After a small search, I've found that we want to find the inverses of both functions. We will find that E(x) does not have an inverse function, and the inverse function of T(x) is h(x) = x/6 - 1/6
Here we have a piecewise function:
T(x) = 6(x-3) + 25 if x > 3
E(x) = 25 if 0 ≤ x ≤ 3
First, remember that two functions f(x) and g(x) are inverses if:
f(g(x)) = x
g(f(x)) = x
From that definition we can see that E(x) does not have an inverse, because for any function g(x), we will have:
E(g(x)) = 25
So E(x) can't meet the condition.
Now let's analyze the function T(x)
T(x) = 6(x-3) + 25
We can rewrite it as:
T(x) = 6x - 6×3 + 25
T(x) = 6x + 1
Note that T(x) is a linear equation, so the inverse will also be a linear equation. Let's assume that the inverse is h(x) = ax + b
We will have:
T(h(x)) = 6×h(x) + 1 = 6(ax + b) + 1
Now, if these are inverses, we have:
6(ax + b) + 1 = x
6ax + 6b + 1 = x
Then we must have:
6b + 1 = 0
6ax = x
From the first equation, we can get:
6b + 1 = 0
6b = -1
b = -1/6
From the second equation we have:
6ax = x
6a = 1
a = 1/6
Then:
h(x) = x/6 - 1/6
And this is the inverse function of T(x)
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calculate the absolute value
| 4 - 3x | = 5x + 4
Recall the definition of absolute value:
• |x| = x if x ≥ 0
• |x| = -x if x < 0
So we have 2 cases to consider:
• If 4 - 3x ≥ 0, then |4 - 3x| = 4 - 3x, and we have
4 - 3x = 5x + 4
8x = 0
x = 0
• If 4 - 3x < 0, then |4 - 3x| = -(4 - 3x) = 3x - 4, which gives
3x - 4 = 5x + 4
2x = -8
x = -4
However, keep in mind that |x| is always non-negative. If x = -4, then the right side of the equation becomes
5(-4) + 4 = -20 + 4 = -16 < 0
so the solution in this case is extraneous.
simplify y + 5 - y - 6
Answer:
-1
Step-by-step explanation:
Subtract the numbers: y+5-y-6
Combine like terms: y-1-y
= -1
The ________ is the actual population of individuals, or clusters, from which a random sample will be drawn.
FIRST TO ANSWER CORRECTLY GETS BRAINLIEST!!!
Answer:
6ft by 15ft
Explanation:
L1 = 10 ft
W1 = 4 ft
L2 = L1*(3/2)
W2 = W1*(3/2)
L2 = 10 ft times (3/2) = 15 ft
W2 = 4 ft times (3/2) = 6 ft
I hope this answer helps you out!
find the derivative of the function y= x^20
Answer:
Step-by-step explanation:
[tex]\frac{dy}{dx} =20x^{19}[/tex]
evaluate the expression
Step-by-step explanation:
13
[tex]3 + (20 \div 5) - ( {2}^{2}) [/tex]
[tex]3 + 4 - 4 = 3[/tex]
15
[tex] \frac{10 - {3}^{2} }{20 - (3 \times 4)} [/tex]
[tex] \frac{10 - 9}{20 - 12} [/tex]
[tex] \frac{1}{8} [/tex]
Show Work! There are 380 students, teachers, and chaperones going on school buses for a field trip. Each school bus can hold 68 passengers. Everyone will ride on a school bus. How many school buses does this group need?
Answer:
6 buses
Step-by-step explanation:
i believe you just have to divide 380/68
then it'll give you 5.5 and then have to round to the nearest integer
f(x)=19x+11 find f(4)
Answer:
87
Step-by-step explanation:
f(x)=19x+11
Let x = 4
f(4) = 19*4 +11
=76 +11
= 87
Answer:
[tex]f(x) = 19x + 11 \\ f(4) = 19 \times 4 + 11 \\ = 76 + 11 \\ = 87 \\ thank \: you[/tex]
Need help with solving please
Answer:
x=8
Step-by-step explanation:
4 ^(1/2x) = 256
Rewriting 256 as a power of 4
4 ^(1/2x) = 4^4
Since the bases are the same, the exponents are the same
1/2x = 4
Multiply each side by 2
1/2x *2 = 4*2
x=8
A. 5x-2+x=x-4 B. 5x+x=x-4
B. -4/6
Step-by-step explanation:
5x+x=-4
6x=-4
x=-4/6
Answer:
x= -2/5 or -0.4 x= -4/5 or -0.8Step-by-step explanation:
If you are solving for x then you should get something like this
A 5x-2+x=x- 4 B. 5x+x=x-4
6x-2=-4. 6x=x-4
6x-2-x=-4. 6x-x=-4
5x-2+2=-4+2. 5x=-4
5x/5=-2/5. 5x/5=-4/5
x=-2/5. x=-4/5
I hope this helped you out!
can you help me to solve this
Answer:
<B = <C(angles in a isoceles traingle)
Answer:
angle B is equal to angle C because it's a isosceles triangle with two equal sides and two equal angles
Solve the equation.
} (a + 2) = {(2-a)
WWW.
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
O A. The solution is
(Type an integer or a simplified fraction.)
B. The solution is all real numbers.
O C. There is no solution.
(Answer quickly)
The university of Michigan football stadium can hold 107,601 people. Michigan states football stadium can hold 75,001 people. 51,000 people can fit in the football stadium at the university of North Carolina and 40,004 people can fit in duke universities stadium which is also in North Carolina. How many more people can fit in the stadiums in Michigan combined than in the stadiums in North Carolina combined
Answer:
56,601
Step-by-step explanation:
What is the y-intercept
Answer:
y-intercept is (0, 9)
Step-by-step explanation:
At y-intercept, x is 0
[tex]y = 9[/tex]
Answer: (0, 9)
Concept:
The y-intercept of a function is the point at which the graph of the function crosses the y-axis.
In other words, the y-intercept is the point when the x value is 0.
Solve:
Find the point where the x value is 0
It is the fourth from the left, where the x value is 0.
The y value is 9.
Finalize the point
x value is 0
y value is 9
Point = [tex]\boxed{(0, 9)}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Find the quotient.
154 divided by 14
Answer:
11
Step-by-step explanation:
[tex]\frac{154}{14} =11\\\\check: 11*14=154[/tex]
154 divided by 14 equals 11.
To find the quotient of 154 divided by 14, we perform long division as follows:
11
14 | 154
First, we consider how many times 14 can be divided into 15, which is 1. We write the quotient, 1, above the line.
Next, we multiply 14 by 1, which equals 14. We subtract 14 from 15, resulting in 1. We bring down the next digit, which is 4.
We now consider how many times 14 can be divided into 14, which is 1. We write the quotient, 1, next to the 1 above the line.
Multiplying 14 by 1 gives us 14. Subtracting 14 from 14 gives us 0.
Since there are no more digits to bring down, we can conclude that the quotient is 11.
Therefore, 154 divided by 14 equals 11.
Long division is a method used to find the quotient and remainder when dividing two numbers. It involves dividing, multiplying, subtracting, and bringing down digits until there are no more digits to bring down. In this case, the quotient is 11, indicating that 154 can be divided by 14 precisely 11 times without any remainder.
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Madura is 25 years younger than her father. Nadira's mother is two years younger than her father. Together Nadira, her mother and father have a combined age of 78. Work out their ages.
just solve by yourself
eg jammu jdndhdbshsbsbs
Answer:
A: [tex]3\frac{1}{3}[/tex]
B: [tex]3\frac{2}{3}[/tex]
I hope this helps!
pls ❤ and mark brainliest pls!
Help please! Describe how figure 20 will look like
9514 1404 393
Answer:
Each colored block in Figure 20 will be a 20×20 square of smaller squares of the same color. The red-green pattern will be identical.
Step-by-step explanation:
Each colored block in Figure N is an N×N array of small blocks the same color. The pattern of red and green N×N blocks is the same from one figure to the next. We expect Figure 20 to fit this description.
Refer to the figure to answer the question.
Name the line of intersection of planes GABH and FEHG
HG
GA
FE
FD
Answer:
It's HG
Step-by-step explanation:
The line of intersection is where they cross, and this line is the line HG
find the defference between 5 2/7 and 2 2/4
Answer: 39/14
Step-by-step explanation:
Given
5 2/7 - 2 2/4
Convert mixed fraction to improper fraction
5 2/7 = (5 × 7 + 2) / 7 = (35 + 2) / 7 = 37/7
2 2/4 = (2 × 4 + 2) / 4 = (8 + 2) / 4 = 10 / 4 = 5/2
Find the common denominator for 37/7 and 5/2
First 10 multiples of 2 = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20
First 5 multiples of 7 = 7, 14, 21, 28, 35
Since 14 is the first common multiple in the lists, 14 would be the common denominator of 37/7 and 5/2
Convert to the common denominator
(37 × 2) / (7 × 2) = 74 / 14
(5 × 7) / (2 × 7) = 35 / 14
Simplify by subtraction of numerator
=74/14 - 35/14
=(74 - 35) / 14
=[tex]\boxed{\frac{39}{14} }[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Any mathematician am giving brainliest for this question
9514 1404 393
Answer:
(x, y) = (1/2, 1)
Step-by-step explanation:
Subtract twice the second equation from the first to eliminate the x-variable.
(2/x +3/y) -2(1/x -4/y) = (7) -2(-2)
11/y = 11 . . . . . . . simplify
y = 1 . . . . . . . . multiply by y/11
__
Substituting into the second equation gives ...
1/x -4/1 = -2
1/x = 2 . . . . . . add 4
1/2 = x . . . . . . multiply by x/2
The solution is (x, y) = (1/2, 1).
_____
Additional comment
The attached graph seems to show that the graphs of the two equations also intersect at (x, y) = (0, 0). However, careful consideration of these equations leads to the conclusion that x=0 and y=0 are not in the domain of either equation. (Division by 0 is undefined.) So, the only solution is (x, y) = (1/2, 1).
If you were to multiply both equations by xy to eliminate fractions, you would, indeed, arrive at the conclusion that (x, y) = (0, 0) is a solution. As we noted, that "solution" is extraneous. Whenever you multiply an equation by an expression that can have the value 0, you need to be careful to exclude any "solution" that makes that expression 0.
which statement best describes f(x)=-2√x-7+1
it is under mapping and function
f of x is equal to -2 root x-7 plus one
Does this picture indicate that < JAC =
Answer:
No
Step-by-step explanation:
<JAC = 93
< DBE = 90
The two angles are not equal
You are wrapping a gift box that is 16 inches long,
7 inches wide, and 9 inches tall. Find the amount of
wrapping paper you need to wrap the gift box to the
nearest square inch.
Answer:
1008 inches
Step-by-step explanation:
Find the area of the rectangle.
(3y+1) miles
25 miles
Answer:
Srectangle: (3y+1)*25=75y+25(cm^2)
Step-by-step explanation:
Srectangle= w*L
A car has been purchased for £5200 and is estimated to have an expected life driving 200,000
miles. At the end of that time its value is estimated to be £200. If the units-of-production
method is used to depreciate the car,
a) What is depreciation cost per mile?
b) What will be book value of the car after it has driven 55000 miles?
Answer:
a) 0.025£ b)3825£
Step-by-step explanation:
a) 5200-200=5000 - of the value will be lost after reaching the milleage of 200000 miles
200000-5000
1-x
200000=5000/x
x=5000/200000= 5/200=1/40=0.025£- the depreciation cost per mile
b)0.025*55000= 1375- the decreasing of the price
5200-1375=3825£- the book value of the car after it has driven 55000 miles
I’ll give you 50 points if it’s answer correctly
Answer:
. The line passes through the quadrants I, II and III. ii. The line intersects the Y-axis at (0, 1).
the length of a rectangle is 8cm and the height is 16cm find the answer of the above figures using this formular...
2(a + b) Perimeter
(B×H) Area
[tex]\\ \sf\longmapsto Perimeter=2(L+B)[/tex]
[tex]\\ \sf\longmapsto Perimeter=2(16+8)[/tex]
[tex]\\ \sf\longmapsto Perimeter=2(24)[/tex]
[tex]\\ \sf\longmapsto Perimeter=48cm[/tex]
Area:-
[tex]\\ \sf\longmapsto Area=Length\times Breadth[/tex]
[tex]\\ \sf\longmapsto Area=8(16)[/tex]
[tex]\\ \sf\longmapsto Area=128cm^2[/tex]
Is square root of 11+10 a rational or irrational number
Answer:
Irrational Number is the answer
Answer:
[tex] \sqrt{11 + 10} = \sqrt{22} = 4.69041576 [/tex]
THIS IS IRRATIONAL
Step-by-step explanation:
The correct answer is irrational and the reason for that is the decimals for sqrt of 22 are non-recurring, are non-terminating and lastly it cannot be expressed in a form of a fraction.
I hope this makes sense
:)
You are looking at your power bill for the month, you pay 12 cents per kilowatt-hour. Running a 60 watt light bulb for 1 hour is .06 KWH, if you leave a light on all the time that has 5 light bulbs in it how much would that cost in a 30 day month? Answer in the form of $2.54 without the dollar sign.
Answer:
$25.92Step-by-step explanation:
1 bulb in 1 hour = 0.06 kWhUnit of cost = 12 cents per kWh = $0.12 per kWh5 bulbs in 30-day month will consume electricity:
5*0.06*30*24 = 216 kWhThe total cost is:
216 * 0.12 = $25.92Total electricity consumed per day
24(0.06)1.44KwhConsumed in 30days
30(1.44)43.2KwhFor 5bulbs
5(43.2)216kwHCost
216(0.12)$25.92