Environment An accident at an oil drilling platform is causing a circular oil slick. The slick is 0.08 foot thick, and when the radius of the slick is 150 feet, the radius is increasing at the rate of 0.5 foot per minute. At what rate (in cubic feet per minute) is oil flowing from the site of the accident?

When f(x)=4x+3 and g(x)=x^2-x+1, the value of f(x) + g(x) is x^2 + 3x + 4.

An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.

It shtbe noted that to get the sum of f(x) and g(x), we merely add the two functions:

f(x) + g(x) = (4x + 3) + (x^2 - x + 1)

Then, it is possible to simplify this expression by combining terms having the same coefficients:

f(x) + g(x) = x^2 + 3x + 4

In conclusion, f(x) + g(x) = x^2 + 3x + 4.

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Let f(x)=4x+3 and g(x)=x^2-x+1    f(x) + g(x)

Answer:

5 inches

Step-by-step explanation:

hypotenuse (h)=13

perpendicular (p)=12

base(b)=√h^2-b^2

=√169-144

=√25

=5

\(\large \maltese \: \: { \underline{ \underline{ \pmb{ \sf{SolutioN }}}}} : - \)

Answer:

Step-by-step explanation:

\( \large \sf \leadsto \: \: 3(5 + x) = 60\)

Now,

\(\large \sf \leadsto \: 15 + 3x = 60\)

\(\large \sf \leadsto \: 3x = 60 - 15\)

\(\large \sf \leadsto3x = 45\)

\(\large \sf \leadsto x= \frac{45}{3} \)

\(\large \bf \leadsto \: x \: = 15\)

\( \underline { \rule{190pt}{5pt}}\)

The dollar amount the school will raise is given by the expression 0.25n, where n is the number of students.

A combination of terms through addition, subtraction, multiplication, division, and other operations is known as an algebraic expression (or variable expression).

A connection that compares two numbers or other mathematical expressions inequitably is known as an inequality in mathematics.

Therefore the dollar amount the school will raise is given by the expression 0.25n or \(\frac{1}{4} n\) , where n is the number of students.

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Answer: you didn’t even say please

explanation: why don’t you ask your mother you make me sad

So we've shown that every pair of vertices in S is connected by an edge in the subgraph induced by S. Therefore, the subgraph induced by S is a complete graph.

To start with, let's clarify what we mean by some of these terms. A graph is just a collection of vertices (or nodes) and edges connecting them. In this case, we're dealing with the complete graph kn, which means that there are n vertices and every possible edge connecting them is included in the graph. So there are a total of n(n-1)/2 edges in the graph.

Now, we're interested in subgraphs of kn. A subgraph is just a subset of the vertices and edges from the original graph. In this case, we're interested in subgraphs induced by nonempty subsets of the vertex set. So if we take some subset of the n vertices in kn, we can look at the edges connecting them and see if they form a complete graph.

So let's say we take some subset of the vertices and call it S. We want to show that the subgraph induced by S is a complete graph. In other words, every pair of vertices in S is connected by an edge.

To see why this is true, let's consider the complement of S, which we'll call S'. This is just the set of vertices in kn that are not in S. Since S is nonempty, S' is also nonempty.

Now, consider any pair of vertices in S. Call them v and w. Since v and w are both in S, they are not in S'. This means that there is an edge connecting v and w in kn, since kn is a complete graph. But since we're only looking at the vertices in S, this edge is also in the subgraph induced by S.

So we've shown that every pair of vertices in S is connected by an edge in the subgraph induced by S. Therefore, the subgraph induced by S is a complete graph.

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Answer:

Patterns

Step-by-step explanation:

Deductive reasoning is used to prove conjectures to be true

Answer:

patterns

Step-by-step explanation:

Deductive reasoning is a simple form of arriving at a conclusion by joining two or more pieces of information. Deductive reasoning is used to prove conjectures to be true.

The area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

Area of regular polygon = 1/2 × apothem × perimeter

perimeter = (s)side length of octagon × (n)number of side.

apothem = s/[2tan(180/n)].

11 = s/[2tan(180/12)]

s = 11 × 2tan15

s = 5.8949

perimeter = 5.8949 × 12 = 70.7388

Area of dodecagon = 1/2 × 11 × 70.7388

Area of dodecagon = 389.0634 in²

Area of pentagon = 1/2 × 5.23 × 7.6

Area of pentagon = 19.874 in²

Therefore, the area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

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The description of the transformation of z on the complex plane that gives the product of and is to scale by a factor of 4, then rotate counterclockwise by /6 radians.

To understand this transformation, let's break it down into its components. Scaling by a factor of 4 means multiplying by 4. This scales the magnitude of by a factor of 4 but does not change its direction. Next, rotating counterclockwise by /6 radians means rotating around the origin by an angle of /6 in the counterclockwise direction. By performing these two transformations in succession, we first scale by a factor of 4, which stretches or compresses it depending on whether it is inside or outside the unit circle, respectively. Then, we rotate counterclockwise by /6 radians, which changes its angle in the counterclockwise direction by /6 radians.

The resulting transformation gives the product of and because scaling and rotation are commutative operations when applied to complex numbers. The order in which the transformations are performed does not affect the result. Therefore, scaling by a factor of 4, then rotating it counterclockwise by /6 radians, will yield the same result as scaling by a factor of 4, then rotating it counterclockwise by /6 radians.

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Answer:

2.05m

Step-by-step explanation:

A better method to determine the more popular sport is by conducting a comprehensive, unbiased survey with a random sample

a. Concluding that baseball is more popular than soccer based on a poll at a championship event is not valid due to potential sample bias, self-selection bias, limited sample size, and question phrasing.

b. A better method to determine the more popular sport is by conducting a comprehensive, unbiased survey with a random sample of students in a neutral setting, using clear and unbiased questions that allow for all preferences

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Answer:135

Step-by-step explanation:

bcs 45x60 is 2700 ÷20= 135

Answer:

the product of 3, and a number increased by 2

The formula for the associative property of multiplication is (a × b) × c = a × (b × c).

This is further explained below.

Generally, The associative property is a feature that certain binary operations have in mathematics. This property indicates that the outcome of an expression will not change even if the parentheses are rearranged in the expression.

Associativity is a legitimate rule that may be used to substitute expressions in logical proofs when working with propositional logic.

In conclusion, (a times b) times c equals a times (b times c), and this is the formula for the associative property of multiplication.

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Answer:

not simplified

Answer:

1)   Adding

2)  x = 1.5   y = 8

Step-by-step explanation:

1. Which would be a more helpful for solving the system: adding the two equations or subtracting one from the other?

Adding.

Would eliminate the y variable

2.solve the system without graphing, show your reasoning

After adding the equations

8x = 12

Divide both sides by 12

x = 1.5

Substitute into the first equation

2(1.5) + (1/2)y = 7

3 + (1/2)y = 7

(1/2)y = 4

y = 8

The required solution of the system of equations is x = 3 / 2 and y = 8.
[Adding the two equations is a more appropriate approach]

The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.

Here,
Given a system of evaluation,

2x+1/2y=7   - - - - - - - - - (1)
6x−1/2y=5   - - -- - - -  - - -(2)

Adding equations 1 and 2
2x + 6x + 1/2y - 1/2y = 7 + 5
8x = 12
x = 12 /8
x = 3 / 2
Put x in equation 1
2 * 3 / 2 + 1/2y = 7
1/2y = 7 - 3
y = 4 * 2
y = 8

Thus, the required solution of the system of equations is x = 3 / 2 and y = 8. [Adding the two equations is a more appropriate approach].

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Answer:

(x + 1)(x + 2) = 7x - 1

{1, 2, 3} and {3, 4, 5}

Step-by-step explanation:

Let the three consecutive integers be x, x + 1, and x + 2.

(x + 1)(x + 2) = 7x - 1

x² + 3x + 2 - 7x + 1 = 0

x² - 4x + 3 = 0

(x - 3)(x - 1) = 0

x - 3 = 0  or  x - 1 = 0

x = 3  or  x = 1

For x = 1,

x = 1, x + 1 = 2, x + 2 = 3

For x = 3,

x = 3, x + 1 = 4, x + 2 = 5

Answer: {1, 2, 3} and {3, 4, 5}

Answer:

a

Step-by-step explanation:

Hope this helps

Answer:

It’s the first one

Step-by-step explanation:

George Washington was reluctant to lead the Continental Army because he was worried about leaving his wife, Martha, alone if he were to be captured or killed during the war.

9514 1404 393

Answer:

Step-by-step explanation:

A terminating decimal has an equivalent denominator that is a power of 10. That is, it is the product of a power of 2 and a power of 5.

Any fraction that has a denominator that is a power of 2 can be expressed as an equivalent fraction with a power of 10 as the denominator.

Example:

  \(\dfrac{7}{2048}=\dfrac{7}{2^{11}}=\dfrac{7\cdot5^{11}}{2^{11}\cdot5^{11}}=\dfrac{7\cdot5^{11}}{10^{11}}=0.00341796875\)

hope this helps.enjoy!!!!!!

this is difficult lol im scared to attempt this so i wont

Answer:

The answer is 0.005.

Step-by-step explanation:

When you divide any number by 10, you move the decimal point over to the left by 1 place.

If, for example, you were instead multiplying by 10, your answer would change to 0.5.

In conclusion, the Mean Value Theorem confirms the inequality holds true.

To prove that (1+h) < (1 + 2h/1),

where h > 0, using the Mean Value Theorem, we can consider the function

f(x) = (1 + x).

According to the Mean Value Theorem, if a function is continuous on a closed interval [a, b] and differentiable on the open interval (a, b), then there exists at least one c in (a, b) such that

f'(c) = (f(b) - f(a))/(b - a).
In this case, we have a = 0 and b = h.

Taking the derivative of f(x), we get f'(x) = 1.

Applying the Mean Value Theorem, we have:
f'(c) = (f(h) - f(0))/(h - 0)
1 = (1 + h - 1)/h
1 = h/h
1 = 1
Therefore, we have proved that (1+h) < (1 + 2h/1) for h > 0.

In conclusion, the Mean Value Theorem confirms the inequality holds true.

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Answer:

B. To swim 200 meters, it takes Jana 120 seconds and Micah 104 seconds.

Answer:

B.

Step-by-step explanation:

because you just read everything and look at the table make sure each statement is fully correct in this case it is B

Answer:

Reducing 420/630

420/630 = (?)

420/630 = (2 x 2 x 3 x 5 x 7)/(2 x 3 x 3 x 5 x 7) How i got this is explained at the bottom*

= 2/3

420/630 = 2/3

The simplest form of 420/630 is 2/3

2/3 is the lowest term of 420/630.

Prime FACTORING:
This should help for visuals for 420:
420

| \  

210   2

| \  

105   2

| \  

35   3

| \  

7   5

This should help for visuals for 630:

630

| \  

315   2

| \  

105   3

| \  

35   3

| \  

7   5

The cost of a CD is $5.94 more than the cost of a DVD. Let's assume that the cost of a DVD is "x" dollars, then the cost of a CD is "x+5.94" dollars.

Using this information, we can write the following equations:

5(x+5.94) + 2x = 113.63 (cost of 5 CDs and 2 DVDs)

6(x+5.94) + 2x = ? (cost of 6 CDs and 2 DVDs)

Solving the first equation for "x", we get x = 12.21. Substituting this value in the second equation, we get the cost of 6 CDs and 2 DVDs as $83.64.

Therefore, the cost of 6 CDs and 2 DVDs would be $83.64 at All Bets Are Off Electronics if 5 CDs and 2 DVDs cost $113.63, and CDs cost $5.94 more than DVDs.

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Answer:

7 inches

Step-by-step explanation:

area of square=l^2

49=l^2

\(\sqrt{49\)=l

7=l

therefore the sides of a triangle is 7 inches.

Answer:

7

Step-by-step explanation:

So to find this you know a square has 4 equal sides. The area is 49, and area is side length multiplied by side length. So what number multiplied by itself is 49? 7 x 7=49!

Step-by-step explanation:

as given,

hari bought,

amount of pure ghee he bought = 25 kg

cost of pure ghee per kg = Rs. 180

so, cost of 25 kg of pure ghee = 180 × 25 = Rs 4,500

amount of vanaspati ghee = 25 kg

cost of per kg of vanaspati ghee = Rs. 80

so, cost of 25 kg of vanaspati ghee = 80 × 25 = Rs. 2,000

he mixed both the ghee and got ( 25 + 25 ) = 50 kg of mixed ghee.

he sold them in cost = Rs. 150 per kg

so, total SP of mixed ghee = 150 × 50 = Rs. 7,500

so,

total CP = ( 4500 + 2000 ) = Rs. 6,500

total SP = Rs. 7,500

so,

Profit = SP - CP

→ 7,500 - 6,500 = Rs. 1000

Profit / gain = ( gain × 100 / CP)

→ (1000 × 100 / 6,500 )

→ 1000/65 = 15.38 ( approx.)

therefore, it's a profit of 15.38%.

hope this answer helps you dear! and may u have a great day ahead! take care!

please check the attachment for solutions

Step-by-step explanation:

Before we find the ninth term, we need to find the common ratio. The common ratio in a geometric sequence is the number that every number after the first one is multiplied by. For example, in the sequence {2, 4, 8, 16, 32, ...}, the common ratio is 2.

Now, for our example, the numbers in the sequence alternate between negative and positive numbers. What does that tell us about the common ratio? Well, the common ratio has to be negative because the negative sign keeps alternating.

So we know the common ratio is negative. But what about the rest of the number? Well, we can see that the ratio has a 1 in the numerator because the numerator is the same throughout the sequence (aside from the alternating negative sign).

Now that we've narrowed down the possibilities to -1/x, let's figure out the denominator of the common ratio. The denominator changes from 3 to 9 to 27 to 81. Do you see a pattern there? Each denominator is 3 times the value of the previous denominator. The denominator of the common ratio, then, must be 3.

Ok. We have our common ratio, -1/3, but the question we still need to find the 9th term in the sequence. Well, we can write out the pattern until we get to the term we want. But what if you were trying to find the one hundredth or the one thousandth term? That would take a very long time to write out. Instead, we can take the first number in the sequence (1/3) and multiply it by the our common factor to the power of the remaining terms. As a formula, this looks like: \(a_{1} *f^{n-1} = a_{n}\), where a is your first term, f is your common factor and n is the number of the term you are trying to find.

So, finally, we can solve the problem.

1/3 * (-1/3)⁸ = a₉

1/3 * 1/6561 = 1/19683

So the value of the ninth term of the given geometric sequence is 1/19683.

I hope you learned something and it wasn't too difficult to understand.

Answer:

^^ what he said xD

Step-by-step explanation:

It was snowing again and I smiled as I stared at the white flakes fluttering by my window. It was (capitalized the C)Christmas, and my day had been one of the best all year. First I (had removed) awakened in the morning to the sound of my brother (added the n to runing)running madly around the house, yelling that it was Christmas. Jumping out of bed, (capitalized the i that was there)I skipped happily down the stairs, with my brother at my heels, and made my way to the Christmas tree in the living room. My parents(apostrophe removed from between the t and s) groggily walked down the stairs to watch us open (up removed) our presents. My Mom sat down on the couch and dad plopped himself on the floor, grumbling something about coffee. I started opening my presents because, after all, its ladies first. Ripping open the wrapping paper, I stared down at my brand(removed dash)new pink boom box. It was beautiful!(question mark changed to exclamation) (capitalized e)Even more, it came with little, stick-on jewels to decorate the boom box. Mom and Dad finally got their coffee and we all took turns watching each other open presents. I got(get turned to got) many more presents that were absolutely amazing. (changed every one into one word)Everyone spends the rest of the day admiring their gifts and playing with their new toys. "I will remember this Christmas forever,"(added endnote) I thought. (capitalized s)Sighing contentedly, I finally turned away from the snow (removed the e from what was danceing)dancing outside the window and rejoined my family.