What property is illustrated by (2x)y = (2y)x?

Answer:

This demonstrates the associative property of addition which states that a + (b + c) = (a + b) + c. Basically, it states that it doesn't matter which order you add numbers in, you will always get the same result.

Answer:

Step-by-step explanation:

Given the differential equation dy/dx = 5y/x subject to the condition y = 4 and x = 1. Using the variable separable method of solving differential equation, we will have;

dy/dx = 5y/x

Separate the variables

dy/5y = dx/x

Integrate both sides of the expression

[tex]\frac{1}{5}\int\limits \frac{1}{y} \, dy = \int\limits \frac{dx}{x} \\ \\\frac{1}{5}lny = lnx + C\\\\lny = 5lnx+5C\\[/tex]

using the initial condition y = 4 while x = 1

ln4 = 5ln1 + 5C

ln4 = 0+5C

C = ln4/5

Substituting the value of C back into the expression;

[tex]lny = 5 lnx+5(ln4/5)\\lny = 5lnx+ln4\\lny = lnx^5+ln4\\lny = ln(4x^5)\\y = 4x^5[/tex]

Hence the solution to the differential equation is y = 4x⁵

b) Given 4(du/dt) = u²

du/dt = u²/4

du/ u² = dt/4

u⁻²du = 1/4 dt

integrate both sides of the equation

[tex]\int\limit {u^{-2}} \, du = \int\limits\frac{1}{4} \, dt\\\\\frac{u^{-1}}{-1} = \frac{t}{4} + C\\\\\frac{-1}{u} = \frac{t}{4} + C[/tex]

Imputing the initial condition u(0) = 7 i.e when t = 0, u = 7

[tex]\frac{-1}{7} = \frac{0}{4} + C\\\\\frac{-1}{7} = C\\[/tex]

[tex]\frac{-1}{u} = \frac{t}{4} - \frac{1}{7}[/tex]

Hence the solution to the DE is [tex]\frac{-1}{u} = \frac{t}{4} - \frac{1}{7}[/tex]

Answer:

256x^8

Step-by-step explanation:

Answer:

X/y = 2/5

Y= x+12

Where y = students

X= adults

Number of adults= 8

Number of students= 20

Step-by-step explanation:

The ratio of adults to students on a class field trip is 2 to 5. If there are 12 more students than adults.

Let adult be x

Let student be y

X/y = 2/5

5x= 2y.... equation one

Y= x+12..... equation two

Substituting equation two into equation one

5x= 2(x+12).

5x = 2x +24

3x= 24.

X= 8

Y= x+12

Y= 8+12

Y= 20

Number of adults= 8

Number of students= 20

Answer:

The maximum possible number of miles traveled by an automobile included in the histogram is 40,000 miles.

Step-by-step explanation:

A histogram is a bar graph reprinting the frequency of various categories.

In a histogram the y-axis represents the frequency and the x-axis represents the categories.

Consider the histogram provided for the number of miles driven by a sample of automobiles in New York City.

The y-axis represents the frequency and the x-axis represents the number of miles driven.

The category 10,000 miles has the highest frequency at 30.

And the maximum possible number of miles traveled by an automobile is 40,000 miles.

Thus, the maximum possible number of miles traveled by an automobile included in the histogram is 40,000 miles.

Answer:

42,500 miles

This is your correct answer

Full question attached

Answer explanation attached

Answer:

bottom right histogram fits the distribution

Step-by-step explanation:

we have chosen the bottom right histogram from the options as this fits the distribution best. It can be observed that probability for each outcome from 1(left from the table) increases till 6(right from the table)

Answer:

170.097

Step-by-step explanation:

1 ounce = 28.3495 grams.

28.3495 x 6 = 170.097

Answer:

170.097 grams            Mark me as brainliest!!!!

Step-by-step explanation:

Answer:

Plato

Step-by-step explanation:

The line segment chosen is HI. Its image is H'I'. The slope of preimage HI is -1.25 and the slope of the image H'I' is -1.25.

