Answers
Answer:
[tex]f(x) = 5x -11[/tex] and [tex]g(x) = \frac{x + 11}{5}[/tex]
Step-by-step explanation:
Required
The inverse pairs
Solving (a):
[tex]f(x) = 5x -11[/tex] [tex]g(x) = \frac{x + 11}{5}[/tex]
Calculate the inverse of f(x)
[tex]f(x) = 5x -11[/tex]
Replace f(x) with y
[tex]y = 5x - 11[/tex]
Swap x and y
[tex]x = 5y - 11[/tex]
Solve for y
[tex]5y = x + 11[/tex]
[tex]y = \frac{x + 11}{5}[/tex]
So, we have:
[tex]g(x) = \frac{x + 11}{5}[/tex]
Hence, f(x) and g(x) in (a) are inverse functions
Others are not
Related Questions
Model 3: Another plan to secure the roller coaster involves placing two concrete struts on either side of the center of the leg of the roller coaster to add reinforcement against southerly winds in the region. Again, using the center of the half-circle as the origin, the struts are modeled by the equations and . A vertical reinforcement beam will extend from one strut to the other when the two cables are 2 feet apart. 8. Algebraically determine the x -value of where the beam should be placed. (15 points) 9. Explain where to place the beam. (10 points)
Answers
Answer:
The beam should be placed 8 feet from the center.
Step-by-step explanation:
According to the Question,
Given That, Another plan to secure the roller coaster involves placing two concrete struts on either side of the center of the leg of the roller coaster to add reinforcement against southerly winds in the region.Again, using the center of the half-circle as the origin, the struts are modeled by the equations y=x+8 and y=x-4. A vertical reinforcement beam will extend from one strut to the other when the two cables are 2 feet apart. Recall that a reinforcement beam will extend from one strut to the other when the two struts are 2 feet apart.
The struts are y = √(x + 8) and y = √(x − 4). The struts are 2 feet apart at the location of the beam:
thus, √(x + 8) − √(x − 4) = 2
on Solving we get,
√(x + 8) = 2 + √(x − 4)
x + 8 = 4 + 4√(x − 4) + x − 4
8 = 4√(x − 4)
2 = √(x − 4)
x − 4 = 4
x = 8
if £2000 is placed into a bank account that pays 3% interest compound into how much will be in the account after 2 years?
Answers
Answer: The answer is £2121.8.
You can check this formula....
The length of the base of an isosceles triangle is x. The length of a leg is 3x-4. The perimeter of the triangle is 97. Find x.
Answers
Answer I do not know i am not there yet i am sorry
Step-by-step explanation:
:(
Math
Help
Will
Give
Brainlist
:))
Answers
Answer:
2/3 mi
Step-by-step explanation:
Multiply the length of one side of a square by 4 to find the perimeter.
(1/6)(4) = 4/6
Simplify. The common factor is 2.
4/6 = 2/3
Angelica and Diego collect Pokémon cards. Angelica has
four more cards than Diego does. Together, they have 18 in total. How many cards does Angelica have?
Answers
Answer:
40Step-by-step explanation:
because 18 + 18 =36 +4=40plese follow meEvaluate e^4 to one decimal place
Answers
Answer:
The answer is going to be the general form for e^x = 1 + x/(1!) + + x^2/(2!) + x^3/(3!) +.....,. till infinity so : e^4 = 1 + 4/1 + 16/ 2 + 64/6 + 256/24 + 1024/ 120 + 4096/720 + 16384/5040 +...till the fraction is<0.1 = 54.6
Write two solutions for the following equation 2x+3y=24.
Answers
Answer: (12, 0) and (0, 8)
Step-by-step explanation:
This equation is in standard form. We can sub in a number for x to solve for y and vice versa.
Let's sub in 0 for x.
[tex]2x+3y=24\\2(0)+3y=24\\3y=24\\\frac{3y}{3} =\frac{24}{3} \\y=8[/tex]
When x is 0 y is 8 giving us the coordinate (0, 8).
Now lets sub in 0 for y
[tex]2x+3(0)=24\\2x=24\\\frac{2x}{2} =\frac{24}{2} \\x=12[/tex]
When y is 0 x is 12 giving us the coordinate (12, 0)
Step-by-step explanation:
Begin by solving for y
3y = -2x + 24 divide by 3
y =-(2/3)x + 24
Choose x so that it is divisible by 3
Let x = 6 which 3 can divide into evenly
y = -(2/3)*6 + 24 3 into 6 is 2 so you are left with
y = - 2 * 2 + 24
y = - 4 +24
y = 20
By a similar mthed, let x = 15
y = -2/3 x + 24
y = -2/3 * 15 +24
y = -2 * 5 + 24
y = -10 + 24
y = 14
So your two solutions are
(6,20)
(15,14)
1.
Write the following to 3.s.f
(a) 2172
(b) 2.066
(c)0.030111
Answers
b)2.060
c)0.030110
X 3 + 3 x 2 − x + 2 x 2 + 6 x − 2. Which expression is equivalent to this product after it has been fully simplified? x3 + 5x2 + 5x – 2 x3 + 2x2 + 8x – 2 x3 + 11x2 – 2 x3 + 10x2 – 2
Answers
Answer:
[tex](x^3 + 3x^2 - x + 2)(x^2 + 6x -2) = x^5 + 9x^4+ 15x^3 + 2x^2 + 10x -4[/tex]
Step-by-step explanation:
Given
[tex](x^3 + 3x^2 - x + 2)(x^2 + 6x -2)[/tex]
Required
The equivalent expression
We have:
[tex](x^3 + 3x^2 - x + 2)(x^2 + 6x -2)[/tex]
Open bracket
[tex](x^3 + 3x^2 - x + 2)(x^2 + 6x -2) = x^5 + 6x^4 - 2x^3 + 3x^4 + 18x^3 - 6x^2 -x^3 + 6x^2 - 2x + 2x^2 + 12x -4[/tex]
Collect like terms
[tex](x^3 + 3x^2 - x + 2)(x^2 + 6x -2) = x^5 + 6x^4 + 3x^4- 2x^3 -x^3 + 18x^3 - 6x^2 + 6x^2 + 2x^2- 2x + 12x -4[/tex]
Evaluate like terms
[tex](x^3 + 3x^2 - x + 2)(x^2 + 6x -2) = x^5 + 9x^4+ 15x^3 + 2x^2 + 10x -4[/tex]
What quadratic equation could be solved to find any solutions to the system of equations?
y = -51 +6
y = 12 + 71 - 11
Replace the values of a, b, and in the equation to formulate the correct equation.
Answers
Answer:
Step-by-step explanation:
x²+7x-11=-5x+6
x²+7x+5x-11-6=0
x²+12x-17=0
[tex]x=\frac{-12\pm \sqrt{12^2-4*1*(-17)} }{2*1} \\=\frac{-12 \pm \sqrt{144+68} }{2} \\=\frac{-12 \pm \sqrt{212}}{2} \\=\frac{-12+2\sqrt{53}}{2}\\=-6 \pm \sqrt{53}[/tex]
need some help with these 2 questions
Answers
Answer:
hear is your answer please mark as brain list
can someone help me with this
Answers
Answer:
Step-by-step explanation:
a) -14 , -9 , -4 , 1 ................
Common difference = d = 2nd term - 1st term
= -9-[-14]
= -9 + 14
d = 5
The next term can be got by adding 5 to the previous term
5th term = 1 + 5 = 6
6th term = 6 + 5 = 11
7th term = 11 + 5 = 16
Next 3 terms are : 6 , 11 , 16
[tex]b) \frac{5}{6},\frac{2}{3},\frac{1}{2},\frac{1}{3},.....\\\\d = \frac{2}{3}-\frac{5}{6}\\\\=\frac{2*2}{3*2}-\frac{5}{6}\\\\=\frac{4}{6}-\frac{5}{6}\\\\=\frac{-1}{6}\\\\a_{5} = \frac{1}{3}+\frac{-1}{6}=\frac{1*2}{3*2}+\frac{-1}{6}=\frac{2}{6}+\frac{-1}{6}=\frac{1}{6}\\\\a_{6}=\frac{1}{6}+\frac{-1}{6}=0\\\\a_{7}=0+\frac{-1}{6}=\frac{-1}{6}\\\\\\Next 3 terms : \frac{1}{6},0,\frac{-1}{6}[/tex]
need help with this asap!
Answers
Answer:
Step-by-step explanation:
1 ) 2 + 7t [ there are no like terms , so no further simplifying ]
2) 6r + ( - 16 r )
= 6 r - 16 r [ both are like terms ]
= - 10 r
3) (3x + 2 ) + ( 2x - 4 )
= 3x + 2 + 2x - 4
= 3x + 2x - 4 + 2 [ arranging like terms together ]
= 5x - 2
4) (8 n² - 3 n + 6 ) + ( n - 2 )
= 8n² - 3n + 6 + n - 2
= 8n² - 3n + n + 6 - 2 [ bringing like terms together ]
= 8n² - 2n + 4
Answer:
1.) 2 + 7 t
2.) - 10 r
3.) 5 x - 2
4.) 8 n² - 2 n + 4
Step-by-step explanation:
1.) 2 + 7 t
No like terms, so no further simplifying.
2.) 6 r + ( - 16 r )
6 r - 16 r. ... ( combine like terms)
- 10 r
3.) ( 3 x + 2 ) + ( 2 x - 4 )
= 3 x + 2 + 2 x - 4
combine like terms
= 3 x + 2 x - 4 + 2
= 5 x - 2
4.) ( 8 n ² - 3 n + 6 ) + ( n - 2 )
= 8 n² - 3 n + 6 + n - 2
combine like terms
= 8n² - 3 n + n + 6 - 2
= 8 n² - 2 n + 4.
The probability that a student takes calculus or is on scholarship is 0.85. The probability that a student is on scholarship is 0.61 and the probability that a student is taking calculus is 0.31. If a student is randomly chosen, find the probability that the student is taking calculus and is on scholarship.
Answers
Answer:
0.07
Step-by-step explanation:
According to the Question,
Let C denote the event that a student takes calculus & S denote the event that a student is on scholarship.
Given, The probability that a student takes calculus or is on scholarship is 0.85 [P(C ∪ S)=0.85] . The probability that a student is on scholarship is 0.61 [P(S)=0.61] . and the probability that a student is taking calculus is 0.31 [P(C)=0.31] .We have,
⇒P(C ∪ S)=0.85 , P(C)=0.31 , P(S)=0.61
We Know, P(C∩S) = P(C) + P(S) − P(C∪S)
Then, Put the Above Values in the Equation, we get
So, P(C∩S) = 0.31 + 0.61 - 0.85 ⇒ 0.07
Thus, The probability that the student is taking calculus and is on scholarship is 0.07A train leaves at 14:56 and arrives at 16:43. It travelled at an average speed of 135 km/h. How far did it travel? Give your answer in km to 1DP.
Answers
Answer:
240.8
Step-by-step explanation:
→ Calculate time taken
16:43 - 14:56 = 1 hour and 47 minutes
→ Write the speed formula and make distance the subject
Speed = Distance ÷ Time ⇔ Distance = Speed × Time
→ Convert 1 hour and 47 minutes into decimal format
1.78333333 or [tex]1\frac{47}{60}[/tex]
→ Substitute values into formula
135 × [tex]1\frac{47}{60}[/tex] = 240.75
What is the same as 3(4 + 5 + 6)?
