How do you think increased distance will affect travel time?

The remainder is 44

The given polynomial is:

The function is to be divided by x - 2

The remainder of the division will be calculated using the remainder theorem

The remainder theorem states that " If a function g(x) is divided by x - a, the remainder of the division will be g(a)"

The remainder when g(x) is divided by x -2 is g(2)

The given statement "Negative is the opposite of an integer" is FALSE.

So, on the number line, opposite values are those that are equally spaced apart from zero.

These numbers' opposites are:

Therefore, the given statement "Negative is the opposite of an integer" is FALSE.

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x = 10 is the value of x as per given in the question.

3x + 6  = 36

3x = 30

x = 10

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Answer: y=2x

Step-by-step explanation:

The equation of the line is y=2x.

AS per the unitary method, the number of freshmen majoring in chemistry are 162.

Unitary method:

Unitary method defied as a process of finding the value of a single unit, and based on the known values.

Given,

In a certain​ country, 9/50 of college freshmen major in chemistry. A community college in a region of the country has a freshman enrollment of approximately 900 students.

Here we need to find the the number of freshmen majoring in chemistry.

As per the concept of unitary method, let us consider x be the number of freshmen majoring in chemistry.

So, we know that, 9/50 of college freshmen major in chemistry.

The total number of students in the community colleges is 900.

Therefore, the number of freshmen in it is calculated as

x = 900 x 9/50

x = 18 x 9

x = 162

Therefore, there are 162 freshmen in chemistry.

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Answer:

834.6m

Step-by-step explanation:

780*1.07=834.6

The law of uninhibited growth is express as:

where N(t) is the population at time t, N0 is the initial population, k is the growth rate and t is the time. In this case we know that after one day, t=1, the population is 800 and that the initial population was 500; plugging these values and solving for k we have:

Now that we have the growth rate, we know that the population growth in this case can be express as:

We want to know the time it takes for the population to be 7000, to find it we equate our expression to this value and solve for t:

Therefore, it takes 5.6 days for the population to reach 7000 individuals.

Next two terms of the sequence 4, 8, -16, -32, 64, ?, ? are 128 and -256.

How to solve question in sequence?

Every sequence has certain logic which can be used to find next terms.

Mainly operations like addition, subtraction, multiplication, squares and cubes are used to find the logic.

Trial and error method is applied to comprehend the logic of sequence.

4, 8, -16, -32, 64, A, B.

According to the given question, the sequence can be split in two separate sequences by taking alternate terms -

1) 4, -16, 64, B

2) 8, -32, A

Now clearly the logic is:

Next term is obtained by multiplying the previous term with -4.

Let's check 4x(-4) = -16x(-4) = 64

∴ B = 64x(-4) = -256

Similarly, 8x(-4) = -32

∴ A = -32x(-4) = 128

Hence completed sequence is 4, 8, -16, -32, 64, 128, -256.

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From the given question

The volume of a cone is:

Now,

We are given with radius and the height of the cone

So,

We can solve for the radius as a function of water level using ratio and proportion

Then,

Substitute the value of r into the above formula

So,

Then,

Taking derivatives

The,

Solving for the dh/dt

So,

Hence, the answer is 9.55.

Answer: 2.5, 5.4

Step-by-step explanation:

[tex]-16t^2 +126t=213\\\\16t^2 -126t+213=0\\\\t =\frac{-(-126) \pm \sqrt{(-126)^2 -4(16)(213)}}{2(16)}\\\\t \approx 2.5, 5.4[/tex]

First, let's draw a sketch of the problem to better understand it:

Since the distances 20, 4√7 and x create a right triangle, we can use the Pythagorean theorem to calculate the value of x.

The Pythagorean theorem states that the length of the hypotenuse squared is equal to the sum of each leg squared.

So we have:

Therefore the wanted distance is 12√2 feet (16.97 ft).

A sandwich store charges a $10 delivery fee and $4.50 for each sandwich.

a) If an office order 6 sandwiches, the total cost is:

10 + 6(4.50) = 10 + 27 = 37

Then, the cost of the order is $37

b) The total cost of x sandwich is given by the following algebraic equation:

f(x) = 10 + 4.50x

because 10 from the delivery fee and x sandwiches cost 4.50x dollars, f(x) is the total cost.

c) The relationship between the number of sandwiches and the cost of the order is proportional, because if the numbers of sandwiches increases, the cost increases too. It can be appreciated in the function f(x), which is a linear function with a unit rate of 4.50.

First, let's calculate the Profit functions which is P(x)=R(x)-C(x)

Let's continue simplifying the function

The profit function is a polynomial function, so the domain is all the real numbers which means x can be any real number

Domain=(-∞,∞)

Calculating x=-10 doesn't make sense because x in all the functions is the number of items, and doesn't make sense to have -10 items, so x shouldn't be negative numbers.

And Calculating x=1000 doesn't make sense either because the problem says "The maximum capacity of the company is 110 items" so if we have x=1000 we are exceeding the limit of items that the company can handle.

Now let's calculate the profit when producing 40 and 50 items (we just need to evaluate those values in the function):

The profit when the company produces 50 items is 500 and the profit when the company produces 40 items is 550.

The company should choose to produce 40 items because is a higher profit in contrast to making 50 items.

According to the function, when we replace the values in X we can see that the term (X^2) grows more than the term X and as you can see the term X^2 is negative which decreases the final result of the profit. Another way to see this is by drawing the function

As you can see the function is a parable and when the number of items "X" is very high the function tends to decrease. The function starts to grow in profit until 40 items (when you find the maximum value of profit) and then the profit function decreases.

Answer:

Step-by-step explanation:

ur mom

x = 113.2941  is the approximate length of the tree's shadow at the same time of a day.

A unit of length is any arbitrarily chosen and widely accepted reference standard for measuring length. The most common units in modern use are metric units, which are used in every country on the planet. In the United States, customary units are also used. British Imperial units are still used in the United Kingdom and other countries for a variety of purposes. SI and non-SI units are subsets of the metric system.

5 feet + 8 inches is equal to 5 feet.

5 feet 8 inches is equal to 5 feet plus (8 inches) * (1 foot 12 inches).

5 feet 8 inches plus (8/12) feet equals 6 feet.

5 feet 8 inches equals 5 feet plus 2/3 feet.

5 feet 8 inches = (5 + (2/3)) feet

5 feet 8 inches = ((15/3) + (2/3)) feet

5 feet 8 inches = ((15+2)/3) feet

5 feet 8 inches = (17/3) feet

5 feet 8 inches = 5.667 feet

A/B = C/D

where

A = height of person

B = length of shadow of person

C = height of tree

D = length of shadow of tree

So we have

A = 17/3

B = 2

C = 321

D = x

A/B = C/D

(17/3)/2 = 321/x

(17/3)*x = 2*321

(17/3)*x = 642

(3/17)*(17/3)*x = (3/17)*642

x = 1926/17 the precise length of the tree's shadow

The approximate length of the tree's shadow is x = 113.2941.

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Answer:

Explanation:

The median is the value corresponding to the line inside the box. Looking at the box plot, the line is between 8 and 9. Thus,

Median = 8.5

To find the measure of variability, we would find the interquartile range, IQR

IQR = third quartile(Q3) - first quartile(Q1)

The first quartile is the value corresponding to the left end of the box. From the box plot, it is between 5 and 6. Thus,

Q1 = 5.5

The third quartile is the value corresponding to the right end of the box. From the box plot,

Q3 = 11

Thus,

IQR = 11 - 5.5

IQR = 5.5

The range is the difference between the minimum and maximum values. On the box plot,

maximum value = 13

minimum value = 1

Range = 13 - 1

Range = 12

answer:

6378/2

step-by-step explanation:

dividing the largest number by the smallest number will allow for the greatest quotient. hope that helps!

Answer:

-1280

Step-by-step explanation:

So, as we can see just by loooing at this geometric sequence, the factor is -2. Let's double check this.

10 * -2 = -20 * -2 = 40

We can just keep multiplying to find the 8th term!

40 * -2 = -80 * -2 = 160 *-2 = -320 * -2 = 640 * -2 = -1280

Sometimes with a short sequence, it is better to just multiply it out. You could also do it like this, though:

[tex]a_{n}=a_{1} *r^{n-1}[/tex]

Here, r = -2. We are looking for the 8th term, which would be 8

Plug in our values:

[tex]a_{8}=10*-2^{7}[/tex]

[tex]-2^{7}=-128\\[/tex]

[tex]10*-128=-1280[/tex]

That is the same answer we got before. I would suggest doing it mathematically if you have a long sequence (15, 100, 300 terms)

Hope this helped!

(x-3) is not a factor of [tex]2x^3-4x^2-6[/tex]

and the Remainder is 32 .

Using the remainder theorem, which asserts that if x is a factor in a polynomial p(x), then p(a) = 0, we may say that.

Therefore, p(x) = 2x3 - 4x2 - 6 p(3) = 0 if x - 3 is a factor.

So, p(x) = 2x³ - 4x² - 6 If x - 3 is a factor, then

p(3) = 0

So, substituting x = 3 into the equation, we have

p(3) = 2x³ - 4x² - 6

= 2(3)³ - 4(2)² - 6

= 2(27) - 4(4) - 6

= 54 - 16 - 6

= 54 - 22

= 32

Since p(3) ≠ 0.

x - 3 is not a factor

2. Since p(3) = 32,

Thus the required remainder is 32.

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Yes, Because the amount charged grows by $35, a fixed amount, every time the number of months increases by 1.

Direct proportion, also known as direct variation, is a relationship between two quantities when their ratio equals a fixed number. The proportional symbol is used to denote it. The fact that the other quantity is inverted here means that the same symbol is really employed to denote inverse proportional.

Direct proportionality applies. This is so that the cost of the membership remains constant no matter how many months you choose to pay for. For instance, the cost is 1 x $35 if you pay for one month. The price increases to 2 x $35 if you pay for two months, which is twice as expensive.

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The greatest common factor or GCF in the expression  4y + xy² + 6y is y.

The given expression is 4y + xy2 + 6y

GCF stands for greatest common factor

Among these three numbers ;

the variable y is common in all three of them

The factors of 4 y = 4 and y

the factors of xy² are x and y

and the factors of 6y are 6 and y

This can also be simply written by taking y common in this

for example; y ( 4 + xy + 6 )

From the above mentioned proof we can establish the fact that the variable y is common in all three of them

Thus the greatest common factor among them is y

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An irrational number is a number that cannot be written as a fraction - the decimal goes on forever without repeating. Therefore:

in this case it cannot be expressed as a fraction and it is decimal, this is the correct option. So,

answer A.

Answer:

A//F

CE

BD

Step-by-step explanation:

since its an equilateral triangle you can split in half easily

Answer: I suppose it is still 60

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

becaus eit the whole nimber

Answer:

2, 3, 5

Step-by-step explanation:

There is no side-side congruence theorem.

There is also no angle-side-side congruence theorem.

That eliminates choices 1 and 4.

The triangles show side-angle-side-angle as congruent corresponding parts.

Also using the vertical angles at vertex C, you get angle-side-angle.

Answer: choices 2, 3, and 5.

ANSWER

81 people

EXPLANATION

Let p be the number of people that attend the party.

Under plan A, the inn charges $30 for each person, so the value y of a party for p people is,

Then, under plan B, the cost is $1300 for a maximum of 25 people - this means that if 1 to 25 people attend the party, the cost is the same, $1300. For each person in excess of the first 25 - this means for 26, 27, 28, etc, the inn charges $20 each. The cost for plan B is,

The last part, (p - 25), is the part of the equation that separates the first 25 attendees. This equation works for 25 people or more, but it is okay to solve this problem. Note that for p = 25, the cost for plan A is,

Which is less than the cost of plan B ($1300).

We have to find for what number of people attending the party, the cost of plan B is less than the cost of plan A,

We have to solve this for p. First, apply the distributive property of multiplication over addition/subtract4ion to the 20,

Add like terms,

Now, subtract 20p from both sides,

And divide both sides by 10,

For 80 people, the costs of the plans are,

Both have the same cost. The solution to the inequation was the number of people, p, is more than 80. This means that for 81 people the cost of plan B should be less than the cost of plan A,

For 81 people, plan B costs $10 less than plan A.

f(x) is a linear function whose slope is equal to -1 and y-intercept is equal to -7.

Here we have f(x) defined as:

f(x) = -x - 7

Now, we define a general linear function as:

g(x) = m*x + b

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

Now, we can rewrite f(x) as:

f(x) = (-1)*x +  (-7)

So f(x) is a linear function with a slope of -1 and a y-intercept of -7.

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Answer:

There are 3 common factors of 63 and 54, that are 1, 3, and 9. Therefore, the greatest common factor of 63 and 54 is 9.

Step-by-step explanation:

In algebra, like terms are terms that have the same variables and powers. The coefficients do not need to match.

Hope this helped:)

There are 144 players in the 12-team league.

Given:

In one basketball league, there are 96 players on 8 teams.

In another basketball league, there are 12 teams.

All of the teams in both leagues have the same number of players.

we are asked to determine the  number of players in the 12-team league.

⇒ 96 player - 8 teams

⇒ 12 team player = ?

⇒ 96/8 = 12 player.

each team:

⇒ 12 × 12

= 144 players in 12 teams.

Hence we get the answer as 144 players.

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