What is the inverse of the function f (x) = 3(x + 5)2 – 4, such that x ≤ –5?
inverse of f of x is equal to negative 5 plus the square root of the quantity x plus 4 all over 3 end quantity
inverse of f of x is equal to negative 5 minus the square root of the quantity x plus 4 all over 3 end quantity
inverse of f of x is equal to negative 5 plus the square root of the quantity x over 3 plus 4 end quantity
inverse of f of x is equal to negative 5 minus the square root of the quantity x over 3 plus 4 end quantity
The equation of the inverse function of the function f(x) = 3(x + 5)^2 - 4 is f-1(x) = -5 + √[1/3(x + 4)]
What are inverse functions?Inverse functions are the opposite of an original equation. This means that for a function f(x), the inverse of the function f(x) is f-(x); it also represents the opposite function
How to determine the inverse functions?The function f(x) is given as
f(x) = 3(x + 5)^2 - 4
Express f(x) as y
So, we have
y = 3(x + 5)^2 - 4
Swap the positions of x and y
So, we have
x = 3(y + 5)^2 - 4
Add 4 to both sides of the equation
So, we have
x + 4 = 3(y + 5)^2
Divide through by 3
So, we have
1/3(x + 4) = (y + 5)^2
Take the square root of both sides
So, we have
√[1/3(x + 4)] = y + 5
Subtract 5 from both sides of the equation
So, we have
y = -5 + √[1/3(x + 4)]
Rewrite as
f-1(x) = -5 + √[1/3(x + 4)]
Hence, the equation of the inverse function of the function f(x) = 3(x + 5)^2 - 4 is f-1(x) = -5 + √[1/3(x + 4)]
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10 8 12 10 14 ? sequence
Answer:
The Sequence
Step-by-step explanation:
the Sequence is a decrease by 2 and a increase of 4. So subtract 2 by 10 to get 8 then add 4 to get 12 and so on.
What is the solution for x² + 4x > 77?
Ox<-7 or x> 11
Ox<-11 or x>7
0-7
0-11
TERENO
TOTAPE
Whilsend
BATTLES
HEYRPRIP
GTHEBEN TEN OF JESHIREMERS
EN ERTER IS BELE RE
A
BODYER an
S
THERE THE
13627
STERIS
MINER
Saca la medida de la pala superior e inferior con respecto a las siguientes medidas
*No son de la misma medida*
La pala inferior y la pala superior tienen longitudes verticales de 55 y 65 centímetros, respectivamente. No es posible encontrar las longitudes horizontales.
¿Cuáles son las medidas de la pala superior y la pala inferior de un arco compuesto?
En esta pregunta debemos saber interpretar las dimensiones geométricas de un arco compuesto y determinar las longitudes de cada pala. Primero, determinamos las longitudes verticales de cada una:
Pala inferior
i = 65 cm - 10 cm
i = 55 cm
Pala superior
s = 65 cm
La insuficiencia de datos sobre longitudes horizontales no permite obtener las longitudes horizontales de cada pala.
La pala inferior y la pala superior tienen longitudes verticales de 55 y 65 centímetros, respectivamente. No es posible encontrar las longitudes horizontales.
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+++++
3
2
0
+++++++
1
-2
-3
Intro
Which statements are true? Check all that apply.
0-2.5=-2/2
0-1.5 -0.5
-0.5 0
-2.5 -2
11.5
Done
Step-by-step explanation:
++++5
+++++++_2
1=false
true
false
false
I need helping solving this :)
Answer: answer is B
Step-by-step explanation:
use Pythagorean theorem to find other side. And sine is opposite side over hypotenuse.
A line is parallel to the line y = x and passes
through the parabola y = x² - 3 at
(4, 13). What is the other point at which the two
functions intersect?
Answer:
Step-by-step explanation:
hello here is an solution
Local extreme Value for each of the Following A) F(x)=x^² - 4x² +5
Answer:
max{x²-4x²+5} = 5 at x = 0
Step-by-step explanation:
1. Find the critical numbers by finding the first derivative of f(x), set it to 0 and solve for x.
[tex]f'(x)=0[/tex]
We get:
[tex]f(x) = -3x^2+5\\f'(x) = -6x\\-6x = 0\\x = 0[/tex]
So the critical number is x = 0.
