PLEASE, I REALLY NEED HELP HOW DO I DO A VERBAL EXPLANATION FOR THIS??? PLEASE

The derivative of a function f(x) at a point x = a is defined as the limit of the difference quotient as h approaches zero:

f'(a) = lim (h → 0) [f(a + h) - f(a)] / h

What is derivative?

The derivative of a function in calculus measures the function's sensitivity to changes in its input variable. Specifically, at a particular point, it represents the function's rate of change with respect to its input variable at that moment.

The derivative of a function f(x) at a point x = a is defined as the limit of the difference quotient as h approaches zero:

f'(a) = lim (h → 0) [f(a + h) - f(a)] / h

This limit represents the instantaneous rate of change or slope of the function at the point x = a. The difference quotient is the change in the function value divided by the change in the input variable (or the distance between two points on the graph of the function).

The derivative is a fundamental concept in calculus, and it has many applications in various fields of science, engineering, and economics. It allows us to calculate important quantities such as velocity, acceleration, and marginal cost, and it is used to optimize functions and solve many real-world problems.

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To find out how many cans of tennis balls the factory packs for the order, we can divide the total number of tennis balls by the number of tennis balls packed into each can.

Given: Total number of tennis balls = 94,500. Number of tennis balls packed into each can = 3. To determine the number of cans of tennis balls the factory packs for the order, we divide the total number of tennis balls by the number of tennis balls packed into each can. Calculation: Number of cans = Total number of tennis balls / Number of tennis balls packed into each can. Number of cans = 94,500 / 3. To find out how many cans of tennis balls the factory packs for the order, we can use the given information. First, we need to divide the total number of tennis balls by the number of tennis balls packed into each can. In this case, there are 94,500 tennis balls and each can contains 3 tennis balls. Dividing 94,500 by 3 gives us the number of cans required. Performing the calculation, we get: Number of cans = 94,500 / 3. Simplifying the expression, we find that the factory needs to pack 31,500 cans of tennis balls for the order.

The factory needs to pack a total of 31,500 cans of tennis balls for the order.

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The equation of the line in slope-intercept form would be; y = -12x + 18

If the slope of a line is m and the y-intercept is c, then the equation of that straight line is given as:

y = MX +c

To find the slope of a line, we the rate at which the value of 'y' is increasing as we increase the value of 'x' by one unit.

We have been given the point (1,6) and (2,-6)

y-y₁ = m(x-x₁)

m = (-6-6)/(2 -1)

m = -12/1

Now substitute;

y-y₁ = m(x-x₁)

y- 6 = -12(x- 1)

y- 6 = -12x + 12

y = -12x + 18

Hence, the equation of the line in slope-intercept form would be; y = -12x + 18

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Answer:

no

Step-by-step explanation:

because more food less active

so if you eat more food, and you are less active you don't exercise off the weight

So you would gain weight not lose weight

The definition of percent helps you write fraction and decimal equivalents by understanding that "per cent" means "per hundred".

For example, if you are asked to write the fraction and decimal equivalent of 25%, you would divide 25 by 100 to get the fractional equivalent of ¼, and divide 25 by 100 to get the decimal equivalent of 0.25.

The decimal equivalent of a fraction or percentage is the numerical value expressed in decimal form. For example, the decimal equivalent of 1/2 is 0.5 and the decimal equivalent of 25% is 0.25. Decimal equivalents are useful for calculations and can be used to convert fractions and percentages into decimal form.

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Answer:

m+10

Step-by-step explanation:

We know that yesterday, eric had m baseball cards. Thus, we can denote that the total number of baseball cards he had yesterday is m.

We know that he got 10 more today. Since he is receiving more, he is adding to his collection. Since he is getting more, we have to add 10 to how many baseball cards he used to have. He used to have m baseball cards, so today he has m+10 baseball cards.

This is the answer as we cannot combine 10 and m. Since m is a variable with no set value as of now, and 10 is a constant number that has no variable, they are not like terms and cannot be added. So the answer is m+10 baseball cards.

I hope this helped.

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Answer:

180

Step-by-step explanation:

Fran raised 2/9 of her goal already meaning you can divide 40 by two so that you can see what 1/9 of her goal was.

