A train leaves chicago and travels east at 60 mph. another train at the same depot leaves at the same time and travels west at 72 mph. how long before the two trains are 330 miles apart?

The equation d = 2r can be rewritten in function notation by replacing 'd' with 'f(r)', giving the function f(r) = 2r.

To rewrite the equation d = 2r using function notation, we first need to understand that function notation is a way to represent a function that is derived from a certain equation. Here, the equation given is d = 2r, where d is in terms of r.

To translate this into function notation, we would change d to f(r). The letter f stands for 'function', and the (r) is the variable that the function is dependent upon. Therefore, the equation d = 2r would be rewritten in function notation as f(r) = 2r.

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Answer:

[tex]25 = f(g(-2))[/tex]

Step-by-step explanation:

[tex]g(-2) = -2 - 3 = -5 \\ \\ f(-5) = {[-5]}^{2} = 25 \\ \\ 25 = f(g(-2))[/tex]

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Answer:

A

Step-by-step explanation:

Answer:

A. Y = 2/9

B. X =  11/24

C. X = 2.64

Question:

Evaluate f(x)= 1.8 X 2^x for x=6

Answer choices:

A: 115.2

B: 2176.78

C: 21.6

Answer:

A:115.2

Step-by-step explanation:

F(x) F(6)

=1 . 8 • 2 • 1

=1 . 8 • 261

=1 . 8 • 64115.2

=115.2

Hence, your answer is A:

The formation of rust on an iron fence is a synthesis reaction, where iron combines with oxygen in the air to create iron oxide. During this process, iron is oxidized and oxygen is reduced, making it an oxidation-reduction (or redox) reaction.

The formation of rust is an oxidation-reduction reaction and a synthesis reaction. Rusting occurs when iron reacts with oxygen in the air, typically in the presence of water, to form iron oxide.

The process can be summarized as iron (Fe) being oxidized to iron(II) ions (Fe2+) which react further with oxygen and water to produce a hydrated iron(III) oxide, commonly known as rust (Fe2O3·xH2O).

This process is classified as a synthesis reaction because it involves the combination of simpler substances - iron and oxygen - to form a more complex compound, namely iron oxide.

In comparison to other types of reactions, decomposition refers to a single compound breaking down into two or more simpler compounds or elements.

Combustion reactions involve fuel (often a hydrocarbon) reacting with oxygen to produce carbon dioxide and water.

Lastly, single-replacement reactions occur when an element replaces another element in a compound. Since the reaction of iron with oxygen adds oxygen to create a new product, rather than decomposing, combusting, or substituting, it is indeed a synthesis reaction.

Answer:

perpendicular lines.

Step-by-step explanation:

Two events are independent if the occurrence of one event does not affect the probability of the other event.

Two events are independent if the occurrence of one event does not affect the probability of the other event. This means that the outcomes of the two events are not related and the probability of one event happening does not change based on whether the other event occurred or not.

For example, if you flip a coin and roll a die, the outcome of the coin flip does not affect the probability of getting a certain number on the die roll. The two events are independent.

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The estimate of cutting 6 ramps from a 12 1/2 feet long board is reasonable. Each ramp will have a length of 2 1/12 feet, and no wood will be left over.

To determine if the estimate of cutting 6 ramps from a 12 1/2 feet long board is reasonable, we can calculate the length of each ramp by dividing the total length of the board by the number of ramps.

12 1/2 feet is equivalent to 12 + 1/2 feet. To divide by a fraction, we can multiply by the reciprocal. So, when we divide 12 1/2 by 6, we get (12 + 1/2) / 6 = 12/6 + 1/2 / 6 = 2 feet + 1/12 feet = 2 1/12 feet.

Therefore, each ramp will have a length of 2 1/12 feet. Since 6 ramps multiplied by 2 1/12 feet is 12 1/2 feet, the estimate is reasonable. No wood will be left over.

Answer: his average speed on the second day is 35 miles per hour

Step-by-step explanation:

Bill spends two days driving from point a to point b

Let x = his speed on the first day.

Let y = his speed on the second day

Speed = distance / time

Time = distance / speed

Total time spent on the trip is 18 hours

Let time that he spent on the first day be t hours

Time that he spent on the second day will be 18 - t

Bill drove 2 hours longer on the second day than on the first day. This means

t = 18 - t + 2

t+t = 18+2

2t = 20

t = 10

He spent 10 hours on the first day.

He spent 18-10 = 8hours on the second day.

Bill drove at an average speed of 5 miles per hour faster than he drove on the second day. This means that

x = y + 5 - - - - - - - -- 1

Distance travelled on the first day = speed on the first day × time spent. This becomes

10 × x = 10x miles

Distance travelled on the second day = speed on the second day × time spent. This becomes

8 × y = 8y miles

He drove a total of 680 miles over the course of the 18 hours. This means that

10x + 8y = 680 - - - - - - - - 2

Substituting equation 1 into equation 2, it becomes

10(y + 5) + 8y = 680

10y + 50 + 8y = 680

10y + 8y = 680 - 50

18y = 630

y = 630/18 = 35 miles per hour

x = y + 5 = 35 + 5

x = 40 miles per hour

The probability that you will roll a 5 on the red cube and a 1 or a 2 on the blue cube will be 1/18.

What is mean by Probability?

The term probability refers to the likelihood of an event occurring.

Given that;

You will roll a 5 on the red cube and a 1 or a 2 on the blue cube.

Now,

Sides of cube dice = 6

Hence, For red cube;

P (r) = 1/6

And, For blue red;

P (B₁ or B₂) = P(B₁) + P (B₂)

                = 1/6 + 1/6

                = 1/3

Thus, The probability that you will roll a 5 on the red cube and a 1 or a 2 on the blue cube = 1/6 x 1/3

                          = 1/18

Therefore, The probability that you will roll a 5 on the red cube and a 1 or a 2 on the blue cube will be 1/18.

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Answer:

[tex]f(x)=3|x-2|-1[/tex]

Step-by-step explanation:

Identify the function that has a vertex of (2,-1) and is stretched vertically by a factor of 3.

The option are absolute function, So the parent function is y=|x|

Vertex form of absolute function is

[tex]y=|x-h|+ k[/tex] where (h,k) is the vertex

vertex of (2,-1) h=2, k =-1

the function becomes

[tex]f(x)=|x-2|-1[/tex]

function is stretched vertically by a factor of 3

when f(x) is vertically stretched by a factor of 'a'.We multiply the factor with f(x)

[tex]f(x)=3|x-2|-1[/tex]

Yes, It is true that a continuous function that is never zero on an interval never changes its sign on that​ interval.

In mathematics, a continuous function is a function such that a continuous variation of the argument causes a continuous variation of the value of the function. This indicates that there aren't any discontinuities or sudden changes in value.

Unchanged sign is a property of continuous functions that are never zero on an interval, hence this is true. This is due to the perennially significant Intermediate value theorem.

Therefore, It is true that a continuous function that is never zero on an interval never changes its sign on that​ interval.

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by using the Pythagorean theorem

 use the height and half the base dimension for the 2 edges of a triangle and the slope ( slant height) would be the hypotenuse

 so:  SQRT(height ^2 + half of base^2) = hypotenuse ( Slant height)

33

[tex]\frac{x-7}{x} = \frac{2x-10}{2x+12}[/tex] → x = [tex]\frac{21}{2}[/tex]

AC = x + x + 12 = [tex]\frac{21}{2} + \frac{21}{2}[/tex] +12 = 33