Given the function f(x) = -2c+cx-x^2, and f^-1(5) = -1, find c

Answers

Answer 1

Answer:

[tex]c=-2[/tex]

Step-by-step explanation:

We are given the function:

[tex]f(x) = -2c + cx - x^2[/tex]

And that:

[tex]\displaystyle f^{-1} (5) = -1[/tex]

And we want to determine the value of c.

Recall that by definition of inverse functions:

[tex]\displaystyle \text{If } f(a) = b, \text{ then } f^{-1}(b) = a[/tex]

So, since f⁻¹(5) = -1, then f(-1) = 5.

Substitute:

[tex]f(-1) = 5 = -2c + c(-1) - (-1)^2[/tex]

Simplify:

[tex]5 = -2c - c - (1)[/tex]

Combine like terms:

[tex]6 = -3c[/tex]

And divide. Hence:

[tex]c = -2[/tex]

In conclusion, the value of c is -2.


Related Questions

Determine the intercepts of the line.
y= 10x - 32
y-intercept:
x-intercept:

Answers

Answer:

see below

Step-by-step explanation:

To find the x intercept set y =0 and solve for x

0= 10x - 32

32 = 10x

Divide by 10

3.2 = x

The x intercept

( 3.2,0)

To find the y intercept set x =0 and solve for y

y= 0 - 32

y = -32

( 0, -32)

Answer:

(0, -32)

(3.2, 0)

Step-by-step explanation:

The line is in slope intercept form. It is easy to identify the y-intercept.

[tex]y=mx+b[/tex]

The y-intercept is (0,-32). '-32' replaces the 'b' in the equation.

To find the x-intercept, set the value of 'y' to zero and solve for 'x'.

[tex]0=10x-32\\\\0 + 32 = 10x-32+32\\\\32=10x\\\\\frac{32}{10}=\frac{10x}{10}\\\\\frac{32}{10}=x\\\\\rightarrow \frac{32/2}{10/2}=\frac{16}{5}\\\\ \boxed{x=\frac{16}{5}}[/tex]

The x intercept is (16/5, 0).

This can also be expressed as (3.2, 0).

Hope this helps.

The chance of Jake winning a 100m race is 3/5. What is the probability of him losing the same race​?

Answers

Answer:

2/5 (because the chance winning the race is 3/5 and the remaining is 3/5 when we add 3/5 , 2/5 the answere is 5/5 when we subtract 3/5 from 5/5 the answere is 2/5

help me please I need
[tex] {x}^{2} + 2x + 6 \\ {x}^{2} + 4x + 2[/tex]

Answers

Step-by-step explanation:

SEE THE IMAGE FOR SOLUTION..

hey, can i please get your intro? would you like to be my friend?

Myself Ojasvi

Class 8, 13

India

Solve for p.

19p–2p+16p+12=

18
p=

Answers

Answer:

6

BRAINLIEST, PLEASE!

Step-by-step explanation:

-19p - 2p + 16p + 12 = -18

-5p + 12 = -18

-5p = -30

p = 6

Answer:

p = 6

Step-by-step explanation:

Given

- 19p - 2p + 16p + 12 = - 18 ( simplify left side )

- 5p + 12 = - 18 ( subtract 12 from both sides )

- 5p = - 30 ( divide both sides by - 5 )

p = 6

Which graph represents the given equation?
y
=
NICO
+ 4r – 2

Answers

Equations can be represented on graphs by plotting the corresponding x and y values. The graph of [tex]y = \frac{3}{2}x^2 + 4x - 2[/tex] is option (B).

Given that:

[tex]y = \frac{3}{2}x^2 + 4x - 2[/tex]

First, we check the y intercept of [tex]y = \frac{3}{2}x^2 + 4x - 2[/tex]

This is when [tex]x = 0[/tex]

So, we have:

[tex]y = \frac{3}{2}x^2 + 4x - 2[/tex]

[tex]y = \frac{3}{2} \times 0^2 + 4\times 0 - 2[/tex]

[tex]y = - 2[/tex]

This point is represented as: [tex](0,-2)[/tex]

Next, check the equation when [tex]x = 1[/tex]

So, we have:

[tex]y = \frac{3}{2}x^2 + 4x - 2[/tex]

[tex]y = \frac{3}{2} \times 1^2 + 4\times 1 - 2[/tex]

[tex]y = 3.5[/tex]

This point is represented as: [tex](1,3.5)[/tex]

From the list of given options (see attachment).

Only graph B has the [tex](0,-2)[/tex] and [tex](1,3.5)[/tex] on its curve.

Hence, option (B) is correct.

Read more about equation of graphs at:

https://brainly.com/question/1971145

Answer:

Equations can be represented on graphs by plotting the corresponding x and y values. The graph of is option (B).

Step-by-step explanation:

y intercept is -2y = 3/2x^2 + 4x – 2y = 3/2(0^2) + 4(0) – 2 = -2and x intercepts are0 = 3/2x^2 + 4x – 2aboutx =  0.43050087, -3.09716754

I'm really confused with this plz help

Answers

Answer:

4 terms

constant 10

third term is -7z

coefficient of the second term is 3

Step-by-step explanation:

-5x+3y -7z +10

There are 4 terms, -5x, 3y ,-7x, 10

The constant is the term without the variable ( letter)

The constant is 10

The third term is -7z

The coefficient is the number in front of the variable

The coefficient of the second term 3y is 3

For part a, we are asked how many terms does this expression have.

Well a term can be a number, a variable, or it can

even be a number times one or more variables.

So the terms would be -5x, +3y, -7z, and +10.

For part b, we are asked what is the constant.

Usually, constants are numbers all by themselves.

So here, the constant would be 10.

In part c, we are asked what is the third term.

Well, looking at the expression, we can see that -7z is the third term.

Finally, what is the coefficient of the second term.

The coefficient is the number before your variable.

So here, the coefficient would be 3.

What is the perimeter (in centimeters) of a rectangle with length 4.5 cm and width 8.2 cm

Answers

Answer:

25.4 cm

Step-by-step explanation:

will make it simple and short

2*b + 2*h

2*4.5 + 2*8.2 = 25.4 cm

Hey there! I'm happy to help!

The perimeter is the distance around the rectangle.

In a rectangle, there are two pairs of opposite sides, and those opposite sides are equal. They are known as the length and the width.

In a rectangle, you have two sides that have the same length and two that have the same width. If you add these all up, you get the perimeter.

If our length is L and our width is W, we can write this equation.

P=2L+2W

So, we can plug in our lengths and widths to find the perimeter!

P=2(4.5)+2(8.2)

P=9+16.4

P=25.4

Therefore, our perimeter is 25.4 cm.

Have a wonderful day! Feel free to message me if you have any questions! :D

The cost of milk is modeled by a linear equation where four quarts (one gallon) costs $3.09 while two quarts
(half-gallon) costs $1.65. Write the linear equation that expresses the price in terms of quarts. How much would
an eight-quart container of milk cost?

Answers

Answer:

linear equation to express the price is:

y=0.72x+0.21

An eight quarts will cost :  $5.97

Step-by-step explanation:

linear equation represent y=mx+b

let x=quarts ( x=4, x=2)

y= price (3.09 and y=1.65 )

two points (4,3.09) and (2,1.65)

need to find the slope m:

y2-y1/x2-x1

(1.65-3.09)/(2-4) ⇒ m=0.72

y=0.72x+b  find b at point (2,1.65)

1.65=0.72(2) +b  ⇒ b=0.21

y=0.72x +0.21

check : point (4,3.09)

y=0.72(4) +0.21

y=3.09  ( correct)

An eight quarts will cost :

y=0.72(8)+0.21

y=5.97 dollars

The Cartesian coordinate system can be applied to three-dimensional solids. Instead of two axes, the coordinate system has three. What are the labels? Check all that apply.
A. z
B. y
C. a
D. x
E. w

Answers

Answer:

its z y and x

Step-by-step explanation:

can i pls get brainliest

PlZ HELP NOW ASAP!!!

Answers

Answer:

x=33

Step-by-step explanation:

x for ?

sinx=opposite/hypotenuse

sinx=162.5/298=0.54530201

convert to degrees using arcsin(0.54530201)= 33.043

33 degrees rounded to the nearest ones

Approximate 0.007349 to 3 significant figures​

Answers

Answer:

Hey there!

That would result in 0.00735.

Let me know if this helps :)

Hence, the significant figures are [tex]0.00735.[/tex]

What is the approximation?

An approximation is anything that is similar, but not exactly equal, to something else. A number can be approximated by rounding. A calculation can be approximated by rounding the values within it before performing the operations.

Here given that,

Approximate [tex]0.007349[/tex] to  significant figures​

So, the significant figures are [tex]0.00735.[/tex]

Hence, the significant figures are [tex]0.00735.[/tex]

To know more about the approximation

https://brainly.com/question/29580932

#SPJ2

Boston wheel chair marathon how long would it take to run a 30 mile race

Answers

G all please come to mpu-xcny-did

Solve the equation for x.
5x - ( 4x - 1) = 2
1
a.
C.
1
9
bi
b. - 1
d.
1

Answers

Answer:

x = 1

Step-by-step explanation:

5x - (4x - 1) = 2

Let's get rid of the parenthesis

Multiply whatever is in the parenthesis by -1 since there is a minus sign before it

5x - 4x + 1 = 2

Move common terms to one side, so subtract 1 from both sides

5x - 4x + 1 = 2

           -  1  - 1

5x - 4x = 1

Subtract the 5x by 4x

x = 1

Answer:

x = 1

Step-by-step explanation:

5x - (4x - 1) = 2

5x - 4x + 1 = 2  {Distribute property  (-1) is distributed with 4x  and (-1)}

Combine like terms

x + 1 = 2

Subtract 1 from both sides

x = 2 - 1

x = 1

I need help in this question

Answers

Answer:

C. 12/15

Step-by-step explanation:

2/3, 6/9, and 18/27 all simplify to 2/3. 12/15 does not.

Answer:

C. 12/15

Step-by-step explanation:

As it is mentioned above, the below text is the explanation, if you were here for the answer, it is above.

The question is asking which ratio is not equivalent. To simplify a ratio, divide all of the numbers in the ratio by the same number until they cannot be divided anymore.

So when we look at A. we see that you can not simplify 2/3 anymore. Hence:

A (simplified version): 2/3

When we look at B. we see that the ratio, or fraction, is 6/9. The numerator, or the top number, is 6, while the denominator (the number on the bottom), is 9. The GCF (The greatest common factor, or GCF, is a term used to describe the biggest number that can divide evenly into two or more numbers. Sometimes, this is also referred to as the greatest common divisor, GCD, or highest common factor, or HCF. A factor is a smaller number that can divide evenly into that number) of 6 and 9 is 3. So we divide the numerator and the denominator (both) by 3 to get to 2/3. Hence:

B (simplified version): 2/3

Now, when we look at C. we see that the ratio is 12/15. What is the GCF of 12/15? The GCF is 3. So we divide the numerator and the denominator by 3 to get:

C (simplified version): 4/5

Moving on to D. Let's make it quick. The ratio is 18/27. The GCF is 9. So we divide the numerator and the denominator by 9 to get::

D (simplified version): 2/3

If:

A (simplified version): 2/3

B (simplified version): 2/3

C (simplified version): 4/5

D (simplified version): 2/3

The one fraction that is not equivalent? I'll let you figure that out for yourself!

Hope I was able to help zahrahimran1 (and anyone else)! Have a nice rest of the day!

If f(x) = 2(x − 5), find f(8). 4 6 8 16

Answers

Answer:

f(8) = 6

Step-by-step explanation:

Plug in 8 as x in the function:

f(x) = 2(x − 5)

f(8) = 2(8 - 5)

f(8) = 2(3)

f(8) = 6

Answer:

[tex]\large \boxed{\mathrm{6}}[/tex]

Step-by-step explanation:

[tex]f(x)=2(x-5)[/tex]

Replace x with 8 to find f(8).

[tex]f(8)=2(8-5)[/tex]

Evaluate.

[tex]f(8)=2(3)[/tex]

[tex]f(8)=6[/tex]

Solve for g.
-3+5+ 6g = 11 – 3g
g =​

Answers

Answer:

g = 1

Step-by-step explanation:

-3 + 5 + 6g = 11 - 3g

Move the variables to one side and the numbers to the other:

9g = 9

Simplify:

g = 1

Answer:

g=1

Step-by-step explanation:

-3+5=2

2+6g=8

11-3g=8

makes sense that g will have to be 1

LAST QUESTION TO MY SUMMER HOMEWORK PLEASE HELP 'BRAINLIEST i will give 25 POINTS at ONCE also its a simple question please answer it quickly I thank you very much and will answer a non math question if you would like.

Answers

Answer:

Step-by-step explanation:

here,

132 degree + 54 degree + x + 90 degree = 360 degree ( angles around a point)

therefore ,

x+ 276 degree =360 degree

x = 360-276

x= 84 degree

hope it helps and pls do mark my answer as the brainliest.............

Using the Distributive Property to factorize the equation 3x2 + 24x = 0, you get

Answers

Answer:

3x(x+8)=0

x=0,-8

This is how to solve for x.

Repost because someone answered without actually giving an answer. What is the mode of the data shown in the table? Scores: 5 12 13 18 Frequency: 3 2 5 4 A. 12 B. 51.5 C. 12.5 D. 13

Answers

Answer:

Option (D) : 13

Step-by-step explanation:

Mode is the observation which occurred the most number of time.

Therefore, mode = 13

I need help. What is (-5/3)²

Answers

Answer:

Exact form:

25/9

Decimal form:

2.(7)

Mixed fraction form:

2 7/9

Step-by-step explanation:

Hope you found this helpful

Answer:

(-5/3)² = 25/9

Step-by-step explanation:

(a/b)ⁿ = aⁿ / bⁿ

(-5/3)² = -5² / 3² = 25 / 9

Please please please help

Answers

Answer:

m = 4

Step-by-step explanation:

9/6=6/m

9m = 36

m = 4

How would you write The difference of 9 and the square of a number

Answers

Answer:

9 - n^2

Step-by-step explanation:

Answer: 9-x^2

Step-by-step explanation:

no work needed

HELP IM BEING TIMED!!

Answers

Answer:

Value of x is 8

Step-by-step explanation:

Given:

[tex]\sqrt{\frac{896z^{15}}{225z^6} }=\frac{xz^4}{15} \sqrt{14z}\\\\Computation: \\\\From\ squaring\ both\ side\\\\ {\frac{896z^{15}}{225z^6} }=\frac{x^2z^8}{225} ({14z})\\\\896z^9=14x^2z^9\\\\896=14x^2\\\\64=x^2\\\\x = 8[/tex]

So, Value of x is 8

In the expression 3v - 8, what is the variable a= V b= - c= 3 d= 8

Answers

Answer:

a. v

Step-by-step explanation:

Given

[tex]3v - 8[/tex]

Required

Identify the variable

Literary, variable means things that change in values;

Going by this definition, we have that:

3 -> This is not a variable because its value will always be 3

v -> This is a variable because its value can change once its value changes, the result of the expression will also change

- -> This is not a variable; it is an arithmetic operator to subtract

8 -> This is not a variable because its value will always be 8

Take for instance

[tex]v = 2[/tex]

[tex]3v - 8 = 3 * 2 - 8 = 6 - 8 = -2[/tex]

When [tex]v =5[/tex]

[tex]3v - 8 = 3 * 5 - 8 = 15 - 8 = 7[/tex]

Notice that there's a difference in both results;

This is as a result of v being a variable

HELP HELP HELP Sally can paint a room in 4 hours. Joe can paint a room in 6 hours. How
long will it take if they paint the room together? I’m not sure if it’s 1.4

Answers

Answer:

2 hrs, 24 min

Step-by-step explanation:

Sally:  in one hour, she can paint 1/4 of the room.

Joe: in one our, he can paint 1/6 of the room

Hour one: 1/4+1/6=3/12+2/12=5/12

1÷5/12=1*12/5=12/5

12/5= 2 & 2/5 hours, or 2.4 hours, or 2 hrs 24 minutes

Answer: 2.4 hours

Step-by-step explanation:

1/4 1/6

LCM

3/12+2/12=5/12 repricical 12/5 =2.4

if the morning temperature started at -7 celsius but warmed during the day to 24 celsius . What is the temperature change

Answers

Answer:

31° change

Step-by-step explanation:

If we want to find the change between two numbers, we need to imagine it like a number line.

<-------------0------------->

Let's plot -7 and 24 on this number line.

<----------[tex]-7[/tex]--0------------24>

If we want to get from -7 to 0, we increase by 7. To get from 0 to 24, we increase by 24.

So the total change is [tex]7 + 24 = 31[/tex].

Hope this helped!

What is the relationship between the area of ABCD and the area of EFGH? Quadrilateral ABCD with side measures 18 for AB, 24 for BC; quadrilateral EFGH with side measures 6 for EF, x for FG The ratio of the area of ABCD to the area of EFGH is 1:9. The ratio of the area of ABCD to the area of EFGH is 3:1. The ratio of the area of ABCD to the area of EFGH is 1:3. The ratio of the area of ABCD to the area of EFGH is 9:1.

Answers

Answer:

The ratio of the area of ABCD to the area of EFGH is 9:1.

Step-by-step explanation:

Let us assume that the shapes are rectangles and they are similar. If the two shapes are similar then their sides are in the same proportion. Therefore the ratio of the sides are in the same proportion.

[tex]\frac{AB}{BC}=\frac{EF}{FG}\\ \\\frac{18}{24}=\frac{6}{x}\\\\18x=24*6\\ \\x=\frac{24*6}{18}=8[/tex]

The area of ABCD = AB × BC = 18 × 24 = 432

The area of EFGH = EF × FG = 6 × 8 = 48

The ratio of the area of ABCD to the area of EFGH = Area of ABCD / Area of EFGH = 432 / 48 = 9/1 = 9 : 1

Simplify: 5^(x+2)-4×5^x÷21×5^x​

Answers

Answer:

(1/21)(21×5^(x+2)-4×5^2x)

Step-by-step explanation:

5^(x+2)-4×5^x÷21×5^x

= 5^(x+2)-4×5^2x/21

= 1/21(21×5^(x+2)-4×5^2x)

Theorem 8.9 : The line segment joining the mid-points of two sides of a triangle is parallel to the third side.
prove this theorem

Answers

Answer:

The essence of Mathematics lies in its freedom


What is the volume of the cylinder?
5767 cm3
2887 cm3
967 cm3
1921 cm3

Answers

Calculate the area of the base circle: pigreco • r^2 = 3,14 • (6)^2 = 3.14 • 36 = 113 cm2
Now you have to moltiplicate to the high, so: 113 • 16 = 1808 cm3
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