In your gym class, your teacher can create teams of 4 for a
relay race and have no students left over. The next day, your
teacher creates teams of 5 for dodge ball and has no
students left over. What are some possible numbers of
students in your class?

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:

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.

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.

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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Answer: 7 handshakes in all.

Step-by-step explanation:

If you and another person have one shake  and there are 14 total people in the cabin that means that there will be 7 handshakes  in all.

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:

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]

Answer:  (a) 720°,  (b)  120°

Step-by-step explanation:

A hexagon is a polygon with six sides.

Formula for finding the interior angle of a polygon = ( 2n - 4 )complementary

                                                                                    = ( 2n - 4 ) 90

complimentary angle is 90°  or

                                                                                     = ( n - 2 )supplementary

supplementary angle is 180° . Now solving the question now since n = 6

we now put it in any of the formula above

       ( 2 x 6 - 4 ) x 90  =  ( 12 - 4 ) x 90

                                   =   8 x 90

                                   = 720°     or

     ( 6 - 2 ) x 180        =  4 x 180

                                  = 720°.

The second part of the question, each size of the interior angle

                                  = ⁷²⁰/₆

                                  = 120°

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:

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:

a. [tex]Total = 4P[/tex]

b. [tex]Gas = 2P[/tex]

c. [tex]2P - 5[/tex]

d. [tex]P = 20[/tex]

Step-by-step explanation:

Given

[tex]Amount\ received = P[/tex]

[tex]Number\ of\ days = 4[/tex]

[tex]Coffee = \$5[/tex]

[tex]Amount\ Left = \$35[/tex]

Calculating (a); the total amount earned;

[tex]Total = Amount * Days[/tex]

[tex]Total = 4 * P[/tex]

[tex]Total = 4P[/tex]

Calculating (b): Money Spent on Gas

From the question, we understand that 1/2 of his earnings is spent on gas;

Hence;

[tex]Gas = \frac{1}{2} * Total[/tex]

Substitute 4P for Total

[tex]Gas = \frac{1}{2} * 4P[/tex]

[tex]Gas = 2P[/tex]

Calculating (c): Expression for coffee

First, we need to calculate the amount left after buying Gas;

[tex]Amount = Total - Gas[/tex]

[tex]Amount = 4P - 2P[/tex]

[tex]Amount = 2P[/tex]

From this amount, he bough coffee of $5;

Hence; he's left with

[tex]2P - 5[/tex]

Calculating (d): Calculating his daily earnings

After (c) above, he has $35 left

So, we have

[tex]2P - 5 = 35[/tex]

Add 5 to both sides

[tex]2P - 5 + 5= 35 + 5[/tex]

[tex]2P = 40[/tex]

Divide through by 2

[tex]P = 20[/tex]

Hence, his daily earnings is $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

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:

(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:

the relation is a function since one input provides us with only one output

outputs are the range since we know that range is the set of all possible outcomes

Answer:

5, -4, and -7

Step-by-step explanation:

5x² = 4x + 7

The standard form of a quadratic equation is

y = ax² + bx +c, where

a, b, and c are the coefficients.

If we convert your quadratic to the standard form, it becomes

5x² - 4x - 7 = 0

The coefficients are 5, -4, and -7.

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:

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:

2000 kilograms

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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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:

[tex]a = \frac{1}{15}[/tex]

Step-by-step explanation:

Hey there!

To solve the given we'll use keep change flip.

[tex]\frac{1}{5} / 3 = a\\\\\frac{1}{5} *\frac{1}{3} = a\\\\\frac{1}{15} = a[/tex]

Hope this helps :)

Answer: 2

Step-by-step explanation:

Find the prime factors of each term

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:

This question is incomplete because the options are missing; here is the complete question:

Which expression is equivalent to (73) 5 • 74?

Select each correct answer:

73 • 5 + 4

73 + 5 + 4

73 + 5 • 74

73 • 5 • 74

The answer to this question is  73 • 5 • 74

Explanation:

The symbol • represents multiplication, this implies the numbers 5 and 74 should be multiplied when solving this operation. Moreover, if the expression is simplified the same symbol or a multiplication symbol should be used.

Moreover, the lack of a symbol between these numbers and 73 indicates multiplication. Indeed, in algebra and some fields of mathematics, the multiplication symbol is omitted, and two numbers standing side by side with no symbol indicate the multiplication. Thus, it is correct to place a multiplication symbol between 73 and the other numbers.

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:

256x^8

Step-by-step explanation: