According to the synthetic division below, which of the following statements are true?

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.

Answer:

C

Step-by-step explanation:

The function C has a range of (-infinity, a] and domain [b, infinity)

Answer:

Find the domain by finding where the equation is defined.

Interval Notation:

(−∞,−4)∪(−4,7)∪(7,∞)

Set-Builder Notation:

{x|x≠−4,7}

Step-by-step explanation:

Answer:

all real numbers except x=-4 or x = 7

Step-by-step explanation:

The domain is the numbers that x can take

We have restrictions for this problem

the denominator cannot be zero

x^2 -3x-28 cannot be zero

(x-7)(x+4) ≠ 0

x-7≠0  x+4≠0

x≠7 x≠-4

Otherwise all real numbers are valid

Answer:

p = 212

Step-by-step explanation:

p-83=129

Add 83 to each side

p-83+83=129+83

p =212

Answer:=212

Step-by-step explanation:

add 83 to both sides and then simplify

−83=129

p-83=129

p−83=129

−83+83=129+83

Answer:

she baked 3 times as many cranberry than blueberry muffins

Step-by-step explanation:

i think that because 9×3=27

the amount of the cranberry muffins are 9

Answer: -78 / 35

Step-by-step explanation:

Given

 2/5 + 3/7 + (-6/5) + (-13/7)

Combine terms that have the same denominator

= 2/5 + (-6/5) + 3/7 + (-13/7)

= -4/5 - 10/7

Convert denominator by Least Common Multiple (LCM)

= (-4 × 7) / (5 × 7) - (10 × 5) / (7 × 5)

= -28/35 - 50/35

= -78 / 35

Hope this helps!! :)

Please let me know if you have any questions

Answer:

[tex] \frac{2}{5} + \frac{3}{7} + ( - \frac{6}{5} ) + ( - \frac{13}{7} ) \\ \frac{2}{5} + \frac{3}{7} - \frac{6}{5} - \frac{13}{7} \\ ( \frac{2}{5} - \frac{6}{5} ) + ( \frac{3}{7} - \frac{13}{7} ) \\ \frac{2 - 6}{5} + \frac{3 - 13}{7} \\ \frac{ - 4}{5} + \frac{ - 10}{7} \\ \frac{ - 4}{5} - \frac{10}{7} \\ \frac{ - 28 - 50}{35} \\ \frac{ - 78}{35} \\ - \frac{78}{35} [/tex]

The equation in point slope form is y - 6 = 2(x + 3)

This is from the general point slope template of [tex]y - y_1 = m(x - x_1)[/tex]

The m is the slope, which in this case is m = 2. The [tex](x_1,y_1)[/tex] is the point the line goes through. In this case, [tex]x_1 = -3 \text{ and } y_1 = 6[/tex]

If you were to solve that equation in bold for y, then you should get y = 2x+12 which is now in y = mx+b form, aka slope intercept form.

Answer:

90

Step-by-step explanation:

To solve this problem we need to set up an expression

35x+20

35 is the cost per hour, and 20 dollars is the visit fee.

x is the amount of hours the CT can work

So if we plug in the amount for the number of hours from the problem we get

35(2)+20

Which becomes 70+20 which is 90.

Hope thsi helps!

The computer technician works for 2 hours will take total charges equal to $90 .

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7

According to the question

The computer technician charges $20 per visit plus $35 per hour.

i.e

Let hours he work = x

therefore,

Total charge of computer technician in equation = 20 +  35x  

Now,

As the computer technician works for 2 hours the cost will be

By using equation

Total charge of computer technician in dollars  = 20 + 35x  

where x = 2

so,

= 20 +  35*2  

= $90  

Hence, the computer technician works for 2 hours will take total charges equal to $90 .  

To know more about equation here:

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Answer:

hello,

answer C

Step-by-step explanation:

area of the rectangle=2b*b=2b²

area of the half cercle= [tex]\\\dfrac{\pi*(\frac{c}{2})^2}{2} =\dfrac{\pi*c^2}{8} \\[/tex]

Area in blue= 2b²-πc²/8

Answer:

The measure of angle JKM is:

JKL - MKL = JKM

⇒80°-25°=55°

so measure of angle JKM is 55°

Step-by-step explanation:

Answer:

Step-by-step explanation:

757 minutes = 12 hours 37 minutes

Answer:

Multiply 800 by 1.022^7 because 1.022^(n-1)

Step-by-step explanation:

Series and sequences.

