Essay writers are okay but seriously just gotta include the answer ;-;
Answer: 6 should be your answer
Explanation: Depending on how many and how large the numbers are, there are a variety of approaches to compute the GCF of a collection of integers.
Simply look at each number's components or multiples to get its largest common multiple for lesser numbers.
These factors look like this for 6 and 42:
1, 2, 3, and 6 are the six factors.
1, 2, 3, 6, 7, 14, 21, and 42 are the 42 factors.
Siobhan’s team is solving the following equation: . Amalia says there are no solutions. Brian says there is one solution, but it is imaginary. Cristina says there are two solutions! Help them out. Determine the solution(s) and justify your answer. You may want to refer to the Math Notes box in Lesson 2.2.2 for help.
There is no real solution of given equation.
There is a special case that will tell us if a quadratic has no real solution: if b = 0 when a and c share the same sign (both positive or both negative), then there will be no real solution. The quadratic formula becomes much simpler when b = 0.
given equation [tex]x^{2} =-16[/tex]
[tex]x=\sqrt{-16},\:x=-\sqrt{-16}[/tex]
[tex]x=4i, x=-4i[/tex]
we get imaginary solutions of given equation
so, there is no real solution equation is exist.
learn more quadratic equation: brainly.in/question/19169616
#SPJ9
A thief steals an atm card and must randomly guess the correct -digit pin code from a -key keypad. Repetition of digits is allowed. What is the probability of a correct guess on the first try?.
The probability of a correct guess on the first try is 0.024%.
What is probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.
A number between 0 and 1 is the probability of an event.
where,
P(E) = Number of Favorable Outcomes/Number of Total Outcomes
Because a thief steals an ATM card and must randomly guess the correct four-digit pin code from an eight-key keypad, and digit repetition is permitted, the following calculation must be performed to determine the probability of a correct guess on the first try:
8 [tex]*[/tex] 8 [tex]*[/tex] 8 [tex]*[/tex] 8 = X
[tex]8 ^ {4 }[/tex] = X
simplifying the above equation, we get
4096 = X
1/4096 = X
0.000244140625 = X
0.000244140625 [tex]*[/tex] 100 = 0.024%
Therefore, the probability of a correct guess on the first try is 0.024%.
The complete question is;
A thief steals an atm card and must randomly guess the correct four-digit pin code from a 8-key keypad. repetition of digits is allowed. what is the probability of a correct guess on the first try?
To learn more about probability, refer to:
https://brainly.com/question/24756209
#SPJ4
What are the answers to this ? HELP ASAP PLS, this is timed ! Please explain as well !
Answer:
b is the answer
Step-by-step explanation:
did I help you