40/2 = 20 (which means that is what 1/9 of her goal is)

Now what you can do is multiply 20 by 9 because when you multiply 1/9 times 9, you get one, which means the fraction is complete.

20 times 9 = 180

Her goal is to raise $180

***you can also double check if the answer is correct if you divide 2/9 and 40/the answer you get. If they match, you got the right answer! both 2/9 and 40/180 equal .22222!

The monthly payment amount is $217.42 and the finance charge is $413.02.

The payment amount and finance charge can be found by using the formula below

Payment amount formula: PMT = (P x R x (1 + R)^N) / ((1 + R)^N - 1)

Finance charge formula: Finance charge = Total payment - Loan amount

Where P = Loan amount

R = Interest rate per period

N = Number of periods

Given that a loan is made for $4800 with an APR of 12% and payments made monthly for 24 months

Therefore,P = $4800R = 12% / 12 = 1% per month

N = 24

Using the Payment amount formula above: PMT = (P x R x (1 + R)^N) / ((1 + R)^N - 1)

PMT = ($4800 x 0.01 x (1 + 0.01)^24) / ((1 + 0.01)^24 - 1)

PMT = $217.42

Hence, the monthly payment amount is $217.42 (rounded to two decimal places).

Using the finance charge formula above: Finance charge = Total payment - Loan amount

Total payment = Payment amount x Number of periods

Total payment = $217.42 x 24 = $5213.02

Finance charge = $5213.02 - $4800

Finance charge = $413.02

Hence, the finance charge is $413.02 (rounded to two decimal places).

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a) The expression to represent this number without computing its value is 2²⁸.

b) Mai has 8 times more coins than Andre.

a)The number of coins that Mai would have on the 28th day can be represented by the formula: 2²⁸. This is because the number of coins doubles each day, and there are 28 days in total.

So, on the first day, Mai has 2 coins, on the second day, she has 2 x 2 = 4 coins, on the third day, she has 2 x 2 x 2 = 8 coins, and so on. Therefore, on the 28th day, she would have 2 x 2 x 2 x ... (28 times) = 2²⁸ coins.

b) Andre's coins lost their magic on the 25th day, so he would have only 2²⁵ coins on the 25th day. To find out how many times more coins Mai has than Andre, we need to divide the number of coins Mai has on the 28th day (2²⁸) by the number of coins Andre has on the 25th day (2²⁵). This gives us:

2²⁸ / 2²⁵  = 2³ = 8

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I'm not going to do all of them for you but I'm basically going to teach you what your teacher taught you.

In division with fractions, the second fraction will be flipped around and then you'll multiply normally.

Example:

(5/3)/(2/3)

You would flip around the 2/3 so it would be 3/2

Then you would multiply:

5/3*3/2

To do multiplication, multiply the top numerator by the top numerator and the bottom numerator by the bottom numerator as I'm sure you've already learned

5*3 = 15

3*2 = 6

15/6

Let me know if you have any questions

If you're wondering why I didn't give you the answer, it's because "Give a man a fish and he'll eat for a day; teach a man to fish and he will eat for a lifetime"

Thank you

The central angle of the sector with a radius of 5 cm and an area of 5π cm² is 72 degrees.

To find the central angle of a sector, we need to use the formula that relates the sector area to the central angle and the radius of the circle. The formula for the area of a sector is:

Area = (θ/360) * π * r^2

Where:

Area is the sector area

θ is the central angle in degrees

π is a mathematical constant (pi)

r is the radius of the circle

In this case, we are given the radius of the circle as 5 cm and the sector area as 5π cm². Let's substitute these values into the formula and solve for θ.

5π = (θ/360) * π * 5^2

Simplifying the equation:

5π = (θ/360) * 25π

To eliminate π, we can divide both sides of the equation by π:

5 = (θ/360) * 25

Now, let's isolate θ by multiplying both sides of the equation by (360/25):

5 * (360/25) = θ

Simplifying the equation:

θ = 72

Therefore, the central angle of the sector is 72 degrees.

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The form of a system of inequalities that would allow you to solve for the number of each type of animal that can be won is 10x + 6y = 12.

Given:

A carnival has a game where players can win stuffed animals. the rules allow for players to win no more than 10 small animals, no more than 6 large animals, and no more than 12 total animals.

x be the number of small animals and y be the number of large animals

The number of small animals = 10x

Number of large animals = 6y

The equation:

= 10x + 6y = 12.

Therefore the form of a system of inequalities that would allow you to solve for the number of each type of animal that can be won is 10x + 6y = 12.

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Answer:

Step-by-step explanation: Vertex Equatiation Por mxa Plus B = X gtex Lp Cneter to 16u8 Killomtrss to ball

12 meters is the correct answer.  I forget the formula XD :)

Answer:

B

Step-by-step explanation: 113.04 divided by 3.14 equals 36

Diameter=2r

Diameter=2(6)

Diameter=12

Answer:

I have solved it and attached in the explanation.

Step-by-step explanation:

Answer:

\(27a^3-54a^2b+36ab^2-8b^3\)

Step-by-step explanation:

To expand the expression (3a - 2b)³, we can use the Perfect Cube Formula.

\(\boxed{\begin{minipage}{6 cm}\underline{Perfect Cube Formula}\\\\$(x-y)^3=x^3-3x^2y+3xy^2-y^3$\\\end{minipage}}\)

Let:

Substitute the values into the formula, and use the exponent rule

\(\boxed{(xy)^n=x^n \cdot y^n}\) :

Therefore:

\(\begin{aligned}(3a-2b)^3&=(3a)^3-3(3a)^2(2b)+3(3a)(2b)^2-(2b)^3\\&=3^3 \cdot a^3-3 \cdot 3^2 \cdot a^2 \cdot 2b+3 \cdot 3a \cdot 2^2\cdot b^2-2^3\cdot b^3\\&=27a^3-3 \cdot 9 \cdot a^2 \cdot 2b+9a \cdot 4b^2-8b^3\\&=27a^3-54a^2b+36ab^2-8b^3\end{aligned}\)

So the expression (3a - 2b)³ expanded is 27a³ - 54a²b + 36ab² - 8b³.

The chart should be completed as follows;

x           \(f(x) = 1.7^x\)               function (x, f(x))               Inverse (f(x), x)

0               1                             (0, 1)                                 (1, 0)

1                1.7                          (1, 1.7)                               (1.7, 1)

-1               0.6                         (-1, 0.6)                            (0.6, -1)

2                2.9                          (2, 2.9)                           (2.9, 2)

3                4.9                          (3, 4.9)                            (4.9, 3)

In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:

\(f(x) = a(b)^x\)

Where:

Based on the given exponential function \(f(x) = 1.7^x\), we would determine the value of f(x) by substituting each of the x-values as follows;

x = 1

\(f(x) = 1.7^1\)

f(x) = 1.7

When x = -1, we have:

\(f(x) = 1.7^{-1}\)

f(x) = 0.6

When x = 2, we have:

\(f(x) = 1.7^{2}\)

f(x) = 2.9

When x = 3, we have:

\(f(x) = 1.7^{3}\)

f(x) = 4.9

In conclusion, the inverse of this exponential function would be determined by interchanging (swapping) the x-value (x) and the y-value f(x) as shown in the chart above.

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The domain of a function is the set of possible input value, the function can take.

The domain is [0,10]

The given parameters are:

\(Flat\ Fee = 15.25\)

\(Rate = 3.45\)

So, the function f(x) is:

\(f(x) = Flat\ Fee + Rate \times x\)

\(f(x) = 15.25 + 3.45 \times x\)

\(f(x) = 15.25 + 3.45x\)

Because x represents the number of orders, the value of x cannot be negative.

The teacher budgets $49.75.

This means that: f(x) = 49.75

So, we have:

\(49.75 = 15.25 + 3.45x\)

Collect like terms

\(49.75 - 15.25 = 3.45x\)

\(34.5 = 3.45x\)

Divide both sides by 3.45

\(10 = x\)

Rewrite as

\(x = 10\)

Hence, the domain is [0,10]

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Answer:

\(\boxed{\underline{\tt B.\:x=-1}}\)

Step-by-step explanation:

\(\tt 8=2^{(x+4)}\)

(First, convert both sides to the same base):-

\(\tt 2^3=2^{x+4}\)

(Now, cancel the base of 2 on both sides):-

\(\tt 3=x+4\)

(Subtract 4 from both sides):-

\(x+4-4=3-4\)

\(\tt x=-1\)

~

Answer: Let x be the number of hours Tay practices the piano. Then, Omar practices for 2/5 less than that, or x - 2/5x = 3/5x hours.