The Scale Factor is used to scale shapes in different dimensions. We study different geometrical shapes in geometry, both two-dimensional and three-dimensional. The scale factor is a metric for comparing figures with similar appearances but differing scales or metrics.

The image of a transformation is the shape after the transformation. The preimage of a transformation is the shape before the transformation. The image is scale factor times preimage.

A line passing through the points (x₁, y₁) and (x₂, y₂) will have a slope

m = (y₂ - y₁)/(x₂ - x₁).

We are asked to select a line segment other than LK, which is not a vertical or horizontal line segment, for the scale factor n = 3.

So, we have to select a preimage( other than LK), and its image (3 times the preimage).

So we select the preimage as HI and its image as H'I', as the scale factor between them is n = 3, and HI is not a vertical or horizontal line segment.

Now, we calculate their slopes.

For the preimage HI (slope is m₁):

HI passes through the points (2, 0) and (0, 2.5). Substituting these values in the slope formula, we get

m₁ = (2.5-0)/(0-2) = -2.5/2 = -1.25.

For the image H'I' (slope is m₂):

HI passes through the points (6, 0) and (0, 7.5). Substituting these values in the slope formula, we get

m₂ = (7.5-0)/(0-6) = -7.5/6 = -1.25.

∴ The line segment chosen is HI. Its image is H'I'. The slope of preimage HI is -1.25 and the slope of the image H'I' is -1.25.

NOTE: The slopes of images and preimages are always the same as the image is just an enlarged or diminished form of the preimage.

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Answer:

[tex]\huge\boxed{(2x+8)(x-3)=2x^2+2x-24}[/tex]

Step-by-step explanation:

[tex]\text{Use FOIL:}\ (a+b)(c+d)=ac+ad+bc+bd\\\\(2x+8)(x-3)=(2x)(x)+(2x)(-3)+(8)(x)+(8)(-3)\\\\=2x^2-6x+8x-24\qquad\text{combine like terms}\\\\=2x^2+(-6x+8x)-24\\\\=2x^2+2x-24[/tex]

Answer:

2x^2+2x-24

Step-by-step explanation:

when you see two parentheses, you should first think : FOIL!

you take the First terms in each of the parentheses which is 2x and x and multiply them. (2x^2)

then you take the Outer terms in the parenthesis which is 2x and -3 and multiply them. (-6x)

then you take the Inside terms which is +8 and x and multiply them. (+8x)

lastly, you take the Last terms which is +8 and -3 and multiply them. (-24)

you should get this : 2x^2-6x+8x-24. combine like terms and there's your answer!

i also advise you to write down all your terms until you are familiar with this foil stuff. don't be ashamed if you need to write them down! you'll get the hang of it! :)

Answer: The number 99.4177 rounded to the nearest hundredth is 99.42.

Step-by-step explanation:

Here's how I got my answer:

Since you need to round to the nearest hundredth, then round to the first two decimal places. So if the number is 5 or greater, then round up. If the number is 4 or lesser, then do not round up.

In this scenario:

99.4177

Round the 1 in the hundredths place up to 2, because 7 is on the greater end. Since they are just asking you for the hundredths place, then do not round anything else.

Hence, your final answer is 99.42.

Answer:

a. x = -2

Step-by-step explanation:

64ˣ = 16⁽ˣ⁻¹)

64 = 4³

16 = 4²

4³⁽ˣ⁾ = 4²⁽ˣ⁻¹)

4³ˣ = 4²ˣ⁻²

3x = 2x - 2

x = -2

Answer:

[tex]\huge \boxed{x=-2}[/tex]

Step-by-step explanation:

64^x = 16^(x-1)

Rewrite the bases with base of 4.

(4^3)^x = (4^2)^(x-1)

Multiply exponents.

4^(3x) = 4^(2(x-1))

Cancel same bases.

3x = 2(x-1)

Expand brackets.

3x = 2x - 2

Subtract 2x from both sides.

x = -2

Answer:

D. The oldest is 92 youngest 49

Step-by-step explanation:

we can get the answer by pairing each of the values on the left hand side that is these values 4 5 6 7  9 with values on the right.

the first age from the top row is 49 the second is 49

from the second row it is 50 50 51 51 52 5 59

from the 3rd row 61 62 63 64 64 65 6

from the forth row t s 71 72 73 73 74 75 7

from the fifth row it is 80 81 83 87

from the sxth row it is 91 92.

each of the numbers  have just written out represents age. the oldest age there is 92 whle the youngest s 49. It is simply each number under attorney paired wth stem to make a number.

I added an attachment with the pairing

Answer:

Cooking., You either end up with great food because you measured the and use the right amount of ingredients or food that isn't the best because you used too little or too much ingredients.

Bonus) For Time Management, it involves math by scheduling activities and other things such things in life at certain times and some things should be met within certain time limits and such.

Answer: Hi!

Shopping! When you're shopping in a store, you have to calculate and estimate the prices of food and items in your head, (or on paper), so you know the total amount of money you are going to use. Many times the amount of money for an item is a fraction, too!

Hope this helps!

Answer: 2

Step-by-step explanation:

Find the prime factors of each term

Answer:

n = 2

Step-by-step explanation:

- 6n - 2n = 16

- 8n = 16

n = 16/-8

n = -2

Answer:

[tex] - 6n \: - 2n \: = 16[/tex]

[tex] = ) - 8n \: = 16[/tex]

[tex] = )n \: = \frac{16}{ - 8} [/tex]

[tex] = )n \: = - 2[/tex]

Answer:

(4, 1 )

Step-by-step explanation:

Given the 2 equations

2x + 3y = 11 → (1)

x - 3y = 1 → (2)

Adding (1) and (2) term by term will eliminate the term in y

3x = 12 ( divide both sides by 3 )

x = 4

Substitute x = 4 into either of the 2 equations and evaluate for y

Substituting into (1)

2(4) + 3y = 11

8 + 3y = 11 ( subtract 8 from both sides )

3y = 3 ( divide both sides by 3 )

y = 1

Solution is (4, 1 )

Answer:

4:5

Step-by-step explanation:

Davina received 50 votes

Binh reveived 40 votes

It asked for ratio of Binh’s votes to Davina’s

so the ratio is first Binh's 40 to Davina's 50     that's 40 to 50

It want it in simplest form so you find the greatest common factor of 40 and 50 which is 10.

40/10 and 50/10 is 4 to 5

So the answer is 4:5(The ":"  means  "to")

The ratio of Binh’s votes to Davina’s votes is 4:5

The comparison of two numbers or quantities by division is known as the ratio.

Given that, In the student council election, Davina received 50 votes, Binh received 40 votes and Eden received 80 votes.

Required ratio = Binh’s votes \ Davina’s votes  

= 40/50

= 4/5

Hence, The ratio of Binh’s votes to Davina’s votes is 4:5

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Answer:

19

Step-by-step explanation:

10 + 9 = 19. If you look at how many students are above the "30 mark", you will count 10 on the first bar and 9 on the second.

Looks like the integral is

[tex]I=\displaystyle\int (4x-6)(x^2-3x+1)^5\,\mathrm dx[/tex]

If you we substitute [tex]y=x^2-3x+1[/tex] and [tex]\mathrm dy=(2x-3)\,\mathrm dx[/tex], we get

[tex]I=\displaystyle2\int(2x-3)(x^2-3x+1)^5\,\mathrm dx=2\int y^5\,\mathrm dy[/tex]

Now use the power rule, and replace y accordingly:

[tex]I=\dfrac{2y^6}6+C=\dfrac{y^6}3+C=\boxed{\dfrac{(x^2-3x+1)^5}3+C}[/tex]

Step-by-step explanation:

To find the distance between two points, we have to use the distance formula:

[tex]d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

Let's solve for line PQ first. We plug in the points into the formula and solve from there.

