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What is the unknown exponent to the 10?
50 X 8,000 = 4 x 10

The expansion of the function \((3x - 4)^4\) simplifies to \(81x^4 - 432x^3 + 864x^2 - 768x + 256.\)

To expand the function \(f(x) = (3x - 4)^4\), we can use the binomial theorem. According to the binomial theorem, for any real numbers a and b and a positive integer n, the expansion of \((a + b)^n\) can be written as:

\((a + b)^n = C(n, 0)a^n b^0 + C(n, 1)a^{(n-1)} b^1 + C(n, 2)a^{(n-2)} b^2 + ... + C(n, n-1)a^1 b^{(n-1)} + C(n, n)a^0 b^n\)

where C(n, k) represents the binomial coefficient, which is given by C(n, k) = n! / (k!(n-k)!).

Applying this formula to our function \(f(x) = (3x - 4)^4\), we have:

\(f(x) = C(4, 0)(3x)^4 (-4)^0 + C(4, 1)(3x)^3 (-4)^1 + C(4, 2)(3x)^2 (-4)^2 + C(4, 3)(3x)^1 (-4)^3 + C(4, 4)(3x)^0 (-4)^4\)

Simplifying each term, we get:

\(f(x) = 81x^4 + (-432x^3) + 864x^2 + (-768x) + 256\)

Therefore, the expanded form of the function \(f(x) = (3x - 4)^4\) is \(81x^4 - 432x^3 + 864x^2 - 768x + 256\).

Note that the coefficient of \(x^3\) is -432, the coefficient of \(x^2\) is 864, the coefficient of x is -768, and the constant term is 256.

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Note the complete question is

Answer:

1) 30 pounds is the weight of the bag all together

2) science book is the heaviest book

Step-by-step explanation:

bag=4 pounds

library book=2 pounds

maths book=2×4=8 pounds

science book=8×2=16 pounds

4+2+8+16=30 pounds all together

heaviest book= science book (16 pounds)

The total area from the graph is 2.737.

Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.

First of all, lets calculate the points of intersection (P, Q, R)

x²+3=(x+2) +5

x²-2=√(x+2)

x⁴+4-4x²=x+2

x⁴-4x²-x+2=0

(x-2)(x³+2x²-1)=0

(x-2)(x+1)(x²+x-1)=0

x=2, -1, -1±√(1+4)/2

Clearly, the x-coordinate of Q is -1, P is -1-√5/2, R is -1+√5/2, S is 2

So the limit of integration will be

P( (-1-√5)/2, (-1-√5/2)² +3)=P((-1-√5)/2, (3+√5/2))

Q(-1, (-1)²+3)=Q(-1, 4)

Area A:

\(\int\limits^\frac{3+\sqrt{5} }{2} _4 {-\sqrt{-y-3}-((y-5)^2 -2)} \, dx\)

= \([\frac{-(y-3)^\frac{3}{2} }{\frac{3}{2} }-\frac{(y-5)^3}{3}+3y]^{\frac{3+\sqrt{5} }{2} }_4\)

= 2.07

Area B:

\(\int\limits^\frac{-1+\sqrt{5} }{2} _4 {-\sqrt{x+2}+5-(x^2+3)} \, dx\)

= \([\frac{-(x+2)^\frac{3}{2} }{\frac{3}{2} }+5x-\frac{x^3}{3}-3x]^{\frac{-1+\sqrt{5} }{2} }_{-1}\)

= 0.667

Total area = 2.07+0.667

= 2.737

Therefore, the total area from the graph is 2.737.

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\((\stackrel{x_1}{2}~,~\stackrel{y_1}{15})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{39}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{39}-\stackrel{y1}{15}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{2}}} \implies \cfrac{ 24 }{ 4 }\implies 6 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{15}=\stackrel{m}{6}(x-\stackrel{x_1}{2})\implies y-15=6x-12\)

\(y=6x+\underset{b}{3}\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\hspace{5em} {\LARGE \begin{array}{llll} \stackrel{y-intercept}{(0~~,~~3)} \end{array}}\)

Answer: 5 weeks

Explanation:

To find out when both siblings will have the same amount of money in their savings accounts, we need to solve the system of equations:

y = 10x + 25

y = 5x + 50

We can set the two equations equal to each other and solve for x:

10x + 25 = 5x + 50

5x = 25

x = 5

Therefore, after 5 weeks, both siblings will have the same amount of money in their savings accounts. So the answer is 5 weeks.

Answer:

Throughout the clarification category elsewhere here, the definition of the concern is mentioned.

Step-by-step explanation:

There seems to be no option for consuming peanut butter oatmeal mixture including apple slices with Meadow voles as well as regular voles.  

Meadow voles tend to consume a combination of peanut butter oatmeal whereas different or specific votes prefer eating slices of apples.

Answer:

natural exponential

natural

quizlet

Answer:

b. natural exponential

c. natural

Step-by-step explanation:

Given function:

\(f(x)=e^x\)

The given exponential function is called the:

The base e is called the:

The number "e" occurs naturally in math and the physical sciences.

It is the base rate of growth shared by all continually growing processes, and so is called the natural base.

It is an irrational number and named after the 18th century Swiss mathematician, Leonhard Euler, and so is often referred to as "Euler's number".

Step-by-step explanation:

the inside expression of an absolute value expression can be positive or negative, but the result is only the positive one.

therefore, for our example here the negative case would be

2.5x - 6.8 = -12.9

which gives us

2.5x = -6.1

x = -6.1/2.5 = -2.44

and the positive case would be

2.5x - 6.8 = 12.9

and that gives us

2.5x = 19.7

x = 19.7/2.5 = 7.88

Answer:

10 e ^10 x

Step-by-step explanation:

Find the derivative using the chain and power rules.

1. An equation that represents "the amount of tax on an item of price p",

t = p x X / 100

2. Marta does pay on an item whose price is $20, $1.6

Percentage is a way to express a number as a fraction of 100. It is often used to represent ratios and proportions in a more convenient and understandable form, especially in financial and statistical contexts. For example, 50% means 50 per 100, or half of a given quantity. It is denoted using the symbol "%".

Given that,

Tax rate = 8%

1. Let's assume that the sales tax rate is X%.

Then, the equation that represents the amount of tax (t) Marta pays on an item whose price is p can be written as:

t = p x X / 100

2. If the price of the item is $20, the amount of tax Marta pays can be calculated as follows:

t = $20 x X / 100

t = $20 x 8 / 100

t = $1.6

So, Marta pays $1.6 in sales tax on an item whose price is $100.

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Answer:

2100

Step-by-step explanation:

area of rectangle = length * width

total area = 80 ft * 15 ft + 30 ft * 30 ft

total area = 1200 ft^2 + 900 ft^2

total area = 2100 ft^2

Answer:

3

Step-by-step explanation:

4a + 2 = 14

      -2    -2

 4a     =   12

4a/4  =  12/4

     a  =  3

Answer:

Step-by-step explanation:

56

Answer:

all of them probly

Step-by-step explanation:

The Volume of the box is 12 cubic unit.

We have,

Height = 1 unit

Width = 2 unit

Length = 6 unit

So, Volume of box

= l w h

= 1 x 2 x 6

= 12 cubic unit

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Answer:

yes

Step-by-step explanation:

Yes, y = 4² is an exponential function.

" An exponential function is a mathematical function which can be expressed as y = \(a^{x}\)  where 'a' is any constant value not equals to 0 and 'x' is a variable which belongs to any real number."

According to the question,

y = 4²

If we compare with general form y = \(a^{x}\) of exponential function we have,

a = 4

x = 2

Hence, we conclude that y = 4² is an exponential function.

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When applying the some rule, we only combine two equal ratios at once. Consequently, we deal with pairs of sides and angles that have equivalent ratios.

When two ratios are equal, a percentage is formed; alternatively, two equal ratios can be said to produce a proportion. When we understand that two ratios are equal, you can write a proportion. The ratios of these two numbers are equal.

When two variables are correlated in a manner that their ratios are equal, this is known as a proportional relationship. In a proportional connection, one variable is always a constant value multiplied by the other, which is another way to think of them. The "constant of proportionality" is the term used to describe that constant. Two angles are said to be complimentary if their sum is 90 degrees. Alternatively put, two angles are said to be complimentary if they combine to make a right angle.

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The length the line segment DF is 21 units

What is Similarity of Triangles?

Two objects are comparable in Euclidean geometry if they have the same form or one has the same shape as the mirror image of the other. More exactly, one can be created by evenly scaling the other, potentially with extra translation, rotation, and reflection.

Since, the question is incomplete I can only assume that the traingles are similar

So, by rule of similarity we can say that ED/BA = DF/AC

by this 15/5 = DF/7

This implies that the length of DF is 21 units

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Answer:

37.68

Step-by-step explanation:

i had this one

Answer:

force applied over a body can compress a body which would change it's density, increase it's density which means decrease it's volume as they are inversely proportional

may this help u

Answer:force applied over a body can compress a body which would change it's density, increase it's density which means decrease it's volume as they are inversely proportional.

Step-by-step explanation:

Part a: The data points appear to follow an exponential pattern. This is because the balance is increasing at a rate that is proportional to the current balance.

Part b: The equation of the best fit is y = 50(1.06)^x. This can be found using a variety of methods, including graphing the data points and fitting a curve to them, or using a statistical software package.

Part c: When x = 32, y = 50(1.06)^32 = $2,499.82.

Years since 1990, x 0 5 10 15 20 25 30

Balance, y $50 $62.31 $77.65 $96.76 $120.59 $150.27 $187.27 $2,499.82

The equation of the fitted curve is y = 50(1.06)^x.

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The required standard deviation of the given data is 54.6.

To find the sample standard deviation for the weights of the offensive linemen, we first need to calculate the mean of the sample and then use that to find the variance and standard deviation.

Mean:

The mean (μ) is the sum of all the values in the sample divided by the number of values in the sample. In this case, the mean is:

(359 + 297 + 350 + 254 + 312 + 250 + 359 + 253 + 254 + 326 + 254 + 331) / 12 = 298.75

Variance:

The variance (σ²) is a measure of the spread of the data. It is calculated as the sum of the squared deviations of each value from the mean divided by the sample size minus one. In this case, the variance is:

( (359 - 298.75)² + (297 - 298.75)² + (350 - 298.75)² + (254 - 298.75)² + (312 - 298.75)² + (250 - 298.75)² + (359 - 298.75)² + (253 - 298.75)² + (254 - 298.75)² + (326 - 298.75)² + (254 - 298.75)² + (331 - 298.75)² ) / (12 - 1) = 2987.5

Standard Deviation:

The standard deviation (σ) is the square root of the variance. In this case, the standard deviation is:

√2987.5 = 54.59

Therefore, the sample standard deviation of the weights of the offensive linemen is 54.59 pounds.

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Answer:

it becomes a 3 unit hight

Answer:No

Step-by-step explanation:

9/12 = 3/4 = .75

6/2 = 3.00

Answer:  No

Step-by-step explanation:

If you reduce each fraction

Divide the top and bottom for 9/12 by 3

=3/4

And 6/2 is 6 divided by 2 =3

3/4 is not bigger than 3  

3/4 is a fraction and 3 is 3 wholes.

Answer:

B. feet/second

Step-by-step explanation:

The units for Ali's final answer will be feet per second.

By identifying the base quantities and units of measure for each physical quantity and tracking these dimensions as calculations or comparisons are made, the dimensional analysis examines the relationships between various physical quantities.

Given that Ali performed the following dimensional analysis to convert a rate of 72 mph.

The units will be calculated as below:-

72 miles/1 hour x 5280 feet/1 mile x 1 hour/60 minutes x 1 minute/60 seconds = 105.6

Miles and miles will cancel out now hour and hour will also be canceled out now the remaining unit will be feet per second.

Therefore, the unit for Ali's final answer will be feet per second.

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Nolan wrote an incorrect value as the y-intercept, the actual linear equation is:

y = -5x + 25

Remember that a general linear equation is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

Here we know that Nolan starts with $25, and then he loses $5 per day, so after x days, he will have:

$25 - $5*x

That is the linear equation he should have written, instead of:

y = -5x + 5

So you can see that the y-intercept is wrong, because Nolan used 5 instead of 25.

Then:

The mistake is that he wrote the y-intercept wrong.

The actual linear equation is:

y = -5x + 25

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Answer:

Tyrone's rate is 1 more mile per hour than John's

Step-by-step explanation:

Given

\(y = 5x\) --- John number of jog

See attachment of Tyrone's number of jog

Required

Select the true option

From the attached graph, we have:

\((x_1,y_1) = (0,0)\)

\((x_2,y_2) = (2,12)\)

Calculate the slope (m); i.e. unit rate

\(m = \frac{y_2 - y_1}{x_2 -x_1}\)

\(m = \frac{12 - 0}{2 -0}\)

\(m = \frac{12}{2}\)

\(m = 6\)

For John, we have:

\(y = 5x\)

A linear equation is represented as:

\(y = mx+ c\)

Where m represents the unit rate. So, by comparison;

\(m = 5\)

\(m = 5\) --- John unit rate

\(m = 6\) --- Tyrone unit rate

Option B is correct because Tyrone's rate is 1 more mile per hour than John's

i.e. 6 - 5 = 1

Answer:

f (x) = (x - 2)² + 3

Step-by-step explanation:

Adding 2 to the constant k would shift the entire equation upwards by 2.

Answer:

h = A/2πr - r

That's the formula. Hopefully it's understandable because I don't know any other way of typing it. You can always search it up and it'll show you. :)