Answer:
The solution is too long. So, I included them in the explanation
Step-by-step explanation:
This question has missing details. However, I've corrected each question before solving them
Required: Determine the inverse
1:
[tex]f(x) = 25x - 18[/tex]
Replace f(x) with y
[tex]y = 25x - 18[/tex]
Swap y & x
[tex]x = 25y - 18[/tex]
[tex]x + 18 = 25y - 18 + 18[/tex]
[tex]x + 18 = 25y[/tex]
Divide through by 25
[tex]\frac{x + 18}{25} = y[/tex]
[tex]y = \frac{x + 18}{25}[/tex]
Replace y with f'(x)
[tex]f'(x) = \frac{x + 18}{25}[/tex]
2. [tex]g(x) = \frac{12x - 1}{7}[/tex]
Replace g(x) with y
[tex]y = \frac{12x - 1}{7}[/tex]
Swap y & x
[tex]x = \frac{12y - 1}{7}[/tex]
[tex]7x = 12y - 1[/tex]
Add 1 to both sides
[tex]7x +1 = 12y - 1 + 1[/tex]
[tex]7x +1 = 12y[/tex]
Make y the subject
[tex]y = \frac{7x + 1}{12}[/tex]
[tex]g'(x) = \frac{7x + 1}{12}[/tex]
3: [tex]h(x) = -\frac{9x}{4} - \frac{1}{3}[/tex]
Replace h(x) with y
[tex]y = -\frac{9x}{4} - \frac{1}{3}[/tex]
Swap y & x
[tex]x = -\frac{9y}{4} - \frac{1}{3}[/tex]
Add [tex]\frac{1}{3}[/tex] to both sides
[tex]x + \frac{1}{3}= -\frac{9y}{4} - \frac{1}{3} + \frac{1}{3}[/tex]
[tex]x + \frac{1}{3}= -\frac{9y}{4}[/tex]
Multiply through by -4
[tex]-4(x + \frac{1}{3})= -4(-\frac{9y}{4})[/tex]
[tex]-4x - \frac{4}{3}= 9y[/tex]
Divide through by 9
[tex](-4x - \frac{4}{3})/9= y[/tex]
[tex]-4x * \frac{1}{9} - \frac{4}{3} * \frac{1}{9} = y[/tex]
[tex]\frac{-4x}{9} - \frac{4}{27}= y[/tex]
[tex]y = \frac{-4x}{9} - \frac{4}{27}[/tex]
[tex]h'(x) = \frac{-4x}{9} - \frac{4}{27}[/tex]
4:
[tex]f(x) = x^9[/tex]
Replace f(x) with y
[tex]y = x^9[/tex]
Swap y with x
[tex]x = y^9[/tex]
Take 9th root
[tex]x^{\frac{1}{9}} = y[/tex]
[tex]y = x^{\frac{1}{9}}[/tex]
Replace y with f'(x)
[tex]f'(x) = x^{\frac{1}{9}}[/tex]
5:
[tex]f(a) = a^3 + 8[/tex]
Replace f(a) with y
[tex]y = a^3 + 8[/tex]
Swap a with y
[tex]a = y^3 + 8[/tex]
Subtract 8
[tex]a - 8 = y^3 + 8 - 8[/tex]
[tex]a - 8 = y^3[/tex]
Take cube root
[tex]\sqrt[3]{a-8} = y[/tex]
[tex]y = \sqrt[3]{a-8}[/tex]
Replace y with f'(a)
[tex]f'(a) = \sqrt[3]{a-8}[/tex]
6:
[tex]g(a) = a^2 + 8a- 7[/tex]
Replace g(a) with y
[tex]y = a^2 + 8a - 7[/tex]
Swap positions of y and a
[tex]a = y^2 + 8y - 7[/tex]
[tex]y^2 + 8y - 7 - a = 0[/tex]
Solve using quadratic formula:
[tex]y = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}[/tex]
[tex]a = 1[/tex] ; [tex]b = 8[/tex]; [tex]c = -7 - a[/tex]
[tex]y = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}[/tex] becomes
[tex]y = \frac{-8 \±\sqrt{8^2 - 4 * 1 * (-7-a)}}{2 * 1}[/tex]
[tex]y = \frac{-8 \±\sqrt{64 + 28 + 4a}}{2 * 1}[/tex]
[tex]y = \frac{-8 \±\sqrt{92 + 4a}}{2 * 1}[/tex]
[tex]y = \frac{-8 \±\sqrt{92 + 4a}}{2 }[/tex]
Factorize
[tex]y = \frac{-8 \±\sqrt{4(23 + a)}}{2 }[/tex]
[tex]y = \frac{-8 \±2\sqrt{(23 + a)}}{2 }[/tex]
[tex]y = -4 \±\sqrt{(23 + a)}[/tex]
[tex]g'(a) = -4 \±\sqrt{(23 + a)}[/tex]
7:
[tex]f(b) = (b + 6)(b - 2)[/tex]
Replace f(b) with y
[tex]y = (b + 6)(b - 2)[/tex]
Swap y and b
[tex]b = (y + 6)(y - 2)[/tex]
