Step-by-step explanation:
We use the symbol f − 1 to denote an inverse function. For example, if f (x) and g (x) are inverses of each other, then we can symbolically represent this statement as:
g(x) = f − 1(x) or f(x) = g−1(x)
One thing to note about the inverse function is that the inverse of a function is not the same as its reciprocal, i.e., f – 1 (x) ≠ 1/ f(x). This article will discuss how to find the inverse of a function.
Since not all functions have an inverse, it is therefore important to check whether a function has an inverse before embarking on determining its inverse.
We check whether or not a function has an inverse in order to avoid wasting time trying to find something that does not exist.
What is the value for y?
Enter your answer in the box.
y=
Answer:
[tex]y =112[/tex]
Step-by-step explanation:
Given
The attached triangle
Required
Find y
The attached triangle is isosceles; so:
[tex]x - 5=34[/tex]
Also, we have:
[tex]y + x - 5 + 34=180[/tex] --- angles in a triangle
Substitute: [tex]x - 5=34[/tex]
[tex]y + 34 + 34=180[/tex]
Collect like terms
[tex]y =- 34 - 34+180[/tex]
[tex]y =112[/tex]
Solve Only estimation
Answer:
3a)1680
b)2620
4a)2130
b)13300
c)460
d)7540
Step-by-step explanation:
3a)1500+180
b)2800-170
4a)1800+330
b)7300+6000
c)670-210
d)8000-460
Answer:
a) 1600
b) 2600
c) 2200
d) 13200
e) 500
Step-by-step explanation:
a) 1463 + 179
1400 + 200
1600
b) 2806 - 176
2800 - 200
2600
c) 1831 + 329
1900 + 300
2200
d) 7345 + 5893
7300 + 5900
13200
e) 665 - 213
700 - 200
500
24×63_64
help me sll
Answer:
1448
Step-by-step explanation:
24 × 63-64
Multiply 24 and 63 to get 1512.
1512-64
Subtract 64 from 1512 to get 1448.
answer
1448
John estimated the height of his office building to be 13m . The actual height of his office building was 14.7m .
Find the absolute error and the percent error of John's estimate. If necessary, round your answers to the nearest tenth.
Answer:
Percent error = 11.6%
Step-by-step explanation:
Given the following data;
Actual height, A = 14.7 m
Estimated height, E = 13 m
a. To find the absolute error;
Absolute error = A - E
Absolute error = 14.7 - 13
Absolute error = 1.7
b. To find the percent error;
Percent error can be defined as a measure of the extent to which an experimental (estimated) value differs from the actual or theoretical value.
Mathematically, it is given by this expression;
[tex] Percent \; error = \frac {experimental \;value - theoretical \; value}{ theoretical \;value} *100[/tex]
Substituting into the equation, we have;
[tex] Percent \; error = \frac {13 - 14.7}{14.7} *100[/tex]
[tex] Percent \; error = \frac {1.7}{14.7} *100[/tex]
[tex] Percent \; error = 0.1157 *100[/tex]
Percent error = 11.57 ≈ 11.6%
The equation y = 50(1.05)x models the growth of a mule deer population introduced into Guadalupe National Park in December 2015. "X" represents the number of years after December 2015 while "y" represents the population at time "x". In what year will the mule deer population first reach 1500?
F.2084
G.2044
H.2043
J.2085
9514 1404 393
Answer:
J. 2085
Step-by-step explanation:
Fill in the desired value for y and solve for x.
1500 = 50(1.05^x)
30 = 1.05^x . . . . . . . divide by 50
log(30) = x·log(1.05) . . . . . take logarithms
x = log(30)/log(1.05) ≈ 69.71
Since x represents years after December 2015, x = 69.7 will be some time in mid 2085.
Which sequence of transformations maps quadrilateral ABCD onto quadrilateral EFGH
Answer:
C. reflection across the x-axis, translation 6 units left
Graph the Image of square KLMN after a translation 3 units left .
Answer:
N' (-8,9) K' (-8,3) L' (-2,3) M' (-2,9)
Step-by-step explanation:
To translate the square 3 units to the left you would subtract 3 from the x-coordinates of the points shown.
The coordinates of the translated square KLMN is given by K' (-8,3) L' (-2,3) M' (-2,9) N' (-8,9)
What is Translation?A translation moves a shape up, down, or from side to side, but it has no effect on its appearance. A transformation is an example of translation. A transformation is a method of changing a shape's size or position. Every point in the shape is translated in the same direction by the same amount.
Given data ,
Let the square be represented as KLMN
Now , the coordinates of the square KLMN is
K ( -5 , 3 ) L ( 1 , 3 ) M' ( 1 , 9 ) N' ( -5 , 9 )
Now , let the translated square be represented as K'L'M'N'
When translating the square to three units to the left , the x coordinate of the square gets reduced by 3
So , the new coordinate of the square will be ( x - 3 , y )
Substituting the values in the equation , we get
K' = K ( -5 - 3 , 3 )
L' = L ( 1 - 3 , 3 )
M' = M ( 1 - 3 , 9 )
N' = N ( -5 - 3 , 9 )
So , on simplifying the equation , we get
The translated square is K' (-8,3) L' (-2,3) M' (-2,9) N' (-8,9)
Hence , the translated square is K' ( -8,3 ) L' ( -2,3 ) M' ( -2,9 ) N' ( -8,9 )
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Name/ Uid:1. In this problem, try to write the equations of the given surface in the specified coordinates.(a) Write an equation for the sphere of radius 5 centered at the origin incylindricalcoordinates.(b) Write an equation for a cylinder of radius 1 centered at the origin and running parallel to thez-axis inspherical coordinates.
To find:
(a) Equation for the sphere of radius 5 centered at the origin in cylindrical coordinates
(b) Equation for a cylinder of radius 1 centered at the origin and running parallel to the z-axis in spherical coordinates
Solution:
(a) The equation of a sphere with center at (a, b, c) & having a radius 'p' is given in cartesian coordinates as:
[tex](x-a)^{2}+(y-b)^{2}+(z-c)^{2}=p^{2}[/tex]
Here, it is given that the center of the sphere is at origin, i.e., at (0,0,0) & radius of the sphere is 5. That is, here we have,
[tex]a=b=c=0,p=5[/tex]
That is, the equation of the sphere in cartesian coordinates is,
[tex](x-0)^{2}+(y-0)^{2}+(z-0)^{2}=5^{2}[/tex]
[tex]\Rightarrow x^{2}+y^{2}+z^{2}=25[/tex]
Now, the cylindrical coordinate system is represented by [tex](r, \theta,z)[/tex]
The relation between cartesian and cylindrical coordinates is given by,
[tex]x=rcos\theta,y=rsin\theta,z=z[/tex]
[tex]r^{2}=x^{2}+y^{2},tan\theta=\frac{y}{x},z=z[/tex]
Thus, the obtained equation of the sphere in cartesian coordinates can be rewritten in cylindrical coordinates as,
[tex]r^{2}+z^{2}=25[/tex]
This is the required equation of the given sphere in cylindrical coordinates.
(b) A cylinder is defined by the circle that gives the top and bottom faces or alternatively, the cross section, & it's axis. A cylinder running parallel to the z-axis has an axis that is parallel to the z-axis. The equation of such a cylinder is given by the equation of the circle of cross-section with the assumption that a point in 3 dimension lying on the cylinder has 'x' & 'y' values satisfying the equation of the circle & that 'z' can be any value.
That is, in cartesian coordinates, the equation of a cylinder running parallel to the z-axis having radius 'p' with center at (a, b) is given by,
[tex](x-a)^{2}+(y-b)^{2}=p^{2}[/tex]
Here, it is given that the center is at origin & radius is 1. That is, here, we have, [tex]a=b=0,p=1[/tex]. Then the equation of the cylinder in cartesian coordinates is,
[tex]x^{2}+y^{2}=1[/tex]
Now, the spherical coordinate system is represented by [tex](\rho,\theta,\phi)[/tex]
The relation between cartesian and spherical coordinates is given by,
[tex]x=\rho sin\phi cos\theta,y=\rho sin\phi sin\theta, z= \rho cos\phi[/tex]
Thus, the equation of the cylinder can be rewritten in spherical coordinates as,
[tex](\rho sin\phi cos\theta)^{2}+(\rho sin\phi sin\theta)^{2}=1[/tex]
[tex]\Rightarrow \rho^{2} sin^{2}\phi cos^{2}\theta+\rho^{2} sin^{2}\phi sin^{2}\theta=1[/tex]
[tex]\Rightarrow \rho^{2} sin^{2}\phi (cos^{2}\theta+sin^{2}\theta)=1[/tex]
[tex]\Rightarrow \rho^{2} sin^{2}\phi=1[/tex] (As [tex]sin^{2}\theta+cos^{2}\theta=1[/tex])
Note that [tex]\rho[/tex] represents the distance of a point from the origin, which is always positive. [tex]\phi[/tex] represents the angle made by the line segment joining the point with z-axis. The range of [tex]\phi[/tex] is given as [tex]0\leq \phi\leq \pi[/tex]. We know that in this range the sine function is positive. Thus, we can say that [tex]sin\phi[/tex] is always positive.
Thus, we can square root both sides and only consider the positive root as,
[tex]\Rightarrow \rho sin\phi=1[/tex]
This is the required equation of the cylinder in spherical coordinates.
Final answer:
(a) The equation of the given sphere in cylindrical coordinates is [tex]r^{2}+z^{2}=25[/tex]
(b) The equation of the given cylinder in spherical coordinates is [tex]\rho sin\phi=1[/tex]
PLEASE CHECK MY WORK
The function given in the table is quadratic:
true***
false
Answer:
false
Step-by-step explanation:
The function given in the table is a linear function:
f(x) = 3x+2
Question 5
Refer to the data that you recorded in part D. In each row, compare the slope of ABto the slope of the perpendicular line. What is the
relationship between the two slopes? What conclusion can you draw about the relationship between the slopes of any two perpendicular lines?
Ok
Answer:
Step-by-step explanation:
Answer:
The product of the slopes of and the line perpendicular to through C is -1 in all cases. So, I can conclude that any two perpendicular lines have slopes that are negative reciprocals of each other.
Step-by-step explanation:
its correct
What is the sum of additive inverse and multiplicative inverse of 2?
answer fast
Answer:
-3/2
Step-by-step explanation:
Additive inverse of 2 = -2
Multiplicative inverse of 2 = ½
→ Sum = -2 + ½
→ Sum = (-4 + 1)/2
→ Sum = -3/2
15 friends want to order pizza for dinner. If each friend can eat 1/3 of a pizza, how many pizzas should they order?
Answer:
5
Step-by-step explanation:
[tex]\frac{15}{3} =5\\3 friends=1 pizza\\15 friends=5 pizzas\\[/tex]
You are having a birthday party and are inviting 6 friends. You have 9 cupcakes, and you are going to share the cupcakes fairly among you and your 6 friends.
Which equation describes how many cupcakes each of you will receive?
Answer:
split the other three in half
Step-by-step explanation:
see image for question
Answer:
no because it is apporxametely 1/4th of the pizza
Step-by-step explanation:
this is not a trick question, anyone adding more than 2 sentances on their explanation is tricking themselves and is thinking too hard
Answer:
No I actually received 1/4 of the pizza
Step-by-step explanation:
Piece B shows 1/4 of the pizza meaning I'm receiving less than half of the pizza
If I receiveed 2/4 of the pizza, it would've maked senes for me to receive 1/2 of the pizza because 2/4 = 1/2
Please please help me please I really need help please just tap on picture and you will see the question
Answer:
No , it is not a right angle triangle
Step-by-step explanation:
according to the pythagoras theorem in right angled triangle sum of square of two sides is equal to the square of it's hypotenuse.
using pythagoras theorem
a^2 + b^2 = c^2
9^2 + 16^2 = 25^2
81 + 256 = 625
337 = 625
since sum of square of two smallest sides of a triangle is not equal to the square of it's hypotenuse it can be concluded that the given figure does not form right angle triangle.
PLZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ HELP MEEEEEEEEEEEEEEEEEEEEEEEEE
Task #1 Creating A Table Task
Create a table of x and y values that represents a proportional relationship.
a) Explain how you know the relationship is proportional.
b) What equation models the values in the table?
2) Create a table of x and y values that represents a linear, non-proportional relationship.
a) Explain how you know the relationship is non-proportional.
b) What equation models the values in the table?
Answer:
b
Step-by-step explanation:
Question 18 of 28 Which of the following equations can be used to find the length of EF in the triangle below? A. (EA)2 = 242-122 B. (ER2 = 242 +122 O C. EF = 24 - 12 D. EF = 24 + 12
Answer: A
Step-by-step explanation:
76 is what percent of 79
Answer:
79
100
0.79%
76
100
0.76%
For f(x) = 4x + 2 and g(x) = x^2 - 6, find (f+g)(x)
Answer:
[tex](f+g)(x) = x^2 + 4x - 4[/tex]
Step-by-step explanation:
We are given these following functions:
[tex]f(x) = 4x + 2[/tex]
[tex]g(x) = x^2 - 6[/tex]
(f+g)(x)
We add the common terms. Thus:
[tex](f+g)(x) = f(x) + g(x) = 4x + 2 + x^2 - 6 = x^2 + 4x + 2 - 6 = x^2 + 4x - 4[/tex]
Thus:
[tex](f+g)(x) = x^2 + 4x - 4[/tex]
Jacob knows that the adult population gets, on average, eight hours of sleep each night. A hypothesis test can help him see if college students are different from the adult population. From a sample of 101 students, Jacob tabulated that his sample of students got an average of 7.3 hours of sleep each night, with a standard deviation of 2.6.
Required:
What is the t- statistic that Jacob calculates?
Answer:
The t-statistic that Jacob calculates is [tex]t = -2.71[/tex]
Step-by-step explanation:
Jacob knows that the adult population gets, on average, eight hours of sleep each night. A hypothesis test can help him see if college students are different from the adult population.
At the null hypothesis, we test if the mean is of 8 hours, that is:
[tex]H_0: \mu = 8[/tex]
At the alternative hypothesis, we test if the mean is different of 8 hours, that is:
[tex]H_1: \mu \neq 8[/tex]
The test statistic is:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation and n is the size of the sample.
8 is tested at the null hypothesis:
This means that [tex]\mu = 8[/tex]
From a sample of 101 students, Jacob tabulated that his sample of students got an average of 7.3 hours of sleep each night, with a standard deviation of 2.6.
This means that [tex]n = 101, X = 7.3, s = 2.6[/tex]
What is the t-statistic that Jacob calculates?
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{7.3 - 8}{\frac{2.6}{\sqrt{101}}}[/tex]
[tex]t = -2.71[/tex]
The t-statistic that Jacob calculates is [tex]t = -2.71[/tex]
PLSSS HELP I WILL GIVE BRAINLIEST
Anita had $400 in her savings account when she went to college. Her parents will add $200 to her account each month.
Miguel had $25 in his savings account. His parents will double the amount in his account each month.
If Anita and Miguel do not take any money from their accounts, whose account will grow faster? Explain why.
Answer:
Miguel's account
Step-by-step explanation:
Miguel's account savings are doubled every month. Hence, they will eventually surpass the savings of Anita, even though Anita's account has more money atm.
Answer:
Miguel's account
Step-by-step explanation:
Even though Anita had more money at first compared to Miguel, Miguel savings will double each month while Anita will get only $200 each month. As a result, Miguel's account will grow faster compared to Anita's.
Find the area and circumference of each circle
Answer:
Step-by-step explanation:
Area = [tex]Area = \pi r^2 = \pi(3)^2 = 9\pi = 28.27\\Circumference = 2\pi r = 2\pi 3 = 6\pi = 18.85[/tex]
Answer:
[tex]area = 28.27 {m}^{2} \\ c = 18.84m[/tex]
Explanation is attached to the picture
Hope this helps you.
I already did the equation for you, but can somebody tell me the answer?
Answer:
if you put that equation into a graphing calculator the answer is 4188.37
What is the surface area of a square pyramid if the base has an area of 16 cm2 and the lateral faces have a slant
height of 12 cm?
O 112 cm
O 208 cm2
O 400 cm?
O 640 cm
Answer:
640
Step-by-step explanation:
pleas check my answer
Answer:
112
Step-by-step explanation:
If you add all the triangle faces and the square.
What is the solution to this inequality?
15 + x 24
O A. x 39
O B. X29
O C. XS 39
O D. XS9
The solution of the inequality will be;
⇒ x ≤ 9
What is Inequality?
A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
The inequality is,
⇒ 15 + x ≤ 24
Now,
Since, The inequality is,
⇒ 15 + x ≤ 24
Solve the inequality as;
⇒ 15 + x ≤ 24
Subtract 15, we get;
⇒ 15 + x - 15 ≤ 24 - 15
⇒ x ≤ 9
Thus, The solution of the inequality will be;
⇒ x ≤ 9
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I need help I’ll give u brainlest
Answer:
[tex]252[/tex] cubic yards
Step-by-step explanation:
[tex]V=lwh[/tex]
Volume = length * width * height
[tex]V=7*4*9[/tex]
[tex]V=252[/tex]
Answer:
252 yd³
Step-by-step explanation:
Volume of rectangular prism = length * width * height
= 9 * 7 * 4 yd³
= 252 yd³
Seven-eighths of a number is -35. What is the number?
Let the number be x
7/8 of the number is 7/8x and it equals -35:
7/8x = -35
Find x by dividing both sides by 7/8
When you divide by a fraction, flip the fraction over and then multiply:
x = -35 x 8/7 = (-35 x 8) / 7 = -280/7 = -40
The number is -40
What is the approximate volume of a cone with a height of 12 inches and a diameter of 10 inches?
Step-by-step explanation:
the answer is in the above image
Answer:
314.2 cubic meters
Step-by-step explanation:
Volume of cone = 1/3 × pi × radius² × height
To find the radius we divide the diameter by two = 5 inches
1 × 3.142 × 25 × 12
3
Ans= 314.2 cubic meters
I hope this helps u
Convert the rational expression to radical form.
x^{4/3}y^{1/3}z^{2/5}
Plz help
Answer:
[tex]a \frac{x}{n} = \sqrt[n]{a}^x .
\sqrt[3]{x}^4 \sqrt[3]{y} \sqrt[5]{z}^2 [/tex]