Given:
The function is
[tex]m(x)=x^2-17x[/tex]
To find:
The inverse of the given function.
Solution:
We have,
[tex]m(x)=x^2-17x[/tex]
Substitute m(x)=y.
[tex]y=x^2-17x[/tex]
Interchange x and y.
[tex]x=y^2-17y[/tex]
Add square of half of coefficient of y , i.e., [tex]\left(\dfrac{-17}{2}\right)^2[/tex] on both sides,
[tex]x+\left(\dfrac{-17}{2}\right)^2=y^2-17y+\left(\dfrac{-17}{2}\right)^2[/tex]
[tex]x+\left(\dfrac{17}{2}\right)^2=y^2-17y+\left(\dfrac{17}{2}\right)^2[/tex]
[tex]x+\left(\dfrac{17}{2}\right)^2=\left(y-\dfrac{17}{2}\right)^2[/tex] [tex][\because (a-b)^2=a^2-2ab+b^2][/tex]
Taking square root on both sides.
[tex]\sqrt{x+\left(\dfrac{17}{2}\right)^2}=y-\dfrac{17}{2}[/tex]
Add [tex]\dfrac{17}{2}[/tex] on both sides.
[tex]\sqrt{x+\left(\dfrac{17}{2}\right)^2}+\dfrac{17}{2}=y[/tex]
Substitute [tex]y=m^{-1}(x)[/tex].
[tex]m^{-1}(x)=\sqrt{x+(\dfrac{189}{4}})+\dfrac{17}{2}[/tex]
We know that, negative term inside the root is not real number. So,
[tex]x+\left(\dfrac{17}{2}\right)^2\geq 0[/tex]
[tex]x\geq -\left(\dfrac{17}{2}\right)^2[/tex]
Therefore, the restricted domain is [tex]x\geq -\left(\dfrac{17}{2}\right)^2[/tex] and the inverse function is [tex]m^{-1}(x)=\sqrt{x+(\dfrac{189}{4}})+\dfrac{17}{2}[/tex].
Hence, option D is correct.
Note: In all the options square of [tex]\dfrac{17}{2}[/tex] is missing in restricted domain.
Answer:
C on edu
Step-by-step explanation:
Help! I honestly dont get this !
Answer:
i don't get that ether
Step-by-step explanation:
Got a #30 question math quiz paying $10 anyone , send your socials or #
This sounds sus to me ┐(￣ヘ￣)┌
Use the properties of logarithms to write the following expression as one logarithm.
3 ln(x) + 2 ln(y) − 4 ln(x + 1)
Please show your work and explain, I would like to learn how to complete this type of problem!
Answer:
Step-by-step explanation:
hi! the log properties say that when logs are multiplied as log(xy), they can be expanded and added like log(x)+log(y). when logs are divided like log(x/y), they can be expanded as log(x)-log(y). when the log has an exponent like log(x^y), the exponent can be added to the front of the log like ylog(x). we can use these properties for this problem.
ln(x^3)+ln(y^2)-ln((x+1)^4)
ln(x^3*y^2)-ln((x+1)^4)
[tex]ln(\frac{(x^3y^2)}{((x+1)^4)})[/tex]
Pls I’m rlly dumb it’s easy math picture here
Answer:
D. 2x, -4y and 8 :)
Step-by-step explanation:
How many cubic yards of dirt will it take to fill a hole that is in the shape of a cube 3 yards on each side?
Answer:
27 yds^3
Step-by-step explanation:
Answer:
27 cubic yards
Step-by-step explanation:
3 x 3 x 3 = 27
which is bigger, 3/5 or 0.625
NEED HELP WITH MATH! Will Give Brainliest! Image is below.
Find all complex solutions (real and non-real). (Enter your answers as a comma-separated list.) x3 8x2 21x 20
Answer:
The answer is "non-real solution: "i-3 and -i-3" and real solution is -2".