Open Brackets
[tex]b = y^2 + 6y - 2y - 12[/tex]
[tex]b = y^2 + 4y - 12[/tex]
[tex]y^2 + 4y - 12 - b = 0[/tex]
Solve using quadratic formula:
[tex]y = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}[/tex]
[tex]a = 1[/tex] ; [tex]b = 4[/tex]; [tex]c = -12 - b[/tex]
[tex]y = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}[/tex] becomes
[tex]y = \frac{-4\±\sqrt{4^2 - 4 * 1 * (-12-b)}}{2*1}[/tex]
[tex]y = \frac{-4\±\sqrt{4^2 - 4 *(-12-b)}}{2}[/tex]
Factorize:
[tex]y = \frac{-4\±\sqrt{4(4 - (-12-b))}}{2}[/tex]
[tex]y = \frac{-4\±2\sqrt{(4 - (-12-b))}}{2}[/tex]
[tex]y = \frac{-4\±2\sqrt{(4 +12+b)}}{2}[/tex]
[tex]y = \frac{-4\±2\sqrt{16+b}}{2}[/tex]
[tex]y = -2\±\sqrt{16+b}[/tex]
Replace y with f'(b)
[tex]f'(b) = -2\±\sqrt{16+b}[/tex]
8:
[tex]h(x) = \frac{2x+17}{3x+1}[/tex]
Replace h(x) with y
[tex]y = \frac{2x+17}{3x+1}[/tex]
Swap x and y
[tex]x = \frac{2y+17}{3y+1}[/tex]
Cross Multiply
[tex](3y + 1)x = 2y + 17[/tex]
[tex]3yx + x = 2y + 17[/tex]
Subtract x from both sides:
[tex]3yx + x -x= 2y + 17-x[/tex]
[tex]3yx = 2y + 17-x[/tex]
Subtract 2y from both sides
[tex]3yx-2y =17-x[/tex]
Factorize:
[tex]y(3x-2) =17-x[/tex]
Make y the subject
[tex]y = \frac{17 - x}{3x - 2}[/tex]
Replace y with h'(x)
[tex]h'(x) = \frac{17 - x}{3x - 2}[/tex]
9:
[tex]h(c) = \sqrt{2c + 2}[/tex]
Replace h(c) with y
[tex]y = \sqrt{2c + 2}[/tex]
Swap positions of y and c
[tex]c = \sqrt{2y + 2}[/tex]
Square both sides
[tex]c^2 = 2y + 2[/tex]
Subtract 2 from both sides
[tex]c^2 - 2= 2y[/tex]
Make y the subject
[tex]y = \frac{c^2 - 2}{2}[/tex]
[tex]h'(c) = \frac{c^2 - 2}{2}[/tex]
10:
[tex]f(x) = \frac{x + 10}{9x - 1}[/tex]
Replace f(x) with y
[tex]y = \frac{x + 10}{9x - 1}[/tex]
Swap positions of x and y
[tex]x = \frac{y + 10}{9y - 1}[/tex]
Cross Multiply
[tex]x(9y - 1) = y + 10[/tex]
[tex]9xy - x = y + 10[/tex]
Subtract y from both sides
[tex]9xy - y - x = y - y+ 10[/tex]
[tex]9xy - y - x = 10[/tex]
Add x to both sides
[tex]9xy - y - x + x= 10 + x[/tex]
[tex]9xy - y = 10 + x[/tex]
Factorize
[tex]y(9x - 1) = 10 + x[/tex]
Make y the subject
[tex]y = \frac{10 + x}{9x - 1}[/tex]
Replace y with f'(x)
[tex]f'(x) = \frac{10 + x}{9x -1}[/tex]
21. M
List the sides of ABC in order from shortest to
longest
Answer:
Ummm... I think it would help if you take a screen shot
Step-by-step explanation:
Answer:
The sum of all angles is 180degrees
100 = 8x +4
X =( 100-4)/8 =12
A = 80
B = 41
C = 59
The largest angle is adjacent to the largest side so
B C A
Step-by-step explanation:
Also can u pls mark me brainliest im new
Please help! Its algebra 2
Answer:
Step-by-step explanation:
1. factor completely
5. simplify first fraction
4. common denominator
2 add the fractions
3. open paranthesis and combine like terms
why is an elephant so wrinkled
Answer:
I have no idea
Step-by-step explanation:
but they beautiul and give good luck
A box of cereal states that there are 90 calories in a 3 4-cup serving. What is the unit rate for calories per cup? How many calories are there in 2 cups of the cereal?
Answer:
Calories per cup = 120 calories
Calories in 2 cups = 240 calories
Step-by-step explanation:
Given that:
Number of calories in a [tex]\frac{3}{4}^{th}[/tex] cup serving = 90 calories
To find:
Unit rate for calories per cup = ?
Number of calories in 2 cups of cereal = ?
Solution:
Here we are given the number of calories in a [tex]\frac{3}{4}^{th}[/tex] cup serving.
To find the calories in one cup, we need to divide 90 calories with [tex]\frac{3}{4}[/tex].
So, unit rate for calories per cup can be given as:
[tex]\dfrac{90}{\frac{3}4}\\\Rightarrow \dfrac{90}{3}\times 4\\\Rightarrow \bold{120 \ calories}[/tex]
To find the calories in 2 cups of cereal, we need to multiply the unit rate for calories per cup with 2.
So, calories in 2 cups of cereal = [tex]120 \times 2[/tex] = 240 calories
Therefore, the answer is:
Calories per cup = 120 calories
Calories in 2 cups = 240 calories
PLEASE HELPPPPP ASAPPP
Answer:
y = (-3/5)x - 7
Step-by-step explanation:
you are given the points (5,-10), (-10,-1)
a slope of (-1+10)/(-10-5) = -9/15 = -3/5 can be determined
using the point (0,-7), we can get y+7=(-3/5)(x - 0)
simplified: y = (-3/5)x - 7
Translate this sentence into an inequality
PLZ HELP ME!
Answer:
Step-by-step explanation:
(b+8)≤18
Mr. Lee is a hotdog and drink vendor at a baseball game. Hot dogs are 3.50 and drinks are 1.50. If Mr. Lee sold enough to make 450 dollars on Monday. He remembers that on Monday he sold three times as many drinks as he did hot dogs. How many hot dogs and how many drinks did Mr. Lee sell on Monday?
Answer:
33 hotdogs and 225 drinks on Monday
Step-by-step explanation:
We would use the ratio of 1:3 hotdogs to drinks
Split the ratio in 450 and we get 112.5:337.5
$112.5 would be the earnings of hotdogs
$337.5 would be the earnings of the drinks
Now we divide each individually by its cost
$112.5/3.5
= 32 1/7,
$337.5/1.5
= 225
We will round the hotdogs to 33 as the word problem says "sold enough to make."
g(x) = 5x – 12. What is g(8)?
Answer:
38?
Step-by-step explanation:
the answer dude lol..............
Twice as many students are in the chess club as in the fencing club.The number of students in the fencing club is one fifth the number of students in the cooking club.There are 42 more students in the cooking club than in the chess club.How many students are in the chess club?
Answer:
28 students
Step-by-step explanation:
Let number of students in cooking club = x
Number of students in fencing club = 1/5 x
Number of students in chess club = 2(1/5)x
Since, There are 42 more students in the cooking club than in the chess club
Then ;
Number of students in chess club = Number of students in cooking club - 42
2(1/5)x = x - 42
(2/5)x - x = - 42
(2/5)x - x = - 42
-0.6x = - 42
x = 42 / 0.6
x = 70
Hence, number of students in chess club :
(2/5) * 70 = 28
3500 calories for 6 servings of pie ________ calories per serving is what?
Answer:
583 rounded to the nearest whole number
Step-by-step explanation:
other wise 583.3333333333333333333333333333
hejabwdychbdscuadsva,syjdh help.
You add 3 to -6 and add 1 to 3 to get -3,4
I WILL MARK BRAINIEST
please answer ASAP
Answer:
It looks like 45 degree for the one on the left and maybe 180 degrees on the right (i'm not sure tbh) but those are my guesses
A cardboard box has edges of length 5.5 in, 3.2in,and 7.25 in.what is the volume of the box?I will gave u Brainliest if u tell me the answer have a nice day
Answer:
The answer is 127.6
Step-by-step explanation:
To find the volume of something, you multiply.
So:5.5 times 3.2 times 7.25 is equal to 127.6
HOPE THIS HELPS YOU!!!! :)
Answer:
127.60 square inches
Step-by-step explanation:
Multiply the diameters all together to get your answers.
5.5 x 3.2 x 7.25
Multiply
5.5 x 3.2 = 17.6
Multiply some more
17.6 x 7.25 = 127.6
You can also just multiply like this:
5.5 x 3.2 x 7.25 = 127.6
Hope this helped :)
Please consider Brainliest :)
Write the equation of the line in point slope form.
(10 Points)
Answer:
y=-1/4(x-4)+3
Step-by-step explanation:
work is in the picture
What is the equation of the line?
Answer:
I believe it should be the second answer
Consider the equation below. What is the discrimination of the equation?
-3x2+27x-63=0
which quadrant will be completely shaded by the graph of 2x+3y ≥-6
Answer:
quadrant I
Step-by-step explanation:
QUICK! Should I wear a hoodie or a coat tomorrow?!!!
Answer:
HOODIEEE u a boy or girl?
Step-by-step explanation:
please helpppp:(((( thank you
Answer:
C
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
Riley earned $5 for 1 2 of an hour babysitting. What is her hourly rate? Simplify your answer and write it as a proper fraction, mixed number, or whole number.
Answer:
Riley's hourly rate is $10
Step-by-step explanation:
Riley earned $5 for 1/2 of an hour babysitting. What is her hourly rate?
1/2 of an hour = $5
1 hour = $x
Cross Multiply
1/2 × x = $5 × 1
x = $5 ÷ 1/2
x = $5 × 2
x = $10
Hence, Riley's hourly rate is $10
halp me :<<<<<<<<<<<<<<
Answer:
4^2+2^2, 5^2, 6^2-6
Step-by-step explanation:
4 to the power of 2 is 16 and 2 to the power of 2 is 4. 16+4 is 20.
5 to the power of 2 is 25 which is greater than 20.
6 to the power of 2 is 36 minus 6 is 30 which is greater than 25 and 20.
Solve for V in V = s^3, if 8 = 4 V =
Answer:
64 units³
Step-by-step explanation:
V = S³
V = 4³
V = 64 Units³
PLEASE HELP ME !
Determine the range of the inequality 4x2 + 3x - 10
Answer:
-22
Step-by-step explanation:
type it in google
A fair spinner has 10 equal sections there is a probability scale
Answer:
1/10
Step-by-step explanation:
Because there is ten different numbers so therefore it would be 10/1
Answer:
{1,2,4}
Step-by-step explanation:
Check image for more help
Thankyou
Find the slope of the line without graphing using the 2 points below.
(-3 , 4) & (13 , 8)
m = _______
Answer:
Step-by-step explanation:
1. use the slope formula --> (y2-y1)/(x2-x1)
2. (8 - 4)/(13 -(-3))
3. 4/16
4. m = 1/4
For triangle ABC with A=103, B=24, a=16, find angle C
Answer:
given A=103° , B=24°
In triangle ABC,
A+B+C=180° [angle sum property of triangle]
103°+24°+C=180°
127°+C=180°
C=180°-127°
C=53°
hope it help u dear...
10pts and I’ll mark brainliest!
(Also EXPLAIN the reasoning you used to write the expression)
I think it is -5................
The height in feet, h, of a base jumper Is jumping off a cliff is given by the equation
h = 3t^2 - 700t + 2000,
where t is the time is seconds. How long will it take the jumper to reach the ground?
Answer:
233 seconds
Step-by-step explanation:
When h = 0 the jumper ends his/her jump. Therefore let h = 0 so that we can solve for t; forming a quadratic equation
0 = 3t^2 - 700t + 200
I am going to solve using the quadratic formula, but there are other approaches--
[tex]t_{1,\:2}=\frac{-\left(-700\right)\pm \sqrt{\left(-700\right)^2-4\cdot \:3\cdot \:200}}{2\cdot \:3},\\\\\sqrt{\left(-700\right)^2-4\cdot \:3\cdot \:200} = 20\sqrt{1219},\\\\t_{1,\:2}=\frac{-\left(-700\right)\pm \:20\sqrt{1219}}{2\cdot \:3}[/tex]
[tex]\:t_2=\frac{-\left(-700\right)-20\sqrt{1219}}{2\cdot \:3}[/tex]
[tex]t=\frac{10\left(35+\sqrt{1219}\right)}{3},\:t=\frac{10\left(35-\sqrt{1219}\right)}{3}[/tex]
Now the solutions are around 233 and 0.3 seconds. Given these two solutions I would find the first one more predictable.
Good morning can anybody help me out with this assignment please and thanks! \
please this if for an grade
Good Morning hope this helped.
Answer:
1: The cost of twelve bottles is $24 cause 12x2=24.
2: The ratio is 24/12 or 2/1
3: $2 every time
The graph of the quadratic function shown on the left is
y = –0.7(x + 3)(x – 4).
The roots, or zeros, of the function are
.
Determine the solutions to the related equation
0 = –0.7(x + 3)(x – 4).
The solutions to the equation are x =
.
Explanation:
We'll use the zero product property. This is the idea where if A*B = 0, then either A = 0 or B = 0.
So if
-0.7(x+3)(x-4) = 0
then either
x+3 = 0 or x-4 = 0
Both of those equations solve to
x = -3 or x = 4
The roots are the locations of the x intercepts, which is where the graph crosses or touches the x axis.
Answer:
1) 3- and 4
2) 3- and 4
Step-by-step explanation: