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Explanation:
The composition of the original function with its inverse will cancel out the operations to yield the input as the output.
Consider the example functions shown below
f(x) = x+5g(x) = x-5The first function adds 5 while the second function does the complete opposite and subtract 5. The two functions are inverses of each other.
We see that,
f(x) = x+5
f(g(x)) = g(x)+5
f(g(x)) = x-5+5
f(g(x)) = x
and you should find that g(f(x)) = x for similar steps.
No matter what the x input is, the output will be identical to the input.
For instance, if we plug in x = 7, then adding 5 to it gets us 12. Then undoing that operation to subtract 5 gets us back to 7 again. This is one example showing why both f(g(x)) and g(f(x)) both equal x, where f and g are inverses of each other.
Greg can complete a landscaping job in six days and Jeff can complete the same job in four days. Working together, and how many days could they complete the job?
Answer:
2.4 days
Step-by-step explanation:
they could complete the job in :
(6×4)/(6+4) = 24/10 = 2.4 days
[tex]\\ \rm\longmapsto \dfrac{ab}{a+b}[/tex]
[tex]\\ \rm\longmapsto \dfrac{6(4)}{6+4}[/tex]
[tex]\\ \rm\longmapsto \dfrac{24}{10}[/tex]
[tex]\\ \rm\longmapsto 2.4days[/tex]
what is cos 0 when sin 0 = 2/5
Answer:
cos 0 = 1
.................
The wood on the back deck of a house needs waterproofing. The shape of the deck
is a rectangle with the length of 40 feet and a width of 3 yards. A gallon can of
waterproof stain covers 50 square feet and costs $19.99 per can plus 8% sales tax.
You go to the hardware store to purchase the waterproof stain needed to complete
the job. You give the cashier $150. How much change do you receive, or how much
additional cash must you find in order to be able to pay for all of the stain you need?
You must show all calculations.
Area of Rectangle = length X width
You cannot split up a can of stain.
You must show all calculations.
Dimensions of a rectangular deck = [tex]40[/tex] feet by [tex]3[/tex] yards
Width of the deck is in yards, so convert it into feet.
Since, [tex]\frac{1}{3}[/tex] yards = 1 foot
Therefore, 1 yard = [tex]3[/tex] feet
And [tex]3[/tex] yards = [tex]3\times 3[/tex] feet
= [tex]9[/tex] feet
Therefore, dimensions of the rectangular deck = [tex]40[/tex] feet by [tex]9[/tex] feet
Area of the deck = Length × Width
= [tex]40\times 9[/tex]
= [tex]360[/tex] square feet
∵ [tex]50[/tex] square feet of deck is stained by number of cans = 1
∴ 1 square feet will be stained by number of cans = [tex]\frac{1}{50}[/tex]
∴ [tex]360[/tex] square feet will be stained by cans = [tex]\frac{360}{50}[/tex] = [tex]7.2[/tex]
We can not purchase can in fractions or parts.
Therefore, number of cans to be purchased = [tex]8[/tex]
Cost of waterproof stain per can = $[tex]19.99[/tex] plus [tex]8[/tex]% sales tax
Therefore, actual cost of 1 can to be paid for the waterproof stain
= [tex](19.99 + 19.99\times \frac{8}{100})[/tex]
= [tex]19.99+1.5992[/tex]
= $[tex]21.5892[/tex]
Cost of [tex]8[/tex] cans = [tex]21.5892\times 8[/tex]
= $[tex]172.71[/tex]
I have paid $[tex]150[/tex] to the cashier.
Therefore, additional money to be paid = [tex]172.71-150[/tex]
= $[tex]22.71[/tex]
Learn more,
https://brainly.com/question/17424783
8 216 899 (nearest million)
Answer:
8 milliom
Step-by-step explanation:
its ez
Reduce the fraction 21 /35
Answer:
3/5
Step-by-step explanation:
21/35
Divide both the top and bottom by 7
21/7 = 3
35/7 = 5
3/5
Answer:
3/5
Step-by-step explanation:
Find gcf for 21 and 35….7
Divide both by 7…. 3 and 5
Arrange 3 as numerator and 5 as denominator….3/5
one half of a number plus 7
Answer:
1/2n + 7
n = unkown number
Step-by-step explanation:
Answer:
1/2(x) + 7
Step-by-step explanation:
x= unknown number
what is the length of the diameter ?
Answer:
you can measure it in ruler
(1)
What is the interest on Rs.1880.90 for one year at simple
interest 5 1/2
%?
Formula for simple interest = total = start value x ( 1 + interest rate x time)
Total = 1880.90 x ( 1 + 0.055 x 1)
Total = 1,984.35
Interest = total - starting amount
Interest = 1984.35-1880.90 = 103.45
Interest: £103.45
Answer:
Given :-Perimeter = 1880.9
Time = 1 years
Rate = 5 (½) years
To Find :-Interest
Solution :-SI = PRT/100
5½ = 11/2 %
» SI = 1880.9 × 11 × 1/2 × 100
» SI = 1880.9 × 11/200
» SI = 103.4
3 If 5 is added to the difference of 3 times of 4 and 7 then find the number.
Answer: 10
Concept:
There are few vocabularies that describe each operation:
Addition: added to, the sum of, plusSubtraction: subtracted from, the difference of, minusMultiplication: multiplied with, the product of, timesDivision: divided by, the quotient of, divideRefer to the list above to answer the question
Solve:
Given worded expression
5 is added to the difference of 3 times of 4 and 7
Convert to numerical expression
3 × 4 - 7 + 5
Simplify by multiplication
=12 - 7 + 5
Simplify by addition/subtraction
=5 + 5
=[tex]\boxed{10}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
The sum of the angle measures of a quadrilateral is 360°. Write and solve an equation to find the value of x.
Answer:
x = 70
Step-by-step explanation:
The sum of the angle measures of a quadrilateral is 360°
76 + 92 + 122 + x = 360
168 + 122 + x = 360
290 + x = 360
x = 360 - 290
x = 70
You can ever CROSS-CHECK
76 + 92 + 122 + 70
290 + 70
= 360
thus cross-checked
Can someone help me please I don’t get this (due today)
Sure, I will help you.
25. Measure of MP=152 degrees.
26. Measure of QNL=208 degrees.
27. Measure of WT=155 degrees.
28. Measure of WTV=205 degrees.
I believe that these answers are correct, but if not, please let me know. If you have any questions, feel free to ask.
what is the value of x in the equation 11+7x=-17
[tex]\\ \rm\Rrightarrow 11+7x=-17[/tex]
[tex]\\ \rm\Rrightarrow 7x=-7-11[/tex]
[tex]\\ \rm\Rrightarrow 7x=-28[/tex]
[tex]\\ \rm\Rrightarrow x=\dfrac{-28}{7}[/tex]
[tex]\\ \rm\Rrightarrow x=-4[/tex]
Answer: x = -4
Step-by-step explanation:
Given equation
11 + 7x = -17
Subtract 11 on both sides
11 + 7x - 11 = -17 - 11
7x = -28
Divide 7 on both sides
7x / 7 = -28 / 7
[tex]\boxed{x=-4}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
4 1/6 = 3 1/3c
WAHT?!? HOW IN THE WORLD DO YOU EVEN DO THIS?!?
Answer:
1 1/4 =c
Step-by-step explanation:
4 1/6 = 3 1/3c
Change the mixed numbers to improper numbers
4 1/6 = ( 6*4+1)/6 =25/6
3 1/3 = ( 3*3+1)/3 = 10/3
25/6 = 10/3c
Multiply each side by 3/10
25/6 * 3/10 = 10/3c * 3/10
3/6 * 25/10 = c
1/2 * 5/2 =c
5/4 =c
Change back to a mixed number
1 1/4 =c
Is the difference of a rational number and an irrational number always irrational? Explain.
Answer:
Step-by-step explanation:
Yes, the irrational number stays irrational.
Make the assumption that this statement is false and that a rational and an irrational can produce a rational. x is irrational. Assume that a, b, c, and d are all integers. If you like, they can be relatively prime to each other.
a/b + x = c/d Subtract a/b from both sides.
x = c/d - a/b Now put the 2 fractions over a common denominator.
x = (c*b - d*a)/(b*d) Investigate what you have.
b*d are two integers multiplied together. multiplication of integers is closed (the answer will be an integer).
cb and da are also integers. subtracted integers are also closed under subtraction.
But
Here's the kicker. An irrational number is one that cannot be expressed as a fraction. Sqrt(2) for example cannot be shown to be rational. There is no fraction that equals sqrt(2)
So our proof is "bogus." It cannot work. An irrational number excludes the possibility of being able to be represented by a fraction by definition.
Is 4.357216436 rational
Answer: It is a rational number.
Step-by-step explanation: Because rational numbers can also be terminating decimals.
Please help explanation if possible
Answer:
x=-2 y=3
Step-by-step explanation:
you should multiple second equation by -5 and collect all terms then put -2 from x
Jade, May and Nel are saving money in a bank account. May has saved €5 more than Jade. Nel has saved twice
as much as May. The three of them have saved €115 in total. How much did each of them save? (Assume that
Jade saved €x)
Answer:
Money saved by Jade = € 25
Money saved by May = € 30
Money saved by Nel = € 60
Step-by-step explanation:
Money saved by Jade = € x
Money saved by May = x + 5
Money saved by Nel = 2* (x + 5) = 2*x + 2*5 = 2x + 10
Total = € 115
x + x + 5 + 2x + 10 = 115
x + x + 2x + 5 + 10 = 115
Combine like terms
4x + 15 = 115
Subtract 15 from both sides
4x = 115 - 15
4x = 100
Divide both sides by 4
x = 100/4
x = € 25
Money saved by Jade = € 25
Money saved by May = 25+ 5 = € 30
Money saved by Nel = 2*25 + 10 = 50 + 10 = € 60
Answer:
Jade=€25
May=€30
Nel=€60
Step-by-step explanation:
Since Nel has 2 units, May has one and you do not know Jane but it is only €5 less, you want to plus 5 to make Jane have one unit like May, so:
115+5=120 (4 units）
120 divide 4= 30 (1 unit)
Jade=30-5=€25
May=€30
Nel=30x2=€60
Hope this helps! Thanks.
please help easy maths
Answer:
A
Step-by-step explanation:
Answer:
Step-by-step explanation:
The y intercept occurs when x = 0.
All you have to do is read the table until you come to x = 0.
When you do, read down to get the y value.
The answer is A (0,2)
2x+7y=-6
4x-y=18\
show step by step how it is solved
Answer: (60/13, 6/13)
Concept:
There are three general ways to solve systems of equations:
Elimination SubstitutionGraphingHere, we are going to use elimination since all the variables are in the corresponding position.
Solve:
Given
[tex]\left \{ {{2x+7y=-6} \atop {4x - y=18}} \right.[/tex]
Multiply the first equation in order to eliminate [x]
[tex]\left \{ {{4x + 14y = -12} \atop {4x - y = 18}} \right.[/tex]
Subtract the second equation from the first equation to eliminate [x]
[tex]14y-y=-12+18[/tex]
[tex]13y=6[/tex]
Divide 13 on both sides
[tex]13y/13=6/13[/tex]
[tex]\boxed{y=\frac{6}{13} }[/tex]
Substitute [y] value in order to get [x] value
4x - y = 18
4x - 6/13 = 18
4x = 18 + 6/13
4x = 240/13
[tex]\boxed{x=\frac{60}{13} }[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Please help me find the value of “ find the value m
Answer:
Add those angles together. PQT is the sum of the angles PQS and SQT
3x+13+6x-2
add like terms
9x-11
angle PQT is equal to 9x-11.
Step-by-step explanation:
A design for a banner includes a striped background. The stripes are colored in the repeating order: yellow, blue, orange, green, and purple. What calor is the 37th stripe?
Answer:
purple.orang.blue.yellow and green
purple.orang.blue.yellow and green
Intersection of 2 lines form a
Answer:
i believe that`s called a linear pair. the opposite sides of the lines create matching angles.
Question 1
A factory has to transport raw materials to a project site. The total weight of the raw material will not be less than 1,500 tons. The factory manager plans
to use two different trucking firms, Big Red has heavy duty trucks that can transport 200 tons at a cost of $50 per truckload. Common Joe is a more
economical firm, costing only $20 per load, but its trucks can transport only 90 tons. The factory manager does not wish to spend more than $450 on
transportation. The availability of trucks is the same for both firms.
Part A
What inequality will show the number of trucks used to transport the required raw material? Replace the inequality sign with the equal sign. Go to
your math tools and open the Graph tool to graph the resulting equation and paste it into the box below. Describe which part of the graph should
be shaded and whether the line should be dashed or not.
Answer:
simple answer
Step-by-step explanation:
hey please help i’ll give brain
Answer:
14 is the correct answer. It is just the inverse of 5+9 but it equals the same
Step-by-step explanation:
Convert 5420 into base five numeral
350 rounded to the nearest hundred is
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\text{350 rounded to the nearest hundred is...}[/tex]
[tex]\huge\text{Rounding is basically is the}\\\huge\text{approximation of the given number.}[/tex]
[tex]\huge\bullet\huge\text{ So, when you are looking at 350, you are}\\\huge\text{asking yourself is it closer to 300 or 400.}\\\huge\text{If you are looking at the number correctly}\\\huge\text{you would see it is closer to \underline{\underline{400}} when you}\\\huge\text{rounded to NEAREST HUNDRED.}[/tex]
[tex]\huge\boxed{\textsf{Therefore, your ANSWER/RESULT is: \bf 400}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\huge\boxed{\frak{Amphitrite1040:)}}[/tex]
. If 26039 apples aré shared equally among 13 boys. How many does each boy receive?
Answer:
2003 apples for each boy
Answer:
26o39÷3 =2,003
therefore; each boy gets 2,003 apples
You work at McDonalds making $12 per hour, this week you are scheduled to work
4:30pm - 10pm Wednesday - Saturday. How much will your gross pay be for the WEEK?
(you are on the clock the entire shift)
Answer:
7$
Step-by-step explanation:
PLS HELP MEEEEE I HAVW TO SUBMIT THIS SOON
Answer:
(100×m) + d
where m is the month number of your birthday
and d is the day number of your birthday
Step-by-step explanation:
[(((m × 4) + 14) × 25) - 230] + d - 120
》[((4m + 14) × 25) - 230] + d - 120
》100m + 350 - 230 -120 + d
》100m + d
Integral sin(3x+3)dx
Step-by-step explanation:
steps are in picture above.
Note:if you have any question please let me know.