Answers
Answer:
45Step-by-step explanation:
3(4 + 5 + 6)
= 3(15)
= 3 × 15
= 45 (Ans)
Solve the following system of equations using all three methods. Must show your work. 4x + y = 2 3x - 3y = 9
Part A: Solve by graphing.
Part B: Solve by substitution.
Part C: Solve by elimination.
Describe the process and steps you used to solve each method.
Answers
Answer:
Step-by-step explanation:
you do part a
Equation 1: 4x+y=2
Equation 2: 3x-3y=9
b
Divide equation 2 by 3
x-y=3
add y to both sides
x=3+y
Sbustitute this into equation 1
4(3+y)=2
12+4y+y=2
5y= -10
y= -2
Plug this into equation 1
4x-2=2
x=1
Part c.
Equation 1: 4x+y=2
Equation 2: 3x-3y=9
divide equation 2 by 3
x-y=3
add the two equations
(x-y)+(4x+y)=2+3
5x=5
x=1
Plug this into equation 1
4(1)+y=2
4+y=2
y= -2
For part a just create a table and graph it
Whats the last info I need?
Answers
Answer:
Step-by-step explanation:
Properties of the similarity of two triangles,
1). Corresponding angles of two triangles should be equal.
2). Corresponding sides of two triangles should be proportional.
By applying second property in the given triangles RTY and CVB,
[tex]\frac{CV}{RT}=\frac{TY}{VB}=\frac{CB}{RY}[/tex]
[tex]\frac{15}{10}= \frac{9}{6}= \frac{CB}{RY}[/tex]
[tex]1.5= 1.5= \frac{CB}{RY}[/tex]
Ratio of sides CB and RY should be 1.5 for the similarity of two triangles.
Therefore, additional information required for the similarity of two triangles is "the measure of third sides of both the triangles should be known"
The total cost of Anfä's trip to the dentist was $628.35. She paid a flat fee of $89.95 which included the checkup:
cleaning and then had 4 cavities filled, each of which cost the same amount. Which shows the correct equation and
value of x, the cost of each cavity filling?
Answers
Answer:
The cost of each cavity filling was $ 134.60.
Step-by-step explanation:
Given that the total cost of Anfa's trip to the dentist was $ 628.35, and she paid a flat fee of $ 89.95 which included the checkup: cleaning and then had 4 cavities filled, each of which cost the same amount, to determine which shows the correct equation and value of x, the cost of each cavity filling, the following calculation must be performed:
(628.35 - 89.95) / 4 = X
538.4 / 4 = X
134.6 = X
Therefore, the cost of each cavity filling was $ 134.60.
Solve the givin proportions
Answers
Answer:
x=(6×6)/9=4
just cross multiply and get your answer
Answer:
x=4
Step-by-step explanation:
Step 1
Represent the ratios as fractions
6/9=x/6
Step 2
Cross-multiply the numerators and denominators
9x=6×6
9x=36
9x/9=36/9
Therefore x=4
what is the answer to 0.7(1.5 + y) = 3.5y - 1.47
Answers
Answer:
0.9
Step-by-step explanation:
0.7*(1.5 + y) = 3.5y - 1.47
or, (0.7*1.5) + 0.7y = 3.5y - 1.47
or, 1.05 + 1.47 = 3.5y - 0.7y
or, 2.52 = 2.8y
or, y = 2.52/2.8
or, y = 0.9
Hope this will help. Please mark me brainliest.
express 96 as the product of prime factors
need it asap
plzz write the method too
Answers
Given:
The given number is:
[tex]96[/tex]
To find:
The product of prime factors of given number.
Solution:
We have,
[tex]96[/tex]
The prime factors of given number are:
2 | 96
2 | 48
2 | 24
2 | 12
2 | 6
3 | 3
| 1
So, 96 can be written as:
[tex]96=2\times 2\times 2\times 2\times 2\times 3[/tex]
Therefore, the 96 as the product of prime factors is [tex]96=2\times 2\times 2\times 2\times 2\times 3[/tex].
The television show September Road has been successful for many years. That show recently had a share of 20, meaning that among the TV sets in use, 20% were tuned to September Road. Assume that an advertiser wants to verify that 20% share value by conducting its own survey, and a pilot survey begins with 11 households have TV sets in use at the time of a September Road broadcast. Find the probability that none of the households are tuned to September Road. P(none)
Answers
Answer:
[tex]P(none) = 0.0859[/tex]
Step-by-step explanation:
Given
[tex]p =20\%[/tex] --- proportion of household that tuned to September
[tex]n =11[/tex] --- selected households
Required
[tex]P(none)[/tex]
Using the complement rule, the proportion that did not tune (q) is:
[tex]q= 1 - p[/tex]
[tex]q= 1 - 20\%[/tex]
[tex]q= 1 - 0.20[/tex]
[tex]q= 0.80[/tex]
So, the probability that none of the 11 tuned in is:
[tex]P(none) = q^{11}[/tex]
[tex]P(none) = 0.80^{11}[/tex]
[tex]P(none) = 0.0859[/tex]
Is the following shape a square? How do you know? A. Yes, the opposite sides are parallel, and all sides are the same length. B. No, because opposite sides are not parallel. C. There is not enough information to determine. D. No, because the sides are not congruent.
Answers
Answer:
A
Step-by-step explanation:
Answer:
NO
Step-by-step explanation:
No, because the sides are not congruent.
Aaron has a combination of nickels, dimes, and quarters in his pocket. Aaron's collection of coins is represented in the matrix below.
1
1
1
14
2 0 -1 0
.05 10 252.15
Which of the following is NOT a correct verbal interpretation of one of the equations in the system?
O Aaron has twice as many quarters as nickels.
O Aaron has no nickels.
O Aaron has a total of 14 coins.
The total value of the coins is $2.15.
6
7
8
8
9
10
Answers
Answer:
Aaron has no nickels
Step-by-step explanation:
eg
Sum of cubes:
(a + b)(a2 – ab + b2) = a3 + b3
Difference of cubes:
(a – b)(a2 + ab + b2) = a3 – b3
Which products result in a sum or difference of cubes? Check all that apply.
(x – 4)(x2 + 4x – 16)
(x – 1)(x2 – x + 1)
(x – 1)(x2 + x + 1)
(x + 1)( + x – 1)
(x + 4)(x2 – 4x + 16)
(x + 4)(x2 + 4x + 16)
Answers
Answer:
C and E
Step-by-step explanation:
Answer:
3 and 5
Step-by-step explanation:
The solution of this problem is in this picture.
What is 1/3 divided into 7 equal parts
Please help I made another one but I said I why on accident
Answers
Answer:
1/21
Step-by-step explanation:
1/3 / 7 = 1/3 / 7/1 = 1/3 * 1/7 = 1/21
Answer:
21
Step-by-step explanation:
1/3 x 7/1 you flip the 7 and you will have 1/3x1/7 and then u 7x3 and u will get 21
If JK = 4, KL = 3x, and JL = 7x, what is JL? Simplify your answer and write it as a proper fraction, mixed number, or integer.
Answers
Answer:
JL = 7
Step-by-step explanation:
If JK = 4, KL = 3x, and JL = 7x, what is JL?
From the diagram given in tbe question,
JK + KL = JL
4 + 3x = 7x
Collect like terms
4 = 7x - 3x
4 = 4x
4x = 4
x = 4/4
x = 1
Since JL from the diagram = 7x
Hence:
7 × 1 = 7
JL = 7
What are the vertices of triangle PQR?
Answers
Answer: D. P, Q and R.
Step-by-step explanation:
The vertices of the triangle PQR - it is P, Q and R.
Does someone know what the answer is? Help, please!
Answers
Answer:
if I'm not wrong it should be A