Find the inverse of these functions
[tex]f(x) = 5 + 2x[/tex]
[tex]f(x) = 4 - \sqrt{2x - 3} [/tex]
as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables and then solving for "y", let's do so.
[tex]\stackrel{f(x)}{y}~~ = ~~5+2x\implies \stackrel{quick~switcheroo}{x~~ = ~~5+2y}\implies x-5=2y\implies \boxed{\cfrac{x-5}{2}~~ = ~~\stackrel{f^{-1}(x)}{y}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{f(x)}{y}~~ = ~~4-\sqrt{2x-3}\implies \stackrel{quick~switcheroo}{x~~ = ~~4-\sqrt{2y-3}}\implies x+\sqrt{2y-3}=4 \\\\\\ \sqrt{2y-3}=4-x\implies \stackrel{\textit{squaring both sides}}{2y-3=(4-x)^2} \\\\\\ 2y=(4-x)^2+3\implies \boxed{\stackrel{f^{-1}(x)}{y}~~ = ~~\cfrac{(4-x)^2 +3}{2}}[/tex]
PLEASE I NEED THIS FAST
Answer:
1. 2 + 3
2. -4 - 8
3. -4 + 8
4. -2 × 2
5. 24 ÷ 2
6. 3 - 8
7. 1 × 7
8. -7 ÷ -1
9. 36 ÷ 4
10. 3 × -3
you're welcome
The winner of a golf tournament made two putts for birdies. The lengths of these putts were 15ft 4 in and 9 ft 2in. What’s the total distance of the putts in yards, feet, and inches?
The total distance of the putts in yards, feets and inches be 8 yd 0 ft 6 inches or 8 yd 0.5 ft 0 inches
What is unit conversion?The conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors.
As,
1 yard = 3 foot,
1 feet = 12 inches.
Now the lengths are given 15ft 4 in and 9 ft 2 in.
So, the total distance of the putts be,
=15 ft 4 in + 9 ft 2 in
= 24 ft 6 inches
= 8 yd 0 ft 6 inches or 8 yd 0.5 ft 0 inches
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Help me
Solve multi-steps equations
42=-8(3-k)+6(k-3)
Answer:
6
Step-by-step explanation:
42=--24+8k+6k-18
42=-24+14k-18
42=-42+14k
14k=-42-42
-14k=-84
k=84/14
K=6.
Hey there!
42 = -8(3 - k) + 6(k - 3)
-8(3 - k) + 6(k - 3) = 42
-8(3 - 1k) + 6(1k - 3) = 42
-8(3) - 8(-1k) + 6(1k) + 6(-3) = 42
-24 + 8k + 6k - 18 = 42
COMBINE the LIKE TERMS
(8k + 6k) + (-24 - 18) = 42
8k + 6k - 24 - 18 = 42
14k - 42 = 42
ADD 42 to BOTH SIDES
14k - 42 + 42 = 42 + 42
SIMPLIFY IT!
14k = 42 + 42
14k = 84
DIVIDE 14 to BOTH SIDES
14k/14 = 84/14
SIMPLIFY IT!
k = 84/14
k = 6
Therefore, the answer is: k = 6
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
In the seahorse tank at an aquarium, 70% of the male seahorses
have eggs in their pouches. There are 20 male seahorses in the
tank. Kennedy uses the expression 0.07 x 20 to find the number of
male seahorses with eggs. Explain why Kennedy's expression is
incorrect. How many male seahorses have eggs in their pouches?
Part A: Kennedy's expression is incorrect because 0.07 is 7 percent, not 70.
Part B: The correct expression would be 0.7 * 20, which equals 14
Randall wants to make a prediction using a linear model with a correlation coefficient of -0.95.
Which statement best describes how accurate he can expect his prediction to be?
O His prediction will probably be very close to the actual value.
O His prediction will probably be very different than the actual value.
O His prediction is likely to be close to the actual value.
His prediction is likely to be different than the actual value.
The statement that describes how accurate he can expect his prediction to be his prediction will probably be very different than the actual value.
What is negative correlation?Correlation is a statistical measure used to measure the relationship that exists between two variables. Negative correlation is when two variables move in different direction. If one variable increases, the other variable decreases. When two variables have a negative correlation, there is a negative sign in front of the number.
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Answer:
His prediction will probably be very close to the actual value.
Step-by-step explanation:
Other answer is wrong. I got it right.
Five children are the following ages: 12, 13, 11, 11, and 13.
What is their mean age?
Answer: Mean is 12
Step-by-step explanation: Mean is adding it all up and then dividing, 12 + 13 + 11 + 11 + 13 is 60
Divide 60 by the amount of numbers, 5
60 divided by 5 is 12
[tex]\rule{50}{1}\large\blue\textsf{\textbf{\underline{Given question:-}}}}\rule{50}{1}[/tex]
Five children are the following ages:-
12, 13, 11, 11, and 13.- What is their mean age?
[tex]\rule{50}{1}\large\blue\textsf{\textbf{\underline{Answer \& how to solve:-}}}\rule{50}{1}[/tex]
In order to find the mean of a set of data, we need to add all the numbers in that set, as follows:-
[tex]\Large\text{12+13+11+11+13}[/tex]
[tex]\bigstar[/tex] On simplification,
[tex]\Large\textit{60}[/tex]
However, that's not our final step; we also need to divide by how many numbers there are (in this case, we have 5, so we divide by 5, as follows:-
[tex]\Large\textsf{60:5}[/tex]
[tex]\bigstar[/tex] As a result, the mean of the children's ages is as follows:-
[tex]\Large\textit{Mean=12}[/tex]
Good luck with your studies.[tex]\rule{50}{1}\smile\smile\smile\smile\smile\rule{50}{1}[/tex]
Find the area of the shaded regions
Answer:
35 area of shaded regions
Answer:
It llooks like its missing some information. I don't think I can find the triangle areas without another angle measure or line length.
Step-by-step explanation:
Dwade is thinking about buying a laptop that costs $559, but he would also have to pay 7% sales tax. How much would Dwade pay in tax?
Answer:
$39.13
Step-by-step explanation:
559 x 7 is 3913 divided by 100 since its a percent is 39.13
The required amount paid for tax is obtained as $39.13.
How to calculate the percent value of the tax?In order to calculate the percent value take the ratio of the tax amount to the amount of the goods and then multiply it by 100.
The tax value is often written in terms of percent.
The price of laptop is given as $559.
And, the percent value of sales tax is 7%.
The amount of tax can be calculated as follows,
7% × Price of laptop
= 7% × 559
= 7/100 × 559
= $39.13
Hence, the amount paid by Dwade for the sales tax is $39.13.
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This pattern follows the rule add 9. What are the next 3 terms?
An image of a pattern. Term one has 9 triangles, term two has eighteen triangles, term three has twenty seven triangles.
Group of answer choices
36, 45, 54
39, 48, 57
42, 51, 60
54, 63, 72
Next three terms after 27 are 36, 45 and 54.
can anyone help me find the area of these two ty
Answer:
11) 49 in.²
13) 4.515 m²
Step-by-step explanation:
11) area of square = (side)²
area = (7 in.)² = 7 in. × 7 in. = 49 in.²
13) area of triangle = base × height/2
area = 4.3 m × 2.1 m / 2 = 4.515 m²
Lisa played soccer for 234 hours on Saturday and for 135 hours on Sunday. How many hours did she play soccer during the weekend?
Answer:
Lisa played 4.35 hours over the weekend :)
Step-by-step explanation:
Find the surface area of the regular pyramid shown in the accompanying diagram. If necessary, express your answer in simplest radical form.
-15
A. 360 + 643 units
B. 720 + 16v3 units'
OC. 720 +61, 3 units
D. 360 + 16,
3 units
The area of the yard is 63 yd.² the length of one side is 7 yards what is the perimeter of the yard
Answer:
32 yd.
Step-by-step explanation:
63 / 7 is 9. 9+7+9+7 is 32.
Rationalise the denominator of (12)/(\sqrt(10)+\sqrt(7)+\sqrt(3))
Answer:
[tex]\frac{12}{\sqrt{10} +\sqrt{7} +\sqrt{3} }=\frac{6\sqrt{147} +6\sqrt{63}-6\sqrt{210} }{21 }[/tex]
Step-by-step explanation:
[tex]\frac{12}{\sqrt{10} +\sqrt{7} +\sqrt{3} }[/tex]
[tex]=\frac{12\left( \sqrt{10} -\left( \sqrt{7} +\sqrt{3} \right) \right) }{(\sqrt{10}+(\sqrt{7} +\sqrt{3 } ))( \sqrt{10} -( \sqrt{7} +\sqrt{3}))}[/tex]
[tex]=\frac{12\left( \sqrt{10} -\sqrt{7} -\sqrt{3} \right) }{\sqrt{10^2} -(\sqrt{7} +\sqrt{3})^2}[/tex]
[tex]\frac{12\left( \sqrt{10} -\sqrt{7} -\sqrt{3} \right) }{10-(10+2\sqrt{21} )} }[/tex]
[tex]=\frac{12\left( \sqrt{10} -\sqrt{7} -\sqrt{3} \right) }{-2\sqrt{21} }[/tex]
[tex]=\frac{-6\left( \sqrt{10} -\sqrt{7} -\sqrt{3} \right) }{\sqrt{21} }[/tex]
[tex]=\frac{-6\left( \sqrt{10} -\sqrt{7} -\sqrt{3} \right) }{\sqrt{21} } \times\frac{\sqrt{21} }{\sqrt{21} }[/tex]
[tex]=\frac{-6\sqrt{21} \left( \sqrt{10} -\sqrt{7} -\sqrt{3} \right) }{21 }[/tex]
[tex]=\frac{-6\sqrt{210} +6\sqrt{147} +6\sqrt{63} }{21 }[/tex]
[tex]=\frac{6\sqrt{147} +6\sqrt{63}-6\sqrt{210} }{21 }[/tex]
Remark:
You can simplify moreover if you want to.
What types of angles are <4 and <5?
A. vertical angles
B. alternate interior angles
C. alternate exterior angles
D. supplementary angles
Answer: Alternate interior angles
Step-by-step explanation:
What value of n makes the inequality true? |n| > |–2.5|
Answer: n > 2.5 or n < -2.5
Step-by-step explanation:
Let's solve your inequality step-by-step.
1. Solve Absolute Value.
|n| > 2.5
We know either n > 2.5 or n < -2.5
n > 2.5 (Possibility 1)
n < -2.5 (Possibility 2)
Your answer is n > 2.5 or n < -2.5
)
A rectangular prism is filled with cubes as shown below. Which expression
represents the volume of the prism in cubic inches?
4 x 2 x 5
4+2 +5
5 in.
2 in.
(4+2) x 5
4 in.
= 1 cubic inch
4x (2+5)
Can someone teach me How to do long division properly?
Step-by-step explanation:
"properly" is very vague.
as your can imagine, particularly in math, where many things are commutative or have other degrees of freedom what do when in what sequence, you will find particularly for the little techniques many different approaches. and most of them are correct.
particularly today I keep scratching my head about what i think is immensely complicated but teachers swear they are helping the students.
anyway, this is how I do divisions by using an example :
73496 ÷ 17
the "window" I use to look at the first number is a long as the second number. in this case 2 digits.
step 1a :
as mentioned, we look at the 2 left most digits (73) and see how often 17 fits inside that as a whole :
73 ÷ 17 = 4
4×17 = 68, so we have a remainder of 73-68 = 5.
I write it like this :
73|496 ÷ 17 = 4
05 (4×7 = 28 and 5 is then 33, carry over 3,
4×1 = 4 plus carry 3 = 7, 0 difference)
step 1b :
pull the next position down
734|96 ÷ 17 = 4
054
step 2a :
we look at the bottom number and divide this by 17.
54 ÷ 17 = 3 and a remainder of 3.
734|96 ÷ 17 = 43
054
03 (3×7 = 21 and 3 is then 24, carry over 2,
3×1 = 3 plus carry 2 = 5, 0 difference)
step 2b :
pull the next position down
7349|6 ÷ 17 = 43
054
039
step 3a :
we look at the bottom number and divide this by 17.
39 ÷ 17 = 2 and a remainder of 5.
734|96 ÷ 17 = 432
054
039
05 (2×7 = 14 and 5 is then 19, carry over 1,
2×1 = 2 plus carry 1 = 3, 0 difference)
step 3b :
pull the next position down
73496| ÷ 17 = 432
054
039
056
step 4a :
we look at the bottom number and divide this by 17.
56 ÷ 17 = 3 and a remainder of 5.
73496| ÷ 17 = 4323
054
039
056
05 (3×7 = 21 and 5 is then 26, carry over 2,
3×1 = 3 plus carry 2 = 5, 0 difference)
step 4b :
pull the next position down. but we have reached the last position before the decimal point. from that moment on we create result numbers after the decimal point.
and because the left number did not have any explicit digits after the decimal point, all the numbers we are pulling down now are 0.
73496.0| ÷ 17 = 4323.
054
039
056
050
step 5a :
we look at the bottom number and divide this by 17.
50 ÷ 17 = 2 and a remainder of 16.
73496.0| ÷ 17 = 4323.2
054
039
056
050
16 (2×7 = 14 and 6 is then 20, carry over 2,
2×1 = 2 plus carry 2 = 4, 1 difference)
step 5b :
pull the next position down. because the left number did not have any explicit digits after the decimal point, all the numbers we are pulling down now are 0.
73496.00| ÷ 17 = 4323.2
054
039
056
050
160
step 6a :
we look at the bottom number and divide this by 17.
160 ÷ 17 = 9 and a remainder of 7.
73496.00| ÷ 17 = 4323.29
054
039
056
050
160
07 (2×7 = 14 and 6 is then 20, carry over 2,
2×1 = 2 plus carry 2 = 4, 1 difference)
step 6b :
pull the next position down. because the left number did not have any explicit digits after the decimal point, all the numbers we are pulling down now are 0.
73496.000| ÷ 17 = 4323.29
054
039
056
050
160
070
step 7a :
we look at the bottom number and divide this by 17.
70 ÷ 17 = 4 and a remainder of 2.
73496.00| ÷ 17 = 4323.294
054
039
056
050
160
070
02 (4×7 = 28 and 2 is then 30, carry over 3,
4×1 = 4 plus carry 3 = 7, 0 difference)
step 7b :
pull the next position down. because the left number did not have any explicit digits after the decimal point, all the numbers we are pulling down now are 0.
73496.0000| ÷ 17 = 4323.294
054
039
056
050
160
070
020
and so on ...
What's the difference between numerical and algebraic expressions? How is the order of operations used to evaluate these expressions?
a numerical expression is a mathematical statement involving only numbers and one or more operation symbols. and a algebraic expession is an expressions that includes at least one variable and at least one operation. Order of operation goes (), exponent, divison, multiplication, addtion and subratcion
Using the graphing function on your calculator, what is the solution to the system of equations show below? y + 2x = 14 2y - x = 3
A. X= 5, y = 4
B. x = 4, y = 5
C. More than 1 solution
D. No solution
Answer:
A. x= 5, y = 4
Step-by-step explanation:
The attachment shows a graphing calculator solution to this system of equations.
(x, y) = (5, 4) . . . . . one solution
2 pts
I have an opening balance of $85.90. I make a deposit of $55. Then the next day, I
withdraw $30. A week later, I earn interest of $1.50. What is my new balance?
Answer:
$2.4
Step-by-step explanation:
85.9-55=30.9
30.9-30=0.9
0.9+1.5=2.4
Solve by factoring
x^2 - 8x - 84 = 0
Show all work
Answer:
X= -6 & x= 14
Step-by-step explanation:
The factors are -14 and 6, these numbers are multiplied to get -84 and added to get -8.
Therefore the new equation is:
x^2 -14x +6x -84 = 0
factorize: x (x -14) 6 (x - 14)
So: (x+6) (x-14) = 0
x = -6 and 14
In a binomial random variable where n=10 and p=.5 what is q?
Group of answer choices
.6
.8
.5
.2
None of these options
Work Shown:
q = 1 - p
q = 1 - 0.5
q = 0.5
Solve the equation for x.
3(x+2)=2(2-x)
Step-by-step explanation:
[tex]3(x + 2) = 2(2 - x) \\ 3x + 6 = 4 - 2x \\ 3x + 2x + 6 = 4 - 2x + 2x \\ 5x + 6 = 4 \\ 5x + 6 - 4 = 4 - 4\\ 5x = 2 \\ x \frac{2}{5} = 0.4[/tex]
d
O
9
9
9
f
f
e
d
Answer: P=
Submit Answer
I need help please!
Answer:
Step-by-step explanation:
Mackenzie chooses one candle and then chooses another candle. What is the probability that Mackenzie selects a polka dot candle both times?
Answer:
1/2
Step-by-step explanation:
because Mackenzie chose two candles and we are to find the probility that he selects a polka dot candle
PLEASE HELP ME
A. 6,000 cm3
B. 3,000 cm3
C. 4,000 cm3
D. 900 cm3
Answer:
A 6000
Step-by-step explanation:
15x20 = 300
300 x 10
since theres two rectangles with the same side lengths
3000 x 2
6000
Answer:
A 6000 cm^3
Step-by-step explanation:
Bottom rectangular prism volume = 15 x 20 x 10 = 3000 cm^3
Top prism = 10 x 20 x 15 = 3000 cm^3
Summed = 6000 cm^3
Which data set contains an outlier?
A. {15, 15, 15, 16, 16, 17, 18}
B. {45, 46, 47, 47, 49, 49}
C. {9, 10, 10, 11.4, 12.1, 12.6}
D. {16, 42, 45, 45, 46, 48}
The data set which contains an outlier from the given answer choices is; Choice D; {16, 42, 45, 45, 46, 48}.
What is an outlier?An outlier in a set of data values is a data value which differs significantly from other data points and hence, tends to affect the mean of such set of data values significantly.
On this note, choice D is the set of data values which contains an outlier.
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f(x)= -4(x-2)^2+100 answer all questions below show work if there is any.
a) find the y-intercept(s) (write your answer(s) as ordered pairs)
b) Find the vertex
c) Find the x-intercept(s) (write your answer(s) as ordered pairs)
e) what is the domain of the function? (use interval notation)
f) what is the range of the function? ( use interval notation)
The vertex of the given function [tex]f(x)= -4(x-2)^2+100[/tex] is (2, -25). the y-intercept is (0,-21). the x-intercept are (-3,0) and (7,0).
What is x-intercept of a function?The x-intercept of a function of variable x ( y = f(x) ) form is an intersection fo the x-axis and the curve of the function.
The x-intercept for a function y = f(x) is a solution to the equation f(x) = 0 because at that value of x, the function f(x) lies on x-axis,
where y is 0. Values of x-intercept for a function f(x) are also called roots or solution of f(x) = 0 equation.
We have the function,
[tex]f(x)= -4(x-2)^2+100[/tex]
On simplifying, we get,
[tex]f(x)= x^2 - 4x -21\\\\f(x) = (x+3)(x-7)[/tex]
Now, the factors of the given functions are (x+3) and (x - 7).
We have,an intercept form of the function is .
[tex]f(x) = (x+3)(x-7)[/tex]
Now, we know that,
Value of x-coordinate of the vertex is -b/2a
= 4 / 2
= 2
x = 2
Then,
[tex]f(2)= 2^2 - 4(2) -21\\\\f(2)= -25[/tex]
So, the vertex of the function is (2, -25).
Further, we know that 'the y-intercept of a function is the point where the function crosses the y-axis'.
So, when x=0, we have, i.e. f(0) = -21
Thus, the y-intercept is (0,-21)
Also, 'the x-intercept of a function is the point where the function crosses x-axis'.
Then, for f(x)=0, we have i.e. i.e. x= -3 and x= 7
Thus, the x-intercept are (-3,0) and (7,0).
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