Answer:

B. 7y - 15

Step-by-step explanation:

Simplifying

10y + -3(y + 5) = 0

Reorder the terms:

10y + -3(5 + y) = 0

10y + (5 * -3 + y * -3) = 0

10y + (-15 + -3y) = 0

Reorder the terms:

-15 + 10y + -3y = 0

Combine like terms: 10y + -3y = 7y

-15 + 7y = 0

Solving

-15 + 7y = 0

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '15' to each side of the equation.

-15 + 15 + 7y = 0 + 15

Combine like terms: -15 + 15 = 0

0 + 7y = 0 + 15

7y = 0 + 15

Combine like terms: 0 + 15 = 15

7y = 15

Divide each side by '7'.

y = 2.142857143

Simplifying

y = 2.142857143

Answer:

b. 7y-15

Step-by-step explanation:

First, write out the expression

1. [tex]10y-3(y+5)[/tex]

To simplify the expression distribute the -3 to the terms within the paratheses.

2. [tex]10y-3y-15[/tex]

Then, combine like terms to simplify further. Since 10y and -3y are like terms they can be subtracted

3. [tex]7y-15[/tex]

This means that B is the correct answer.

The depth of the mirror of the cross-section of a searchlight would be 8.33 cm if the light bub has a vertex at 3 cm and the mirror is 20 centimeters across at the origin.

A cross-section is perpendicular to the axis of the symmetry goes through the vertex of the parabola. The cross-sectional shape of the mirrored section of most searchlights or spotlights is parabolic.

Given:

a = 3

y = [tex]\frac{20}{2}[/tex] cm = 10 cm

Solution:

from the equation [tex]y^{2} = 4ax[/tex]

[tex]y^{2} = 4*3*x\\ y^{2} = 12x[/tex]

putting x, 10 cm in the equation

[tex]x=\frac{10^{2} }{12} \\\\x= \frac{100}{12} \\\\x= 8.33 cm[/tex]

thus, the depth of the mirror would be - 8.33 cm

Learn more about other problems of the parabola:

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Answer:

see below

Step-by-step explanation:

2^30

-------

8^9

Rewriting

8^9

2^3 ^ 9

We know a^b^c = a^(b*c)

2^(3*9) = 2^27

2^30

-------

2^27

We know a^b / a^c = a^(b-c)

2^(30-27) = 2^3

Assuming you mean 2^x

2^3 = 2^x

x=3

If you mean 2x

2^3 = 8

8 = 2x

Divide by 2

4 =x

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{\dfrac{2^{30}}{8^9}=2x}[/tex]

[tex]\mathsf{2^{30}}\\\mathsf{= \bf 1,073,741,824}\\\\\mathsf{8^9}\\\mathsf{= \bf 134,217,728}[/tex]

[tex]\mathsf{\rightarrow \dfrac{1,073,741,824}{134,217,728}= 2x}\\\\\\\mathsf{\dfrac{1,073,741,824}{134,217,728}= \bf 8}\\\\\\\mathsf{\rightarrow \ 8 = 2x}\\\\\\\\\large\textsf{TURN\ the\ EQUATION\ around}\\\\\\\mathsf{\rightarrow\ 2x = 8}\\\\\\\large\textsf{DIVIDE 2 to BOTH SIDES}\\\\\\\mathsf{\dfrac{2x}{2}=\dfrac{8}{2}}\\\\\\\large\textsf{CANCEL out: }\mathsf{\dfrac{2}{2}}\large\textsf{ because it gives you 1}\\\\\\\large\textsf{KEEP: }\mathsf{\dfrac{8}{2}}\large\textsf{ because it gives you the answer of x}[/tex]

[tex]\mathsf{x = \dfrac{8}{2}}\\\\\\\mathsf{x = 8\div 2}\\\\\\\mathsf{x = \bf 4}\\\\\\\\\\\boxed{\boxed{\huge\text{Therefore, your answer is: \textsf{x = 4}}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

(I'll leave cm out to save space and time in the answer)

the perimeter is 500, there are 5 sides. so on average a side will be 100.

that's already the important key idea.

it's indeed 100 for the third side, the second will be 10 less, the fourth 10 more (making the 2and and the 4th side 200 in sum, and therefore still 100 on average).

repeat this for the 1. and 5. side and we get:

80

90

100

110

120

Answer:

-13 1/2 < -6/8

Step-by-step explanation:

*Any negative in either the numerator or denominator will make the entire fraction negative.

1/2  = .5

-13 1/2 = -13.5

-6/8 = -3/4

-3/4 = -0.75

-6/8 = -0.75

-13 1/2 = -13.5

Which means:

-13 1/2 < -6/8

Hope this helped.

Answer:

[tex] < [/tex]

Step-by-step explanation:

[tex] \frac{6}{8} [/tex]

Is close to 0 (to positive) you can use a time line to determine which is a correct answer

Answer:

37.5%

Step-by-step explanation:

150/450 = .375 = 37.5%

The percentage is 150 grams out of 400 grams will be 37.5%.

The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol '%' is used to symbolize it.

The percentage is given as,

Percentage (P) = [Initial value - Final value] / Initial value x 100

It is given that the difference between the initial and final value is 15 grams and the initial value is 400 grams.

Then the percentage is 150 grams out of 400 grams will be

P = (150 / 400) x 100

P = 0.375 x 100

P = 37.5%

Thus, the percentage is 150 grams out of 400 grams will be 37.5%.

More about the percentage link is given below.

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Answer:

a + b =1

Step-by-step explanation:

Write the given quadratic as x^2 – 1x – 90 = 0.  This factors into

(x - 10)(x + 9) = 0, and so the roots/solutions are {-9, 10}.

If we call -9 "a" and 10 "b," then the sum a + b is -9 + 10, or a + b =1.

Answer:

c

Step-by-step explanation:

come on ! you can literally see that in the chart.

how many parts of the gray 3/8 are covered by the gray 1/4 ?

2 parts = 2/8 are clearly covered by 1/4.

2/8 is what part of 3/8 ?

it is the same question as "2 is what part of 3" ?

is 2 a quarter (1/4) of 3 ? no, 1/4×3 = 3/4 and not 2.

is 2 one third (1/3) of 3 ? no, 1/3 of 3 = 1/3×3 = 1 and not 2.

is 2 two thirds (2/3) of 3 ? ah, 2/3 × 3 = 2. that is correct !

is 2 three quarters (3/4) of 3 ? no, 3/4×3 = 9/4 and not 2.

once you have the same denominator, you can easily compare the numerators and ignore the denominators for such problems.

Answer:

[tex]we \: know \: that \: commutative \: prop \\ = x + y = y + x \\ then \\ 4xy + 0 = 0 + 4xy \\ thank \: you[/tex]

Answer:

B

Step-by-step explanation:

here we use trigonometric ratio involving soh,cah,toa

Answer:

22 m/s

Step-by-step explanation:

Take the distance and divide by the time

1210 m/55s

22 m/s

Answer:

Step-by-step explanation:

[tex]speed = \frac{distantce}{time} \\ = \frac{1210m}{55s} \\ = 22m {s}^{ - 1} [/tex]

Answer:

x=1

Step-by-step explanation:

3x+9 = 12

Subtract 9 from each side

3x+9-9=12-9

3x = 3

Divide by 3

3x/3 = 3/3

x=1

Hi there!  

»»————-　★　————-««

I believe your answer is:  

[tex]x = 1[/tex]

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\boxed{\text{Calculating the answer...}}\\\\3x + 9 = 12\\-------------\\\rightarrow 3x + 9 - 9 = 12 - 9\\\\\rightarrow 3x = 3\\\\\rightarrow \frac{3x=3}{3}\\\\\rightarrow \boxed{x=1}[/tex]

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

wyatt

Step-by-step explanation:

4:30 mins is 270 seconds

On the last option, since you can substitute y=3x+1 into the other equations to solve for x.