P: (-5, 1)

Q: (-2, -5)

[tex]PQ=\sqrt{(-2+5)^2+(-5-1)^2 }[/tex]

[tex]PQ=\sqrt{(3)^2+(-6)^2 }[/tex]

[tex]PQ=\sqrt{9+36}[/tex]

[tex]PQ=\sqrt{45}[/tex]

[tex]PQ=3\sqrt{5}[/tex]

Now, let's solve line ML.

M: (5, 3)

L: (2, -3)

[tex]ML=\sqrt{(2-5)^2+(-3-3)^2 }[/tex]

[tex]ML=\sqrt{(-3)^2+(-6)^2}[/tex]

[tex]ML=\sqrt{9+36}[/tex]

[tex]ML=\sqrt{45}[/tex]

[tex]ML=3\sqrt{5}[/tex]

Answer: 3√5, 3√5, yes, they are congruent.

Answer:

4d+56

Step-by-step explanation:

4(d+14)       you must do distributive property to simplify this answer.

4d + 56      after distributing remove parentheses

Answer:

Answer = 72.46

Answer: 72.46

Step-by-step explanation:

Nearest hundredth is second place to the right of decimal point

- 72.46387

- The second place to the right of decimal point is 6.

Look at the place after 6 to determine whether or not to move up.

- The next place is 3, and 3 is less than 5, so we keep the place.

72.46

Hope this helps!! :)

Please let me know if you have any question or need further explanation

Answer:  x = 34

Step-by-step explanation:

⁴ ⁻ˣ/₅ + ˣ + 2/₃ = 6

Now resolve into fraction and convert to a linear equation

4 - x /₅ + x + 2/₃ = 6

3( 4 -x ) + 5( x + 2 )/15 = 6

3( 4 - x ) + 5( x + 2 )    = 6 x 15

12 - 3x + 5x + 10         = 90

        2x + 22              = 90

                             2x  = 90 - 22

                             2x  = 68

                                x = 34

Joanne has to pay monthly membership fees = $24.72 per month

And registration fee = $49.95

Here,

The given expression is 24.72 m + 49.95

Joanne has to pay registration fee as well as monthly membership.

And, m denotes the number of months.

We have to explain the different part of given expression.

What is linear expression?

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.

Now,

The given expression is ;

⇒ 24.72 m + 49.95

Joanne has to pay registration fee as well as monthly membership.

Where, m denotes the number of months.

From the expression;

⇒  24.72 m + 49.95

We can see that,

Joanne has to pay monthly membership fees = $24.72 per month

And registration fee = $49.95

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I'm not sure what you're really talking about.

But I think you are talking about fractions.

In fractions there are two places

The number that goes on the top is numerator.

Answer:

2000 kilograms

Step-by-step explanation:

Answer:

The average rate of function of f on the given interval is -1.

Step-by-step explanation:

Recall that the average rate of change is simply the slope of the function between two points.

We are given the function:

[tex]f(x)=x^2-4[/tex]

And we want to find its average rate of change on the interval [-4, 3].

Evaluate the two endpoints:

[tex]\displaystyle \begin{aligned} f(-4) & = (-4)^2 - 4 \\ \\ & = 16 - 4 \\ \\ & = 12\end{aligned}[/tex]

Likewise:
[tex]\displaystyle \begin{aligned} f(3) & = (3)^2 - 4 \\ \\ & = 9 - 4 \\ \\ & = 5\end{aligned}[/tex]

Recall that slope is given by:

[tex]\displaystyle m = \frac{\Delta y}{\Delta x}[/tex]

Hence, the average rate of change is:
[tex]\displaystyle\begin{aligned} \text{Avg Rate of Change} & = \frac{(5)-(12)}{(3)-(-4)} \\ \\ &= \frac{-7}{7} \\ \\ & = -1\end{aligned}[/tex]

In conclusion, the average rate of function of the given function on the given interval is -

Answer:

Step-by-step explanation:

Using the distance formula

the distance between (-10, 12) and (5, 3) is

d = 17.492855

We have the final answer as

Hope this helps you

Answer:17.5

Step-by-step explanation: