Which of the pairs of functions and their inverses will always have a domain and range of all real numbers?
Answer:
A pair of linear functions
Step-by-step explanation:
Given
See comment for options
Required
Which has real numbers as its range and domain
The answer to this is, the linear functions
Take for instance
[tex]f(x) = mx + b[/tex]
The above function is real for all values of x
The inverse is calculated as thus:
[tex]f(x) = mx + b[/tex]
Replace f(x) with y
[tex]y = mx + b[/tex]
Swap y and x
[tex]x = my + b[/tex]
Make y the subject
[tex]my = x - b[/tex]
Divide by m
[tex]y = \frac{x - b}{m}[/tex]
Replace y with the inverse function
[tex]f^{-1}(x) = \frac{x - b}{m}[/tex]
The above function (i.e. the inverse function) is real for all values of x
This is not true for other options
Sam and Mary collect marbles. “If you give me 5 marbles I’ll have twice as many as you.” said Sam to Mary.
“But if you give me 4 marbles wwe would have the same number said Mary to Sam.
How many marbles do they have altogether?
Answer:
54 marbles
Step-by-step explanation:
The question is a word problem leading to a simultaneous equation
Let 'x' represent the initial number of marbles with Sam, and let 'y' represent the initial number of marbles with Mary,
If Mary gives Sam 5 marbles, we have;
x + 5 = 2 × (y - 5)...(1)
If Sam gives Mary 4 marbles, we get;
x - 4 = y + 4...(2)
From equation (1), we get;
x + 5 = 2 × (y - 5) = 2·y - 10
x = 2·y - 10 - 5 = 2·y - 15
x = 2·y - 15...(3)
From equation (2), we have;
x - 4 = y + 4
∴ x = y + 4 + 4 = y + 8
x = y + 8...(4)
Equating the two values of 'x' in equation (3), and equation (4), we get;
2·y - 15 = y + 8
2·y - y = 8 + 15 = 23
∴ y = 23
From equation (4), we get;
x = y + 8 = 23 + 8 = 31
x = 31
The total number of marbles they have altogether = x + y
However, x + y = 23 + 31 = 54
Therefore;
The total number of marbles they have altogether = 54 marbles.
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20
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s)
The equation of a line is 2[v+ 1) = 10x* 3.
The yuntercept of the line is
and the slope of the line is
Answer:gotta go sorry
Step-by-step explanation:
The measures, in degrees, of the three angles of a triangle are given by 2x+1, 3x - 3, and 9x. What is the
measure of the smallest angle?
Answer:
Step-by-step explanation:
27 degrees
helpppp please!!!!!!
Answer:
x-8
Step-by-step explanation:
since we dont know how much gas is in the tank, lets make that X.
and since we subtract 8 gallons from how much is in the tank, we make that X-8
Answer:
Inequality:
x < 8
The Graph Would be the Hallow Dot on the 8, then it would go the left way.
Which expression is equivalent
Answer:
[tex]\sqrt[6]{2\\}[/tex]
Step-by-step explanation:
Rewriting
2 ^1/2 ÷ 2 ^ 1/3
We know a^ b ÷ a^c = a^ (b-c)
2 ^ (1/2 -1/3)
Getting a common denominator
2^ ( 3/6 - 2/6)
2^ 1/6
[tex]\sqrt[6]{2\\}[/tex]
Answer:
[tex]\sqrt[6]{2}[/tex]
Step-by-step explanation:
We can start by writing the expression as one power of two, and then comparing it to the options. The square root of two is the same and [tex]2^{\frac{1}{2} }[/tex] and the cube root of two is the same as [tex]2^{\frac{1}{3} }[/tex]. Therefore, we can rewrite the expression:
[tex]\frac{2^{\frac{1}{2} }}{2^{\frac{1}{3} }}[/tex]
Now, to write them as one power of two, we can use the quotient rule which states, [tex]\frac{x^m}{x^n} = x^{m-n}[/tex]:
[tex]2^{\frac{1}{2} -\frac{1}{3}}[/tex]
We just need to subtract 1/3 from 1/2 to get:
[tex]2^{\frac{1}{6} }[/tex]
This is the same as the 6th root of 2, which is the second option.
Shirts-2-Go sells t-shirts for a base price of $12 per shirt plus a fixed fee of $3 shipping and handling for the whole order. Shirts PLUS sells t-shirts for a base price of $8 per shirt plus a fixed fee of $23 shipping and handling for the whole order. Let x represent the number of shirts ordered and let y represent the total cost of the order.
y = 12x + 3
y = 8x + 23
How many shirts would you have to purchase for the total cost to be the same at both companies?
Answer:
5 shirts
Step-by-step explanation:
Y=12x+3 equation 1
y=8x+23 equation 2
12x+3=8x+23 substituting y value will cause equations to equal
4x=20
x=5 shirts
check answer
y=12x+3
y=12(5)+3
y=60+3
y=63
y=8x+23
y=8(5)+23
y=40+23
y=63
CAN SOMEONE HELP ME OUT WITH THIS PLEASE AND THINK YOU
Answer:
[tex]10\frac{7}{18}[/tex]
Step-by-step explanation:
First revert it to improper fraction.
[tex]\frac{13}{2} +\frac{35}{9} \\\\[/tex]
Now put them to a common denominator.
[tex]\frac{187}{18}[/tex]
=> [tex]10\frac{7}{18}[/tex]
The weekly amount of money spent on maintenance and repairs by a company was observed, over a long period of time, to be approximately normally distributed with mean $400 and standard deviation $20. How much should be budgeted for weekly repairs and maintenance to provide that the probability the budgeted amount will be exceeded in a given week is only 0.1?
Answer:
$425.6 should be budgeted for weekly repairs and maintenance.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean $400 and standard deviation $20.
This means that [tex]\mu = 400, \sigma = 20[/tex]
How much should be budgeted for weekly repairs and maintenance to provide that the probability the budgeted amount will be exceeded in a given week is only 0.1?
This is the 100 - 10 = 90th percentile, which is X when Z has a p-value of 0.9, so X when Z = 1.28.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.28 = \frac{X - 400}{20}[/tex]
[tex]X - 400 = 20*1.28[/tex]
[tex]X = 425.6[/tex]
$425.6 should be budgeted for weekly repairs and maintenance.
¿Cuánto mide el lado de un terreno cuadrado, si su área 144 m2?
Answer:
72
Step-by-step explanation:
all you had to do was divide by 2
Thang decided to borrow $90 from his local bank to help pay for a car. His loan was for 3 years at a simple interest rate of 40%. How much interest will Thang pay?
Answer:
Step-by-step explanation:
P = 90
r = 40% = 40/100 = 0.4
t = 3 years
It is not clear to me what this means. Is the 40% for each year for 3 years or is the interest rate = 40% period. I know that in some of the poorer countries, this is not an unusual amount to pay for each year he holds the loan.
I will take it as 40% for each year for 3 years.
i = prt = 90 * 0.4 * 3
i = 108
What measure is represented by 17 feet in the figure below?
A cylinder with diameter 17 feet.
the radius of the base
the diameter of the base
the area of the base
the height of the cylinder
Answer: The answer is the diameter.
Step-by-step explanation:
Answer:
diameter
Step-by-step explanation:
the diameter goes straight through the center of the circle
find the value of x and y
Answer:
x = 58
y = 39
Step-by-step explanation:
x = 58 (Vertically opposite angles)
x + 2y + (x-14) = 180 (Angles in a straight line)
=> x + 2y + x - 14 = 180
=> 2x + 2y = 180 + 14
=> 2(58) + 2y = 194
=> 116 + 2y = 194
=> 2y = 194 - 116
=> 2y = 78
=> y = 78/2
=> y = 39
I need help very quickly, please!!
Answer:
32ft
Step-by-step explanation:
Tan = opp/adj
Tan(65) = n / 15
Tan(65) x 15 = n
n = 32.16 = 32ft
Answer:
32 feet
Step-by-step explanation:
Hi there!
We are given a right triangle and the angle of elevation (one of the acute angles in the triangle) as 65°, as well as one of the legs (sides that make up the right triangle) as 15
We need to find the height of the triangle.
Let's make the height of the triangle (the side we need to find) x
Since we need to find the height of the triangle, let's use tangent. As we have the angle of elevation given, we'll use that.
Recall that tangent is [tex]\frac{opposite}{adjacent}[/tex]
in reference to the angle of elevation, the opposite side is x, and the adjacent side is 15
that means that:
tan(65)=[tex]\frac{x}{15}[/tex]
plug tan(65) into your calculator (make sure it's on degree mode!)
tan(65)≈2.14
2.14=[tex]\frac{x}{15}[/tex]
multiply both sides by 15 to clear the fraction
32.1=x
The problem asks us to round to the nearest foot, so the height of the building is 32 feet
Hope this helps! :)
plz anser this nathanmalhotra (if your not them dont anserw) From midnight to 7:00 am, the temperature rose 3/10 °C each hour. If the temperature at midnight was −1°C, what was the temperature at 7:00 am?
