Does this table represent a function? Why or why not?
X
у
2.
1
3
4.
4
4
5
2
5
5

Answer:

Jenn runs faster at 9 minutes/mile.

Step-by-step explanation:

Jana runs 3 miles in 1/3 hour.

1/3 hour is equivalent to 1/3*60 = 20 minutes

The ratio time/distance is the reciprocal of the speed and is greater as the speed is lower and vice-versa.

This ratio for Jana is 20/3=16.7 minutes/mile

As for Jenn, she runs 5 miles in 3/4 hour.

3/4 hour is equivalent to 3/4*60=45 minutes

The ratio time/distance is 45/5=9 minutes/mile

Since Jenn has a lower ration, her speed is greater than Jana's, thus Jenn runs faster.

Answer:

[tex]\mathbf{y(x) = \dfrac{(c_1 + c_2) \ cos (x)}{e^{6x} }+ \dfrac{i(c_1 -c_2) \ sin (x)}{e^{6x}}+ c_3e^{3\ x}}[/tex]

Step-by-step explanation:

The objective of this question is to solve:

[tex]\dfrac{dy(x)}{dx}+ 9\dfrac{d^2y(dx)}{dx^2}+\dfrac{d^3y(x)}{dx^3}-111y(x) = 0 :[/tex]

Suppose the general solution is proportional to [tex]e^{\lambda x}[/tex] for [tex]\lambda[/tex] is constant; Then:

Let's replace [tex]y(x) = e^{\lambda\ x}[/tex] into the above equation:

i.e.

[tex]\dfrac{d^3}{dx^3}(e ^{\lambda x} )+ 9 \dfrac{d^2}{dx^2}(e ^{\lambda x} ) + \dfrac{d}{dx}(e ^{\lambda x} )- 111 \ e ^{\lambda x} = 0[/tex]

To Replace:

[tex]\dfrac{d^3}{dx^3}(e ^{\lambda x} )[/tex] with [tex]\lambda^3 e ^{\lambda x }[/tex]

[tex]\dfrac{d^2}{dx^2}(e ^{\lambda x} ) \ with \ \lambda^2 e^{\lambda\ x}[/tex]

[tex]\dfrac{d}{dx}(e ^{\lambda x} ) \ with \ \lambda e ^{\lambda \ x}[/tex]

Thus;

[tex]\lambda^3 e ^{\lambda x }[/tex] + [tex]9 \lambda^2 e^{\lambda\ x}[/tex] + [tex]\lambda e ^{\lambda \ x}[/tex] - 111 [tex]e ^{\lambda \ x}[/tex] = 0

[tex]e ^{\lambda \ x} (\lambda ^3 + 9 \lambda ^2 + \lambda - 111 )= 0[/tex]

∴

In as much as [tex]e^{ \lambda x}\neq 0[/tex] for any finite [tex]\lambda[/tex]; Then:

[tex]\lambda ^3 + 9 \lambda ^2 + 111 = 0[/tex]

By Factorization:

[tex](\lambda - 3) ( \lambda ^2 + 12 \lambda + 37) = 0[/tex]

[tex]\lambda = -6 + i \ or\ \lambda = -6 - i \ or \ \lambda = 3[/tex]

However;

The root [tex]\lambda = -6 \pm i[/tex] yield;

[tex]y_1 = (x) = c_1 e ^ {(-6+i)x}[/tex]

[tex]y_2 (x) = c_2e^{(-6-i)x}[/tex]

The root [tex]\lambda = 3[/tex] yield;

[tex]y_3(x) = c_3 e^{3x}[/tex]

∴

The general solution is:

[tex]y(x) = y_1(x) + y_2(x) + y_3(x) = \dfrac{c_1}{c^{(6-i)}x}+\dfrac{c_2}{c^{(6+i)}x}+ c_3e^{3x}[/tex]

Using Euler's Identity ;

[tex]e^{\alpha+i \beta} = e^\alpha \ cos (\beta ) + i \ e^\alpha \ sin ( \beta)[/tex]

[tex]y(x) = c_1 ( \dfrac{cos (x) }{e^{6x}}+ \dfrac{i \ sin x }{e^{6x} }) + c_2 ( \dfrac{cos (x)}{e^{6x}}- \dfrac{-i \ sin (x)}{e^{6x}})+c_3 e^{3x}[/tex]

[tex]\mathbf{y(x) = \dfrac{(c_1 + c_2) \ cos (x)}{e^{6x} }+ \dfrac{i(c_1 -c_2) \ sin (x)}{e^{6x}}+ c_3e^{3\ x}}[/tex]

Answer:

How to Easily Calculate the Serving Size in Recipes

Weigh the Food. Before you can accurately divide your recipe into servings, you need to know how much it weighs in total. ...

Divide the Recipe into Servings. ...

Calculate Calories. ...

Save the Information.

Step-by-step explanation:

1280 cones because you would add 60 +4 and multiply by 20, and would get 1280 cones.

Answer:

-4( 3a+4)

Step-by-step explanation:

-12a - 16

-4*3a -4*4

Factor out a -4

-4( 3a+4)

Answer:

The answer is 11

hence 5 + 6 = 11

Answer:

hi

Step-by-step explanation:

[tex]5 + 3(2) = 11[/tex]

probably…

Answer: 19 months

Step-by-step explanation:

given data:

amount paid initially when joining the club = $50.

monthly payments made = $10.

total amount paid since joining the club = $240.

Solution:

= 10X + 50 = 240

collect like terms

= 10X = 240 – 50

10X = 190

divide both sides by 10

10X/10 = 190/10

X = 19

isabella has been a member of the club for 19 months.

Answer:

Step-by-step explanation:

13/16 dived by 5/6 = 9/40

7 dived by 1/6 = 42

2 1/5 dived by 1 1/3 = 1 13/20

2 1/7 dived by 3/28 = 20

9514 1404 393

Answer:

  y = x +7

Step-by-step explanation:

The slope of the given line can be found as ...

  m = (y2 -y1)/(x2 -x1)

  m = (3 -7)/(-1 -3) = -4/-4 = 1

Then the point-slope form of the equation for the desired line is ...

  y -k = m(x -h) . . . . . . line with slope m through point (h, k)

  y - 9 = 1(x -2)

  y = x -2 +9

  y = x + 7 . . . . slope-intercept form

__

The attachment shows a graphing application that will write the equation of the line. Here, it shows the desired line has the equation ...

  x -y = -7 . . . . desired line equation in standard form

Answer:

21.97025026/250

Answer:

38 units.

Step-by-step explanation:

Perimeter of the polygon EFGHJK = 38 unit

Perimeter of a shape is defined as the total length of its boundary. The perimeter of a shape is determined by adding the length of all the sides and edges enclosing the shape. It is measured in linear units of measurement like centimeters, meters, inches, or feet.

Given,

In graph of polygon EFGHJK

EF = 2 unit

FG = 10 unit

GH = 9 unit

HJ = 8 unit

JK = 7 unit

KE = 2 unit

Perimeter of EFGHJK = EF + FG + GH + HJ + JK + KE

                                    = 2 + 10 + 9 + 8 + 7 + 2

                                    = 38 unit

Hence, 38 unit is the measure of perimeter of polygon EFGHJK.

Learn more about perimeter here:

https://brainly.com/question/6465134

#SPJ2

Answer:

x=20°

Step-by-step explanation:

1.) m<DOB = m<DOE + m<BOE (or m<EOB)    

2.) m<DOB = 90°+x

3.) m<AOC = m<DOB

4.) 110° = 90° + x

5.) x = 20°

1.) given

2.) substitution

3.) vertical/reflexive

4.) substitution

5.) algebra

Answer:

3

Step-by-step explanation:

You just divide 27 by 3, then divide that answer by 3, and keep doing that until you get to 1:

27/3

9

9/3

3

3/3

1

3^x = 27

3^3 = 27

3 x 3 x 3 = 27

9 x 3 = 27

27 =27

Answer:

x=12

Step-by-step explanation:

multiply 2 from both sides to isolate x

then u should end up with 1x=12

Answer: It has one solution (8, 2).

Step-by-step explanation:

I put both equations in Desmos and the solution was (8,2)

Answer:

x = 39

Step-by-step explanation:

A circle is made up of 360 degrees

235+ 54+ x+32 = 360

Combine like terms

x+321=360

Subtract 321 from each side

x+321-321 = 360-321

x = 39

Answer:

2.35 hamburgers

Step-by-step explanation:

H6.25 + H18.75 = 58.75

Answer:

bout 7

Step-by-step explanation:

Answer:3.049533e+44 to be exact

Step-by-step explanation:

Answer:

I not see the number 2

I think that is number 2

Answer:

first and last one should be the answer (not sure about the first, cant see it too good)

Answer:

269.75

Hope this helps:)

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

Following PEMDAS you would do the equation in the parentheses first.

1 - 15 = -14

13 - 2  ⋅ (-14) divided by 14

-2 ⋅ (-14) = 28

13 + 28 divided by 14

28 divided by 14 = 2

13 + 2 = 15

Your answer is 15

Hope I helped :)

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Answer:

-

Step-by-step explanation:

I took the test

The correct operator that enters a circle is a subtraction sign.

Given the expressions

[tex](4x^5-8x) ()(3x^2-8x+9)[/tex]

We need to know which sign goes into the bracket that will give a trinomial when simplified.

A trinomial is a function containing 3-terms.

Using the subtraction sign.

[tex](4x^5-8x) - (3x^2-8x+9)[/tex]

Expand

[tex]= 4x^5-8x - 3x^2+8x-9\\= 4x^5-3x^2-8x+8x-9\\=4x^5-3x^2+0-9\\=4x^5-3x^2-9[/tex]

Since the resulting term is a trinomial (3 terms), hence the correct operator that enters a circle is a subtraction sign.

Learn more here: https://brainly.com/question/1320408

Answer:

-3.21

Step-by-step explanation:

If you pay close attention the numbers are 5 points away from each other, so after -3.2 is -3.21! Hope that helped love :)

Answer:

f(x) = x2 – p(x + 1) – c, then (α + 1)(β + 1)f(x) = x2 – p(x + 1) – c, then (α + 1)(β + 1)f(x) = x2 – p(x + 1) – c, then (α + 1)(β + 1)f(x) = x2 – p(x + 1) – c, then (α + 1)(β + 1)f(x) = x2 – p(x + 1) – c, then (α + 1)(β + 1)f(x) = x2 – p(x + 1) – c, then (α + 1)(β + 1)

Step-by-step explanation: