Answers
Answer:
10. D. 5 1/3
11. C. 285 cm
12. A. 42 units
Step-by-step explanation:
The first two are simple addition problems. (In problem 11, you can replace the addition of 5 identical numbers with a multiplication by 5.) The last problem is also an addition problem, but figuring out what to add can take a little effort.
___
10. The segment addition theorem tells you that for R between S and T:
ST = SR + RT
ST = 3 2/3 + 1 2/3 = (3 +1) + (2/3 +2/3) = 4 + 4/3 = 4 + 1 1/3
ST = 5 1/3
__
11. The definition of a regular polygon is that all of its sides and angles are congruent. A "pentagon" is 5-sided polygon, so your regular pentagon will have 5 sides, each of measure 57 cm. The perimeter is the total length of the sides, so is ...
P = 57 cm +57 cm +57 cm +57 cm +57 cm
P = 5×57 cm
P = 285 cm
__
12. Again, the perimeter is the sum of the side lengths. Here, the length of the top side is easily figured by the difference of x-coordinates (6 units). The length of the left side is recognizable as double the length of the hypotenuse of a 3-4-5 right triangle (10 units). The lengths of the other two sides can be found using the distance formula with the end point coordinates:
MN = √((-10-8)^2 +(-6-(-3))^2) = √(324 +9) = √333 ≈ 18.248
LM = √((8-2)^2 +(-3-2)^2) = √(36 +25) = √61 ≈ 7.810
So, the perimeter is ...
P = 6 + 10 + 18.248 +7.810 = 42.058 ≈ 42 units
_
Here, it is helpful to be familiar with the 3-4-5 right triangle. It has several interesting properties, one of which is that it shows up in algebra problems a lot. Any triangle with this ratio of side lengths is also a right triangle.
In this problem, the difference in coordinates K - N = (-4-(-10), 2-(-6)) = (6, 8) which we recognize as having the ratio 3:4. We could continue with the distance formula:
NK = √(6^2 +8^2) = √100 = 10
or, we can simply recognize this will be the result based on our familiarity with this triangle.
_
An alternate approach to this problem will also work. You can estimate the length of the perimeter.
The distance between two points is more than the maximum difference of their coordinates and less than the sum of differences of their coordinates. For example, the distance between points N and K will be more than 8 and less than 8+6=14.
If you need to refine this very crude estimate further, you can add 40% of the smallest difference to the largest difference. In this case, that would be ...
8 + 0.40·6 = 10.4 . . . . . we already know the length is actually 10, so we see this estimate is within 4% of the real length.
For the coordinates in this problem, we can see that the perimeter will be more than the sum of the longest coordinate differences: 6+6+18+8 = 38. This is an important fact, because it eliminates all of the answer choices except 42. If there were any remaining ambiguity as to the answer, we could refine our estimate by adding 40% of the sum of the shortest coordinate differences: 0.40·(0+5+3+6) = 5.6. That would bring our estimate to 38+5.6 = 43.6, within 4% of the actual value of the perimeter.
Related Questions
the club's total number of members will grow exponentially each month. She uses the given expression to model the number of club members, in hundreds, after advertising for t months.
1.8(1.02)^12t
What does the value 1.8 represent?
Answers
Answer:
1.8 represents the initial number of the club members in hundreds.
Step-by-step explanation:
* Lets revise the exponential grows
- If a quantity grows by a fixed percent at regular intervals,
the pattern can be depicted by this function.
- The function of the exponential growth is:
y = a(1 + r)^x
# a = initial value (the amount before measuring growth)
# r = growth rate (most often represented as a percentage and
expressed as a decimal)
# x = number of time intervals that have passed
* Now Lets study the problem to solve it
- The club's total number of members will grow exponentially
each month
- The expression to model the number of club members, in
hundreds, after advertising for t months is
1.8(1.02)^12t
* Lets compare between this model and the function above
# a = 1.8 ⇒ initial number of members in hundreds
# r = 1.02 - 1 = 0.02 ⇒ growth rate
# x = 12t ⇒ number of time intervals
* 1.8 represents the initial number of the club members in hundreds.
a rectangle is 6 meters longer than it is wide. The area of the rectangle is 315 square meters. find the length
Answers
Answer:
The length is 21 meters
Step-by-step explanation:
* Lets use variable to represent the dimensions of the rectangle
- The length of the rectangle is 6 meters longer than its width
# Let the width of the rectangle = x meters
∴ The length of the rectangle = x + 6 meters
- The area of the rectangle = Length × width
∵ The area of the rectangle = 315 meters²
∵ The length of the rectangle = x + 6
∵ The width of the rectangle = x
∴ x(x + 6) = 315 ⇒ open the brackets to solve the equation
∴ x² + 6x = 315 ⇒ subtract 315 from both sides
∴ x² + 6x - 315 = 0
- Lets factorize the quadratic equation to find the value of x
∵ The last term of the quadratic is negative
∴ The brackets have different sign
# x² = x × x ⇒ 1st terms in the two brackets
# -315 = -15 × 21 ⇒ 2nd terms in the two brackets
# x × -15 = -15x ⇒ 1st term in the first bracket and 2nd term in
the second bracket
# x × 21 = 21x ⇒ 1st term in the second bracket and 2nd term
in the first bracket
# 21x - 15 x = 6x ⇒ the middle term of the quadratic equation
∴ The factoriz of x² + 6x - 315 = 0 is
(x + 21)(x - 15) = 0
∴ x + 21 = 0 OR x - 15 = 0
# x + 21 = 0 ⇒ subtract 21 from both sides
∴ x = -21 ⇒ neglect this answer because there is no negative
value for the dimensions
# x - 15 = 0 ⇒ add 15 to both sides
∴ x = 15
- The value of the width is x
∴ The width = 15 meters
- The value of the length is x + 6
∴ The length = 15 + 6 = 21 meters
Find the solution set for the equation, given the replacement set.
5x + 2y = –3; {(–2, 9.5), (–3, 11.5), (–4, 8.5), (–5, 6.5)}
a.
{(–2, 9.5), (–3, 11.5)}
c.
{(–4, 8.5)}
b.
{(–3, 11.5)}
d.
{(–4, 8.5), (–5, 6.5)}
Answers
Answer:
c. {(–4, 8.5)}
Step-by-step explanation:
A plot of the equation and the offered points is attached.
__
It might be helpful to put the equation into slope-intercept form.
2y = -5x -3
y = -5/2x -3/2
This shows you that y will be an odd multiple of 1/2 only for even values of x. So, we only need to check the points (-2, 9.5) and (-4, 8.5).
At x=-2, y = -5/2(-2) -3/2 = 5 -3/2 < 9.5 . . . . . (-2, 9.5) is not a solution
At x=-4, y = -5/2(-4) -3/2 = 10 -3/2 = 8.5 . . . . (-4, 8.5) is a solution
Of the offered choices, the only one in the solution set is (-4, 8.5).
Substitute the value x = -1 into the first equation and solve for y.
{ y= 2x - 1
-2x - y = 5
Answers
Answer:
y = -3
Step-by-step explanation:
Following the directions, we have ...
y = 2·(-1) -1 = -2-1 . . . . . . put -1 where x is in the equation
y = -3
Please help
must show work
there are 5 that I'm stuck on
Answers
you cannot show too much "work"
basically, you remove what is common to all of the factors, and then put brackets, as it will be multiplied back in, remember that when you multiply exponents with the same base, its same as adding them, so subtract to remove...
you can seperate two of the variables , then factor, then subtract the last one from those two, because it cannot be factored out , as in part2 #2
MATH GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG
Answers
Answer:
Option C is correct.
Step-by-step explanation:
The equation used to represent the slop-intercept form is
y= mx + b
where m is the slope
and b is the y-intercept.
So, in the given question y-intercept = (0,8)
b= 8 and
slope =m= 1/2
the equation will be:
y = mx + b
y= (1/2)x + 8
So, Option C is correct.
if g(x)= 2x -1 then g(4)=
Answers
g(4)=2×4_1
8-1
=9
hence the answer is 9
hope it helps you!!!!!!!!!
Answer:
g(4) = 7
Step-by-step explanation:
To evaluate g(4) substitute x = 4 into g(x), that is
g(4) = (2 × 4) - 1 = 8 - 1 = 7
Which of the following points is a solution of the inequality y < -|x|?
A. (1,-2)
B. (1,-1)
C. (1,0 )
Answers
ANSWER
The correct choice is A
EXPLANATION
The given inequality is
y < -|x|
We substitute each point into the inequality to determine which one is a solution.
Option A
-2 < -|1|
-2 < -1.
This statement is true.
Hence (1,-2) is a solution.
Option B.
-1 < -|1|
-1 < -1.
This statement is false.
Option C
0 < -|1|
0 < -1.
This statement is also false.
What is the x-intercept and the y-intercept of the line in the graph
Answers
Answer:
x intercept= 3
y=-2
Step-by-step explanation:
the intercept is the point when the line crosses the axis
PLEASE HELP 70 POINTS
4a. An experiment had the following result for 20 flips of a coin: P(Tails) 12/20 P(Heads) = 8/20. If you flip 90 more times, how many would be tails?
4b. Explain how many flips would be tails if you flip 100 more times.
Answers
Answer:
4a. About 54 times NOT INCLUDING THE FIRST TRIAL
4b. About 60 times NOT INCLUDING THE FIRST TRIAL
Step-by-step explanation:
I say about because we don't know if it's ALWAYS going to be the same results.
4a. Also 12*4 because it's 20 times so 20*4=80 then you add half of it to become 90 and you get 54
4b. 12*5 because 100/5=20 for the 20 trials of them
What is the length of the third side of the window frame below?
(Figure is not drawn to scale.)
A picture of a right triangular window frame is shown. The longest side has length labeled as 39 inches. The height of the frame is labeled as 36 inches.
15 inches
27 inches
25 inches
32 inches
Answers
Answer:
15 inches
Step-by-step explanation:
The longest side of the right triangular window frame is 39 inches
The height is 36 inches
Let the base of the window frame be x inches
So according to Pythagoras theorem,
x² + 36² = 39²
x² = 39² - 36² = 225
x = [tex]\sqrt{225}[/tex] = 15 inches
The third side of the window frame is therefore equal to 15 inches.
The length of the third side of the window frame will be 15 inches. Then the correct option is A.
What is a Pythagoras theorem?The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.
The Pythagoras theorem formula is given as
H² = P² + B²
The longest side has a length labeled as 39 inches. The height of the frame is labeled as 36 inches.
Let x be the length of the third side of the window frame. Then we have
39² = x² + 36²
x² = 39² - 36²
x² = 1521 - 1296
x² = 225
x = 15 inches
Then the correct option is A.
More about the Pythagoras theorem link is given below.
https://brainly.com/question/343682
#SPJ2
GEOMETRY!!! 15 PTSSSSS
Answers
Answer:
23) option c
JL ≈ 9.3
25) option c
y ≈ 9.6
Step-by-step explanation:
25)Given in the question that,
cos(21°) = 9 / y
y = 9/cos(21°)
y = 9.64
y ≈ 9.6(nearest tenth)
23)Given in the question that the hypotenuse of right angle triangle = 12
To find,
height of the right angle triangle
angle k = 39°
so by using trigonometry identity
cos(39) = opp/hypo
cos(39) = JL / KL
JL = cos(39)(12)
JL = 9.32
JL ≈ 9.3
Answer:
Q 23. Last option 7.6
Q 25 Third option
Step-by-step explanation:
To solve Q 23
From the figure we can write,
Sin 39 = Opposite side/Adjacent side
= JL/KL
= JL/12
JL= 12 * Sin 39
= 12 * 0.629 = 7.55
= 7.6
To solve Q 25
Cos 21 = 9/y
y = 9/Cos 21 = 9/0.9335
= 9.64
= 9.6
I need help on this
Answers
Answer:
none of the above
Step-by-step explanation:
The transformation ...
g(x) = k·f(x -a) +b
vertically stretches the function f(x) by a factor of "k", translates it to the right by "a" units and up by "b" units. There won't be any reflection across the x-axis unless the stretch factor (k) is negative.
You have k=2, a=2, b=-2, so the function is stretched by a factor of 2, then translated to the right and down by 2 units each.
_____
The stretch is done first. If it is done last, then the translation factor(s) are also stretched. All the answer choices given in your problem statement list the stretch last, so none is correct. (You are probably expected to choose d.)
What is the domain and range of the function shown
Answers
Answer:
• domain: x ≥ 0
• range: y ≥ 0
Step-by-step explanation:
The graph shows a ray that starts at the origin and extends to infinity in both the +x and +y directions. The domain (horizontal extent) is [0, ∞), as is the range (vertical extent).
HELP PLZ 20 POINTS PLZ DUE TM!!!
Answers
Answer:
40 (cm)
Step-by-step explanation:
0. make up a new picture with additional elements (radius of the inscribed circle, it's 'x'; and some elements as shown in the attached picture);
1. the formula of the required perimeter is P=a+b+c, where c- hypotenuse.
2. apply the Pythagorean theorem: a²+b²=c², where c - hypotenuse, then calculate value of 'x' (attention! x>0, the length is positive value !)
3. substitute 'x' into the formula of the required perimeter. The result is 40.
PS. All the details are in the attached picture, answer is marked with red colour.
what is the discriminant of the polynomial below 4x^2-20x +25
Answers
Answer:
The discriminant D=0
Step-by-step explanation:
For the duadratic polynomial [tex]ax^2+bx+c[/tex] the discriminant is
[tex]D=b^2-4ac.[/tex]
In your case, for the polynomial [tex]4x^2-20x+25,[/tex]
[tex]a=4;[/tex][tex]b=-20;[/tex][tex]c=25;[/tex][tex]D=(-20)^2-4\cdot 4\cdot 25=400-400=0.[/tex]Answer:
The answer is 0 D
Decimal Calculations (Multiplication). An employee earns a salary of $380 for a 40-hour work week. If the employee worked 40 hours plus 14 hours of overtime at the overtime rate of 12.50 for each hour overtime worked, find her total income for the week.
Answers
Answer:
$ 555
Step-by-step explanation:
Salary for a 40-hour work week = $380
Total income for the week will be = Salary of regular 40 hours + Salary of 14 hours overtime
Salary per hour for the overtime work = $ 12.50
So,
The salary for 14 hours of overtime will be = $ 12.50 x 14 = $ 175
Therefore,
Total income for the week will be = $ 380 + $175 = $ 555
Thus, for a 40 hour work week and 14 hours of overtime the total income of the week will be $ 555
Please help me on this please
Answers
Answer:
㏒3(14) = 2.402 ⇒ 3rd answer
Step-by-step explanation:
* Lets revise some rules of the logarithmic functions
- log(a^n) = n log(a)
- log(a) + log(b) = log(ab) ⇒ vice versa
- log(a) - log(b) = log(a/b) ⇒ vice versa
* Lets solve the problem
- We have the value of ㏒3(2) and ㏒3(7)
- We must change the problem to these logarithm to solve
∵ 14 = 2 × 7
∴ We can write ㏒3(14) as ㏒3(2 × 7)
∴ ㏒3(14) = ㏒3(2 × 7)
* Now lets use the rules above
∵ log(ab) = log(a) + log(b)
∴ ㏒3(2 × 7) = ㏒3(2) + ㏒3(7)
∵ ㏒3(2) = 0.631 and ㏒3(7) = 1.771
∴ ㏒3(2 × 7) = 0.631 + 1.771 = 2.402
* ㏒3(14) = 2.402
Please help I've failed this many times
Answers
Answer:
x-intercept (9, 0)y-intercept (0, 17.5)Step-by-step explanation:
You can compute the slope from two of the points, then write the point-slope form of the equation of the line.
slope = (change in y)/(change in x)
= (15 -20)/(3 -1) = -5/2
Then the equation of the line, using the first point) is ...
y = m(x -h) +k . . . . . . for slope m through point (h, k)
y = -5/2(x -1) +20
The x-intercept is the value of x where y=0:
0 = -5/2(x -1) +20 . . .put 0 where y is in the equation, then solve for x
0 = (x -1) -8 . . . . . . . . multiply by -2/5 (the inverse of the x-coefficient)
9 = x . . . . . . . . . . . . . simplify, add 9
The x-intercept is (9, 0).
__
The y-intercept is the value of y where x=0:
y = -5/2(0 -1) +20 . . . . . . put 0 where x is in the equation, then solve for y.
y = -2.5 +20 = 17.5
The y-intercept is (0, 17.5).
_____
Comment on the problem
Your question page seems to offer both lesson and video help. Either or both may be better than the written solution here.
The equation h(t)=−16t2+19t+110 gives the height of a rock, in feet, t seconds after it is thrown from a cliff.
What is the initial velocity when the rock is thrown?
Answers
[tex]\bf ~~~~~~\textit{initial velocity} \\\\ \begin{array}{llll} ~~~~~~\textit{in feet} \\\\ h(t) = -16t^2+v_ot+h_o \end{array} \quad \begin{cases} v_o=\stackrel{}{\textit{initial velocity of the object}}\\\\ h_o=\stackrel{}{\textit{initial height of the object}}\\\\ h=\stackrel{}{\textit{height of the object at "t" seconds}} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ h(t)=-16t^2+\stackrel{\stackrel{v_o}{\downarrow }}{19}t+110~\hspace{10em}19~\frac{ft}{sec}[/tex]
The initial velocity of the rock when thrown from the cliff is represented by the coefficient of the t term in the quadratic equation, which is 19 feet per second.
The equation h(t) = -16t² + 19t + 110 describes the height of a rock in feet, as a function of time in seconds after it is thrown from a cliff. To find the initial velocity of the rock when it is thrown, we look at the coefficient of the linear term in this equation, which represents the initial velocity in feet per second (since the equation is quadratic and the coefficient of the t2 term corresponds to half the acceleration due to gravity in feet per second squared).
The initial velocity of the rock is given by the coefficient of the t term, which is 19 feet per second.
Find the equation of the line that is perpendicular to the line 4x + 2y = 1 and passes through the point (−4, 3).
A) y=2x+5
B) y=2x+2
C) y=1/2x+2
D) y=1/2x+5
Answers
Answer:
y=1/2x+5 or d
Step-by-step explanation:
Answer is D
Step-by-step explanation:
*algebra* What is (f−g)(x)?
Answers
Answer:
x^3 -6x^2 +18x-10
Step-by-step explanation:
f-g (x) = f(x) -g(x)
f(x) = x^3 -2x^2 +12x-6
g(x) =4x^2 -6x +4
f(x) -g(x) =x^3 -2x^2 +12x-6 - (4x^2 -6x +4)
Distribute the minus sign
x^3 -2x^2 +12x-6 - 4x^2 +6x -4
Combine like terms
x^3 -2x^2- 4x^2 +12x+6x-6 -4
x^3 -6x^2 +18x-10
If the distance covered by an object in time t is given by s(t)=t^2+5t , where s(t) is in meters and t is in seconds, what is the distance covered in the interval between 1 second and 5 seconds?
A. 24 meters
B. 30 meters
C. 40 meters
D. 42 meters
E. 44 meters
Answers
Answer:
E. 44 meters
Step-by-step explanation:
The function that models the distance covered by the object is
[tex]s(t)=t^2+5t[/tex]
where s(t) is in meters and t is in seconds.
The distance covered by the object after 1 second is
[tex]s(1)=1^2+5(1)=6m[/tex]
The distance covered by the object after 1 second is
[tex]s(1)=5^2+5(5)=50m[/tex]
The distance covered between 1 second and 5 seconds is
50-6=44m
Answer:
person above is right
Step-by-step explanation:
right on plato
Consider the function f(x) = sin(x) and the function g(x) shown below.
Answers
Answer:
C
Step-by-step explanation:
g(x) = f(x - π/3), so g(x) is f(x) shifted to the right π/3 units.
Answer C.
a home building contractor bought 4 2/8 acres for $165,000. What was the cost of each acre? (round to nearest dollar.)
Answers
Answer:
$ 38,824
Step-by-step explanation:
Total Area of land that was bought = [tex]4\frac{2}{8}[/tex] acres
Total Cost of this area = $ 165,000
We have to find the cost of 1 acre of land.
Cost of [tex]4\frac{2}{8}[/tex] acres of land = $ 165,000
Dividing both sides by [tex]4\frac{2}{8}[/tex], we get:
Cost of 1 acre of land = $ 165,000 ÷ [tex]4\frac{2}{8}[/tex]
= $ 38,824
Thus the cost of each acre of land is $ 38,824 (rounded to nearest dollar)
Answer: $38,824
Step-by-step explanation:
Convert the mixed number [tex]4\ \frac{2}{8}[/tex] as a decimal number.
Divide the numerator by the denominator and add it to the whole number 4. Then:
[tex]4+0.25=4.25acres[/tex]
Then, knowing that 4.25 acres cost $165,000 , divide this amount by 4.25 acres to find the cost of each acre.
Therefore, you get that the cost of each acre rounded to nearest dollar is:
[tex]cost=\frac{\$165,000}{4.25}\\cost=\$38,824[/tex]
An architect created the blueprints for the Chin's house. The scale factor is 1 inch: 40 inches. The length and width of the living room on the blueprint are 4 inches and 8 inches respectively. WHat is the area of the actual living room?
Answers
Step 1: Find the area of the living room on the blueprint with the formula Area = length x height
A = 4 x 8
A = 32
Step 2: We now know that the area of the living room on the blueprint is 32 inches, but we have to convert it into the actual answer. To do this multiply 32 by 40 (you have to do this because 1 inch is 40 inch in reality meaning that each inch in the 32 inches is times 40 <<< Does that make sense?), so...
40 x 32 = 1,280
Hope this helped!
Answer:
The measurements for the actual room are, in inches, 160 x 320
Step-by-step explanation:
If you want the computed area, then multiply those numbers together since A=bh. I assumed you were just looking for the measurements of the actual room. Set up a ratio for the scale first, the model info in the numerator and the actual room info in the denominator:
[tex]\frac{m}{a}: \frac{1}{40}[/tex]
Here, the m is the model on paper and the a is the actual room. So if the length of the room on paper is 4 inches, that will go on top with the model stuff and we will solve for the missing equivalent length of the actual room:
[tex]\frac{m}{a} :\frac{1}{40} =\frac{4}{x}[/tex]
Cross multiply to get that the length of the actual room is 160 inches long. Divide by 12 if you need that number in feet.
Doing the same with the width:
[tex]\frac{m}{a} :\frac{1}{40}=\frac{8}{y}[/tex]
Cross multiply to get that the width of the actual room is 320 inches. Again, if you need that in feet, divide by 12.
Mrs. Robinson, an insurance agent, earns a salary of $4,800 per year plus a 3% commission on her sales. The average price of a policy she sells is $6,100.
Write an inequality to find how many policies Mrs. Robinson must sell to make an annual income of at least $8,000.
4800+183x<(line under the arrow)=8000
4800+183x=8000
4800+183x>=8000
4800+186>(ine under the arrow)=8000
Answers
Answer:
[tex]4800+183x\geq 8000[/tex]
She must sell at least 18 policies to make an annual income of at least $8,000
Step-by-step explanation:
Let [tex]x[/tex] be the number of policies Mrs. Robinson must sell
We know that Mrs. Robins makes 3% on commission for each policy sold. We also know that the average price of a policy is $6,100, so she makes 3% of $6,100 per policy sold. To find the 3% of $6,100 we just need to multiply 3% and $6,100; then dive the result by 100%:
[tex]\frac{3*6,100}{100} =183[/tex]
Now we know that she makes $183 per policy sold. Since [tex]x[/tex] is the number of policies sold, [tex]183x[/tex] is her total commission for selling [tex]x[/tex] policies.
We also know that She makes $4,800 per year, so her total annual income is her salary plus her commissions, in other words:
[tex]4800+183x[/tex]
Finally, we know that she wants to make at least $8,000, so her salary plus her commissions must be greater or equal than $8,000:
[tex]4800+183x\geq 8000[/tex]
Let's solve the inequality:
1. Subtract 4800 from both sides
[tex]4800-4800+183x\geq 8000-4800[/tex]
[tex]183x\geq 3200[/tex]
2. Divide both sides by 183
[tex]\frac{183x}{183} \geq \frac{3200}{183}[/tex]
[tex]x\geq 17.48[/tex]
Since she can't sell a fraction of a policy, we must round the result to the next integer:
[tex]x\geq 18[/tex]
We can conclude that she must sell 18 policies to make an annual income of at least $8,000.
What is the point of maximum growth rate? Round to the nearest tenth.
Answers
Answer:
(x, f(x)) ≈ (5.5, 4)
Step-by-step explanation:
You can go to the trouble to find the point where the second derivative is zero (the derivative has a maximum), or you can realize the function is symmetrical about y=4, which is where the point of inflection is. The x-value there is ...
4 = 8/(1 +3e^(-0.2x))
1 +3e^(-0.2x) = 8/4 = 2
e^(-0.2x) = 1/3
x = ln(1/3)/-0.2 = 5ln(3) ≈ 5.493 ≈ 5.5
We already know the value of f(x) is 4 there.
The point of maximum growth is about (5.5, 4).
Law of sines: sin(A)/a=sin(B)/b=sin(C)/c How many distinct
Answers
Answer:
According to the given question if one of the angle of the triangle is 75 degree and the other two sides are of length 2 and 3 units respectively then option C is correct. Only One triangle can be formed where Angle B will be 40 degree. You can figure it out from the steps mentioned below first of all draw an Arc with the length either 3cm or 2 cm that will be the base of a triangle and then from the ending point again cut an arc then after from the starting point that is the point draw an angle of 75 degree with the help of protactor and extend it to meet the Arc finally you can get the 40 degree.
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What are the vertical and horizontal asymptotes for the function f(x)= x^2+x-6/x^3-1?
a) vertical asymptote: x = 1
horizontal asymptote: none
b) vertical asymptote: x = 1
horizontal asymptote: y = 0
c) vertical asymptote: x = –2, x = 3
horizontal asymptote: y = 0
d) vertical asymptote: x = –2, x = –3
horizontal asymptote: none
Answers
Answer:
Option B
Step-by-step explanation:
Given
f(x)= (x^2+x-2)/(x^3-1)
For vertical asymptotes we have to put the denominator of the function equal to zero:
x^3-1=0
x^3=1
So,
x=1
As the degree of denominator is greater than the degree of numerator, there will be only horizontal asymptote which will be y=0 because all the y values will be dragged down to the x-axis.
So the horizontal asymptote: y=0
And Vertical asymptote: x =1
Answer:
b
Step-by-step explanation: