Alyssa purchased 3 pounds of peanuts for $8.25. Write an equation that shows the relationship between the cost and the number of pounds purchased

Given that

[tex]g(x) = x^3 + x[/tex]

the inverse [tex]g^{-1}(x)[/tex] is such that

[tex]g\left(g^{-1}(x)\right) = g^{-1}(x)^3 + g^{-1}(x) = x[/tex]

or

[tex]g\left(f(x)\right) = f(x)^3 + f(x) = x[/tex]

Differentiating both sides using the chain rule gives

[tex]3f(x)^2f'(x) + f'(x) = 1 \\\\ f'(x) \left(3f(x)^2+1\right) = 1 \\\\ f'(x) = \dfrac1{3f(x)^2+1}[/tex]

Then the derivative of f at 2 is

[tex]f'(2) = \dfrac1{3f(2)^2+1} = \boxed{\dfrac14}[/tex]

Answer:

The geometric sequence is decreasing by 0.5 * each term

common ratio = 0.5

an equation for this exact sequence would be

50(0.5)^x-1

Step-by-step explanation:

To find the common ratio for a geometric sequence we can divide the previous term value by the next term value

so 50 / 25 = 0.5

and to check we can divide

25 / 12.5 = 0.5

So our common ratio is 0.5

Step-by-step explanation:

Given sequence:

The first term is 50 and the common ratio is:

The equation:

Find the 8th and 10th terms:

Answer:

35

Step-by-step explanation:

1.5x30=45 -

45-10= 35

month=30 days

Movie costs 1.5 for a day and it will cost 10 for a month so you have to do 1.5x30=45 then you have to subtract 10 becuses that's the monthly pay so your answer would be 35 please (give brainless)

Answer:

The top of the ladder is sliding down at a rate of -1.25 ft/s.

Step-by-step explanation:

From the Pythagorean Theorem:

[tex]\displaystyle a^2 + b^2 = c^2[/tex]

(Where a is the height, b is the distance between the bottom of the ladder and the wall, and c is the length of the ladder itself.)

Note that the hypotenuse c is a constant value at 26 feet. Substitute:

[tex]\displaystyle a^2 + b^2 = (26\text{ ft})^2 = 676 \text{ ft}^2[/tex]

We want to determine how fast the top of the ladder is sliding down the wall at the instant of time when the bottom of the ladder is 10 feet from the wall and sliding away from the wall at the rate of 3 ft/s.

In other words, we want to find da/dt given that b = 10 ft, and db/dt = 3 ft/s.

First, we can differentiate both sides with respect to t, where a and b are both functions of t:

[tex]\displaystyle \frac{d}{dt}\left[ a^2 + b^2\right ] = \frac{d}{dt}\left [ 676 \text{ feet}^2\right ][/tex]

Implicit differentiation yields:

[tex]\displaystyle 2a \frac{da}{dt} + 2b \frac{db}{dt} = 0[/tex]

Next, since we know that b = 10 ft, we can find a:

[tex]\displaystyle \begin{aligned} a^2 + b^2 & = 676\text{ ft}^2 \\ \\ a^2 +(10 \text{ ft})^2 & = 676\text{ ft}^2 \\ \\ a & = 24\text{ ft} \end{aligned}[/tex]

Substitute and solve for da/dt:

[tex]\displaystyle \begin{aligned} 2a \frac{da}{dt} + 2b\frac{db}{dt} & = 0 \\ \\ 2(24 \text{ ft}) \frac{da}{dt} + 2(10 \text{ ft})(3 \text{ ft/s}) & = 0 \\ \\ 48 \text{ ft} \cdot \frac{da}{dt} & = -60 \text{ ft$^2$/s} \\ \\ \frac{da}{dt} & = -1.25 \text{ ft/s} \end{aligned}[/tex]

Since the ladder is sliding down the wall, da/dt is expected to be negative.

In conclusion, the top of the ladder is sliding down at a rate of -1.25 ft/s.

Assuming the given number is in base 2, we have

111.01₂ = 2² + 2¹ + 2⁰ + 2⁻²

111.01₂ = 4 + 2 + 1 + 0.25

111.01₂ = 7.25

Answer:

41/5

Step-by-step explanation:

First we change the 8 and 1/5% to 8.2%

Write the fraction down as a number over one = 8.2/1

Multiply both top and bottom by 10 for every number after the decimal point:

As we have 1 numbers after the decimal point, we multiply both numerator and denominator by 10. So,

8.2/1 = (8.2 × 10)

(1 × 10) = 82/10

Reduce the above fraction by dividing both numerator and denominator by the GCD (Greatest Common Divisor) between them. In this case, GCD (82,10) = 2. So, (82÷2)/(10÷2) = 41/5 when reduced to the simplest form.

As the numerator is greater than the denominator, we have an IMPROPER fraction, so we can also express it as a MIXED NUMBER, thus 82/10 is also equal to 81/5 when expressed as a mixed number.

Answer:

17

Step-by-step explanation:

(11+14÷2)−1

 (11+7)−1

    18−1

       17

Parallel lines have the same slope

The equation of the line is: [tex]\mathbf{y = \frac 23x + 8}[/tex]

From the question, we have:

[tex]\mathbf{2x - 3y = 5}[/tex]

Make y the subject

[tex]\mathbf{- 3y = 5 - 2x}[/tex]

Divide through by -3

[tex]\mathbf{y = \frac 23 x - 5}[/tex]

Because the required equation is parallel to [tex]\mathbf{2x - 3y = 5}[/tex], then they must have the same slope

A linear equation is represented as:

[tex]\mathbf{y=mx + c}[/tex]

Where:

m represents the slope

So, by comparison:

[tex]\mathbf{m = \frac 23}[/tex]

This means that:

The required equation has a slope of 2/3

The equation of the line is:

[tex]\mathbf{y = m(x - x_1) + y_1}[/tex]

Where:

[tex]\mathbf{m = \frac 23}[/tex]

[tex]\mathbf{(x_1,y_1) = (-9,2)}[/tex]

So, we have:

[tex]\mathbf{y = \frac 23(x + 9) + 2}[/tex]

Open brackets

[tex]\mathbf{y = \frac 23x + 6 + 2}[/tex]

[tex]\mathbf{y = \frac 23x + 8}[/tex]

Hence, the equation of the line is: [tex]\mathbf{y = \frac 23x + 8}[/tex]

Read more about equations of parallel lines at:

https://brainly.com/question/402319

Answer:

Step-by-step explanation:

If he washes his dads car alone it takes 6hrs, If his dad helps him it takes 2hrs.

6-2= 4

4hrs?

I dont understand the question lol.

Answer:

for the table

x y

0 260

1 240

2 220

3 200

Unit Rate is -20

we know this because the question tells us, he reads 20 pages per hour

the equation would be

y = -20x + 260

Answer:

it's 64,116

Step-by-step explanation:

ur welcome

Answer:

2. 2xy-2y

Step-by-step explanation:

4xy-2y(x+1)=4xy-2xy-2y

=2xy-2y

Answer:

16 robots

Step-by-step explanation:

Each worker can move 12 boxes/minute and there are 24 workers.

24 x 12 =  288

Divide the total work by 18 (since a robot can move 18 boxes/minute)

288 ÷ 18 = 16

Answer:

true

Step-by-step explanation:

it is because 1 and 3 in set A are in sat B

Answer:

a straight line has an angle of 180

therefore 180-109=71

71÷2 = 35.5

x is 35.5 degrees

The measure of x is 29 degree.

As, Parallel line have property

As, <CBA = <BAD (Alternate Interior Angle)

So, <BAD = 42

Now, <BAD + <BAC + <CAE = 180 (Linear Pair)

42 + 109 + x = 180

151 +x = 180

x = 180- 151

x = 29

Learn more about Parallel line here:

https://brainly.com/question/16701300

#SPJ7

Answer:

sorry i am not sure

Step-by-step explanation:

sorry i am not sure

Answer:

x = [tex]\frac{y}{7}[/tex], y = 7x

Step-by-step explanation:

hope this helps

9514 1404 393

Answer:

  1a: $84; 1b: 30,000A +15,000B; 1c: 37,000A +18,500B

  2: 4,000 composite units

Step-by-step explanation:

We assume your "composite unit" consists of the smallest set of units in the ratio in which they are sold.

A "composite unit" is 1B +2A. The contribution margins are the difference between the selling price and the variable cost per unit:

  A: 72 -40 = 32

  B: 48 -28 = 20

  composite unit: 2A+B = 2(32) +20 = 84

(a) The contribution margin per composite unit is $84.

__

(b) The break-even point is the number of composite units that have a total contribution margin equal to the total fixed costs:

  84n = 1260000

  n = 1260000/84 = 15000

30,000 units of A and 15,000 units of B must be sold to break even.

__

(c) The additional number of composite units required to achieve pre-tax income of 294000 is ...

  294,000/84 = 3500

37,000 units of A and 18,500 units of B must be sold for a pretax income of $294,000.

__

Contribution margins per unit are ...

  H: 6 -4 = 2

  C: 8 -6 = 2

  I: 10 -7 = 3

A composite unit is 3H +2C +I, so the contribution margin per composite unit is ...

  3(2) +2(2) +1(3) = 6 +4 +3 = 13 . . . dollars

The break-even point is 52,000/13 = 4,000 composite units

Answer:

46.3

Step-by-step explanation:

Mean is the average of all values. You add all the values on the table and divide them by the amount of values (here there are 10 land animals so you would divide by 10).

[tex]\frac{70+61+50+48+45+43+40+39+35+32}{10} =\frac{463}{10} = 46.3[/tex]

Answer:

x= 13

Step-by-step explanation:

can i please get branlist? if not thats okay.

nonrigid

segment lengths are not

Answer:

1 Nonrigid

2 segment lengths are not

Answer:

Step-by-step explanation:

2/7 + 4/5 mixed forms

2/7 + 4/5 =

38/35 or 1 3/35

Answer:

38/35

Step-by-step explanation:

1. convert to like fractions

2/7-> 10/35

4/5-> 28/35

2. add fractions

10/35 + 28/35 = 38/35

Answer: Im pretty sure its B

(/ ^_^/) .....

Did you use the formula

gradient =

[tex] \frac{y2 - y1}{x2 - x1} [/tex]

??

I'm not shear but i think that run to -6 then 3 is the correct sorry am learning it

Answer:

y=-2/5x-1

Step-by-step explanation:

I started by looking for the y-intercept of the line, where the line intersects with the y-axis and saw it was -1.

Then I looked at the slope of the line and used the rise/run strategy. From the y-intercept to the point it was 2 units down and 5 units across (2/5) and since it is going down it's negative

Plugging it in: y=mx+b

m=slope

b=y-intercept

y=-2/5x-1

Hope this helps :)

Answer:

6.5555 months

Step-by-step explanation:

$415-$120= $295

Micah will need $295 from his paycheck earnings to be able to afford the guitar.

$295/$45= 6.5555months

Answer:

19.5

Step-by-step explanation:

3r+(7+8)/(t-3)

3(4)+(15)/(5-3)

12+(15/2)

12+7.5

19.5

Answer:

1200

Step-by-step explanation: