34. Find the average rate of change for x 0.5 to 35 for the following temperatures in degrees Fahrenheit
recorded beginning at noon. Also interpret the meaning of x = 3.5.

Rational root theorems are used to determine the potential roots of a polynomial function

The function is given as:

[tex]f(x) = 2x^2 + 2x - 24[/tex]

Expand

[tex]f(x) = 2x^2 + 8x - 6x - 24[/tex]

Expand

[tex]f(x) = 2x(x + 4) - 6(x + 4)[/tex]

Factor out x + 4

[tex]f(x) = (2x -6)(x + 4)[/tex]

Set to 0

[tex](2x -6)(x + 4) = 0[/tex]

Split

[tex](2x -6) = 0\ or\ (x + 4) = 0[/tex]

Make x the subject in both cases

[tex]2x = 6\ or\ x= -4[/tex]

Solve for x

[tex]x = 3\ or\ x= -4[/tex]

So, the actual roots are 3 and -4

Recall that, the function is:

[tex]f(x) = 2x^2 + 2x - 24[/tex]

For a function,

[tex]f(x) = px^n + ax^{n-1} +.......+q[/tex]

According to rational root theorem, the roots of f(x) are:

[tex]Roots = \pm \frac{Factors\ of\ q}{Factors\ of\ p}[/tex]

The roots of 24 are:

[tex]24 = \pm1, \pm2, \pm 3, \pm 4, \pm 6, \pm 8, \pm12,\pm 24[/tex]

The roots of 2 are:

[tex]2 = \pm1, \pm2[/tex]

So, the possible roots are:

[tex]Roots = \frac{\pm1, \pm2, \pm 3, \pm 4, \pm 6, \pm 8, \pm12,\pm 24}{\pm 1, \pm 2}[/tex]

This gives:

[tex]Roots = \pm1, \pm2, \pm 3, \pm 4, \pm 6, \pm 8, \pm12,\pm 24,\pm0.5, \pm1, \pm 1.5, \pm 2, \pm 3, \pm 4, \pm6\pm 12[/tex]

Remove repetitions

[tex]Roots = \pm0.5, \pm1, \pm 1.5, \pm2, \pm 3, \pm 4, \pm 6, \pm 8, \pm12,\pm 24[/tex]

Read more about rational root theorem at:

https://brainly.com/question/11015301

3 and -4 dudes and dudettes

edg2022

Step-by-step explanation:

-8 - 6x < 1

Bringing like terms on one side

-6x < 1 + 8

-6x < 9

x < 9/-6

x < 3/-2

I think the correct answer is none

Answer:

  a. 3942 kWh

  b. $473.04

  c. 1314 kWh

  d. $157.68

Step-by-step explanation:

There are 1000 W in 1 kW, so 450 W = 0.450 kW. The energy used per day is ...

  (0.45 kW)(24 h) = 10.8 kWh . . . . energy per day

Then in a 365-day year, the energy used is

  (365 da/yr)(10.8 kWh/da) = 3942 kWh/yr

__

At the rate of $0.12/kWh, the cost of running the pump is ...

  ($0.12/kWh)(3942 kWh/yr) = $473.04/yr

__

Switching the pump off for 1/3 of the time will save 1/3 of the energy found in part (a):

  1/3(3942 kWh) = 1314 kWh . . . . energy saved by switching off the pump

__

The savings will be 1/3 of the cost of running the pump full time:

  1/3($473.04/yr) = $157.68/yr

Answer: It is 0.73 my friend. Very good work.

Step-by-step explanation:

The answer is for this question is A

Answer:

Step-by-step explanation:

4x = 3yz^2

4x/3y = z^2

To undo an exponent you root it.

[tex]\sqrt{4x/3y} = z[/tex]

I believe this is it. you basically just have to divide by the numbers to get z by itself. If you have any questions please comment.

Answer:

171,254

Step-by-step explanation:

calculate it

------------------------

Answer:

y = 1/2x - 1

slope = 1/2

y-intercept is

(0,-1)

Answer:

3hrs 15 minutes

Step-by-step explanation:

10:45

-07:30

------------

03:15

------------

Step-by-step explanation:

given, ¾-½= ¼gallon milk.

hope this helps you.

Answer:

$30

Step-by-step explanation:

Over 5 years she will have been paid $30 in interest. To find the amount of interest first find the total amount the account has after 5 years. The formula for simple interest is A=P(1+rt). Where A is the total amount, P is the principal (initial amount), r is the rate in decimal form, and t is the time in years.

Plug in the values to solve, A=200(1+0.03*5). Then, simplify to get A=230. Finally, to get only the interest, I, use the formula A-P=I. So, 230-200=30. Therefore, the interest Leila earned was 30 dollars.

Answer:

do u even still need the answer its been aweek since you asked it and it was due that same day

Step-by-step explanation:

Answer:

All of them are equal to 2.427

Step-by-step explanation:

A = 2.427

B = 2.427

C = 2.427

D = 2.427

Answer:

jjjjStep-by-step explanation:

Answer:

3x+8=17                                  2x+8=2(x+4)                         x+4=x-4

3x=17-8                                    2x+8=2x+8                          No solution

3x/3=9/3                                  All Real numbers

x= 3                                                

infinitely many solution

Q2) It means this equation  has no answer to it and no solution

Q3)  x+ 4=x-4 has no solution

Q4) It means that it has many answers to it and many steps to it to get the answer

Q5) By doing the answer for example 3x+9=17 it has many solutions and we can get the answer by

Answer:

The first 10 digits of pi (π) are 3.1415926535. The first million digits of pi (π) are below, got a good memory? Then recite as many digits as you can in 30 ...

Step-by-step explanation:

Answer:

12, or if its yearly, 48.

Answer:

$140

Step-by-step explanation:

Total Amount of chocolate = 100 Pounds

Amount of chocolate in one box = 1 1/4 Pounds =  5/4 Pounds

Number of boxes = 100/(5/4) = 80 boxes

Cost of one box = $1.75

Total selling price = 80×1.75 = 140

The total selling price for all the boxes of chocolate is $140

Answer: $140

Step-by-step explanation:

Convert

1 1/4 --> 1.25

Solve

100/1.25= 80

80*1.75= $140

Answer: Associative property

Answer:

yes

Step-by-step explanation:

its D

Proof:-

In ∆XYZ and ∆VWZ

[tex]\because\sf\begin{cases}\sf XZ\cong VZ(Given)\\ \sf YZ\cong WZ(Given)\\ \sf <XZY\cong <WZV(Opposite angles)\end{cases}[/tex]

Hence

∆XYZ[tex]\cong[/tex]∆VWZ(Side-Angle-Side)

The equilibrium constant of the reaction is 0.0030.

The equation of the reaction is given as;

N2(g) + 3H2(g) ⇆ 2NH3 (g)

We have the following information at equilibrium;

[NH3] = 0.105 M

[N2] = 1.1 M

[H2] = 1.50 M

Hence, we can calculate the equilibrium constant using the relation;

K = [NH3]^2/ [N2]  [H2]^3

Substituting values;

K = [0.105]^2/[ 1.1] [1.50]^3

K =0.011025 /3.7125

K= 0.0030

Learn more: https://brainly.com/question/17960050

Answer:

I think it;s 9.8

Step-by-step explanation:

You divide 35 and 28 i think

Answer:

Part A: The scale factor of the dilation that transforms Triangle PQR to Triangle P'Q'R' is 1/4

Part B:

P''(-1, 0)

Q''(0, -1)

R''(2, -1)

Part C:

The two Triangles PQR and P''Q''R'' are not congruent.

Answer: There are no solutions

Answer:

Two

Step-by-step explanation:

x^2 = 4x - 5 is equivalent to x^2 - 4x + 5 = 0 in standard quadratic form.

All quadratics have exactly two roots/solutions.

In this case the coefficients of the polynomial are 1, -4 and 5, and so the discriminant is b^2 - 4ac, or (-4)^2 - 4(1)(5), or 16 - 20 = -4.

Since the discriminant is negative, we conclude that this polynomial has two complex roots/solutions.

Answer: 0.04 is exactly 10 times as much as 0.004. If we multiply 0.004 by 10, we will get 0.04 as an answer. In other words, we can say that 0.004 is exactly 1/10th of 0.04. It means that if we divide 0.04 by 10, we will get 0.004 as an answer.

Answer:

Look below

Step-by-step explanation:

0.04 means 4 hundredths since if you divide 4 by 100 you get 0.04. You can try it yourself on a calculator. 0.004 is 4 thousandths. Same thing with 0.04, if you divide 4 by 1000 you will get 0.004. Hope this helps! If you want me to explain a bit more I can try

Answer:

Step-by-step explanation:

1. 4x° + 4x° + 4x° = 180° ( The sum of all interior angles of any triangle is equal to 180° )

[tex]4x + 4x + 4x = 180 \\ 12x = 180 \\ x = \frac{180}{12} \\ x = {15}^{o} \\ [/tex]

4x° + 4x° = y° ( An exterior angle of a triangle is equal to the sum of its two interior opposite angles. )

[tex]4x + 4x = y \\ 4(15) + 4(15) = y \\ 60 + 60 = y \\ {120}^{o} = y[/tex]

2. y° + 60° + 60° = 180° ( The sum of all interior angles of any triangle is equal to 180° )

[tex]y + 60 + 60 = 180 \\ y + 120 = 180 \\ y = 180 - 120 \\ y = {60}^{o} \\ [/tex]

All three internal angles are also congruent to each other and are each 60°. Therefore this is a equilateral triangle.

Perimeter = 4x + 4x + 4x ( An equilateral triangle is a triangle with all three sides of equal length. )

[tex]54 = 4x + 4x + 4x \\ 54 = 12x \\ \frac{54}{12} = x \\ x = 4.5[/tex]

Answer:

 8A + 11A  = A(19)

Step-by-step explanation:

   8A + 11A

 = A(8 + 11)                      Factor out the common factor A

= A(19)

Answer:

X=4

Step-by-step explanation:

28−(3x+4)=2(x+6)+x

28+−1(3x+4)=2(x+6)+x(Distribute the Negative Sign)

28+−1(3x)+(−1)(4)=2(x+6)+x

28+−3x+−4=2(x+6)+x

28+−3x+−4=(2)(x)+(2)(6)+x(Distribute)

28+−3x+−4=2x+12+x

(−3x)+(28+−4)=(2x+x)+(12)(Combine Like Terms)

−3x+24=3x+12

−3x+24=3x+12

Step 2: Subtract 3x from both sides.

−3x+24−3x=3x+12−3x

−6x+24=12

Step 3: Subtract 24 from both sides.

−6x+24−24=12−24

−6x=−12

Step 4: Divide both sides by -6.

−6x

−6

=

−12

−6

x=2

Answer:

x = 2

Step-by-step explanation:

28 - 3x + 4 = 2x + 12 + x

24 - 3x = 3x + 12

     + 3x   +3x

24 = 6x + 12

-12          -12

12 = 6x

x = 2

What do you mean? What’s the question?

Answer:

Unknown

Step-by-step explanation:

Question, not provided.