The inverse function [tex]f^{-1}(x)[/tex] is such that
[tex]f\left(f^{-1}(x)\right) = x[/tex]
Plugging [tex]f^{-1}(x)[/tex] into [tex]f(x)[/tex] gives us
[tex]f\left(f^{-1}(x)\right) = \dfrac{3f^{-1}(x) + 3}{5f^{-1}(x) + 6} = x[/tex]
Solve for [tex]f^{-1}(x)[/tex] :
[tex]\dfrac{3f^{-1}(x) + 3}{5f^{-1}(x) + 6} = x \\\\ 3f^{-1}(x)+3=x\left(5f^{-1}(x)+6\right) \\\\ 3f^{-1}(x) + 3 = 5x f^{-1}(x)+6x \\\\ 5xf^{-1}(x)-3f^{-1}(x) = 3 - 6x \\\\ (5x-3)f^{-1}(x)=3-6x \\\\ \boxed{f^{-1}(x)=\dfrac{3-6x}{5x-3}}[/tex]
A bat and a ball cost 1.10$ in total. The bat costs 1 dollar more than the ball. How much does the ball cost?
Answer:
$0.5
Step-by-step explanation:
A + B = 1.10
A=1 +B
now A + B = 1.10
A - B = 1 (B cancels out)
2A = 2.10
A= 1.05
A + B = 1.10
substitute A value
1.05 + B = 1.10
B= 1.10-1.05
B=$ 0.5
Which equation represents a line that passes through ( -2 , 4 ) and has the slope of 2/5
Answer:
y = 2/5x +24/5
Step-by-step explanation:
The slope intercept form of a line is
y = mx+b where m is the slope and b is the y intercept
y = 2/5 x +b
Substitute the point into the equation and solve for b
4 = 2/5(-2)+b
4 = -4/5 +b
Add 4/5 to each side
20/5 +4/5 = b
24/5 = b
y = 2/5x +24/5
3/z when z=2 SORRY FOR HAVING 2 QUESTIONS IN A ROW
3/z when z = 2
= 3/2
= 1.5
This is the answer
Answer:
[tex]3/z\: when\:z=2[/tex]
[tex]\frac{3}{z}=2[/tex]
[tex]\frac{3}{z}z=2z[/tex]
[tex]2z=3[/tex]
[tex]\frac{2z}{2}=\frac{3}{2}=z=\frac{3}{2}[/tex]
[tex]z=1.5\right[/tex]
OAmalOHopeO
Which table shows a proportional relationship between a and b?
Answer:
It is c
Step-by-step explanation:
Solve: f(x) = (x + 1)(x + 1)
Answer:
f(x) = x² + 2x + 1
Step-by-step explanation:
you know how to multiply 2 expressions ?
let's say in general we have
(a + b)(c + d)
you take one part of one expression and multiply it with all parts of the other expression, then you take the second part of the first expression and multiply it with all parts of the other expression, then a potential third part, then a fourth part and so on, and you add all these things together (well, depending on the actual signs, of course).
so, we get for this simple generic example
a×c + b×c + a×d + b×d
now we use that understanding for our question here.
(x+1)(x+1) = x×x + 1×x + x×1 + 1×1 = x² + x + x + 1 = x² + 2x + 1
Help!! Please! appreciate it !!
Answer:
I'm pretty sure you are intended to pick AAS.
Step-by-step explanation:
As it stands, AAS. But this can be an unreliable theorem. If you show that the third angles are equal (which they are) using the fact that if two angles of a triangle are equal to the corresponding angles of another triangle, then the third angle is as well. That means that you can use the much more reliable ASA.
|7-4x|>1 como se resuelve está inecuación con valor absoluto??
Answer:
Step-by-step explanation:
te da x<3/2 y x<2, pero la segunda solucion abarca la primera. Por lo tanto creo q seria x<2
Please help!!!!
Oak wilt is a fungal disease that infects oak trees. Scientists have discovered that a single tree in a small forest is infected with oak wilt. They determined that they can use this exponential model to predict the number of trees in the forest that will be infected after t years.
f(t) = e^0.4t
1. The scientists believe the forest will be seriously damaged when 21 or more of the forest’s 200 oak trees are infected by oat wilt. According to their model, how many years will it take for 21 of the trees to become infected?
Type the correct answer in the box. Use numerals instead of words. Round your answer to the nearest tenth.
2. Rewrite the exponential model as a logarithmic model that calculates the number of years g (x) for the number of infected trees to reach a value of x.
To solve this question, we need to solve an exponential equation, which we do applying the natural logarithm to both sides of the equation, both to find the needed time and to find the inverse function. From this, we get that:
It will take 7.6 years for 21 of the trees to become infected.The logarithmic model is: [tex]g(x) = \frac{\ln{x}}{0.4}[/tex]Number of trees infected after t years:
The number of trees infected after t years is given by:
[tex]f(t) = e^{0.4t}[/tex]
Question 1:
We have to find the number of years it takes to have 21 trees infected, that is, t for which:
[tex]f(t) = 21[/tex]
Thus:
[tex]e^{0.4t} = 21[/tex]
To isolate t, we apply the natural logarithm to both sides of the equation, and thus:
[tex]\ln{e^{0.4t}} = \ln{21}[/tex]
[tex]0.4t = \ln{21}[/tex]
[tex]t = \frac{\ln{21}}{0.4}[/tex]
[tex]t = 7.6[/tex]
Thus, it will take 7.6 years for 21 of the trees to become infected.
Question 2:
We have to find the inverse function, that is, first we exchange y and x, then isolate x. So
[tex]f(x) = y = e^{0.4x}[/tex]
[tex]e^{0.4y} = x[/tex]
Again, we apply the natural logarithm to both sides of the equation, so:
[tex]\ln{e^{0.4y}} = \ln{x}[/tex]
[tex]0.4y = \ln{x}[/tex]
[tex]g(x) = \frac{\ln{x}}{0.4}[/tex]
Thus, the logarithmic model is:
[tex]g(x) = \frac{\ln{x}}{0.4}[/tex]
For an example of a problem that uses exponential functions and logarithms, you can take a look at https://brainly.com/question/13812761
Given sin
=
=
V23 and tan o
find cos 0.
23
11 )
12
?
COS 0 =
TO
Answer: [tex]\frac{11}{12}[/tex]
Step-by-step explanation:
Use trigonometry (shown in image below) to find the 3 side-lengths:
The side opposite of θ = [tex]\sqrt{23}[/tex]The base side adjacent to θ = 11The hypotenuse = 12According to right triangle trigonometry:
cos θ = [tex]\frac{adjacent}{hypotenuse}[/tex]
Substitute in the values:
cos θ = [tex]\frac{11}{12}[/tex]
Complete the statements for the graph of f(x)=|x|.
The domain of the function is
______________
The range of the function is
______________
The graph is ____ over the interval (0,♾)
The graph is ____ over the interval (♾,0)
below
Step-by-step explanation:
all real numbers
[0,∞]
increasing
decreasing
HELP?h?e?l?pppppppppppppppppppppp
Answer:
Yes
Step-by-step explanation:
N is the centroid of the triangle. Find XN if XG = 33
Answer:
XN = 22
Step-by-step explanation:
Recall: the Centroid theorem states that the Centroid of a triangle is ⅔ of the distance any vertex of the triangle to the midpoint of the side opposite to it.
This implies that:
XN = ⅔(XG)
XG = 33
Substitute
XN = ⅔(33)
XN = 2*11
XN = 22
In ΔFKR, which side is included between ∠F and ∠R?
Answer:
First choice
Step-by-step explanation:
It gives you the endpoints of the included side, F and R. Therefore, the side is FR or RF.
No idea how to do
[tex]\frac{4r + 20}{r + 5}[/tex]
when r ≠ 5 ?
Factorize the numerator:
4r + 20 = 4r + 4×5 = 4 (r + 5)
I think you meant to say r ≠ -5, which means r + 5 ≠ 0, so that the denominator is never zero and so the expression is defined (no division by zero). This lets you cancel the factor of r + 5 in the numerator with the one in the denominator:
(4r + 20)/(r + 5) = 4 (r + 5)/(r + 5) = 4
Choose the correct simplification of the expression b5 ⋅ b4.
b
b9
b20
b−1
Answer:
b20
Step-by-step explanation:
Whats his mistake and the correct awnser
Answer:
θ ≈ 35.7°
Step-by-step explanation:
His mistake was in using the wrong trig. ratio
Instead of using cosine he should have used the sine ratio
sinθ = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{7}{12}[/tex] , then
θ = [tex]sin^{-1}[/tex] ([tex]\frac{7}{12}[/tex] ) ≈ 35.7° ( to the nearest tenth )
Part B
Question
Type the correct answer in the box.
The y-intercept of the parent function, f(x), is
I
The y-intercept of the child function, g(x), is
Answer:
The y-intercept of the parent function, f(x), is 0
The y-intercept of the child function, g(x), is 7
Step-by-step explanation:
Since the parent function passes through the origin, its y-intercept is 0. Once the function is translated 7 units up, its y-intercept is 7.
The solution is :
Vertex is (-2, 0)
y-intercept is 4.
What is vertex?In geometry, a vertex is a point where two or more curves, lines, or edges meet. As a consequence of this definition, the point where two lines meet to form an angle and the corners of polygons and polyhedra are vertices.
here, we have,
to find the function translated 2 units left, we just need to substitute the 'x' in the equation by 'x+2':
f(x) = (x+2)^2 = x2 + 4x + 4
Then, to find the vertex, we can use the formula:
x_v = -b / 2a
x_v = -4 / 2 = -2
Now, finding the y_vertex, we have:
f(x_v) = (-2)^2 + 4*(-2) + 4 = 0
So the vertex is (-2, 0)
To find the y-intercept, we make x = 0 and then find f(x):
f(0) = 0 + 0 + 4 = 4
So the y-intercept is 4.
To learn more on vertex click:
brainly.com/question/12563262
#SPJ2
complete question:
Identify the vertex and y-intercept of the graph of the function translated 2 units left from the parent function f(x) = x².
vertex: ( ? , ? )
y-intercept: ?
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
If x+2 is a factor of x^3-6x^2-11x+k then k=
Answer:
k=10
Step-by-step explanation:
Brainliest please~
Answer:
K=10
Step-by-step explanation:
Correct on Plato
find area of shaded region by using formula a^2-b^2.
Answer:
216 cm^2
Step-by-step explanation:
15^2 -3^2 = 225 -9
= 216
What is the length of side s of the square shown below? 450 90" A. 4-3 B. 1 C. 4 D. 2 E F. 2.5
Answer:
E
Step-by-step explanation:
Using Pythagoras' identity in the right triangle
s² + s² = 2²
2s² = 4 ( divide both sides by 2 )
s² = 2 ( take the square root of both sides )
s = [tex]\sqrt{2}[/tex]
Answer:
E.
Step-by-step explanation:
we know the diagonal of the square : 2
as you can see in the picture, there is a right-angled triangle with the baseline of Hypotenuse being the diagonal, and 2 times s being the 2 sides.
that means we can use Pythagoras to calculate s :
2² = s² + s²
4 = 2s²
2 = s²
s = sqrt(2)
Algebra is hard for me
Answer: Third Choice. 9
Step-by-step explanation:
Concept:
Here, we need to understand the idea of evaluation.
When encountering questions that gave you an expression with variables, then stated: "If x = a, y = b, z = c" (a, b, c are all constants), this means you should substitute the value given for each variable back to the expression.
Solve:
Given
4x + 2y -1
x = 3, y = -1
Substitute the value of x and y
4(3) + 2(-1) - 1
Simplify by multiplication
12 - 2 - 1
Simplify by subtraction
9
Hope this helps!! :)
Please let me know if you have any questions
Answer:
Step-by-step explanation:
Hello!
4x= 4*3 = 12
2y = 2*-1 = -2
12-2 -1= 9
pls answer fast i need help
Do it by your self ok ???
find the value of x
4x - 7 = 3x + 9
x = 16
they're equal because they are opposites by the vertex.
hope it helps :)
Please help!! Thank you!
Answer:
[tex]\text{As }x\rightarrow \infty, f(x)\rightarrow -\infty,\\\text{As }x\rightarrow -\infty, f(x)\rightarrow -\infty[/tex]
Step-by-step explanation:
This question is asking for the function's end behavior. An even degree power function with a negative leading coefficient forms a parabola concave down. This means, its vertex represents the maximum and the parabola opens downward (towards negative infinity).
Thus,
[tex]\lim_{x\rightarrow \infty}f(x)=-\infty,\\\lim_{x\rightarrow-\infty}f(x)=-\infty[/tex]
This corresponds with the first answer choice listed:
[tex]\text{As }x\rightarrow \infty, f(x)\rightarrow -\infty,\\\text{As }x\rightarrow -\infty, f(x)\rightarrow -\infty[/tex]
When a boy stands on the bank of a river and looks across to the other bank, the angle of depression is 12°. If he climbs to the top of a 10 ft tree and looks across to other bank, the angle of depression is 15°. What is the distance from the first position of the boy to the other bank of the river? How wide is the river? Give your answers to the nearest foot.
Please look at the scanned picture.
Which of the integers shown is the greatest?
Answer:
-3
Step-by-step explanation:
because as you vo more to the negative side the less.it gets and more to the positive side it gets moe
Fine FG , given that line HF is perpendicular bisector or EG
Answer:
FG = 7
Step-by-step explanation:
We'll begin by calculating HF. This can be obtained by using the pythagoras theory as illustrated below:
EF = 7
EH = 3
HF =?
EF² = EH² + HF²
7² = 3² + HF²
49 = 9 + HF²
Collect like terms
49 – 9 = HF²
40 = HF²
Take the square root of both side
HF = √40
Finally, we shall determine FG. This can be obtained as follow:
GH = 3
HF = √40
FG =.?
FG² = GH² + HF²
FG² = 3² + (√40)²
FG² = 9 + 40
FG² = 49
Take the square root of both side
FG = √49
FG = 7
If p =(3x+1) and q = ( 3x-1),show that : pq+1 =x2
Answer:
See explanation
Step-by-step explanation:
It should be 9x² not x²
p = (3x + 1) and q = (3x - 1)
pq + 1 = (3x + 1)(3x - 1) + 1
= (9x² - 3x + 3x - 1) + 1
= (9x² - 1) + 1
= 9x² - 1 + 1
= 9x²
Therefore,
pq + 1 = 9x²
The blue dot is at what value on the number line?
Answer:
[tex]8[/tex]
Step-by-step explanation:
Hope it helps you:D
*copied*
Answer:
"8"
4,6,8
Step-by-step explanation:
use a double angle or half angle identity to find the exact value of each expression
θ is given to be in the fourth quadrant (270° < θ < 360°) for which sin(θ) < 0 and cos(θ) > 0. This means
cos²(θ) + sin²(θ) = 1 ==> sin(θ) = -√[1 - cos²(θ)] = -3/5
Now recall the double angle identity for sine:
sin(2θ) = 2 sin(θ) cos(θ)
==> sin(2θ) = 2 (-3/5) (4/5) = -24/25