2. Evaluate the first derivative by plugging in the critical number and see if the derivative is positive or negative on both sides:
[tex]f'(x)[/tex] is positive when the x < 0 (for example: -6*(-1)=+)
[tex]f'(x)[/tex] is negative when the x > 0 (for example: -6*(1)=-)
Therefore, you have a local maximum.
Now just get the Y value by plugging in the critical number in the original function. [tex]f(0)=5[/tex]
local maximum is (0,5)
1) A random sample of n = 12 individuals is selected from a population with
µ = 70 and a treatment is administered to each individual in the sample. After treatment the sample mean is found to be M = 74.5 with S = 5.20
Based on the sample data, does the treatment have a significant effect.?
Use a two tailed test with α = 0.05
steps
a) State the Null and the Alternate Hypotheses
A random sample of n = 12 individuals is selected from a population with
µ = 70 and a treatment is administered to each individual in the sample. After treatment the sample mean is found to be M = 74.5 with S = 5.20. Based on the sample data, the treatment has a significant effect as per the deduced test statistic. Following are the statements for Null and the Alternate Hypotheses,
H₀: The treatment does not have a significant effect
Hₐ: The treatment has a significant effect
According to the given information,
Size of the sample, n = 12
Population Mean, μ = 70
Sample Mean, M = 74.5
Standard Deviation, S = 5.20
The Null hypothesis is given by,
H₀: The treatment does not have a significant effect (μ = 70)
The Alternate hypothesis is given by,
Hₐ: The treatment has a significant effect (μ ≠ 70)
Since the population standard deviation is unknown, we will use one-sample t-test here.
Test statistic, TS = (M-μ) / (s/√n)
Substituting the given values of M, μ, S, and n, we get,
TS = (74.5-70) / (5.20/√12)
TS = 4.5 / 1.5
TS ≈ 3
The t table now provides critical values of -2.131 and 2.131 at 15 degrees of freedom for a two-tailed test using α = 0.05 (significance level).
Since our test statistic, TS does not fall in the range of the critical values, it falls in the rejection region. Thus, we can reject the null hypothesis and say that the treatment has a significant effect.
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Length of the lot is 7 5/8 inches 1/2in=16ft
A.) 234ft
B.) 245 ft
C.) 244 ft
D.) 254 ft
Answer:
244 ft
Step-by-step explanation:
Scale: 1/2 in = 16 ft
Scale length = 7 5/8 inches
Real length = ?
We can use a proportion.
1/2 in : 16 ft = 7 5/8 in. : x
(1/2)/16 = (7 5/8)/x
(1/2)x = 16 × 7 5/8
(1/2)x = 122
x = 244
Answer: C. 244 ft
find y' if x^y = y^x
The answer is [tex]\boxed {\frac{dy}{dx} = \frac{y^{x}logy-yx^{y-1}}{x^{y}logx-xy^{x-1}}}[/tex].
Apply logarithmic differentiation on each side.
LHS
u = x^ylog u = y log x1/u du/dx = y/x + log x (dy/dx)du/dx = x^y (y/x + log x dy/dx)du/dx = yx^(y - 1) + x^y logx dy/dxRHS
v = y^xlog v = x log y1/v dv/dx = x/y dy/dx + logydv/dx = y^x (x/y dy/dx + logy)dv/dx = xy^(x - 1) dy/dx + y^x logyEquating both sides
yx^(y - 1) + x^y logx dy/dx = xy^(x - 1) dy/dx + y^x logydy/dx (x^y logx - xy^(x - 1)) = y^x logy - yx^(y - 1)[tex]\boxed {\frac{dy}{dx} = \frac{y^{x}logy-yx^{y-1}}{x^{y}logx-xy^{x-1}}}[/tex]Which transformations must be applied to object A to place it in the position of object B?
rotation and reflection
rotation and translation
reflection and translation
rotation, reflection, and translation
In order for object A to be placed in the position of object B, there needs to be a rotation and translation.
