The domain of the provide function where the function is defined is x less than the number three.
What is the domain of the function?Domain of a function is the set of all the possible input values which are valid for that function.
The function given in the problem is,
[tex]y=\ln\left(\dfrac{-x+3}{1}\right)[/tex]
The above function is the function of logarithm. For the logarithmic function, it is defined for all the real numbers except 0.
Thus, the function should be greater than zero as,
[tex]\left(\dfrac{-x+3}{1}\right) > 0\\(-x+3) > 0\\-x > -3[/tex]
Change the sign of both side, by changing the inequality,
[tex]x < 3[/tex]
Thus, the domain of the provide function where the function is defined is x less than the number three.
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Answer:
x<3
Step-by-step explanation:
edge 2022
what is the property of equality of 2y − 40 = -18?
Answer:
Given the equation 2y-40=-18 to simplify the equation further we need to first add 40 to both sides of the equation thereby justifying the addition property as shown;
2y-40 + 40 =-18+40
2y = 40-18
2y = 22
We will also apply the division property here. Division property is used when both sides of an equation is divided by a number without affecting the equality rule.
Dividing the resulting equation by 2:
2y/2 = 22/2
y = 11
Step-by-step explanation:
What is the equivalent decimal? Drag the answer into the box to match the fraction. 5/45
Answer:
0.11111111111
Reason :
When you divided 5 by 45, you get 0.11111111111
Help ????????????????????
Answer:
first one is 90
second one is 108
Step-by-step explanation:
Susan says that a solution to the equation x + 5 = 15 must also be a solution to the equation 2(x+1) = 22 write an explanation why this is true
9514 1404 393
Answer:
each equation can be transformed to the other
Step-by-step explanation:
Starting with the given equation, we can subtract 4, then multiply by 2:
x + 5 = 15
x + 5 - 4 = 15 - 4
x + 1 = 11
2(x + 1) = 2(11)
2(x +1) = 22 . . . an equivalent equation
The properties of equality allow one equation to be transformed into the other.
An airline sells all the tickets for a certain route at the same price. If it charges 200 dollars per ticket it sells 10,000 tickets. For every 15 dollars the ticket price is reduced, an extra thousand tickets are sold. This if the tickets are sold for 185 dollars each then 11,000 tickets sell. It costs the airline 100 dollars to fly a person. (a) Express the total profit P in terms of the number n of tickets sold. (b) Express the total profit P in terms of the price p of one ticket.
The function that gives the amount of profit at a given price and number
given are obtained from the relationship between the variables.
a) The profit in terms of the number of tickets sold, P = -0.015·n² + 250·n
(b) The profit in terms of ticket price, is P = -66.[tex]\overline 6[/tex]·p² + 3000·p + 2,333,333.[tex]\overline 3[/tex]
Reasons:
Number of tickets sold at x = $200, is y = 10,000 tickets
Number of extra tickets sold for every $15 price reduction = 1,000 tickets
Number of tickets sold at $185 = 11,000
The cost to fly a person = $100
(a) The rate of change, [tex]\frac{\Delta y}{\Delta x}[/tex], of the number of ticket sold wit price is given as
follows;
[tex]\dfrac{\Delta y}{\Delta x} = \dfrac{11,000 - 10,000}{185 - 200 } = -66. \overline 6[/tex]
The equation in slope and intercept form is therefore;
n - 11,000 = -66.[tex]\overline 6[/tex]·(p - 185)
n = -66.[tex]\overline 6[/tex]·p + 12,333.[tex]\overline 3[/tex] + 11,000 = -66.[tex]\overline 6[/tex]·p + 23,333.[tex]\overline 3[/tex]
Number of tickets sold, n = -66.[tex]\overline 6[/tex]·p + 23,333.[tex]\overline 3[/tex]
[tex]Price \ per \ ticket, \ p = \dfrac{23,333.\overline {3} - n}{66. \overline{6}}[/tex]
The revenue, R = n·x
Therefore;
[tex]R = \dfrac{23,333.\overline {3} \cdot n- n^2}{66. \overline{6}}[/tex]
The profit = Revenue - Cost
The cost = 100·n
[tex]Profit, P = \dfrac{23,333.\overline {3} \cdot n- n^2}{66. \overline{6}} - 100 \cdot n = -0.015 \cdot n^2 + 250 \cdot n[/tex]
Total profit, P = -0.015·n² + 250·n(b) The total profit, P, in terms of the price p, for one ticket
Number of tickets sold, n = -66.[tex]\overline 6[/tex]·p + 23,333.[tex]\overline 3[/tex]
The revenue, R = n·p
∴ R = -66.[tex]\overline 6[/tex]·p² + 23,333.[tex]\overline 3[/tex]·p
Cost = 100·n
∴ Cost = 100·(-66.[tex]\overline 6[/tex]·p + 23,333.[tex]\overline 3[/tex])
Therefore, the profit is given as follows;
Profit = -66.[tex]\overline 6[/tex]·p² + 23,333.[tex]\overline 3[/tex]·p - (100·(-66.[tex]\overline 6[/tex]·p + 23,333.[tex]\overline 3[/tex]))
Therefore;
Total profit, P = -66.[tex]\overline 6[/tex]·p² + 3000·p + 2,333333.[tex]\overline 3[/tex]Learn more here:
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We want to express the total profit in two different ways.
The answers are:
a) P(n) = n*[n - 23,333.3]*(-15/1,000) - n*100
b) P(p) = n(p)*p - n(p)*100 = [ (-1,000/15)*p + 23,333.3]*(p - 100)
The given information is:
If the ticket price is $200, they sell 10,000 tickets.If the ticket price decreases $15, they sell 1,000 tickets more.It costs $100 to fly a person, then the cost of each ticket is $100.a) We want to get the profit in terms of the number n of tickets sold.
The number of tickets sold depends on the price, we know that it is a linear relation like:
n(p) = a*p + b
where p is the price.
we know that:
n(200) = 10,000
n(185) = 11,000
If this is a linear relation, the slope is known:
a = -1,000/15$
Then the line is something like:
n(p) = (-1,000/15)*p + b
We know that if k = 200, then n = 10,000
Replacing that we have:
n(200) = 10,000 = (-1,000/15)*200 + b
10,000 + (1,000/15)*200 = b = 23,333.3
Then the number of tickets sold as a function of the price is:
n(p) = (-1,000/15)*p + 23,333.3
Then the revenue is given by the number of tickets sold times the price, this is:
r(n) = n*p
We can write k in terms of n as:
k = [n - 23,333.3]*(-15/1,000)
Then the revenue as a function of the number of tickets sold is:
r(n) = n*[n - 23,333.3]*(-15/1,000)
The profit is the difference between the revenue and the cost, then the profit function is:
P(n) = n*[n - 23,333.3]*(-15/1,000) - n*100
Where n*100 is the cost.
b) now we want to write the same equation, but this time as a function of the price.
now the revenue is:
r(p) = n*p = [ (-1,000/15)*p + 23,333.3]*p
Then the profit is:
P(p) = n(p)*p - n(p)*100 = [ (-1,000/15)*p + 23,333.3]*(p - 100)
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PLS HELP FAST 20 PTS Identify the length of MN.
Answer:
Try 6.5
Step-by-step explanation:
Maybe that might work out
What is the equation of the line that goes through (-3,-1) and (3,3)?
A. 3x + 2y = 15
B. 3y + 2x = 15
C. 3x − 2y = 3
D. 2x − 3y = -3
Answer:
It’s D : 2x - 3y= -3
Step-by-step explanation: I got a 100 on the test.
A helicopter hovers 950 feet above a small island. The figure shows that the angle of depression from the helicopter to point P is 47 °. How far off the coast, to the nearest foot, is the island?
let x rep the foot of the island
Using trig formula
SOHCAHTOA
sin 47° = 950/x
xsin47° = 950
x = 950/sin47°
Please help I need just 4 Correct for answers to pass
Answer:
Hey!
Your answer is 14m (2sf)
Step-by-step explanation:
WE HAVE TO USE PYTHAGORAS! ⇒ a²+b²=c² THEN √c = (unknown side)
Here: 12² + 8²= 208
Now SQUARE-ROOT 208! ⇒ √208
ANSWER: 14.42220510185596
The answers there are rounded up so we round this number to get 14m!
B IS YOUR OPTION!
I HOPE THIS HELPED YOU!simplify -4/5 divided by 3/-2
Answer:
[tex]\frac{8}{15}[/tex]
Step-by-step explanation:
Answer:6/36
Step-by-step explanation:
Which graph represents a function?
Answer:
the answer is the top right one
If a supplement of an angle is 20 more than 3 times a complement, then the measure of the angle is?
240 chocolates are put into three boxes. The chocolates are
put into either a red, yellow or blue box in the ratio 2:5:1
Work out the number of chocolates in each box.
Answer:
red: 20
yellow: 50
blue:10
Step-by-step explanation:
find number of chocolate in one box
240÷3=80
add the ratiios
2+5+1=8
divide the number of chocolate in one box by the sum of the ratio
80÷8=10
multiply the quotient by each of the quatities in the ratio
red:2x10=20
yellow:5x10=50
blue:1x10=10
Solve 3[-x + (2 x + 1)2 = x - 1
X=?
Answer:
x=−7/8
Step-by-step explanation:
Type A is five feet tall and grows at a rate of 12 Inches per year?
Answer: it is 5 years old
Step-by-step explanation: because 12 inches is 1 foot long and5feetis5yearsfootlongfoot
The length of a rectangle is units greater than its width. If the width is w, which expression gives the perimeter of the rectangle in terms of its width?
A. 4w + 3
B. w – 3
C. 5w
D. 6w + 4
Answer: i got C sorry if its not right
Blake is saving up to buy a
new par of headphones. He
has $20 saved aready, and
he earns $10 for every lown
he mows. How many lawns will
he have to mow to have at
least $90 saved?
Answer:
7 lawns
Step-by-step explanation:
90 - 20 = 70
70 / 10 = 7
7 lawns will need to be mowed to save at least $90
Bus Stop #2: initial value: 9 miles rate of change: 0.5 miles each minute Friend’s House: A 2-column table with 3 rows. Column 1 is labeled Time (minutes) with entries 3, 6, 9. Column 2 is labeled Distance (miles) with entries 4, 6, 8. Seth can also get dropped off at Bus Stop #2, which is closer to his school. Which will get him to school faster? (School is 17 miles away.)
Answer:
bust stop #2 6.5 minutes
Step-by-step explanation:
Answer:
bust stop #2 6.5 minutes
Step-by-step explanation:
Caitlyn has a credit card with a spending limit of $1500 and an apr (annual percentage rate) of 18%. during the first month, caitlyn charged $375 and paid $250 of that in her billing cycle. which expression will find the amount of interest caitlyn will be charged after the first month? (0.18) (250 dollars) (0.015) (375 dollars) (0.18) (375 dollars) (0.015) (125 dollars)
The amount of interest Caitlyn will be charged after the first month is $1.875.
Annual percentage rate(APR) of the credit card = 18%
What will be the Monthly Percentage Rate of the credit card?The monthly percentage rate will be 1/12th of APR.
The Amount charged in the first month =$375
Amount paid in billing cycle = $250
So, the amount on which interest will be levied = $375 - $250 = $125
The interest levied on $125 = 125* (18/12)* (1/100)
The interest levied on $125 = $1.875
Therefore, the amount of interest Caitlyn will be charged after the first month is $1.875.
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what is 3|(18-3)+4((5-(-7)|
Answer:
37
Step-by-step explanation:
Expand the equation
3 x (18 - 3) + 4 x (5 - 7)
Use BODMAS
First find the sum of brackets
18 - 3 = 15
3 x 15 = 45
then
5 - 7 = -2
-8
so
45 + - 8 = 37
BODMAS
B - Brackets
O - Power
D - Divison
M - Multiplication
A - Addition
S - Subtraction
Hope this helped you
:-)
Please Graph y<1−3x.
PLEASE HELP! WILL CROWN!! I need statements and reasons on DC and EF!!! plzzz
Answer:
DC⊥EF as the 2 angles in smallest triangle are 30 and 60 degrees, so the last one is 90 making Line DC perpendicular to Line EF.
Step-by-step explanation:
DC⊥EF means that Line DC is perpendicular (90 degrees) to EF.
To prove this, we can use the two angles of the small triangle created by the intersection of the triangles AEF and DCB.
The remaining angle of triangle AEF is 60, as all angles of triangles add up to 180 (so 180 - 12 = 60). This angle at F is shared with the little triangle.
Now we will get the angle at D using the triangle DCB. Since we are given two angles 90 and 60, angle D has to be 30.
So of our little triangle, we have angles 30 and 60, meaning the last one is 90 degrees and hence, DC⊥EF
A video game costs £42.
A new version of the game is released.
The price has increased by 15%.
Work out the cost of the new version. £ |
Help!!!
Answer:
48.30
Step-by-step explanation:
42(1.15) = 48.30
Which three lengths can NOT be the lengths of the sides of a triangle?
A.) 24 m, 16 m, 10 m
B.) 8 m, 9 m, 8 m
C.) 20 m, 6 m, 11 m
D.) 13 m, 10 m, 15 m
Answer:
I would say C.)
Mark is painting the ceiling of a square room. If the area he paints is 400 sq. feet, what are the dimensions of the room?
Answer:
20 by 20
Step-by-step explanation:
square root of 400 is 20
20 times 20 = 400
The temperature is 8 degrees if the dropping rate is 3.5 degrees an hour. How many hours until it is -20degrees?
What is the Volume of this polygon ?
Answer:
100 cm^3
Step-by-step explanation:
Volume = 10x5x2 = 100
Answer:
100cm3
Step-by-step explanation:
To calculate the volume you have to to 2x5x10=10x10=100
Pls rate brainliest!
can someone please help me with number 2 and 3? i just have to put them in a sentence
it’s something like this I think
Rewrite the expression using only positive exponents.
PLEASE HELP!!!!
Answer:
Step-by-step explanation:
[tex]\frac{1}{5^{12} } \frac{1}{32^{3} } \frac{1}{9^{15} } \\[/tex]
???? ????? ?????????????
Answer:
12/5
Step-by-step explanation:
tan(G) = opposite side ÷ adjacent side
⇒ tan(G) = 24/10 = 12/5