Step-by-step explanation:
In the given equation there is some mistype error so, its correct equation can be defined as follows:
Given value:
[tex]\bold{ f(x) = x^3+ 8x^2 +22x +20}[/tex]
use hit and trial method we put x value are -2:
[tex]f(-2) = (-2)^3+ 8(-2)^2 +22(-2) +20\\\\[/tex]
[tex]= -8 + 8 \times 4 +22 \times -2 +20\\\\= -8 + 32 -44 +20\\\\= -52 + 52\\\\=0[/tex]
So, the real solution to the equation is "-2".
In the above solution, we calculate the f(x) =-2 is its real solution. so, the calculation for non-real solution:
divide the value [tex]x^3+8x^2+ 22x +20[/tex] by ([tex]x+2[/tex]):
Quotient: [tex]x^2+6x+10[/tex]
Remainder: 0
[tex]\to x^2+6x+10 \\\\compare \ with \ ax^2+bx+c: \\\\a= 1\\b= 6\\c=10\\\\\bold{Formula:}\\\\\to D= b^2-4ac\\\\[/tex]
[tex]= 6^2- 4 \times 1 \times 10\\\\ = 36- 40\\\\ = -4[/tex]
Formula for calculate non-real solution:
[tex]\bold{\frac{-b\pm \sqrt{D}}{2}}[/tex]
non-real solution: "i-3 and -i-3"
A sphere has a diameter of 8cm. Which statements about the sphere are true? Check all that apply.
• the sphere has a radius of 4cm.
• the sphere has a radius of 16 cm.
• The diameter’s length is twice the length of the radius.
• The radius’s length is twice the length of the diameter.
• The volume of the sphere 2048/3 pi. cm. cubed
• the volume of the sphere is 256/3 pi. cm. cubed
Answer:
The sphere has a radius of 4 cm.The diameter’s length is twice the length of the radius.The volume of the sphere is StartFraction 256 Over 3 EndFraction pi centimeters cubed.Step-by-step explanation:
Answer:
1. The sphere has a radius of 4 cm.
3. The diameter length is twice the length of the radius.
6. The volume of the sphere is StartFraction 256 Over 3 EndFraction pi centimeters cubed.
48minutes to 1hour
This is a ratio plz simplify it
Answer:
48/60=24/30=15/12=4/5 or 4:5
So your final answer is 4/5 or 4:5
Step-by-step explanation:
Help. This is graded lol. Also due in 1 hour soooooo pls go quick. Also explain, since I actually wanna know how to do this.
40 POINTS ON THE LINE (idk if that's a lot)
Answer:
[tex]m\angle1 =47^o[/tex]
[tex]m\angle2 =119^o[/tex]
[tex]m\angle ABC =97^o[/tex]
[tex]m \angle FED = 62^o[/tex]
Step-by-step explanation:
angle 1 and the angle 133 degrees are supplementary angles, then added should give 180 degrees.
angle1 + 133 = 180 then angle1 = 180-133 = 47 degrees
[tex]m\angle1 = 180^o - 133^o=47^o[/tex]
Angle 2 is of the same measure as the angle marked as 119 degrees since they are what is called "corresponding angles between parallel lines."
Angle ABC plus angle that measures 83 degrees should add to 180 since their sum gives a straight line, then:
ABC + 83 = 180
ABC = 180 - 83 = 97 degrees
Last image:
The two angles with algebraic denomination should be equal because they are alternate internal angles, Then this equality can be written as:
8 x - 34 = 5 x + 2
solve for x by subtracting 5 x from both sides:
3 x - 34 = 2
add 34 to both sides:
3 x = 2 + 34
3 x = 36
x = 36/3
x = 12
and now knowing x we can find angle DEF
DEF = 5 x + 2 = 5 (12) + 2 = 60 + 2 = 62 degrees
mass and weight math
Answer: There is 1,000 milligrams in 1 gram.
Answer:
1000mg
Step-by-step explanation:
to be honest that's the obvious answer
and in advance
1kg=1000000mg
1kg=1000g
1g=1000g
solve the equation
–12p = 24
Answer:
p = -2
Step-by-step explanation:
24 divided by -12
p= -2
The ratio of Vicki's savings to Donna's savings is 4 : 7. Vicki saved $225 less than Donna. How much money did Vicki save?
Answer:
300
Step-by-step explanation:
4:7
7-4=3
225/3=75
75x4=300
The annual fundraising goal of a sports team is $100,000. So far $41,317 has been raised. How much more money is needed to reach the goal?
Answer:
58,683
Step-by-step explanation:
subtract
The points (-2,-10) and (-1, v) fall on a line with a slope of 8. What is the value of v?
The required value of v is -2 for a given line with a slope of 8.
What is the slope of the line?The slope of a line is defined as the angle of the line. It is denoted by m
Slope m = (y₂ - y₁)/(x₂ -x₁ )
Consider two points on a line—Point 1 and Point 2. Point 1 has coordinates (x₁,y₁) and Point 2 has coordinates (x₂, y₂)
Given data as :
The points given are (-2,-10) and (-1, v).
Since the line with a slope of 8.
So in this case, we have:
m = (v - (-10)) / (-1 - (-2))
Solving for v:
8 = (v + 10) / 1
8 = (v + 10)
v = -10 + 8
Apply the subtraction operation, and we get
v = -2
Thus, the required value of v is -2.
Learn more about the Slope of the Line here:
brainly.com/question/14511992
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60th Term of -10,8,26,...
Answer:
60th term is 1052
Step-by-step explanation:
position to term rule : position number multiplied by 18 then minus 28 ( position number × 18 - 28)
60 × 18 - 28
twice a number is three more than nine
Answer:
6
Step-by-step explanation:
Let that number be x.
[tex]2x = 9 + 3[/tex]
[tex]2x = 12[/tex]
[tex]x = 6[/tex]
(4,-8)and(6,-9) written in point-slope form,slope-intercept form, and standard form
Answer:
Point slope- y + 8 = − 1 2 ⋅ ( x − 4 )
Slope Intercept Form- y = − 1/ 2 x − 6
Slope- m=-1/2
Step-by-step explanation:
Point slope- y-y₁=m(x-x₁)
Slope Intercept form- y=mx+b\
Slope- rise/run= y2-y1/x2-x1
during a sale, 20 cent bars of soap were sold at the rate of 3 for 50 cents. how much is saved on 9 bars?
Answer:
30 is saved
Step-by-step explanation:
20 x 3 = 60 - 50 = 10, you get 10 three times because of 9 / 3 = 3 you get 10 x 3 = 30
Help me! What is the value of x in the matrix equation below?
Answer:
A. -3
Step-by-step explanation:
edge test
The value of x in the matrix equation comes to be 1.
What is a matrix?A matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object.
The given matrix equation is:
[tex]-2\left[\begin{array}{cc}x&-1&3&5\\\end{array}\right] + \left[\begin{array}{cc}3&8&-1&6\\\end{array}\right] =\left[\begin{array}{cc}x&10&-7&-4\\\end{array}\right][/tex]
Multiply -2 with each element of the first matrix i.e. first matrix on the left side of the equation followed by the addition of matrices we get:
[tex]\left[\begin{array}{cc}-2x+3&2+8&-6-1&-10+6\\\end{array}\right] =\left[\begin{array}{cc}x&10&-7&-4\\\end{array}\right][/tex]
[tex]\left[\begin{array}{cc}-2x+3&10&-7&-4\\\end{array}\right] =\left[\begin{array}{cc}x&10&-7&-4\\\end{array}\right][/tex]
On comparing both matrices
-2x+3 = x
3x=3
x=1
Hence, the value of x in the matrix equation comes to be 1.
To get more about matrices visit:
https://brainly.com/question/1821869
An airplane is flying overhead at a constant elevation of 4090 ft. A person is viewing the plane from a position 3010 ft from the base of a radio tower. The airplane is flying horizontally away from the person. If the plane is flying at the rate of 700 ft/s, at what rate is the distance between the person and the plane increasing when the plane passes over the radio tower
Answer:
415 ft/s
Step-by-step explanation:
I've attached a diagram showing the triangle formed between the plane, the person and the radio tower.
From the attached diagram, x represents the position between the person and the position on the ground directly below the airplane while s represents the distance between the person and the plane.
The constant elevation remains 4090 ft while the value of x and s varies with time.
Thus, x varies with respect to time as dx/dt while s varies with respect to time as ds/dt.
Now, we are told that the plane is flying at the rate of 700 ft/s. This means that; dx/dt = 700 ft/s
Now we want to find the rate at which the distance between the person and the plane is increasing when the plane passes over the radio tower.
This means that we want to find ds/dt when x = 3010 ft
From pythagoras theorem if x = 3010 ft and the Elevation remains 4090 ft, we can find s as;
s = √(4090² + 3010²)
s = √25788200
s ≈ 5078.21 ft
Since we want to find ds/dt at x = 3010 ft, from the diagram, we can say from pythagoras theorem that;
x² + 4090² = s²
Differentiating x and s with respect to t, we have;
2x(dx/dt) = 2s(ds/dt)
2 will cancel out to give;
x(dx/dt) = s(ds/dt)
ds/dt = (x/s)(dx/dt)
Plugging in 700 for dx/dt, 3010 for x and 5078.21 for s, we have;
ds/dt = (3010/5078.21) × 700
ds/dt ≈ 415 ft/s
Pls I need help ASAP
Answer:
the answer is 1/8
thank you
if you loved my answer then please like it and mark as brainliest
Shonda painted 3 walls in her home. She used 34 of her paint. She used the same amount of paint on each wall.
How much of her paint was used on each wall?
Drag and drop the correct answer to complete the statement.
Shonda used ________ area of her paint on each wall.
Please help me
Answer:
en que exactamente necesitas mi ayuda????
Step-by-step explanation:
???????
Answer: Shonda used 1/4 of her paint on each wall.
Step-by-step explanation:
If she used 3/4 of her paint on 3 walls, then each wall used up 1/4 of her paint.
3/4 divided by 3 = 1/4
Hope this helps!
3/5 x 1/7 please help
Answer:
3/35
Step-by-step explanation:
3*1=3
5*7=35
3/35
Find an explicit formula for the arithmetic sequence
81
,
54
,
27
,
0
,
.
.
.
81,54,27,0,...81, comma, 54, comma, 27, comma, 0, comma, point, point, point.
Note: the first term should be
a(1)
a(1)start text, a, left parenthesis, 1, right parenthesis, end text.
Answer:
Can you redo it so I can answer it's kind of confusing
Answer:
81 - 27(n-1)
Step-by-step explanation:
Question 1 Part A: How many beads did Jiao send out? *
Wooden Beads
Oak
4,525
Maple
6,950
Ash
3,720
Ebony
2,475
Bayong
1,250
Answer:
Jiao sent out 18,920 beads.
Step-by-step explanation:
All I did was add.
</3 hope this helps.
Two lines in the same plane that do not intersect are.
A.line segment
B.perpendicular
C.parallel
D.midpoint
Evaluate the expression 12- x when x=8
[tex]given \: that \ :[/tex]
[tex]x = 8[/tex]
[tex]then \:12 - x \: will \: be \: :[/tex]
[tex]12 - 8[/tex]
[tex] = 4[/tex]
[tex]∴ \: 12 - 8= 4 [/tex]
Answer:
The result of 12-x when x=8, is 4
Step-by-step explanation:
Numerical Evaluation
Evaluate an algebraic expression means substituting the variables present in the expression by their respective numerical values, operate and report the result.
The given expression is
12 - x
Substituting x = 8, we get:
12 - 8 = 4
The result of 12-x when x=8, is 4
PLEASE HELP WITH THIS WILL GET EXTRA POINTS
Answer:
1.2
2.4
3.6
4.8
5.9
6.4
7.3
8.6
Step-by-step explanation: