Give an example of a function which represents all types of a function. Find the composite function (fog)(x) given that f = {(1,6), (4,7), (5,0)) and g = {(6,1), (7,4), (0,5)}
Answer:
(fog)(x) = x
Step-by-step explanation:
Composite function:
[tex](f \circ g)(x) = f(g(x))[/tex]
Composite of a function and its inverse.
The composition of a function and it's inverse is the straight line x. So
[tex](f \circ f^{-1})(x) = x[/tex]
f = {(1,6), (4,7), (5,0)) and g = {(6,1), (7,4), (0,5)}
We can see that the x-values in f are the y-values for g, and the y-values for f are the x-values for g, that is, f and g are inverse functions. Thus:
(fog)(x) = x
find any 4 rational number between -1/2 and -1/3
Given:
The two numbers are [tex]-\dfrac{1}{2}[/tex] and [tex]-\dfrac{1}{3}[/tex].
To find:
The 4 rational numbers between the given numbers.
Solution:
We have,
[tex]-\dfrac{1}{2}[/tex] and [tex]-\dfrac{1}{3}[/tex]
First we need to make common denominators. So multiply and divide the first fraction by 3 and second fraction by 2.
[tex]-\dfrac{1\times 3}{2\times 3}=-\dfrac{3}{6}[/tex]
[tex]-\dfrac{1\times 2}{3\times 2}=-\dfrac{2}{6}[/tex]
We need to find 4 rational numbers between the given numbers. So, multiply and divide both fractions by five, (4+1=5).
[tex]-\dfrac{3\times 5}{6\times 5}=-\dfrac{15}{30}[/tex]
[tex]-\dfrac{2\times 5}{6\times 5}=-\dfrac{10}{30}[/tex]
Now, the four numbers between -15 to -10 are -14, -13, -12, -11.
[tex]-15<-14<-13<-12<-11<-10[/tex]
[tex]-\dfrac{15}{30}<-\dfrac{14}{30}<-\dfrac{13}{30}<-\dfrac{12}{30}<-\dfrac{11}{30}<-\dfrac{10}{30}[/tex]
[tex]-\dfrac{1}{2}<-\dfrac{14}{30}<-\dfrac{13}{30}<-\dfrac{12}{30}<-\dfrac{11}{30}<-\dfrac{1}{3}[/tex]
Therefore, the 4 rational number between the given numbers are [tex]-\dfrac{14}{30},\ -\dfrac{13}{30},\ -\dfrac{12}{30}\ -\dfrac{11}{30}[/tex].
What is the answer for this question?
Answer:
a/e
~~~~~~~~~~
[tex]\frac{(18) ab (20)cd}{ (15) bc (24) de}[/tex]
[tex]\frac{(3) ab (4)cd}{ (3) bc (4) de}\\[/tex]
[tex]\frac{ ab cd}{ bc de}\\[/tex]
[tex]\frac{ a }{ e}\\[/tex]
Step-by-step explanation:
A container in the shape of this cuboid holds 2 litres of water.
The container has a square base.
Its height is double the length of each edge on its base.
Work out the height of the container, in cm.
Given:
Volume of cuboid container = 2 litres
The container has a square base.
Its height is double the length of each edge on its base.
To find:
The height of the container.
Solution:
We know that,
1 litre = 1000 cubic cm
2 litre = 2000 cubic cm
Let x be the length of each edge on its base. Then the height of the container is:
[tex]h=2x[/tex]
The volume of a cuboid is:
[tex]V=l\times w\times h[/tex]
Where, l is length, w is width and h is height.
Putting [tex]V=2000,\ l=x,\ w=x,\ h=2x[/tex], we get
[tex]2000=x\times x\times 2x[/tex]
[tex]2000=2x^3[/tex]
Divide both sides by 2.
[tex]1000=x^3[/tex]
Taking cube root on both sides.
[tex]\sqrt[3]{1000}=x[/tex]
[tex]10=x[/tex]
Now, the height of the container is:
[tex]h=2x[/tex]
[tex]h=2(10)[/tex]
[tex]h=20[/tex]
Therefore, the height of the container is 20 cm.
[tex]1,6 + 6,13[/tex]
= 1,6 + 6,13
= 7,73 .
FollowMe? FollowBack.
Answer:
7,73Step-by-step explanation:
1,6
6,13 +
7,73
[tex] \: \: \: [/tex]Can someone help me with this please ?
given that cot(θ)= -√5/3 and cos(θ) < 0, find sin(θ)
D. 3√14 /14
Step-by-step explanation:
given that cot(θ)= -√5/3 and cos(θ) < 0
cot(θ)= -√5/3 and cos(θ) < 0, the angle should be on quadrant II.
cot(θ)= -√5/3 => x = -√5 , y = 3
h = √(-3)²+5 =√14
so, sin(θ) = y/h = 3/√14 = 3√14 /14
A 15 foot ladder leans against a building and reaches a window 12 feet above the ground. What is the measure of the angle, to the nearest degree, that the ladder forms with the ground?
Answer:
paki sagot naman po para my isagot ako sa module ko
Answer:
it should be 37°
Step-by-step explanation:
cos=adj/hypo
cis-1(12/15)
=36.8
=37
help asap please im failing
Step-by-step explanation:
The y intercept is when x=0 what is the y value.
When x=0, the y intercept is 1.
b. A gradient is the slope of the line. We need to find the rise and run of the line between two points.
Let use points 0,1 and 1,3
Our y values rise by 2 values and our x values change by 1 value so our slope is
[tex] \frac{2}{1} = 2[/tex]
Answer:
a. At the y-intercept,x=0
This implies the y-intercept=1
b. Taking points (0,1) and (1,3), the gradient of the line is given by (3-1)/(1-0) =2/1 =2
Find the volume and surface area of the cone (to the nearest tenth)
Answer:
Surface area of cone = 286.55 cm² (Approx.)
Volume of cone = 263.89 cm³ (Approx.)
Step-by-step explanation:
Given:
Height of cone = 7 cm
Diameter of cone = 12 cm
Find:
Surface area of cone
Volume of cone
Computation:
Radius of cone = 12 / 2 = 6 cm
Surface area of cone = πr(l +r)
Surface area of cone = (3.14)(6)[(√7² + 6²) + 6]
Surface area of cone = 18.84[15.21]
Surface area of cone = 286.55 cm² (Approx.)
Volume of cone = (1/3)(π)(r²)(h)
Volume of cone = (1/3)(3.14)(6²)(7)
Volume of cone = (1/3)(3.14)(36)(7)
Volume of cone = 263.89 cm³ (Approx.)
Please help me-
The graphs below have the same shape. What is the equation of the blue
graph?
Answer:
[tex]\text{C. }g(x)=(x-5)^2[/tex]
Step-by-step explanation:
The function [tex]y=(x-c)^2[/tex] has a phase shift of [tex]c[/tex] to the parent function [tex]y=x^2[/tex]. Since [tex]g(x)[/tex] has moved to the right 5 units from the parent function [tex]f(x)=x^2[/tex], we're looking for a value of [tex]c=5[/tex].
Therefore, we have:
[tex]g(x)=\boxed{(x-5)^2}[/tex]
Fill in the blank with the correct response. The slope of the graph of y = -7x is
Answer:
The slope is -7
Step-by-step explanation:
[tex]y = mx + c[/tex]
The [tex]m[/tex] indicates the slope/gradient of a graph
Answer:
m = -7
Step-by-step explanation:
y = -7x is a typical slope-intercept equation of a straight line. Comparing it to
y = mx + b, we see that the slope, m, is -7 and the y-intercept, b, is 0.
Solve for O pls and thank you
Answer:
a) 67.4°
Step-by-step explanation:
since this is a right triangle you can use the sine trigonometric ratio of opposite/hypotenuse
sin⁻¹(Ф) = 12/13 which equals 67.4°
Find the measurement of the missing side in each right triangle.
Answer:
12
Step-by-step explanation:
[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]
in this case its
[tex]5^{2}[/tex] + [tex]b^{2}[/tex] = [tex]13^{2}[/tex]
25 + [tex]b^{2}[/tex] = 169 subtract 25 from both sides
[tex]b^{2}[/tex] = 144 take square root of each side
b = 12
Answer:
[tex]12[/tex]
Step-by-step explanation:
----------------------------------------
In order to find the missing side of the triangle, we would need to use the Pythagorean theorem: [tex]a^2+b^2=c^2[/tex]
So,
[tex]5^2+b^2=13^2[/tex]
[tex]25+b^2=169[/tex]
[tex]b^2=144[/tex]
[tex]b=12[/tex]
--------------------
Hope this helps.
T= 3x +4y work out the value of T when x = 5 and y = -7
Answer:
T=-13
Step-by-step explanation:
substitute T=3*5+4*(-7)
the product:T=15-28
the sum:T=-13
area of a triangle: sine formula just please help i’m stuck and i don’t know what to do this was due yesterday
Answer:
269.0
Step-by-step explanation:
Trigonmetric area formula: 0.5 * a* b* sin(C)
a = 46
b=19
c = 38 degrees
0.5 * 46 * 19 * sin(38)
Pulg it into a calculator and you get 269.0441
Then round to the nearest tenth to get 269.0
A store sells a certain tile for $2 per tile and a pint of paint for $3. A second store sells the same items for $1 per tile and $4 per pint of paint. Ari bought the same number of tiles and pints of paint at both stores, costing him $26 at the first store and $18 at the second store, before tax. Which system of equations can be used to find the number of tiles, x, and the number of pints of paint, y, that Ari bought at each store? A system of equations. 3 x plus 4 y equals 18. X plus 2 y equals 26. A system of equations. X plus 3 y equals 18. 2 x plus 4 y equals 26. A system of equations. 2 x plus 3 y equals 26. X plus 4 y equals 18. A system of equations. 3 x plus 2 y equals 26. 4 x plus y equals 18.
Answer:
2 x plus 3 y equals 26. X plus 4 y equals 18
Step-by-step explanation:
Number of tiles, = x
Number of pints of paint, = y
Store 1:
Cost per tile = $2 ; cost per pint = $3 ; total cost = $26
Store 2 :
Cost per tile = $1 ; cost per pint = $4 ; total cost = $18
System of equation:
2x + 3y = 26 - - - (1)
x + 4y = 18 - - - - - (2)
bill has the following test scores in science: 82% 88% and 96%. he hasn’t one more test to take this quarter. if bill wants husband test average to be 90% what score does he need to earn on his last test?
Answer:
He needs to earn a 94%.
Step-by-step explanation:
[tex]\frac{82+88+96+x}{4} = 90\\ \\ \frac{266+x}{4} =90\\\\ 4(\frac{266+x}{4}) =(90)4\\ \\ 266+x = 360\\ \\ 266+x-266 =360-266\\ \\ \\x = 94[/tex]
He must earn a 94% on his latest test for a test average of 90%
Write an equation to represent the relationship between x and y:
Answer:
y = 1/3 x - 1
Step-by-step explanation:
use slope formula then substitute an x and y and the m to find b
y=mx+b
HELP please i need this done by thursday
help me find this answer
Answer:
37.6 cm
Step-by-step explanation:
5.6m = 560cm
3.8m = 380cm
560/50 = 11.2 cm
380/50 = 7.6 cm
11.2 + 11.2 + 7.6 + 7.6 = 37.6 cm
The drama club sold $779 worth of tickets to the school play. Student tickets cost $3 apiece and tickets for everyone else cost $5 each. What equation relates the number of student tickets that were sold, s, and the number of other tickets that were sold, t, written in standard form?
s +
t =
Answer:
3s + 5t = 779
Step-by-step explanation:
Answer:
3 5 779
Step-by-step explanation:
A= P(1+rt)
A= 27 and t=3 solve for r.
Answer:
(27 - P) / 3P = r
Step-by-step explanation:
A = P(1 + rt)
A = 27
27 = P(1 + 3r)
27 = P + 3Pr
27 - P = 3Pr
(27 - P) / 3P = r
someone please help me ASAP!
Answer:
(-7,-1)
Step-by-step explanation:
bcoz coordinates of a is (-6,-2) and x=-6 we use the x-1 to find the new x which is
-6-1=-7
and to find y you should use y-3 and replace y with 2 which will be
2-3=-1
and y =-1
so the new coordinates are -7 for x-axis and -1for y-axis
What is the nth term rule of the linear sequence -5,-7,-9,-11,-13
Answer:
-7
Step-by-step explanation:
cause I took the test and got it right in my first try
Ms. Mackey records the number of math problems that each of her students gets correct on a math fact quiz.
The numbers of correct problems on the quizzes for the 15 students are listed below.
Answer and also explanation:
Use the drawing tool(s) to form the correct answer on the provided plot.
In order to construct a dot plot representing the number of correct problems on each student's quiz, first find the range of the data.
The maximum number of correct problems is 10. The minimum number of correct problems is 2. Therefore, the number of correct problems ranges from 2 to 10.
Next, determine how many students had each number of correct problems in the range.
No. of Correct Problems
0 1 2 3 4 5 6 7 8 9 10
No. of Students 0 0 1 1 2 0 3 2 2 2 2
The number of correct problems, from 0 to 10, will be the values on the number line. The number of students will be the number of dots above each value on the number line.
The dot plot showing the correct number of math problems for Ms. Mackey's students is shown on your question.
1. Find 3 rational numbers between −1//3 and 1/−5
Step-by-step explanation:
-1×5 1×3
------ -----
3×5 -5×3
=
-5/15 -3/15
-5/15×4/4 ;
-3/15×4/4
=
-20/60 ;
-12/60
you can write any 8 rational no. between them
please mark as brainliest answer as it will also give you 3 pts
HELP WITH THIS SOMEONE!!!
Answer:
to blury
Step-by-step explanation:
Which expression is equivalent to (x^-6/x^2)^3
1/x
1/x^5
1/x^9
1/x^24
Step-by-step explanation:
1/x^24 is the correct expression
Sabe-se que o preço a ser pago por uma corrida de táxi inclui uma parcela fixa, que é denominada bandeirada, e uma parcela variável, que é função da distância percorrida. Se o preço da bandeirada é R$4,60 e o quilômetro rodado é R$0,96, qual a distância percorrida por um passageiro que pagou R$19,00?
a) 15 km
b) 16 km
c) 17 km
d) 18 km
e) 19 km
Answer:
El pasajero recorrió 15 kilómetros.
Step-by-step explanation:
Dado que se sabe que el precio a pagar por un viaje en taxi incluye una parte fija, que se denomina bajada de bandera, y una parte variable, que es función de la distancia recorrida, si el precio de la bajada de bandera es de R $ 4,60 y el kilómetro recorrido es de R $ 0,96, para determinar cuál es la distancia recorrida por un pasajero que pagó R $ 19,00 se debe realizar el siguiente cálculo:
Costo total = (0.96 x cantidad de km recorridos) + 4.60
19 = 0.96X + 4.60
19 - 4.60 = 0.96X
14.4 = 0.96X
14.4 / 0.96 = X
15 = X
Por lo tanto, el pasajero recorrió 15 kilómetros.