Trudy bought a $20 prepaid long distance phone card. for every minute that she talks, $0.25 is deducted from her card. The function f(m)=20-0.25m represents the amount of money f(m) she has left after talking m minutes.FInd the zero and explain what it means in the context of the situation.

Answer:

1,360,000

Step-by-step explanation:

1,700,000-340,000 = 1,360,000 or 1.36×10^5

Answer:

x=76

Step-by-step explanation:

-4(x - 26) = -200

x-26=50

x=50+26

x=76

I hope this helped you! If it did, please consider rating, pressing thanks, and giving my answer 'Brainliest.' Have a great day! :)

Step-by-step explanation:

-4x+104=-200

-4x=-200-104

-4x=-304

x=-304÷(-4)

×=76

===============================================

Work Shown:

Let

g(x) = ax^3 + 2

h(x) = bx^2 + 1

Plug x = 1/2 into each function

g(x) = ax^3 + 2

g(1/2) = a(1/2)^3 + 2

g(1/2) = (1/8)a + 2

and

h(x) = bx^2 + 1

h(1/2) = b(1/2)^2 + 1

h(1/2) = (1/4)b + 1

In order for f(x) to be differentiable at x = 1/2, the function f(x) must be continuous at x = 1/2. If we had a jump discontinuity here, then there is no way the function is differentiable here.

f(x) is continuous at x = 1/2 when g(1/2) = h(1/2).

This means,

g(1/2) = h(1/2)

(1/8)a + 2 = (1/4)b + 1

8*[(1/8)a + 2] = 8*[(1/4)b + 1]

a+16 = 2b+8

a = 2b+8-16

a = 2b-8

We'll keep this in mind for later.

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

Now let's compute the derivatives

g(x) = ax^3 + 2

g ' (x) = 3ax^2

h(x) = bx^2 + 1

h ' (x) = 2bx

Now plug in x = 1/2

g ' (x) = 3ax^2

g ' (1/2) = 3a(1/2)^2

g ' (1/2) = (3/4)a

and

h ' (x) = 2bx

h ' (1/2) = 2b(1/2)

h ' (1/2) = b

Equate the two items. We do so because we want f(x) to be differentiable at x = 1/2, so that means g ' (1/2) = h ' (1/2)

So,

g ' (1/2) = h ' (1/2)

(3/4)a = b

3a = 4b

a = (4b)/3

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

Earlier we found a = 2b-8.

Since both a = 2b-8 and a = (4b)/3, this means we can equate the right hand sides to solve for b

2b-8 = (4b)/3

3*(2b-8) = 3*(4b)/3

6b-24 = 4b

6b-4b = 24

2b = 24

b = 24/2

b = 12

Which leads to

a = 4b/3

a = 4*12/3

a = 48/3

a = 16

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

The piecewise function

[tex]f(x) = \begin{cases}ax^3+2, \ \ x < \frac{1}{2}\\bx^2+1, \ \ x \ge \frac{1}{2}\end{cases}[/tex]

will update to

[tex]f(x) = \begin{cases}16x^3+2, \ \ x < \frac{1}{2}\\12x^2+1, \ \ x \ge \frac{1}{2}\end{cases}[/tex]

To verify f(x) is differentiable at x = 1/2, you should check to see if both pieces evaluate to the same output when you plug in x = 1/2. In other words, you should check to see if g(1/2) = h(1/2).

Also, you should check to see if g ' (1/2) = h ' (1/2) so that f(x) is fully differentiable here. I'll let you do the check portions.

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

After getting our a and b values, we can finally say that

a+b = 16+12 = 28

Answer:

The locus of the moving end of the minute hand of the clock will be a circle where radius will be the length of the minute hand

Answer:

A

Step-by-step explanation:

slope is (y2-y1)/(x2-x1)

anyhow that comes out to -3/2

the only place that actually applies is in A

Answer:

A

Step-by-step explanation:

6=-3/2×-2+3

6=3+3

6=6

-3=-3/2×4 + 3

-3=-6+3

-3=-3

Answer:

REEEEEEEEEEEE

Step-by-step explanation:

===========================================================

This equation is written in slope-intercept form, which looks like so:-

[tex]\bigstar{\boxed{y=mx+b}[/tex]

where

m is the slope

b is the y-intercept

Now, what is the slope?

Hint:- The slope is the coefficient of x, and the y-intercept is the constant.

That's right! The slope is 3, and the y-intercept is -4.

=========================================================

Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I will comment and/or edit my answer :)

Answer:

y=55x+160

Step-by-step explanation:

i might be wrong, but i think it would be y=55x+160

Answer:

y=55x+160

Step-by-step explanation:

she starts at 160 mi which is like your y-intercept so the "b" in y=mx+b. the slope or "m" would be 55 because thats how much she's travelling per 1 x or 1 hour

Answer:

First, collect the like terms

36x+34x=180+2-2

Solve,

74x=180

x=180/74

2.43243243243

When you round it, it will be approximately,

x≅2.43

Step-by-step explanation:

I hope it helped please give me brainliest

Answer:

[tex]x = \frac{18}{7} [/tex]

Answer:

0

Step-by-step explanation:

Because there are two negatives of the same number, we can instantly know that this would be 0.

Answer: 0

on this one it can’t be undefined so put 0 and you will get it correct

Answer:

Step-by-step explanation:

Yes plzz give me brainliest

Answer:

if he leave at 2pm 45 miles in the first hr is the correct answer 3 pm

Step-by-step explanation:

Answer:

0.91

Step-by-step explanation:

Answer:

I would say B

Step-by-step explanation:

Some inland areas can be warm but cold where-as some places near the coast stay warm most of the time

Answer:

x=90

Step-by-step explanation:

it is a square so: 360/4=90

Answer:

The largest size of the teams would be 6 if you wanted all teams to be the same size and consist of only members from their own room.

Step-by-step explanation:

In order to solve this, you need to find the greatest common factor. The highest number that can go into 12, 18, and 24 evenly would be 6.

Answer:

2 teams of 6 for class A, 3 teams of 6 for class B. and 4 teams of 6 for class C

Step-by-step explanation:

We are given the total amount of students in each class. 12,18,24. In order to separate these we have to find the common denominator among all the classes total numbers. 6 is a common denominator between them all as we can break it down to the number thats most common. Take the total number of students in each class and divide it by six. That is the total number of groups to be equal among them all.

Answer:

The answer is 1/20

Step-by-step explanation:

Answer: 1/20 in fraction form. 0.05 in decimal form.

Step-by-step explanation:

1/5 ÷ 4 = 1/20 in fraction form. 1/5 ÷ 4 = 0.05 in decimal form.

Answer:

can't really do that.

Step-by-step explanation:

whats the numbers lol

Answer:

0, -5, 3 = Integers 8.1, 1/2, =2.5 = Not an Integer

Step-by-step explanation:

Edge 2021

Answer:

a = 2 - 3b

        2

Step-by-step explanation:

3(a + b) = a + 2   expand

3a + 3b = a + 2

3a - a = 2 - 3b

2a = 2 - 3b

a = 2 - 3b

        2

Answer:

75%

Step-by-step explanation:

Answer:

Step-by-step explanation:

7000 - 4000 = 3000

percentage of increase = 3000 / 4000

                                       = 0.75 x 100

                                       = 75%

check:

= 4000 x 1.75

= 7000  ok

Answer:

A=184

Step-by-step explanation:

Answer:

49

Step-by-step explanation:

Add up all the numbers and divide by how many numbers there are.

Answer:

49

Step-by-step explanation:

the sum of all the numbers is 294

294÷6=49

========================================

Work Shown:

(small vertical)/(large vertical) = (small horizontal)/(large horizontal)

8/x = 16/40

8*40 = x*16 .... cross multiply

320 = 16x

16x = 320

x = 320/16  .... divide both sides by 16

x = 20

Note: there are other proportions you could set up such as 8/16 = x/40. The key here is that whatever equation you set up, it must cross multiply to 16x = 320 so that you get the same solution.

Answer:

11 players

Step-by-step explanation:

In a football tryouts at a local school there are 16 coaches and 44 players

Therefore spilliting then into group with similar numbers can be illustrated as follows

= 16/4

= 4 coaches each

= 44/4

= 11 players each

Hence sharing them into groups will result in 4 coaches and 11 players for each group

Answer:

240 yd

Step-by-step explanation:

Let A, B, C, and D represent location 1, location 2, location 3, and location 4 respectively.

Consider the figure in the attached file.

We need to find the total distance traveled by Betsy.

The distance covered by Betsy is

length of segment AB length of segment BC length of segment CD length of segment DA.

To find the distance AB, we need to find the distance from A to B on y-axis.

So, length of segment AB units

To find the distance BC, we need to find the distance from B to C on x-axis.

So, length of segment BC units

To find the distance CD, we need to find the distance from C to D on y-axis.

So, length of segment CD units

To find the distance DA, we need to find the distance from D to A on x-axis.

So, length of segment DA units

Hence, the total distance covered is units

It is given that 1 unit equals 10 yd, so distance traveled by Besty is yd