Solve for x:
3x - 6y = 9

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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.

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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

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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

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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.

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

a+b = 16+12 = 28

Answer:

the answer is -3 because -3 is closer to 0 than -4

Answer:

x = -121

Step-by-step explanation:

(7/2)*x+(1/2)*x = (9/2)*x+121/2 // - (9/2)*x+121/2

(7/2)*x+(1/2)*x-((9/2)*x)-(121/2) = 0

(7/2)*x+(1/2)*x+(-9/2)*x-121/2 = 0

-1/2*x-121/2 = 0 // + 121/2

-1/2*x = 121/2 // : -1/2

x = 121/2/(-1/2)

x = -121

Answer:

A=184

Step-by-step explanation:

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

Answer:

the answer is D

Step-by-step explanation:

edu 2021

Answer:

180

Step-by-step explanation:

Keep multiplying 45 until you get a number divisible by 36. This is called the least common multiple.

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:

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:

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

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

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:

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

Step-by-step explanation:

Answer:

1.75

Step-by-step explanation:

5x + 3x - 4 = 10

Add Four To Both Sides To Begin Simplifying.

5x + 3x = 14

Now, Combine Like Terms.

8x = 14

Divide:

8x/8 = 1X = X

14/8

X = 14/8

14/8 = 1.75

X = 1.75

Check:

(5 * 1.75) + (3*1.75) - 4 = 10

8.75 + 5.25 - 4 = 10

14 - 4 = 10

10 = 10.                 This Is True, So X Does Equal 1.75

Answer:

The answer should be B; one answer

Step-by-step explanation:

After solving this equation, I came up with the answer 0.75, therefore there is only one answer.

Answer:

Step-by-step explanation:

Yes plzz give me brainliest

Answer:

REEEEEEEEEEEE

Step-by-step explanation:

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:

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:

GCF=   2 x 5 x 11 = 110

LCM=   2 x 2 x 5 x 11 = 220

Step-by-step explanation:

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:

i think your right

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:

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:

0.91

Step-by-step explanation:

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