Answer:
[tex]f^{-1}(6) = 2[/tex]
Step-by-step explanation:
Given
[tex]f(2) = 6[/tex]
[tex]f(3) = 7[/tex]
Required
[tex]f^{-1}(6)[/tex]
First, we need to determine the slope of the function using;
[tex]m = \frac{y_1 - y_2}{x_1 - x_2}[/tex]
From the given parameters;
In [tex]f(2) = 6[/tex]
x = 2; y =6 --- Take this as x1 and y1
In [tex]f(3) = 7[/tex]
x = 3; y = 7 --- Take this as x2 and y2
[tex]m = \frac{y_1 - y_2}{x_1 - x_2}[/tex] becomes
[tex]m = \frac{6 - 7}{2 - 3}[/tex]
[tex]m = \frac{- 1}{ - 1}[/tex]
[tex]m = 1[/tex]
Next, we determine the equation of the function using
[tex]y - y_1 = m(x - x_1)[/tex]
Substitute the values of x1,y1 and m
[tex]y - 6 = 1(x - 2)[/tex]
Open bracket
[tex]y - 6 = x - 2[/tex]
Add 6 to both sides
[tex]y - 6 + 6 = x -2 +6[/tex]
[tex]y = x + 4[/tex]
Next is to determine the inverse function by swapping the positions of x and y
[tex]x = y + 4[/tex]
Make y the subject of formula;
[tex]y = x - 4[/tex]
Replace y with [tex]f^{-1}(x)[/tex]
[tex]f^{-1}(x) = x - 4[/tex]
Now, we can solve for [tex]f^{-1}(6)[/tex]
Substitute 6 for x
[tex]f^{-1}(6) = 6 - 4[/tex]
[tex]f^{-1}(6) = 2[/tex]
Jill paid $36 for calendars marked down $5 apiece from the original price, she could have gotten 5 fewer calendars. How many cards did she buy
Answer:
she bought 7 cards
Step-by-step explanation
7x5=35 and im sure there is tax
Question 5
Kate is finding the factors of a large number. Using
a calculator, she has just worked out that 66 is a
factor of this number.
Suddenly, she realises that 22 must be a factor of
the large number as well. Explain why Kate is
correct.
Explanation : If 66 is a factor of this unknown value, then 22 must be as well considering that 22 is a factor off 66. Let's say that this large value is 330. It is a multiple of 66, as 66 [tex]*[/tex] 5 = 330. At the same time 22 [tex]*[/tex] 15 = 330, so 330 is a multiple of 22 as well - or vice versa, 12 is a factor of 330.
We can also tell that 15, 22 fit into 330 through another approach. 22 [tex]*[/tex] 3 = 66, and 66 [tex]*[/tex] 5 = 330, so 5 [tex]*[/tex] 3 = 15 - the same value. This proves that 22 will always be a factor of a value that is the factor of 66.
Write the geometric sequence in function notation.
7, 14, 28, 56, 112, ...
3
Ax) = (7). ()x-1
f(x) = (7) · (2)X-1
O AX) = (7) . (3)X-1
Rx) = (2) (+)*-1
Answer:
a(n) = 7*2^(n - 1)
Step-by-step explanation:
The first term of the given geometric sequence, 7, 14, 28, 56, 112, ... , is 7, and the common ratio is 2. Each new term is twice the previous term.
Thus the general formula for the geometric sequence becomes
a(n) = 7*2^(n - 1).
As a check, let's see whether this formula correctly predicts the fourth term (56): Here n = 4, and so a(4) = 7*2^(4 - 1) = 7*2^3 = 7*8 = 56. Yes.
Answer:
f(x) = (7) ∙ (2)x–1
Step-by-step explanation:
The first term in the sequence is 7, and the common ratio is 2. Using the explicit formula and writing it in function notation results in f(x) = (7) ∙ (2)x–1.
Which table represents a linear function? A, B, C, D
Answer:
Table B represents a linear function.
Step-by-step explanation:
Table B is a linear function because y goes up by a constant, steady rate of 4 every time x goes up by one.
Find the sine and cosine of each angle as a fraction and as a decimal. Round to the nearest hundredth.
Answer:
1st triangle:
sin(C): 0.64, [tex]\frac{16}{25}[/tex]
cos(C): 0.8, [tex]\frac{4}{5}[/tex]
Second triangle:
sin(C): 0.75, [tex]\frac{\sqrt{5} }{3}[/tex]
cos(C): 0.67, [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
Using SOH CAH TOA, we know that to find the sin of an angle, it's Opposite/Hypotenuse.
To find the cos of an angle, it's adjacent/hypotenuse.
In the 1st triangle:
The adjacent to C is 16, the hypotenuse is 25.
[tex]\frac{16}{25} = 0.64[/tex] is the sin of C.
The adjacent to C is 20, and the hypotenuse is 25.
[tex]\frac{20}{25} = 0.8[/tex] is the cos of C.
In the second triangle:
The opposite to C is [tex]\sqrt{5}[/tex] and the hypotenuse is 2.
[tex]\frac{\sqrt{5} }{2} \approx0.75[/tex] is the sin of C.
The adjacent to C is 2 and the hypotenuse is 3.
[tex]\frac{2}{3} \approx 0.67[/tex] is the cos of C.
Hope this helped!
Which statements are true based on the diagram? Check all that apply.
Points A, B, and D are on both planes.
Point H is not on plane R.
Plane P contains point F.
Points C, D, and A are noncollinear.
The line containing points F and G is on plane R.
The line containing points F and H is on plane R.
Answer:
The answer to this is a, b, d, e
Step-by-step explanation:
Answer:
A, B, D, E
Step-by-step explanation:
PLEASE HELP! 10 POINTS Which line would be the line of best fit for the scatter plot?
Answer:
The first one
Step-by-step explanation:
This line is the best fit for the scatter plot because it touches a lot more points than the second
Answer:
The first line
Step-by-step explanation:
Hey there!
Well the first lie is a positive slope just like the dots whereas,
the second line is a negative slope.
Therefore, the first line is the line of best fit.
Hope this helps :)
Two functions, A and B, are described as follows: Function A y = 9x + 4 Function B The rate of change is 3 and the y-intercept is 4 How much more is the rate of change of function A than the slope of function B? 3 6 2 9
Answer:
6
Step-by-step explanation:
Function A
y = 9x + 4
Function B
y = max+b
m = 3 and b = 4
y = 3x+4
The difference in the slopes is 9-3 = 6
Answer:
6
Step-by-step explanation:
The two functions are A and B.
A's equation is khown
● y =9x + 4
B is also khown. We should only gather tge information.
● the rate of change is 3
●the y-intercept is 4
So B's equation is:
● y = 3x + 4
3 is the rate of change wich is khown as the slope.
Divide A's slope by B's slope to khow how much A's slope is bigger than B's.
● 9/3 = 3
Substract 3 from 9 and you get the difference 9-3= 6
What is the value of y?
Answer:
63 degrees
Step-by-step explanation:
(180-54)/2=126/2=63
Answer:
The value of y is 63
Step-by-step explanation:
The sum of angles in a triangle is 180°.
The angles in the triangle are 54°, y°, y°
Sum of angles in the triangle = 54° + y° + y° = 54 + 2y°
To find y, equate the sum of the angles in the triangle to 180°
54° + 2y° = 180°
2y° = 180° - 54°
2y° = 126°
y = 126/2 = 63
Sue's ice cream has 6 more scoopsthan Tessa's ice cream cone.
Sue's ice cream cone has 9 scoops.
How many scoops are on Tessa's ice cream cone?
Answer:
Tessa has 3 ice-cream scoops
Step-by-step explanation:
What’s x ?? Help plzzz
Answer:
x = 69°
Step-by-step explanation:
1). JFGHI is a pentagon, every angle in a Pentagon is equal to 108°.
2). angle JIH + angle HIE = 180°; angle JIH = 108, so angle HIE = 72°.
3). angle JDI is equal to 39° and angle IEH; so angle IEH = 39°
4). Now we know 2 out of the three angles in the triangle IHE, so we can find x!
5). x + angle HIE + angle IEH = 180°
x + 72° + 39° = 180°
x = 69°
The net of a right rectangular prism is shown below: Find the volume of the prism with the given net (in cubic inches).
Answer:
240 inches cubed
Step-by-step explanation:
Volume equals length times width times height. Imagine the net is folded into its shape. The product of the base, 6 x 10 = 60, and the height, 4, equals 240. Remember that each square accounts for two inches. Hope this helps.
5. Find the measures of the following. Round to the nearest whole number
Answer:
a - HT = 17
b - ∠T = 62
c - ∠H = 28
Find the measure of c.
Answer:
140°
Step-by-step explanation:
The circle has a central angle of 80. This means that the arc it intercepts is also 80°. Therefore, the rest of the circle not intercepted by the arc is 360-80=280°
Remember that inscribed angles have one-half of the arc-length it intercepts. We can see that Angle C intercepts the entire circle except for the arc intercepted by Angle O. Therefore, the arc intercepted by Angle C is 280°. This means that Angle C is the half of 280, or 140°.
URGENT!!!! PLEASE HELP NOW!!! WHO EVER GIVES THE CORRRECT ANSWER WILL GET BRAINLIEST!!!
Items Sold at a Clothing Store
The bar graph shows the number of each item sold at a clothing store. Which
statement about the graph is true?
Answer:
The correct ans is..... ( which i believe )
3rd option
Hope this helps...
Pls mark my ans as brainliest
If u mark my ans as brainliest u will get 3 extra points
Answer:
3rd option
Step-by-step explanation:
because 2/5 of 40 is equal to 16, and thats the equivelent of the pants sold.
Can someone please help me please and thanks.
Answer:
The probability of 3 students having blood type A is 1.23 , having blood type B is 0.3 and having blood type AB is 0.12
Step-by-step explanation:
If 120 is divided into 3 parts which are proportional to 1, [tex]\frac{1}{2} [/tex], and [tex]\frac{1}{6}[/tex], what is the middle part?
[tex]k+\frac{k}{2}+\frac{k}{6}=120\\\\6k+3k+k=720\\10k=720\\k=72[/tex]
72,36,12
answer: 36
solve for m. √m-7 = n+3 It is worth like 40 points
Answer:
sqrt of (m-7) = n+3
m = (n+3)^2 + 7 or m= n^2 + 6n + 16
sqrt of (m)-7 = n+3
m = (n+10)^2 or m =n^2 + 20n + 100
Step-by-step explanation:
(2) move the constants to the other side, and square
or (1) square and move constants
then you can solve for m
Answer:
[tex]n^2+6n+16[/tex]
Step-by-step explanation:
I'm going to assume you meant [tex]\sqrt{m-7} = n+3[/tex], not [tex]\sqrt{m} - 7 = n+3[/tex].
[tex](\sqrt{m-7}) ^2 = (n+3)^2\\\\(\sqrt{m-7}^2) = (n+3)^2\\\\(m-7)^{\frac{2}{2} } = (n+3)^2\\\\m - 7 = (n+3)^2\\\\m - 7 = n^2 + 2n\cdot3 + 3^2\\\\m - 7 = n^2 + 6n + 9\\\\m - 7 + 7 = n^2 + 6n + 9 + 7\\\\m = n^2 + 6n + 16[/tex]
Hope this helped!
The coefficient of 6x is
1
6
Х
Answer:
6
Step-by-step explanation:
If a number and a variable were together in a term, the number would the the coefficient. The coefficient would multiply the variable.
In '6x', the number '6' is the coefficient. '6' would be multiplying 'x'.
The correct answer should be 6.
0 3C = n
Use the data in the table to give an equation to represent the proportional relation
ship.
X Y
0.5 7
1. 14
1.5 21
2 28
y = 14x
y = 7x
7y = x
21y = x
Answer:
[tex]\huge \boxed{y=14x}}[/tex]
Step-by-step explanation:
x=0.5, y=7
x=1, y=14
x=1.5, y=21
x= 2, y=28
Let’s take the first equation.
y = 14x
y = 14(0.5) = 7
When x is 0.5, y is 7.
y = 14(1) = 14
When x is 1, y is 14.
y = 14(1.5) = 21
When x is 1.5, y is 21.
y = 14(2) = 28
When x is 2, y is 28.
h(x+1)=x^2-4 evaluate function by substuting x+1
Answer:
h(x + 1) = (x+3)(x-1)
Step-by-step explanation:
Simply plug the value of x+1 into the equation for x.
h(x) = x^2 - 4
h(x + 1) = (x + 1)^2 - 4
h(x + 1) = x^2 + 2x + 1 - 4
h(x + 1) = x^2 + 2x - 3
h(x + 1) = (x+3)(x-1)
Cheers.
Answer:
h(t)= t² - 2t -3
Step-by-step explanation:
h(x+1)= x²-4 is the given function
We can write it x²-4 as:
(x+2)(x-2)= (x+1+1)(x+1 - 3)Substituting x+1 with t. Then function is:
h(t)= (t+1)(t-3)= t² - 2t -3or
h(t)= t² - 2t -3Tamara walked 3/4 mile in 1/2 hour. Which of the following represents the unit rate that Tamara walked? A. 1/2 mi/h B. 2/3 mi/h C. 3/4 mi/h D. 1 1/2 mi/h Include ALL work please!
Answer:
1 1/2 miles / hour
Step-by-step explanation:
We want distance / time
3/4 miles
---------------
1/2 hour
3/4 ÷ 1/2
Copy dot flip
3/4 * 2/1
3/2
1 1/2 miles / hour
Answer:
D
Step-by-step explanation:
Multiple (3/4) by 2 to find the information for one hour)
6/4 in one hour
3/2 or 1 + 1/2 mi/h
D is the answer
Name five fractions whose values are between 3/8 and 7/12
Answer:
convert them to decimasls
Step-by-step explanation:
convert thhem to decimals to make it easier
Answer:
1/2 2/4 4/8 6/12 9/18
Step-by-step explanation:
for n prove by
[tex]3 + 3 {}^{2} + 3 {}^{3} ... + 3 {}^{n} = \frac{3(3 {}^{n} - 1) }{2} [/tex]
thank you
Answer:
[tex]3 + 3^2 + 3^3 ...+ 3^n = \frac{3(3^n - 1)}{2}[/tex]
Step-by-step explanation:
Given
[tex]3 + 3^2 + 3^3 ...+ 3^n[/tex]
Required
Show that the sum of the series is [tex]\frac{3(3^{n}-1)}{2}[/tex]
The above shows the sum of a geometric series and this will be calculated as shown below;
[tex]S_n = \frac{a(r^n - 1)}{r - 1}[/tex]
Where
a = First term;
[tex]a = 3[/tex]
r = common ratio
[tex]r = \frac{3^2}{3} = \frac{3^3}{3^2}[/tex]
[tex]r = 3[/tex]
Substitute 3 for r and 3 for a in the formula above;
[tex]S_n = \frac{a(r^n - 1)}{r - 1}[/tex] becomes
[tex]S_n = \frac{3(3^n - 1)}{3 - 1}[/tex]
[tex]S_n = \frac{3(3^n - 1)}{2}[/tex]
Hence;
[tex]3 + 3^2 + 3^3 ...+ 3^n = \frac{3(3^n - 1)}{2}[/tex]
The following dot plot shows the number of books each student checked out from the library last month. Each dot represents a different student. Which of the following is a typical number of books one student checked out?
Answer:
The answer isn't 1 because most of the students checked out more than 1 bookThe answer isn't 4 because most of the students checked out more than 4 booksThe answer isn't 12 because most of the students checked out fewer than 12 booksThe answer is 7 because most of the students checked out more books than 1, 4, and 12In 7, seven kids checked out 7. [tex]7*7=49[/tex] (Correct answer because 49 is the biggest number here)
In 1, only two kids checked out 1. [tex]1 *2=2[/tex] (Wrong answer because 2 is lower than 49)
In 4, only eight kids checked out 4. [tex]4*8=32[/tex] (Wrong answer because 32 is lower than 49)
In 12, only two kids checked out 12. [tex]12*2=24[/tex] (Wrong answer because 24 is lower than 49)
So 7 is the correct answer because [tex]7*7=49[/tex] is the greatest equation here.
The 0 and 11 number book is the typical book one student checked out.
Given, the dot plot shows the no. of book each student checked out from the library last month.
Since each dot represent a different student, so clearly from the dot plot the 8 number book is checked out by the most of the students because it has most of the dots.
Since the number 0 and 11 has only one dot it represent that only 1 student checked out these books last month.
Hence the 0 and 11 number book is the typical book one student checked out.
For more details on dot plot follow the link:
https://brainly.com/question/4398979
The box plots display the same data set for the number of touchdowns a quarterback threw in 10 seasons of play. Including outlier: A number line goes from 5 to 30. The whiskers range from 5 to 29, and the box ranges from 18 to 26. A line divides the box at 21.5. Excluding outlier: A number line goes from 5 to 30. The whiskers range from 17 to 29, and the box ranges from 19 to 27. A line divides the box at 21. There is an asterisk at 5. Complete the statements describing the effect of the outlier on the measures of variability. The outlier of the data set is . The range of the data set including the outlier is more than the one excluding the outlier. The interquartile range of the data set including the outlier is more than the one excluding the outlier. The outlier had the most effect on the .
Answer:
5
12
0
range
Step-by-step explanation:
i just did it, these are the right answers.
Answer:
5,12,0, and the last answer is range
Step-by-step explanation:
Did it on Edge2021. Hope this helps!
help me plz can i have help
Answer:
6×[tex]10^{-4}[/tex]
Step-by-step explanation:
What is h decreased by 20
Answer:
h minus 20
Step-by-step explanation:
Jo kept track of how much TV she watched each day for two weeks. How many hours in all did she spend watching TV?
Answer:
12 1/2 hours
Step-by-step explanation:
This is because (0*1) + (1/4*1) + (1/2*1) + (3/4*3) + (1*3) + (1 1/4*4) + (1 1/2*1) = 12 1/12.
please solve this fast
Answer:
69
Step-by-step explanation:
