Write an equivalent expression to 2x+3x+4(x-2)

Answer:

1 hole 2 1/8 and 2 1/ 8 you add them together and it equal 1 hole

The length of the side between the vertices A' and B' is 3.75 inches

In order to find the length of the side between the vertices A' and B', we need to use the fact that the ratio of corresponding side lengths between the pre-image and the image is the same as the ratio of the scale factor used in the dilation.

The ratio of the side length between the vertices B'C' and BC is 9/12. If we call this ratio k, then the ratio of the side length between the vertices A'B' and AB is also k.

So we can use the side length between AB = 5 inches and k = 9/12 to find the side length between A'B'

A'B' /AB = k

A'B' = k × AB

A'B' = (9/12) × 5

A'B' = 3.75 inches

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(a) Concerning the coefficients of the equation for the volume of the eggplant ( \(V(ft^{3}) = 3.53\times 10^{-2}\cdot e^{2\cdot t^{2}}\)), the units of the coefficients with values \(3.53 \times 10^{-2}\) and 2 are cubic feet and \(\frac{1}{h^{2}}\), respectively.

(b) Regarding the determination of the coefficients by linear regression, the scientist must plot the square of time versus the natural logarithm of the volume and he would have obtained that the intercept is the natural logarithm of constant A and the slope is constant B.

(c) After the solicitation of the European distributor of the film, the new formula is \(V' = 9.884\times 10^{-4}\cdot e^{1.543\times 10^{-7}\cdot t'^{2}}\), where volume is in cubic meters and time is in seconds.

Note - The statement reports typing mistakes. We present the correct statement below:

The climatic moment in the film "The Eggplant that Ate New Jersey" comes when the brilliant young scientist announces his discovery of the equation for the volume of the eggplant: \(V(ft^{3}) = 3.53\times 10^{-2}\cdot e^{2\cdot t^{2}}\), where \(t\) is the time in hours from the moment the vampire injected the eggplant with a solution prepared from the blood of the beautiful dental hygienist.

(a) What are the units of \(3.53\times 10^{-2}\) and \(2\)?

(b) The scientist obtained the formula by measuring \(V\) and \(t\) and determining the coefficients by linear regression. What would he have plotted versus what on what kind of coordinates? What would he have obtained as the slope and intercept of his plot?

(c) The European distributor of the film insists that the formula must be given for the volume in cubic meters (\(m^{3}\)) as a function of time, in seconds. Derive the formula.

(a) In this exercise, we must make use of principles for dimensional analysis. We know that the equation for the volume of the eggplant is represented by:

\(V(ft^{3}) = 3.53\times 10^{-2}\cdot e^{2\cdot t^{2}}\) (1)

Dimensionally speaking, we have the following case:

\([L]^{3} = [A]\cdot e^{[B]\cdot [t]^{2}}\) (2)

By direct inspection and some algebraic handling, we conclude that:

\([A] = [L]^{3}\)

\([B] = [t]^{-2}\)

Therefore, the units of \(3.53 \times 10^{-2}\) and 2 are cubic feet and \(\frac{1}{h^{2}}\), respectively.

(b) The curve fit for the exponential expression used by the scientist is of the form:

\(V = A\cdot e^{B\cdot t^{2}}\) (3)

If we apply logarithms on both sides of the expression above, then we have the following form:

\(\ln V = \ln A\cdot e^{B\cdot t^{2}}\)

\(\ln V = \ln A + B\cdot t^{2}\) (4)

The scientist must plot the square of time versus the natural logarithm of the volume and he would have obtained that the intercept is the natural logarithm of constant A and the slope is constant B.

(c) An hour equals 3600 seconds and a cubic feet equals 0.028 cubic meters. Hence, we can adapt (1) to fulfill the requirements of the European film distributor by using the following conversions:

\(t' = 3600\cdot t\) (5)

\(V' = 0.028\cdot V\) (6)

Where:

By applying (5) and (6) in (1), we have the resulting formula:

\(V' = 0.028\cdot [3.53\times 10^{-2}\cdot e^{2\cdot \left(\frac{t'}{3600} \right)^{2}}]\)

\(V' = 9.884\times 10^{-4}\cdot e^{1.543\times 10^{-7}\cdot t'^{2}}\)

The new formula is \(V' = 9.884\times 10^{-4}\cdot e^{1.543\times 10^{-7}\cdot t'^{2}}\), where volume is in cubic meters and time is in seconds.

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After a small online search, I've found that the volume equation is:

\(V[ft^3] = 3.53 \cdot10^{-2} \cdot exp(2 \cdot t^2)\)

a) We want to see what are the units of the first factor:

\(3.53 \cdot10^{-2}\)

You can see that the volume is in cube feet, and the only part in the equation that can have units is this one, so the units of this factor should be cube feet.

b) On the vertical coordinate he would see the volume and on the horizontal coordinate he would see the time.

The graph of this function is an increasing exponential function, that grows slow at the beginning and then grows faster.

c) Remember that the term with the units is:

\(3.53 \cdot10^{-2}\)

So we should write this as:

\(3.53 \cdot10^{-2} ft^3\)

Now we know that:

\(1m^3 = 35.3 ft^3\\\\1 = \frac{1 m^3}{35.3 ft^3}\)

Now we can multiply our measure by this to get:

\(3.53 \cdot10^{-2} ft^3 = ( \frac{1 m^3}{35.3 ft^3})*(3.53 \cdot10^{-2} ft^3) = 0.1 m^3\)

Then the equation is:

\(V = 0.1m^3\cdot exp(2 \cdot t^2)\)

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Answer:

Rounded to the nearest dollar, Robert will have $ 505 more than Cooper on his account.

Step-by-step explanation:

Given that Cooper invested $ 3,100 in an account paying an interest rate of 2% compounded quarterly, while Robert invested $ 3,100 in an account paying an interest rate of 3% compounded continuously, to determine, after 12 years, how much more money would Robert have in his account than Cooper to the nearest dollar, the following calculation must be made:

Compound interest formula: Initial x (1 + interest / composition) ^ composition x years

Continuous compound interest formula: Initial x exp ^ (interest x years)

Cooper:

3,100 x (1 + 0.02 / 4) ^ 12x4 = X

3,100 x (1 + 0.005) ^ 48 = X

3,100 x 1,005 ^ 48 = X

3,100 x 1,270 = X

3,938.51 = X

Robert:

3,100 x 2.71828182845904 ^ (3x12) = X

4,443.32 = X

4,443.32 - 3,938.51 = X

504.51 = X

Therefore, rounded to the nearest dollar, Robert will have $ 505 more than Cooper on his account.

Answer:

$139

Step-by-step explanation:

Answer:

61 ft

Step-by-step explanation:

I'm assuming that the diver simply walked off the cliff since we were not given any information about the jump itself.

If the distance between the cliff and the surface of the water is 48.5 feet, and if the distance between the surface of the water and the place where the diver stopped descending is 12.5 feet, you would add those two distances up.

48.5 ft + 12.5 ft = 61 ft

The total distance of her jump from her was 61 feet.

Given that a diver jumps from a cliff that is 48.5 feet above the surface of the water, and she stops descending 12.5 feet under the water, to determine what was the total distance of her jump, the following calculation must be performed:

The height of the cliff and the depth at which it reached under the water must be added.

Therefore, the total distance of her jump from her was 61 feet.

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B — No

A function can only have one output value.

The expression Salina created using the greatest common factor in addition and distributing the property is

9(4 + 6)

9x4 + 9x6

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

36 + 54

Taking out the greatest common factor.

9(4 + 6)

Using the distributive property over addition

9 x 4 + 9 x 6

Thus,

9 x 4 + 9 x 6 is the expression Salina created.

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This question is incomplete, the complete question is;

You decide to record the hair colors of people leaving a lecture at your school. What is the probability that the next person who leaves the lecture will have blonde hair ?

Express your answer as a simplified fraction or a decimal rounded to four decimal places.

Blonde Red Brown Black Gray

31          25       18      40     42

Answer: the probability that the next person who leaves the lecture will have blonde hair is 0.1987

Step-by-step explanation:

Given that;

HAIR COLOR      FREQUENCY

Blonde                         31

Red                              25

Brown                          18

Black                           40

Gray                            42

Total                           156

So

there were 156 people all together

and out of the 156, 31 of them were blonde.

now the probability that the next person who leaves the lecture will have blonde hair will be;

⇒ 31 / 156 = 0.1987

Therefore, the probability that the next person who leaves the lecture will have blonde hair is 0.1987

The correct equivalent expression to the square root containing a variable is 2a³/5 and the correct option is E.

We shall simplify the expression of the square root containing a variable by carrying out basic mathematics operations to derive its equivalent as follows:

squre root of (36a⁸/255a²) = square root of (36a⁶ × a²/255 × a²)

a² is common and can be cancel out

square root of (36a⁸/255a²) = square root of (36a⁶/255)

square root of (36a⁸/255a²) = square of 36 multiplied by the square root of a⁶ all divided by the square root of 255 {take square root of each}

square root of (36a⁸/255a²) = 6a³/15

square root of (36a⁸/255a²) = 2a³ × 3/5 × 3

we divide through by the common factor 3

square root of (36a⁸/255a²) = 2a³/5

Therefore, the equivalent expression to square root of (36a⁸/255a²) is derived as 2a³/5 which is option E.

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After eliminating the parameter, the rectangular equation is y = x³ – 3x² + 3x – 1. Option C is the correct option.

What is a rectangular equation?

An equation in rectangular form, also known as a rectangular equation, is a single equation written in the standard form in mathematics that uses variables like x, y, and z.

Given parametric equations are

y = t³  .......(i)

x = t + 1  .....(ii)

Calculate the value of t from equation (ii):

x = t + 1

t = x - 1

Putting t = x - 1 in equation (i):

y = (x - 1)³

Applying algebric identity (a - b)³ = a³ – 3a²b + 3ab² – b³:

y = x³ – 3x² + 3x – 1

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Answer:

c

cubic

all real numbers

Step-by-step explanation:

Answer:

\(\huge\boxed{\sf 38}\)

Step-by-step explanation:

= a³ + b (6 + c)

Put a = 2, b = 3 and c = 4

= (2)³ + 3 (6 + 4)

= 8 + 3(10)

= 8 + 30

\(\rule[225]{225}{2}\)

Answer:

Step-by-step explanation:

the requied answer is 38.

according to the question the value of a=2,b=3,c=4.

here,

to find the value of   a³ + b (6 + c)we have to do it in steps:

step 1: solve the bracket (6+4) =10.

step 2:  solve the value of a³ =8.

now put these values ,

=8+3(10)

=38.

Answer:

the answer is

C)-9/15-2/5=-1/5

Answer:

Yes because no same x-value resulted in different y-values.

Answer:

Yes

Step-by-step explanation:

Answer:

-4/10

Step-by-step explanation:

Negative X Positive = Negative

2 x 2 = 4

5 x 2 = 10

Put negative: -4/10

Answer:

83

Step-by-step explanation:

3x³+2y-6

x= 3 and y = 4, we will plug in what x equals to for the x value, then we will plug in what y equals to for the y value

3(3³) + 2(4) - 6

now let's use order of operations (PEMDAS: parenthesis exponent multiplication division addition subtraction)

parenthesis first

3³ = 3·3·3= 27

3(27) + 2(4) - 6

there are no exponents so we will use multiplication

3·27 = 81

2·4=8

81 + 8 - 6

83

Answer: exponential decay

Step-by-step explanation:

Exponential decay means that it's getting smaller and you can see that the numbers are getting smaller on the y axis.

Hope this helps :)

The solution to the system of linear equations is (x, y, z) = (64/11, 37/11, 9/11). The system has exactly one solution.

Let's solve the system of linear equations correctly.

The given system of linear equations is:

x = y + 3z = 6

x - 2y = 5

2x - 2y + 5z = 9

To determine the number of solutions, we can analyze the system using the method of elimination or substitution. Let's use the method of elimination:

From equation 1, we have:

x = y + 3z

Substituting this value of x in equation 2:

(y + 3z) - 2y = 5

y + 3z - 2y = 5

-z + 3z = 5 - y

2z = 5 - y

Now, let's substitute the value of x in equation 3:

2(y + 3z) - 2y + 5z = 9

2y + 6z - 2y + 5z = 9

11z = 9

Simplifying the equation, we find:

z = 9/11

Now, substituting this value of z back into the equation 2z = 5 - y, we get:

2(9/11) = 5 - y

18/11 = 5 - y

18/11 - 5 = -y

18/11 - 55/11 = -y

-37/11 = -y

y = 37/11

Finally, we can substitute the values of y and z into equation 1 to find the value of x:

x = y + 3z

x = 37/11 + 3(9/11)

x = 37/11 + 27/11

x = 64/11

Therefore, the solution to the system of linear equations is (x, y, z) = (64/11, 37/11, 9/11).

The system has exactly one solution.

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Answer:

x=23, y=14

Step-by-step explanation:

The triangles are indeed simular

Answer:

there are 5 red marbles, 8 blue marbles, and 12 green marbles in a bag.

Step-by-step explanation:

Answer:

I believe its 52.94% (53 rounded)

Step-by-step explanation: First add all the numbers to see the total amount of marbles (34) Second is add the marbles that are NOT red or yellow (18).Then the final step is divide 18/34

Hope this helps and have a great day

The range of the equation f(x) = 3ˣ ⁻ ¹ - 2 is  y > -2

From the question, we have the following parameters that can be used in our computation:

f(x) = 3ˣ ⁻ ¹ - 2

The above equation is an exponential function

The rule of an exponential function is that

In this case, it is -2

So, the range is y > -2

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Answer:

true

Step-by-step explanation:

if the ball lands on the team who served the ball's side of the court they are allowed to replay it. :)

Answer:

Step-by-step explanation:

Answer:

Ok so the b is a coefficient which means it needs to be replaced by a number.

The 7 is gonna be multiplied by that coefficient then subtracted by 3.

Hope this helped.

Step-by-step explanation:

Answer:

the third option

Step-by-step explanation:

It is saying that seven is being multiplied to the variable b which is then being subtracted from 3. Hope this helped. Happy Holidays!

Answer:

abcdefg

Step-by-step explanation:

Step-by-step explanation:

For drawing the graph , we Firstly need to find the equation of the line . We can find the line using Slope intercept form . Here ,

We know slope intercept form as ,

\(\implies y = mx + c \\\\\implies y = (3)x + (-6) \\\\\implies \boxed{\boxed{y = 3x - 6 }}\)

Now we need to plot the graph of y = 3x -6. Refer to attachment for graph .

The stem and leaves display the image and distribute information continuously. These charts are similar to histograms, but instead of using lines, they show numbers. It is a useful tool, especially when searching for statistical information.

The stem and leaf diagram, also known as the stem and leaf diagram, is a method of organizing data in a way that makes it easy to observe the frequency of importance of different species. A chart that shows numerical data arranged in a series. Each data value or number is divided into stems and leaves.

Rows and sheets are represented in the form of a special table in which each first digit or digit of the document value is divided by the stem and the last digit of the document in sheets. The letter is used to represent the stem and leaf, called stem and leaf values.

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Answer:

c = 5

Step-by-step explanation:

3c - 8c + 7 = -18

-5c + 7 = -18

-5c = -25

c = 5

Answer:

ANSWER: Yes. They have enough to pay their bill: 21 dollars times 1.06 = 22 dollars and 26 cents and 22 dollars and 26 cents times 1.15 = 25 dollars and 60 cents.

Step-by-step explanation:

convert all % to decimals

0.06 x 21 = $1.26 tax

0.15 x 21 = $3.15 tip

1.26 + 3.15 = $4.41 added payment

4.41 + 21 = = $25.41 total bill

(yes i am aware i did the method differently since i learned it another way but the answer should till be correct.)

Answer:

Yes. They have enough to pay their bill: 21 dollars times 1.06 = 22 dollars and 26 cents and 22 dollars and 26 cents times 1.15 = 25 dollars and 60 cents. Otherwise B.

Answer:

The answer is M + 2, if thats wat ur asking for.

Step-by-step explanation:

Answer:

M+2

Step-by-step explanation:

M+12-10

Since there are only 12 and -10 that are the same you can add them together to get 2 and that is pretty much what you could do unless you find what M is.

Hope this helps!