How would object A get to object B?The first step would be to rotate object A to the left to give it the same orientation as object B.
Then, translate object A to the coordinates of object B. This would lead to object A fitting into object B.
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f(x)= x+28/x-7 for inverse functions
The inverse function of the given function is [tex]\mathbf{= \dfrac{28+7x}{x-1}}[/tex]
What is the inverse of a function?A function g is the inverse of a function f, if and only if the values of y= f(x), x = g(y).
From the formula given:
[tex]\mathbf{y=f(x) = \dfrac{x+28}{x-7}}[/tex]
Let's substitute x with y;
[tex]\mathbf{y= \dfrac{x+28}{x-7}}[/tex]
[tex]\mathbf{x=\dfrac{y+28}{y-7}}[/tex]
Solve for y;
[tex]\mathbf{= \dfrac{28+7x}{x-1}}[/tex]
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Harry is building a decking area in his garden.
250 cm
150 cm
4 m
7m
150 cm
He needs to build a wooden frame in the shape of the decking.
Calculate the perimeter of the decking area.
The perimeter of the decking area is 800cm.
How to determine the perimeterIt is important to note that the decking area takes the shape of a rectangle
The formula for determining the perimeter of the decking area is given as;
Perimeter = 2 multiplied by the sum of the length and width of the rectangle
It is mathematically written as;
Perimeter = 2 ( length + width)
Where;
length = 250cmwidth = 150 cmNow, let's substitute the values into the formula
Perimeter = 2 ( 150 + 250)
Sum the bracket
Perimeter = 2 ( 400 )
Perimeter = 2 × 400
Perimeter = 800 cm
Thus, the perimeter of the decking area is 800cm
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the graph shown below expresses a redical function that can be written in the form f(x)= a(x+k)^1/n + c. what does the graph tell the value of a in this function?
The value of n given the form of the function is (b) positive odd number
How to interpret the graph?The form of the graph is given as:
f(x) = a(x + k)^1/n + c
For the given graph, we have the following features:
a > 0 --- a is positive
k > 0 --- k is positive
c < 0 --- c is negative
If n is an even number, the function would be undefined because the even root of a number is undefined
However, the function is defined if n is an odd number,
Hence, the value of n given the form of the function is a positive odd number
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A farmer with 3380 ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle. What is the largest possible total area of the four pens?
The largest possible total area of the four pens is 285610 ft²
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let y represent the length of the pen and x represent the width of the pen.
Hence:
Perimeter = x + y + x + y + x + x + x = 2y + 5x
2y + 5x = 3380
y = (3380 - 5x)/2 (2)
Area (A) = xy
A = x * (3380 - 5x)/2
A = (3380x - 5x²)/2
The maximum area is at A' = 0, hence:
A' = (1/2)(3380 - 10x)
0 = (1/2)(3380 - 10x)
10x = 3380
x = 338 ft.
2y + 5(338) = 3380
y = 845 ft.
Largest possible total area = 338 * 845 = 285610 ft²
The largest possible total area of the four pens is 285610 ft²
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please help me on this question!!
Answer:
B
Step-by-step explanation:
The domain is the set of input values, which is typically shown on the horizontal axis.
The answer is B.
The domain of the function refers to the possible values of the horizontal axis of the graph.
Hence, the domain is : 6 ≤ g ≤ 12
Solve the following problems using Pythagoras. Include a diagram . a. How long must a ladder be to reach 12 ft up the wall, if thefoot of the ladder is placed 2.5 ft away from the wall
Answer:
sqrt(601)/2 ft
Step-by-step explanation:
The legs of the right triangle are 12 and 2.5. by the Pythagorean Theorem, the length of the ladder is sqrt(12^2 + 2.5^2) = sqrt(150.25). Simplified is sqrt(601)/2 ft.
The length of ladder used is 12.25 ft.
What is Pythagoras theorem?Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse .
The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.
example:
The hypotenuse of a right-angled triangle is 16 units and one of the sides of the triangle is 8 units. Find the measure of the third side using the Pythagoras theorem formula.
Solution:
Given : Hypotenuse = 16 units
Let us consider the given side of a triangle as the perpendicular height = 8 units
On substituting the given dimensions to the Pythagoras theorem formula
Hypotenuse^2 = Base^2 + Height^2
16^2 = B^2 + 8^2
B^2 = 256 - 64
B = √192 = 13.856 units
Therefore, the measure of the third side of a triangle is 13.856 units.
given:
base= 2.5 ft,
perpendicular= 12 ft
Using Pythagoras theorem,
H² = B² + P²
H² = 2.5² + 12²
H² = 6.25+ 144
H= 12.25 ft
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In June 2020, Parks Canada closed the Bow Valley Parkway (Highway 1A) to vehicle traffic
between Banff and Castle Junction near Johnston Canyon. This made for a bike ride that cut
through a small piece of Canada’s beautiful Rocky Mountains. A group of friends decide to cycle
the trip, 25 km each way, from Banff to Johnston Canyon and back. They ride towards Johnston
Canyon straight into the wind, and then have the wind at their backs on the return trip. The wind
adds or subtracts 5 km/h from their speed. If the group of friends wants to complete the round trip
in 3 hours, algebraically find the average speed with no wind the group needs to cycle. Complete
the distance speed time chart to help solve the question. Round your answer to the nearest
hundredth of a km/h.
The average speed with no wind that the group needs to cycle between Banff and Castle Junction is 16.67 km/h.
What is the average speed of travel?The average speed (S) of travel is the distance (D) traveled divided by the time taken(T).
What is an algebraic equation?An algebraic equation is a statement of the equality of two expressions that have variables, using algebraic operations, known as addition, subtraction, multiplication, division, raising to a power, and extraction of a root.
Data and Calculations:Distance to Castle Junction and from Banff = 50 km (25 x 2)
Time required to cycle = 3 hours
Effect of wind on cyclists = -+5 km/h
The algebraic equation for speed, S, is D/T
Where:
D = Total distance
T = Total time
Therefore, S = D/T = 50/3
S = 16.6667 km/h
Thus, the average speed with no wind that the group needs to cycle between Banff and Castle Junction is 16.67 km/h.
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What is the most precise name for quadrilateral ABCD with vertices
A(-1,0), B(4, 0), C(5, 4), and D(0, 4)?
A. rhombus
B. rectangle
C. square
D. parallelogram
Parallelogram is the quadilateral ABCD with vertices A(-1,0), B(4, 0),
C(5, 4), and D(0, 4)
What is parallelogram?A parallelogram is a quadrilateral whose opposite sides are parallel and equal.
first, find the length of the sides of the quadilateral.
AB = [tex]\sqrt{(4-(-1))^2+0-0^2} \\[/tex]= [tex]\sqrt{5^2+0}[/tex] = [tex]\sqrt{25}[/tex] = 5
BC = [tex]\sqrt{(5-4)^2+(4-0)^2}[/tex] = [tex]\sqrt{1^2+4^2}[/tex] = [tex]\sqrt{1+16} = \sqrt{17}[/tex]
CD = [tex]\sqrt{(0-5)^2+(4-4)^2} = \sqrt{(-5)^2+0} = \sqrt{25-0} = 5[/tex]
DA = [tex]\sqrt{(-1-0)^2+(0-4)^2} = \sqrt{(-1)^2+(-4)^2} = \sqrt{1+16} = \sqrt{17}[/tex]
opposite side length is equal.
so quadilateral is parallelogram.
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The most precise name for quadrilateral ABCD with vertices
A(-1,0), B(4, 0), C(5, 4), and D(0, 4) is parallelogram.
What is the most precise name for quadrilateral ABCD with vertices A(-1,0), B(4, 0), C(5, 4), and D(0, 4)?The most precise name for quadrilateral ABCD with vertices A(-1,0), B(4, 0), C(5, 4), and D(0, 4) is parallelogram.The parallelogram has opposite parallel sides.A parallelogram is a flat 2d shape that has four angles.The opposite interior angles are equal.If the parallelogram has anyone of the angles is a right angle, then all the other angles will be at a right angle.Hence, the most precise name for quadrilateral ABCD with vertices A(-1,0), B(4, 0), C(5, 4), and D(0, 4) is a parallelogram.
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12. The brakes on a vehicle can slow it down at a rate of 15m/s 2. Remember that slowing down is also a rate of change of speed. If this vehicle is travelling at 40 m/s how long would it take the brakes to bring the vehicle to a standstill? Show all steps and formulae used
Step-by-step explanation:
there are several formulas that could play a role.
but in our case, where we have velocities and the deceleration, we are going to use
fV = iV + at
fV = final velocity (0 on our case)
iV = initial velocity (40 m/s in our case)
a = acceleration (-15 m/s² in our case)
t is the time it takes to reach fV.
0 = 40 + (-15)t = 40 - 15t
15t = 40
3t = 8
t = 8/3 = 2.666666666... seconds
so, it takes 2.6666666... or 2 2/3 seconds to bring the vehicle to a standstill.
Grocer Edwards graphs the relationship between the
diameter and heights of different cans in his store. The
graph is below.
Height (cm)
18-
D
16+
14+
12+
10+
8+
6+
4+
2+
2
Choose 1 answer:
4
●
6
8
A
●
10 12
What is the meaning of point A?
●
Diameter (cm)
●
14 16 18
A can with an 10 cm diameter has an 18 cm height.
A can with an 18 cm diameter has an 11 cm height.
A can with an 11 cm diameter has an 18 cm height.
A can with an 18 cm diameter has an 10 cm height.
Considering the given graph, the meaning of point A is given by:
A can with an 11 cm diameter has an 18 cm height.
What does the graph gives?The graph gives the height of the can as a function of the diameter. Both measures are in cm. Then, the axis are given as follows:
The x-axis is the diameter.The y-axis is the height.Point A has coordinates (11,18), that is, x = 11, y = 18, hence the interpretation is:
A can with an 11 cm diameter has an 18 cm height.
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Answer:
A
Step-by-step explanation:
just took the quiz and can confirm the other guy is valid :D
find the slope of this line
Answer:
Undefined (DNE)
Step-by-step explanation:
Any vertical line has an undefined slope.
need help with this asap
The converse, inverse and contrapositive of each conditional statement include:
Converse: If two angles have a common side, then they are adjacent.Inverse: If two angles are not adjacent, then they do not have a common side.Contrapositive: If two angles do not have a common side, then they are not adjacent.What is a conditional statement?
A conditional statement can be defined as a type of statement that can be written to have both a hypothesis and conclusion. Thus, it typically has the form "if P then Q."
Where:
P and Q represent sentences.
In this scenario, we would write the converse, inverse and contrapositive of each conditional statement as follows:
Converse: If two angles have a common side, then they are adjacent.Inverse: If two angles are not adjacent, then they do not have a common side.Contrapositive: If two angles do not have a common side, then they are not adjacent.Read more on conditional statement here: brainly.com/question/16951916
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What is the approximate length of the line segment?
Answer:
18.4 units
Step-by-step explanation:
We can use the distance formula, d = [tex]\sqrt{(x_{1}-x_{2}) ^{2} +(y_{1}-y_{2}) ^{2}}[/tex] to find the length of the line segment.
d = [tex]\sqrt{(x_{1}-x_{2}) ^{2} +(y_{1}-y_{2}) ^{2}}[/tex] = [tex]\sqrt{(5+12) ^{2} +(-10+3) ^{2}}[/tex] = [tex]\sqrt{(17) ^{2} +(7) ^{2}}[/tex]=[tex]\sqrt{338}[/tex]=18.38
Find the eighth term of the
geometric sequence, given the
first term and common ratio.
a1=6 and r=-1/3
Answer:
7
Step-by-step explanation:
haha
for
for
haha
but
birthday
can
7 answer
Answer:
the answer is -2/729
Step-by-step explanation:
When you're given the first term and the common ratio, you just need to multiply the first term by the common ratio and then raise to the power of the nth term minus 1.
In this case, 6(-1/3)^7
I NEED THE ANSWERS PLEASE ANYONE ANSWERS WILL DO
Answer:
1. x = -1 y= -2
2. infinitely many solutions
3. x = 6 y= -7
4.no solution
5. x = -3 y = -17
6. x= 3 y = 7
Step-by-step explanation:
1) y=x-1
7x+6y= -19
6y= -19 -7x
y= (-7x-19)/6
since x-1 and (-7x-19)/6 are both equal to y they are equal to each other
this is how to get x
x-1 = (-7x-19)/6
6x-6 = -7x-19
13x = -13
x = -1
now put back -1 in the equation to get y
y=x-1
y = -1 -1
y= -2
2)-10x+2y=-12
y=5x-6
2y= -12 + 10x
y= -6 + 5x
y = 5x - 6
5x-6 = 5x - 6
0 = 0
when something is
equal to itself its
infinitely many solutions
(when something is not equal to something its no solution)
((when something is equal to just one answer its one solution)
3) y= -4x+17
y=x-13
-4x+17 = x-13
30 = 5x
x = 6
y=x-13
y=6-13
y= -7
4) -3x-15y=8
x+5y=5
-3x-15y=8 -> y = -1/15(3x-8)
5y=5-x -> y= 1/5 (5-x)
-1/15(3x-8) = 1/5 (5-x)
-x-8/3 = 5-x
0 = 23/3
(when something is not equal to something its no solution)
5) -3x+6y=-3
3x-y=8
-3x+6y= -3 -> y = 1/6(3x-3)
3x-y=8 -> y = 3x-8
1/6(3x-3) = 3x-8
3x-3 = 18x-48
x-1 = 6x - 16
5x = -15
x = -3
3x-y=8
3(-3)-y=8
-9-8 = y
y = -17
6) -6x+6y=24
-3x-8y=1
-6x+6y=24 -> y = 1/6(6x+24) -> y = x+4
-3x-8y=1 -> -3x-1 = 8y -> y = 1/8 (-3x-1)
1/8 (-3x-1) = x+4
-3x-1 = 8x+32
11x = 33
x= 3
-6x+6y=24
-6(3)+6y=24
-18 + 6y = 24
6y = 24 + 18
6y = 42
y = 7
f f(x) = 3x + 2 and g(x) = x2 + 1, which expression is equivalent to (f circle g) (x)?
hi
f°g mean apply g(x) and then use result of g(x) as "x" in f(x)
so as g(x) = x² +1 and f(x) = 3x+2
so if we call g(x) X we have
f( X) = 3 X +2
now we replace " X" for it's value
f(X) = 3 ( x² +1) +2
f(X) = 3x² +3 +2
f(X) = 3x² +5
so f°g = 3x² +5
Match the expressions to their solutions or equivalents. -1/9 / (-1/3)
The quotient of the given expression is 1/3
Difference and division of fractionsFractions are written as a ratio of two integers
Given the expression below'
-1/9 / (-1/3)
Change the division to multiplication
-1/9 * -3/1
1/9 * 3/1
1/3
Hence the quotient of the given expression is 1/3
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you received an invoice for 3,000 with terms of 3/10 1/20 n/30. how much will you have to pay if you the bill in 12 day
The customer will to pay $2,970 in 12 days.
What does 3/10 mean?
3/10 is cash discount term which means that a discount of 3% would be given to the customer if payment for the goods purchased is made within 10 days of purchase.
In this case, 3% is not applicable since the payment was made after 12 days.
What does 1/20 mean?
1/20 is cash discount term which means that a discount of 1% would be given to the customer if payment for the goods purchased is made within 20 days of purchase, the payment is within this range, hence, a 1% discount would be applied to invoice price so as to determine the cash payable
cash payable=$3,000*(1-1%)
cash payable=$3,000*0.99
cash payable=$2,970
What does n/30 mean?
It means a payment is expected latest after 30 days which does not entitle the customer no discount.
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