Answer:
11/10°C
Step-by-step explanation:
7 x 3/10 = 21/10
Temperature at midnight = -1°C
Temperature at 7.00 am = 21/10°C -1°C = 11/10°C
Answer:
1.1°C
Step-by-step explanation:
Assuming we are starting at midnight, we know that at midnight it is -1°C. We want to find the temperature at 7:00 AM. Or 7 hours later than midnight. The question says that every hour the temperature rises by 3/10°C. In 7 hours, we need to multiply 3/10*7=21/10=2.1 °C. So, it rises by 2.1 °C. Next add that to the -1 from midnight. Do 2.1+-1=1.1 °C.
Hope this helps!
Simplify 3a²b³x 4a³b
If using the method of completing the square to solve the quadratic equation
22 + 2x + 16 = 0, which number would have to be added to "complete the
square"?
Answer:
complete the square 2 x + 38 = 0
Step-by-step explanation:
Dan, Harry and Regan sell cars.
Dan sells x cars.
Harry sells 5 more cars than Dan.
Regan sells twice as many cars as Dan.
Write an expression, in terms of x, for the mean number of cars Dan, Harry and Regan sell.
binomial theorem to expand (x+4)^4
Answer:
Step-by-step explanation:
(x+4)^2.(x+4)^2
= x^4 +16x^3+96x^2+256x+256
Equations of parallel lines
Answer: c
Step-by-step explanation:
In order to be parallel, the slope must be the same. This means slope is 2
Now one of the point is 5,-1, so do 2x5 + x = -1, so x = -11
meaning b is -11
so the equation should be y=2x-11
Algebra
write down the coefficient of x in 3(x)4x
A 12
B 3
C 0
by Emmanuel okorie
Answer:
nah its a.
Step-by-step explanation:
bakit?(#boyinthebrainly)
Please answer quickly
Answer:
10
Step-by-step explanation:
given :
length WX ≅ (congruent means equal) length XY
therefore , WX = 3
WZ = WX + XZ
WZ = 3 + 7
WX = 10
PLEASE HELP ME!! its a pretty easy question
Answer:
V= 936m³
Step-by-step explanation:
Formula:
Volume = L * W * H
Volume1= L * W * H
= 16 * 9 * 6
= 864m³
Volume2= L * W * H
= 6 * 2 * 6
= 72m³
Add both volumes to get total volume.
= 864m³ + 72m³ = 936m³
Hope this helps!
Have a nice dayy! :)
Practice D. Factor each trinomial.
1.
x² – 2x- 8
I
2.
y2 – 13y + 42
3.
m2 - 6m - 7
Help me answer those three factor please
Answer:
So 1) x²-2x-8
= x(x-2-8/x)
2) y²-13y+42
= y(y-13+42/y)
3) m²-6m-7
= m(m-6-7/m)
Hope it helps
Which number(s) below belong to the solution set of the equation? Check all
that apply
x + 9 = 26
A. 17
B. 234
C. 52
D. 35
E. 26
F. 3
Answer:
A
Step-by-step explanation:
x + 9 = 26
x = 17
Answer:
A.17
Step-by-step explanation:
17+9=26
verify that :- 5/8x(7/9-11/6)=(5/8x7/9)-(5/8x11/6)
please answer
!!!10 POINTS I KNOW IT IS NOT ENOUGH BUT PLEASE ANSWER!
AND IF YOU CAN SHOW AT LEAST A LITTLE WORK THAT WOULD BE GREAT I NEED TO SHOW WORK!!!
Answer:
B) 376 units squared
Step-by-step explanation:
Imma put a picture that has a fully explanation. Hope this helps, good luck! ;)
Btw saw your other one got deleted •_• *sigh*
HURRY !!!!!! Which describes the correlation shown in the scatterplot?
Which set of numbers is arranged in increasing order? A. , , , B. , , , C. , , , D. , , ,
Answer:
its B
Step-by-step explanation:
3.14 then pi (3.14159) then 22 ÷ 7 (3.1428) then square root of 10 (3.16)
Answer:
B
Step-by-step explanation:
pi=3.141592654
square root of 10=3.16227766
3.14=3.14
22/7=3.142857143
Consider the trapezoid shown below.
6 in.
4 in.
6 in.
6 in.
(not drawn to scale)
Answer:
36
Step-by-step explanation:
1/2bh
1/2 (6*4) =12
Considering there are three triangles we will multiply by 3
12*3=36
