Let f(x) = (2 - x)/(2 + x). By definition of the derivative,
[tex]\displaystyle f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}h[/tex]
[tex]\displaystyle f'(x)=\lim_{h\to0}\frac{\frac{2-(x+h)}{2+(x+h)}-\frac{2-x}{2+x}}h[/tex]
[tex]\displaystyle f'(x)=\lim_{h\to0}\frac{\frac{(2-x-h)(2+x)-(2-x)(2+x+h)}{(2+x+h)(2+x)}}h[/tex]
[tex]\displaystyle f'(x)=\lim_{h\to0}\frac{-4h}{h(2+x+h)(2+x)}[/tex]
[tex]\displaystyle f'(x)=-4\lim_{h\to0}\frac1{(2+x+h)(2+x)}=\boxed{-\frac4{(2+x)^2}}[/tex]
Need help ASAP!
What is the volume of the right rectangular prism?
9 mm
6 mm
8 mm
O 23 mm
O 46 mm
O 432 mm
O 864 mm
Answer:
He's correct its 432
Step-by-step explanation:
The net below represents a container. What solid figure does it show.
Answer:
Looks like a cuboid
Hope it helps :)
Have a great day!
The net below represents a container. What solid figure does it show?
____________________Solution :-We can see that the given net has 12 edges, 6 faces and 8 vertices if we compile it up. These number of edges, faces and vertices are found in a cuboid or a rectangular prism. With this we can conclude that if we compile the given net, it will form a cuboid or a rectangular prism. So, the given net is of a cuboid or a rectangular prism.
____________________Final Answer :-The given net is of a cuboid or a rectangular prism.
____________________f(x)= square root of x-5. find f-1 (x) and it’s domain
Answer:
Option B.
Step-by-step explanation:
Inverse function:
Suppose we have a function y = f(x). To find the inverse function, we exchange x and y on the original function, and then isolate y.
The domain of the inverse function(x values) is the range of the original function(y values).
Original function:
[tex]f(x) = \sqrt{x} - 5[/tex]
Domain is [tex][0,\infty)[/tex], and when [tex]x = 0, f(x) = -5[/tex]. So the range is [tex][-5,\infty][/tex], that is, [tex]y \geq -5[/tex]
Inverse function:
[tex]y = \sqrt{x} - 5[/tex]
Exchanging x and y
[tex]x = \sqrt{y} - 5[/tex]
[tex]\sqrt{y} = x + 5[/tex]
[tex](\sqrt{y})^2 = (x+5)^2[/tex]
[tex]y = (x+5)^2[/tex]
The inverse function is [tex]f^{-1}(x) = (x+5)^2[/tex]
Domain:
Range of the original function is [tex]y \geq -5[/tex], so the domain of the inverse function is [tex]x \geq -5[/tex]. The correct answer is given by option B.
Answer:
B. f ^ -1 (x) = (x + 5) ^ 2;
x > -5
Step-by-step explanation:
Ap e x
somebody help me please in the photo
Answer:
93 degrees
Step-by-step explanation:
alternate interior angles are congruent so 39+x=132 x=93
Answer:
Step-by-step explanation:
According to Alternate Interior Angles Theorem (in a graph that shows a transversal crossing two parallel lines, the alternate interior angles are congruent), The angle that includes the sum of 39° and x° is congruent to 132°.
So: 39° + x° = 132°, and x = 93
What is the equation of this parallel line?
Answer:
y = 5x - 6
Step-by-step explanation:
y - 9 = 5 ( x - 3 )
y = 5x - 15 + 9
y = 5x - 6
Pls help me ASAP no scamming:-)
Hi this was a different question from normal but okay.
Answer:
There has been an high speed chase that lead to an injury of a young girl. Isaac midway had fled the seen at North West 22nd, around 2:56 pm. With the girl laying in the street with a broken leg and fractured ankle. Have any evidence call crime stoppers.
Step-by-step explanation:
This provides criminal, time and location and injury. Good luck.
One Night, The Criminal Mastermind, Arnold "Laughing" Jack Escapes From The Facility In New Orleans, And Proceeds To Murder 70 People, The Most Famous Spot Was His Murder Hotel Where He Mutilated 5 People In The Kitchen. The Injuries On The Bodies Were Similar To What Forensics Is The Equivalent Of, How Being Struck With A Curved Sword Would Be.
4053 x 6
...........
Answer:
24318
Step-by-step explanation:
That's all what you were asking for?
Consider the function shown below.
g(x) = 2^x
If the function gis horizontally compressed by a factor of 1/2 and reflected across the x axis to obtain function f, which of the following graphs
matches the above transformation?
9514 1404 393
Answer:
see attached
Step-by-step explanation:
The only graph that shows a proper vertical reflection is the one attached. (It also correctly shows the horizontal compression.)
Answer:
It's Y
Step-by-step explanation:
I got it right. Hope this helps.
3. Jayne, Carlos, June, and Pedro each measured their dogs' weights, but each used a different measurement. Place the four dogs in order from lightest to heaviest.
Jayne's Dog 42 lbs
Carlos' Dog 624 oz
June's Dog 41 lbs,
7 oz Pedro's Dog
665 oz
Answer:
Carlos, June, Pedro, Jayne
least to greatwst
x+1/2(x-4)=1/2x+6(x-2)
how many solutions does the equation have?
A. 0
B. 1
C. 2
D. 4
PLEASE HURRY
Answer:
B) 1
Step-by-step explanation:
x+1/2(x-4)=1/2x+6(x-2)
x+1/2x-4/2=1/2x+6x-12
x+1/2x-1/2x-2=6x-12
x-2=6x-12
x-6x-2=-12
-5x-2=-12
-5x=-12+2
-5x=-10
5x=10
x=10/5
x=2
Question 26 of 40
How does the graph of f(x) = -45% - 3 differ from the graph of g(x) = -45%?
O A. The graph of f(x) is shifted three units to the right of the graph of
g(x).
O B. The graph of f(x) is shifted three units down from the graph of
g(x).
C. The graph of f(x) is shifted three units to the left of the graph of
g(x).
O D. The graph of f(x) is shifted three units up from the graph of g(x).
SOLVE THE SYSTEM USING ELIMINATION!!!!
HURRY ILL GIVE BRAINLIEST!!
Answer:
(5,3)
Step-by-step explanation:
add the equations to eliminate to x's and get 8y=24
divide both sides by 8 to get y=3
then substitute in -2x+3(3)=-1 to solve for x
so x=5 so the solution is (5,3)
Answer:
[tex]x=5 \\y=3[/tex]
Step-by-step explanation:
[tex]-2x+3y=-1\\2x+5y=25[/tex]
Add these equations to eliminate x:
[tex]8y=24[/tex]
Then, solve [tex]8y=24[/tex] for y:
[tex]8y=24[/tex]
[tex]\frac{8y}{8} =\frac{24}{8}[/tex] (divide both sides by 8)
[tex]y=3[/tex]
Now let's find the value of x:
Substitute 3 for y in [tex]-2x+3y=-1[/tex]
[tex]-2x+(3)(3)=-1[/tex]
[tex]-2x+9=-1[/tex] (simplify both sides of the equation)
[tex]-2x+9+-9=-1+-9[/tex] (add both sides by -9)
[tex]-2x=-10[/tex]
[tex]\frac{-2x}{-2} =\frac{-10}{-2}[/tex] (divide both sides by -2)
[tex]x=5[/tex]
Therefore, the value of x = 5 and y = 3
the simple interest on a sum of money is 25% of the rate percent per annum find the rate
si =25%*p
rate =term=t
from si= ptr/100
term = rate = 5
What is the volume of the rectangular prism?
3. Shyann is flipping a quarter and flips 8 tails in a row. Should the next flip most likely be a
heads to balance it out? Explain your reasoning.
In ΔWXY, the measure of ∠Y=90°, YX = 40, XW = 41, and WY = 9. What ratio represents the cosine of ∠W?
Answer:
[tex]\cos(W) = \frac{9}{41}[/tex]
Step-by-step explanation:
Given
[tex]\angle Y = 90^o[/tex]
[tex]YX = 40; XW = 41; WY = 9[/tex]
Required
Determine [tex]\cos(W)[/tex]
The question is illustrated with the attached image.
So:
[tex]\cos(W) = \frac{Adajacent}{Hypotenuse}[/tex]
[tex]\cos(W) = \frac{WY}{XW}[/tex]
This gives:
[tex]\cos(W) = \frac{9}{41}[/tex]
describe and correct the error in solving the equations below
9514 1404 393
Answer:
19. wrong multiplier was used, and used incorrectly; x = -324
20. wrong multiplier was used, and used incorrectly; y = 5
Step-by-step explanation:
In each case, the equation was multiplied by the coefficient of the variable, instead of divided. In each case, the square of the coefficient was evaluated incorrectly (so the error wasn't noticed).
__
19) As described above.
(-36)(9) = (x/9)(9)
-324 = x
__
20) In addition to the errors described above, the variable was changed from y to x.
15/3 = (3y)/3
5 = y
A square pyramid is rotated about a line perpendicular to the base and through the vertex. What angle of rotation maps the pyramid onto itself?
30º
45º
60º
90º
Answer:
I think the answer is 30°. Please tell me if I'm wrong.
Answer: 90 Degrees
Step-by-step explanation:
The fish population is decreasing at a rate of 3% per year. In 2002 there were about 1600 fish. Find the fish population in 2010. Round to the nearest whole number
Answer:
Population of fish in
Which equation has the same solution as x2 - 6x - 14 = 0?
А
(x + 3)2 = 23
B
(x - 3)2 = 23
С
(x + 3)2 = 5
D
(x - 3)2 = 5
Answer:
i think it is option c
Step-by-step explanation:
2x is subtracted from the square of a number
Answer:
let the number be x
x²-2x=0
here it is your quadratic equation
L 10.1.2 Exam: Semester Exam
Find the value of x.
20°
(3x + 2)
O A. 6
O B. 20
O c. 7
O D. 5
Answer:
A
Step-by-step explanation:
The requried simplified value of x in the intersection of two lines is 6.
What are opposite angles?Opposite angles are a pair of angles that are formed when two lines intersect. The two angles are located on opposite sides of the point where the two lines intersect.
Opposite angles are also called vertical angles, and they have equal measures. This means that if we know the measure of one opposite angle, we can find the measure of the other opposite angle by setting them equal to each other.
Here,
When two lines intersect, opposite angles are equal. So, we can set the two opposite angles equal to each other and solve for x.
Given that the opposite angles are 3x + 2 and 20 degrees, we have:
3x + 2 = 20
Subtracting 2 from both sides, we get:
3x = 18
Dividing both sides by 3, we get:
x = 6
Therefore, the value of x is 6.
Learn more about opposite angles here:
https://brainly.com/question/2687431
#SPJ7
This is part two of the problem go check part one so it makes sense
Answer:Execute Order 66
Step-by-step explanation:
Answer:
Step-by-step explanation:
Assuming that the original figure is the black one
Area of the original figure = 2 x 3 = 6
A (0,1) -> A’ (0,3)
B (2,1) -> B’ (6,3)
C (2,4) -> C’ (6, 12)
D (0,4) -> D’ (0,12)
AB = 6
BC = 9
Area of the final figure = 9 x 6 = 54
b)
area of the final figure = 9 x area of the original figure
c)
true, because their side are proportional
The stadium vending company finds that sales of hot dogs average 35,000 hot dogs per game when the hot dogs sell for $2.50 each. For each 25 cent increase in the price, the sales per game drop by 2000 hot dogs. Determine a function R x that models the total revenue per game, where x is the number of $0.25 increases in the price of a hot dog.
Answer:
A function R x that models the total revenue per game is as follows:
Rx = 87,5000 + 3,750x – 500x^2.
Step-by-step explanation:
Based on the information in the question, we have:
Rx = Total revenue per game
x = Number of $0.25 increases in the price of a hot dog
Average sales of hot dogs = 35,000
Effect of each 25 cent increase in the price on average sales = 35,000 - 2000x
Effect of each 25 cent increase in the price on selling price = 2.5 + 0.25x
Therefore, we have:
Rx = (35,000 - 2000x)(2.5 + 0.25x)
This can be solved further by opening the brackets as follows:
Rx = 87,5000 + 8,750x - 5,000x - 500x^2
Rx = 87,5000 + 3,750x – 500x^2
Therefore, a function R x that models the total revenue per game is Rx = 87,5000 + 3,750x – 500x^2.
What is the area of the given trapezoid?
9)
2.9 km
5.6 km
10.9 km
O 38.64 km2
O 19.3 km2
O 77.28 km?
O 46.44 km2
PLEASE HELP
Answer:
38.64 km^2
Step-by-step explanation:
The formula for the area of a trapezoid is:
[tex]\frac{(b_{1}+b_{2})*h}{2}[/tex]
Where b1 and b2 are the bases and h is the height. We are given 2.9 and 10.9 as the bases and 5.6 as the height. We can plug these values into the formula:
[tex]\frac{(2.9+10.9)*5.6}{2}[/tex]
After entering the expression in the calculator, you get:
38.64 km^2
This is the first option.
How high is the end of the ladder against the building?
Answer:
D.
Step-by-step explanation:
its a right triangle, so we can use the pythagorean theorem to find h
(pythagorean theorem is a^2+b^2=c^2, c is the hypotenuse)
h^2+4^2=13^2
h^2+16=169
h^2=153
h=sqrt153
h≈ 12.4ft
Caroline puts $400 into a savings account that earns 6% annually. Write a function that represents this situation, where t is the time in years. Solve algebraically after how many years she will get $1200 in her account (round it to the nearest year).
Answer: 19 years
Step-by-step explanation:
Given
Amount invested [tex]\$400[/tex]
Rate of interest [tex]R=6\%[/tex]
after 1-year amount becomes
[tex]A=400\left (1+6\%\right)\\A=400\left (1+0.06\right)\\A=400\times 1.06\\A=\$424[/tex]
After n years it is
[tex]A=400\left (1.06\right)^n[/tex]
Sum accumulated is [tex]\$1200[/tex]
[tex]\Rightarrow 1200=400\left(1.06\right)^n\\\Rightarrow 3=\left(1.06\right)^n\\\text{Taking log both sides}\\\Rightarrow n=\dfrac{\ln 3}{\ln 1.06}\\\\\Rightarrow n=18.85\approx 19\ \text{years}[/tex]
the spinner shown below has 12 congruent sections. the spinner spun 150 times. what is a reasonable prediction for the number of items the spinner will land on an even number. (pls help asap!!)
Answer:45
Step-by-step explanation:
There are 3 even numbers out of A total of 8 numbers.
Each spin would have a 3/8 chance of landing in an even number.
Multiply the chance of landing on even by number of spins:
120 x 3/8 = 360/8 = 45
The answer would be 45 times.
Find the area of the parallelogram in square meters
Answer: 27
Step-by-step explanation:
9*3
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