Step-by-step explanation:

Answer: option c

Using the given percentage we can see that the minimum and maximum numbers are:

N-  = 967

N+ = 1,150

The total number of students is 3,650, and we know that the average percentage is 29% ± 2.5%

The minimum value is what we get when we use the minus sign:

29% - 2.5% = 26.5%

The 26.5%  of 3,650 is:

N- = (0.265)* 3,650 = 967

The maximum value is what we get when we use the plus sign:

29% + 2.5% = 31.5%

The 31.5% of  3,650 is:

N+ = (0.315)*3,650 = 1,150

These are the two values.

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The fraction of the hour that remained is 1/4 hour.

The portion or part of the complete item is represented by a fraction. It stands for the equal components of the whole. The denominator and numerator are the two components of a fraction. The top number is referred to as the numerator, and the bottom number is referred to as the denominator.

The students have to submit the book reports in 1 hour.

After the first report, 2/3 hours remained. The next two reports took 1/6 hour and 1/4 hour respectively.

After the first report, 2/3 hours remained.

The next two reports took 1/6 and 1/4 hours.

So, the total time to complete the next two reports is:

= 1/6 + 1/4

= 10/24

= 5/12 hours

Therefore, the fraction of hour remained will be:

= 2/3 - 5/12

= ( 2/3 ) × ( 4/4 ) - 5/12

= 8/12 - 5/12

= 3/12

= 1/4 hour

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Answer:

b.2/6.

Step-by-step explanation:

Simplify each fraction

a.3/3 =1

b.2/6. Divide the top and bottom by 2  1/3

c.3/12 Divide the top and bottom by 3  1/4

d.7/12 Does not simplify

Answer:

\(\frac{1}{3}\)

Step-by-step explanation:

I don't think that there are two answers. I think there's only one.

Answer: 2:7

Step-by-step explanation:

Vanilla icecream = 4

Chocolate icecream = 14

4:14=2:7

2X2=4

7X2=14

Step-by-step explanation:

a ratio is simply relating 2 (or more) groups and their sizes.

in our case here the ratio is

4/14 = 2/7

this is often written as

4:14 = 2:7

it means that for every 2 people liking (I assume "preferring") vanilla ice cream there are 7 people liking (preferring) chocolate ice cream.

FYI

in total, a ratio also tells us about the size of the sample for the observation or analysis. 4/14 tells us there are 18 (4+14) people in the survey. and the simplified form 2/7 tells us that we can split the whole survey group into units of 9 (2+7) people with the same behavior as the total group.

a ratio is a fraction (incl. all the calculation and comparison rules) with a special meaning.

so, don't mix the ratio up with e.g. the fractions of the different behaviors in the group :

4/18 = 2/9 of the whole group prefer vanilla.

14/18 = 7/9 of the whole group prefer chocolate.

the ratio is now the relative size relationship between both : 2/9 / 7/9 = 2/7

Answer:

The mass of 3.5 moles of Ca (Sodium)  is 140 g to two significant figures.

Answer:

ty

Step-by-step explanation:

Answer:

sec² [㏑(ax + b)] X a/(ax +b)

Step-by-step explanation:

chain rule is if y = f(c) and z = f(e), and y = f[f(e)], then:

dy/de = dy/dc X dc/de

This might look complicated. Much easier with example, as in this question.

y = tan [㏑(ax + b)]

y = tan (u),

where u =㏑(v), v = ax + b

so we have y = tan (u), u = ㏑(v), v = ax + b.

dy/du = sec² (u), du/dv = 1/v, dv/dx = a.

dy/dx = dy/du X du/dv X dv/dx

        = sec² (u) X (1/v) X a

        = sec² [㏑(v)] X (1/(ax + b)) X a

        = sec² [㏑(ax + b)] X a/(ax + b)

Answer:

6 km.

Step-by-step explanation:

Lets say moving west is negative and moving east is positive. This is thus equal to -4+6-4+6-4+6, which is equal to 6.

Answer: ❘-168 - 115❘

you’re finding difference so we set up a subtraction problem.

We can’t have a negative answer so we must take the absolute value of that number