f(x) = 6x + 4. Find the inverse of f(x).
A. f^-1(x) = 6x - 4
B. f^-1(x) = x-6/4
C. f^-1(x) = 4 - 6x
D. f^-1(x) = x-4/6
D. f-1(x) = x-4/6
Step-by-step explanation:
y = 6x + 4
-4
y-4 = 6x
÷6
y-4/6 = x
(Swap y and x around to find the inverse)
Inverse will be:
x - 4/6 = y
So, f-1(x) = x-4/6
Hope this helps!
8 ounces ____ 1/4 pound
Which one is bigger,equal or less
Answer: GREATER
Step-by-step explanation:
1/4 of a pound is 0.125 divided by 4 please correct if wrong 8 ounces to a pound would be 0.5/0.50
Find the derivative of the function. f(x) = (tan5(x) + 2)^2
[tex]f(x) = (tan(5x)+2)^2\\\\f'(x) = 2(tan(5x) +2)*\frac{d}{dx}(tan(5x)+2) = 2(tan(5x)+2)*5sec^2(5x)\\ =(2tan(5x)+4)*5sec^2(5x)\\ =10tan(5x)*sec^2(5x)+20sec^2(5x)[/tex]
Hope that helps!
[tex]\begin{gathered} \rm Prove \: that :- \\ { { \rm { f ( x ) = f ( 0 ) + \dfrac{x}{1!} f'(0) + \dfrac{x²}{2!} f''(0) + \dfrac{x³}{3!} f'''(0) + \cdot \cdot \cdot \cdot \cdot \cdot \cdot }}}\end{gathered}[/tex]
The series you had provided is generally the Maclaurin's series , and we want to prove the series , this series is very very much useful in calculus , especially when you have to substitute a function by it's series . So now let's start !
Consider the function f(x) as series of a polynomials of nth (n ≥ 1) degree as
[tex]{\boxed{\bf{f(x)=a_{0}+a_{1}x+a_{2}x^{2}+a_{3}x^{3}+a_{4}x^{4}+\cdots \cdots \infty}}}[/tex]
Now , at x = 0
[tex]{:\implies \quad \sf f(0)=a_{0}+a_{1}(0)+a_{2}(0)^{2}+a_{3}(0)^{3}+a_{4}(0)^{4}+\cdots \cdots \infty}[/tex]
[tex]{\boxed{:\implies \quad \sf f(0)=a_{0}}}[/tex]
Now , again consider the function that we assumed
[tex]{:\implies \quad \sf f(x)=a_{0}+a_{1}x+a_{2}x^{2}+a_{3}x^{3}+a_{4}x^{4}+\cdots \cdots \infty}[/tex]
Differentiating both sides w.r.t.x will yield
[tex]{:\implies \quad \sf f^{\prime}(x)=0+a_{1}\times 1+a_{2}\times 2\times x+a_{3}\times 3\times x^{2}+a_{4}\times 4\times x^{3}+\cdots \cdots \infty}[/tex]
[tex]{:\implies \quad \sf f^{\prime}(x)=a_{1}+2a_{2}x+3a_{3}x^{2}+4a_{4}x^{3}\cdots \cdots \infty}[/tex]
Now , put x = 0 ;
[tex]{:\implies \quad \sf f^{\prime}(0)=a_{1}+2a_{2}(0)+3a_{3}(0)^{2}+4a_{4}(0)^{3}\cdots \cdots \infty}[/tex]
[tex]{:\implies \quad \sf f^{\prime}(0)=a_{1}}[/tex]
[tex]{\boxed{:\implies \quad \sf a_{1}=\dfrac{f^{\prime}(0)}{1!}}}[/tex]
Now , consider ;
[tex]{:\implies \quad \sf f^{\prime}(x)=a_{1}+2a_{2}x+3a_{3}x^{2}+4a_{4}x^{3}\cdots \cdots \infty}[/tex]
Differentiating both sides w.r.t.x now ;
[tex]{:\implies \quad \sf f^{\prime \prime}(x)=0+2\times a_{2}\times 1+3\times a_{3}\times 2\times x+4\times a_{4}\times 3\times x^{2}\cdots \cdots \infty}[/tex]
[tex]{:\implies \quad \sf f^{\prime \prime}(x)=2a_{2}+6a_{3}x+12a_{4}x^{2}+\cdots \cdots \infty}[/tex]
Now , putting x = 0 will yield ;
[tex]{:\implies \quad \sf f^{\prime \prime}(0)=2a_{2}+6a_{3}(0)+12a_{4}(0)^{2}+\cdots \cdots \infty}[/tex]
[tex]{:\implies \quad \sf f^{\prime \prime}(0)=2a_{2}}[/tex]
[tex]{\boxed{:\implies \quad \sf a_{2}=\dfrac{f^{\prime \prime}(0)}{2!}}}[/tex]
Now , similarly we can prove that ;
[tex]{\boxed{:\implies \quad \sf a_{n}=\dfrac{f^{n}(0)}{n!}}}[/tex]
Now , as we had considered ;
[tex]{:\implies \quad \sf f(x)=a_{0}+a_{1}x+a_{2}x^{2}+a_{3}x^{3}+a_{4}x^{4}+\cdots \cdots \infty}[/tex]
Now , putting the values we obtained above ;
[tex]{:\implies \quad \sf f(x)=f(0)+\dfrac{x}{1!}f^{\prime}(0)+\dfrac{x^2}{2!}f^{\prime \prime}(0)+\dfrac{x^3}{3!}f^{\prime \prime \prime}(0)+\dfrac{x^4}{4!}f^{\prime \prime \prime \prime}(0)+\cdots \cdots \dfrac{x^n}{n!}f^{n}(0)+\cdots \cdots \infty}[/tex]
Hence , Proved
+
Question 9 (Multiple Choice Worth 5 points)
(05.02 MC)
The angles shown below are supplementary:
10x
70°
What is the value of x?
O 100
O 110
O 20°
021
Answer:
x=11
Step-by-step explanation:
supplementary angles add up to 180 degrees
10x + 70 =180
10x = 110
x=11
11x10 = 110
110+70 = 180
The measure of the
central angle of a circle
is 74°. What is the
measure of the
intercepted arc?
Answer: 74 degrees
Step-by-step explanation:
The measure of a central angle is equal to the measure of the arc that it intercepts.
Given: ABCD is a parallelogram GEC ∠GEC≅∠HFA and AE ≅ FC .
Prove: △GEC≅△HFA.
Answer:
Step-by-step explanation:
3) Congruent segments added to congruent segments form congruent segments
4) [tex]\overline{AD} \parallel \overline{BC}[/tex] (opposite sides of a parallelogram are parallel)
5) [tex]\angle FAH \cong \angle GCE[/tex] (if 2 parallel lines are cut by a transversal, the alternate interior angles are congruent)
6) [tex]\triangle GEC \cong \triangle HFA[/tex] (ASA)
If 60% of a number is 90, what is the number
Answer:
60% in a fraction is: 60/100
60/100 of a variable, x, is equal to 90.
So we format it this way and solve for x;
60/100 * x = 90
60/100x = 90
0.6x = 90
/0.6 /0.6
x = 150, is the number.
NEED HELP ASAP WILL MARK BRAINLIEST Read the following scenario and answer the questions. Your manufacturing company incurs several costs to make the finished product, which are cans of eco-friendly paint. You purchase 100 empty cans at $2.00 each and 200 labels for the cans of paint at $1.00 each. You have two employees who bottle the paint into the cans and one additional employee who places a label on each can. You take a printout from your clock where the employees have entered their time and find that the wages due to these three employees is $2,000.00. You must also pay payroll taxes in the amount of $140.00 total for these three employees. A number of other costs incurred must be taken into consideration as well: depreciation on the factory machine of $150.00, utilities of $200.00, prepaid insurance of $600.00, and property taxes on your building of $2,000.00. Prepare the journal entries to record the purchase of the raw materials, the labor incurred, and the overhead incurred. Assume that $100.00 of the raw materials and $1,000.00 of the indirect materials were used. Prepare the journal entries to assign these materials to the jobs and overhead. Of the $2,140.00 in factory labor, $500.00 was attributed to indirect labor costs. Prepare the journal entry to assign the labor to jobs and overhead. You determine that direct labor cost is the activity base for determining the predetermined overhead rate. The following information is known about the estimated annual costs: overhead costs: $18,000.00 direct labor costs: $25,000.00 What is the predetermined overhead rate? What is the journal entry to assign overhead to jobs? Prepare the journal entry to transfer costs to Finished Goods. A sale of the goods takes place. The goods are sold for $5,000.00. Prepare the journal entry to record this sale.
Answer:
answer is 2.8 im not sure so check with another person mark me as brainliest
Step-by-step explanation:
if you divide 10 divided by 2 it gives you 5 and then subtract it by 2.2 = 2.8
there goes your answer.
Factor the expression. 81x^2 - 121
[tex]81x^{2} -121=(9x-11)(9x+11)[/tex]
Hope that helped!
Factoring:
[tex]81x^2-121=(9x+11)(9x-11)[/tex]
Hope that helps!
An ostrich is
running at a speed
of 43 miles per
hour
Is it proportional or non proportional
The relationship iof the ostrich running at 43 miles per hour is proportional.
Speed of the ostrichSince speed = distance per unit time
The speed of the ostrich is 43 miles per hour. This means that the ostrich covers a distance of 43 miles every hour.
Since the ostrich always covers a distance of 43 miles every hour, we see that distance is proportional to time.
So, the relationship iof the ostrich running at 43 miles per hour is proportional.
Learn more about proportionality here:
https://brainly.com/question/24868934
PLEASE ANSWER ASAP WILL MARK BRAINLIEST!!!
Answer:
option c
Step-by-step explanation:
Quadratic function in vertex form:
y = a(x - h)² + k
Where (h, k) is the vertex
vertex(5 , 12)
y = a(x - 5)² + 12
This passes through (8, 9)
9 = a(8 - 5)² + 12
9 = a(3)² + 12
9 = 9a + 12
9 - 12 = 9a
9a = -3
a = -3/9
a = -1/2
[tex]Answer:\ y = \dfrac{-1}{3}(x - 5)^{2}+12[/tex]
1. Assume that segments that appear to be tangent are tangent.
Find ML to the nearest tenth.
2. Assume that segments that appear to be tangent are tangent.
Find WY.
1. Applying the pythagroean theorem, ML = 6.4.
2. Applying the two tangents theorem, WY = 37.
What is the Two Tangents Theorem?The two tangents theorem states that two tangents drawn from a circle to meet at a point outside the circle are congruent.
Thus:
1. ΔJKL is a right triangle, find JL using the Pythagorean theorem:
JL = √(16² - 9.6²)
JL = 12.8
Therefore:
ML = 1/2(JL)
ML = 1/2(12.8) (radius of circle)
ML = 6.4.
2. Based on the two tangents theorem, we have:
43 - 2x = 12x + 1
-2x - 12x = -43 + 1
-14x = -42
x = 3
WY = 43 - 2x
Plug in the value of x
WY = 43 - 2(3)
WY = 37
Learn more about the two tangents theorem on:
https://brainly.com/question/9892082
A cloud directly above you is about 10° across. From the weather report, you know that the cloud is at an altitude of 2200 m. How wide is the cloud?
The width of the cloud is 12500 meters wide.
The situation forms a right angle triangle.
What is a right angle triangle?Right angle triangle are triangle that has one of its sides as 90 degrees. The sides can be found using trigonometric ratios.
Therefore, the altitude is the opposite side of the triangle formed. The width of the cloud is the adjacent side of the triangle formed.
tan 10 = opposite / adjacent
Therefore,
tan 10° = 2200 / a
cross multiply
a = 2200 / tan 10°
a = 2200 / 0.1763269807
a = 12500 meters
Therefore, the width of the cloud is 12500 meters .
learn more on right triangle here: https://brainly.com/question/2883415
Logan has a budget of $400 to have family pictures taken. There is a sitting fee of $38. Prints cost $25 per page. How many pages of prints can Logan order?
Answer:
14
Step-by-step explanation:
You take the 400 and you minus 38 you get 362 then u divide that by 25 you get 14.48. I personally would just go with 14
I don't understand how the problem wants me to set up the equation, much less how to find the right answer.
PLEASE HELP HURRY! I HAVE AN F IN MATH!!!
A prism is completely filled with 64 cubes that have edge lengths of 12 in.
What is the volume of the prism?
Enter your answer in the box.
__ in³
Answer:
Step-by-step explanation:
Volume of cube = edge³
= 12*12*12
= 1728 in³
Volume of prism = volume of 64 cubes
= 64 * volume of a cube
= 64 * 1728
= 110592 in³
help please, i dont know how to do this
Answer:
they are not simular
Step-by-step explanation:
one has longer sides then the other and one has shorter sides
A line passes through the point (-10,-7) and has a slope of
2 Write an equation in slope-intercept form for this line.
Answer: Below
Step-by-step explanation:
so using slope intercept form, we know that y = mx + b. We plug in our values. Since -10 is the x value and -7 is the y value, and 2 is the slope:
-7 = 2(-10) + b
Simplify.
-7 = -20 + b
13 = b
We plug b into the slope intercept form, this time without an x or y value to make it apply to all points on the line.
y = 2x + 13
That's our answer.
10. The number of people who have heard a rumor increases exponentially. If all who hear a rumor repeat it
to two people per day, and if 20 people start the rumor, the number N(t) of people who have heard the
rumor after t days is given by N(t) 20(2).
a. After what amount of time will 1000 people have heard the rumor?
=
1000 people will have heard the rumor
by 6 days.
1000 = 2012)
20
20
Soat
2t - 50
10g (50) = +
5.643856
b. What is the doubling time for the number of people who have heard the rumor?
+
Answer:
2000 is the answers.............
A dilation produces a smaller figure. Which is a possible scale factor? –2 One-third 1 4
Answer:
1/3 (one-third)
Step-by-step explanation:
A scale factor that produces an image smaller than the original figure is less than 1. A scale factor that produces an image bigger than the original figure is more than 1.
Thus, the only option that's less than 1 is one-third.
Change 7 square yard to feet
It is never helpful to rewrite a quadratic equation in standard form as a first
step in solving it.
True or False
Answer:
false and can you please help me on my last question i posted its bout john henry
Step-by-step explanation:
A piece of art is in the shape of an equilateral triangle with sides of 15 in.
What is the area of the piece of art to the nearest tenth?
O 73.45 inches squared
84.5 inches squared
O 97.4 inches squared
169 inches squared
Answer:
97.4 inches squared
Find the commission on a sale of $600 with a 5% commission rate.
$15
$30
$50
$45
Pls help me
Answer:
30
Step-by-step explanation:
5% of 600 is 30 so that should be ur answer
Explain how to use the Zero-Product Property to find the solution of the equation 3x(x – 6) = 0.
Answers: set the expression 3x equals to 0 and set the expression x-6 equal to 0, then solve both equations for x
Step-by-step explanation: x = 0, x = 6
Simplify Expression:
3b+8b+9b
Answer:
20b
Step-by-step explanation:
3+8+9
3+8=11
9+11=20
3b+8b+9b
3b+8b=11b
11b+9b=20b
Answer:
Since they all have the same variable, you add them all together. so it would be 20b !!
Step-by-step explanation:
Eric recorded the total number of push-ups he did each minute for four minutes write the order number pairs as ordered pairs
Answer:
(1, 15), (2, 30), (3, 45), (4, 60)
Step-by-step explanation:
So the values are already given to you in the table, it's just a matter of turning them into ordered pairs. Ordered pairs are a set of numbers that represent a point on the coordinate plane. On the graph, the x-axis (horizontal) is for time and the y-axis (vertical) is for the amount of push-ups. An ordered pair is (x, y) so you put (amount of minutes, amount of push-ups). For how they're related, how many push-ups he did increases by 15 for every minute. So, the y-value increases by 15 when the x-value increases by 1.
What does mean mean on sports teams
Answer:
Physical activy used for pleasure.
Step-by-step explanation:
It's just a meaning so I can't provide an explanation.
The line of best fit for a scatter plot is shown (6.04)
Answer:
y- 1/2x+8
Step-by-step explanation:
the slope is negative 1/2