A train leaves the station at time t=0. Traveling at a constant speed, the train travels 420 kilometers in 2 hours. Write a function that relates the distance traveled d to the time.

Answer:

[tex]y = 20\times 2^{x}[/tex].

Step-by-step explanation:

Let [tex]y = (a)\, (b)^{x}[/tex] denote this exponential function for some constant [tex]a[/tex] and [tex]b[/tex] ([tex]b > 0[/tex]) that need to be found.

Assume that the graph of the function [tex]y = (a)\, (b)^{x}[/tex] goes through the point [tex](x_{0},\, y_{0})[/tex]. Substituting in [tex]x = x_{0}[/tex] and [tex]y = y_{0}[/tex] should satisfy the equation of this function:

[tex]y_{0} = (a)\, (b)^{x_{0}}[/tex].

For example, [tex]y = (a)\, (b)^{x}[/tex] goes through the point [tex](0,\, 20)[/tex]. Substituting in [tex]x = 0[/tex] and [tex]y = 20[/tex] should then satisfy the equation of this function:

[tex]20 = (a)\, (b)^{0}[/tex].

Similarly, since the graph of this function goes through [tex](7,\, 2560)[/tex] where [tex]x = 7[/tex] and [tex]y = 2560[/tex]:

[tex]2560 = (a)\, (b)^{7}[/tex].

In general, the constant [tex]a[/tex] in such systems could be eliminating by dividing one equation by the other. For example, dividing [tex]2560 = (a)\, (b)^{7}[/tex] by [tex]20 = (a)\, (b)^{0}[/tex] gives:

[tex]\displaystyle \frac{2560}{20} = \frac{(a)\, (b)^{7}}{(a)\, (b)^{0}}[/tex].

Simplify to obtain:

[tex]\displaystyle 128 = b^{7 - 0}[/tex].

[tex]\displaystyle 128 = b^{7}[/tex].

[tex]b^{7} = 128[/tex].

Since the exponent of [tex]b[/tex] is an odd number, the sign of [tex]b[/tex] should also be positive- same as the sign of [tex]128[/tex]. Extra steps would be required if the exponent of [tex]b[/tex] is even.

Raise both sides to the [tex](1/7)[/tex]th power to find the (unique) value of [tex]b[/tex]:

[tex]b = 128^{1/7} = 2[/tex].

Substitute [tex]b = 2[/tex] back into either equation (for example, [tex]2560 = (a)\, (b)^{7}[/tex]) to find the value of [tex]a[/tex]:

[tex]2560 = (a)\, (2)^{7}[/tex].

[tex]\begin{aligned}a &= \frac{2560}{2^{7}} \\ &= \frac{2560}{128} \\ &= 20\end{aligned}[/tex].

Thus, this exponential function would be [tex]y = 20\times 2^{x}[/tex].

Answer:

so is volume length times width

Answer:

Using Pythagorean theorem a2 + b2 = c2 15002 + 20002 = C2; c is 2,500 feet

Answer:

x = 7

Step-by-step explanation:

The 2 right triangles are similar by the AA postulate, then the ratios of corresponding sides are in proportion, that is

[tex]\frac{x}{4}[/tex] = [tex]\frac{3.5}{2}[/tex] ( cross- multiply )

2x = 14 ( divide both sides by 2 )

x = 7

Will recommend to see attached picture as name of angles are based on it.

[tex] \\ [/tex]

We can only find value of x if both triangles i.e triangle DOC and triangle AOB are similar.

[tex] \\ [/tex]

[tex]\sf \underline{In \: \triangle \: DOC \: and \: \triangle\:AOB: }[/tex]

[tex] \\ [/tex]

[tex] \sf1. \angle DOC = \angle AOB[/tex]

Reason :-

VOC (Vertically opposite angle)

How to recognize either it is VOC (Vertically opposite angle) or not?

So it's basically very easy to recognize, when ever u see lines intersect each other just like a multiply sign ( × ) either horizontal or parallel they are considered as VOC ans are always equal.

[tex] \\ [/tex]

[tex] \sf2. \angle CDO = \angle BAO[/tex]

Reason:-

Both are of 90°.

So how we recognized that these both angles were in 90°?

When ever you see that angle is marked in square ( □ ) like shape instead of curve shape then it means the angle is 90°.

[tex] \\ [/tex]

[tex]\sf\triangle \: DOC\simeq \triangle\:AOB: [/tex]

By :- AA (angle angle)

[tex] \\ \\ [/tex]

Now Finally Let's find value of x.

[tex] \\ [/tex]

[tex] \dashrightarrow \sf\dfrac{DC}{AB} = \dfrac{OC}{OB} = \dfrac{OD}{OA} [/tex]

Reason :- Corresponding sides of similar triangle are in proportion.

[tex] \\ [/tex]

So:-

[tex] \\ [/tex]

[tex] \dashrightarrow \sf\dfrac{DC}{AB} = \dfrac{OC}{OB}[/tex]

[tex] \\ \\ [/tex]

[tex] \dashrightarrow \sf\dfrac{2}{3.5} = \dfrac{4}{x}[/tex]

[tex] \\ \\ [/tex]

[tex] \dashrightarrow \sf\dfrac{3.5}{2} = \dfrac{x}{4}[/tex]

[tex] \\ \\ [/tex]

[tex] \dashrightarrow \sf\dfrac{35}{2 \times 10} = \dfrac{x}{4}[/tex]

[tex] \\ \\ [/tex]

[tex] \dashrightarrow \sf\dfrac{ \cancel{35}}{2 \times \cancel{10}} = \dfrac{x}{4}[/tex]

[tex] \\ \\ [/tex]

[tex] \dashrightarrow \sf\dfrac{7}{2 \times 2} = \dfrac{x}{4}[/tex]

[tex] \\ \\ [/tex]

[tex] \dashrightarrow \sf\dfrac{4 \times 7}{2 \times 2} = x[/tex]

[tex] \\ \\ [/tex]

[tex] \dashrightarrow \sf\dfrac{ \cancel4 \times 7}{\cancel2 \times 2} = x[/tex]

[tex] \\ \\ [/tex]

[tex] \dashrightarrow \sf\dfrac{ 2 \times 7}{1 \times 2} = x[/tex]

[tex] \\ \\ [/tex]

[tex] \dashrightarrow \sf\dfrac{\cancel 2 \times 7}{1 \times \cancel2} = x[/tex]

[tex] \\ \\ [/tex]

[tex] \dashrightarrow \sf\dfrac{1 \times 7}{1 \times 1} = x[/tex]

[tex] \\ \\ [/tex]

[tex] \dashrightarrow \sf\dfrac{7}{1 } = x[/tex]

[tex] \\ \\ [/tex]

[tex] \dashrightarrow \sf7= x[/tex]

[tex] \\ \\ [/tex]

[tex] \dashrightarrow \bf x = 7[/tex]

[tex] \\ \\ [/tex]

.°. length of x is equal to 7(unit)

Answer:

The percentage of the adult racehorses weigh more than 570 kg is 1.7% ⇒ 1st answer Step-by-step explanation: Adult racehorse weights are normally distributed, with a mean of 500 kg and a standard deviation of 33 kg We need to find the percentage of the adult racehorses weigh more than 570 kg To solve the problem do these steps 1. Find z-score 2. Use z-score to find the corresponding area which represented P(x) 3. Change P(x) to percentage ∵ z = (x - μ)/σ ∵ The mean μ = 500 kg ∵ The standard deviation σ = 33 kg ∵ x = 570 kg Substitute these values in the rule above ∴ z = Let us use the normal distribution table to find the corresponding area ∵ The area corresponding to z-score of 2.12 is 0.98300 ∵ We need x > 570 , then we need the area to the right of the z-score ∴ P(x > 570) = 1 - 0.98300 = 0.017 Change it to percentage by multiplying the answer by 100% ∴ The percentage of x > 570 = 0.017 × 100% = 1.7% The percentage of the adult racehorses weigh more than 570 kg is 1.7%

Step-by-step explanation:

The percentage of the adult racehorses weigh more than 570 kg is 1.7% ⇒ 1st answer Step-by-step explanation: Adult racehorse weights are normally distributed, with a mean of 500 kg and a standard deviation of 33 kg We need to find the percentage of the adult racehorses weigh more than 570 kg To solve the problem do these steps 1. Find z-score 2. Use z-score to find the corresponding area which represented P(x) 3. Change P(x) to percentage ∵ z = (x - μ)/σ ∵ The mean μ = 500 kg ∵ The standard deviation σ = 33 kg ∵ x = 570 kg Substitute these values in the rule above ∴ z = Let us use the normal distribution table to find the corresponding area ∵ The area corresponding to z-score of 2.12 is 0.98300 ∵ We need x > 570 , then we need the area to the right of the z-score ∴ P(x > 570) = 1 - 0.98300 = 0.017 Change it to percentage by multiplying the answer by 100% ∴ The percentage of x > 570 = 0.017 × 100% = 1.7% The percentage of the adult racehorses weigh more than 570 kg is 1.7%

Answer:

yes it is correct good work

Answer:

31/30 or 1 1/30

Step-by-step explanation:

1/3+1/5+1/2

Answer:

factor the polynomial

6 (7x-3)

Step-by-step explanation:

[tex] - 18 + 42x \\ divide \: both \: sides \: by \: 6 \\ 2(7x -3)[/tex]

The probability of the event that the number picked is less than or equal to 16 is 33.33%. Then the probability of the complement of event A is 66.67%.

Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.

A number is randomly selected from {15, 16, 17, 18, 19, 20}.

A is represented by the event that the number picked is less than or equal to 16.

Total event = 6 {15, 16, 17, 18, 19, 20}

Favorable event = 2 {15, 16}

Then the probability of the event that the number picked is less than or equal to 16 will be

[tex]\rm P(x\leq 16) = \dfrac{2}{6}\\\\P(x\leq 16) = \dfrac{1}{3} \\\\P(x\leq 16) = 0.3333\\\\ P(x\leq 16) = 33.33 \ \%[/tex]

The probability of the complement of event A will be

[tex]\rm P(x > 16) = \dfrac{4}{6}\\\\P(x > 16) = \dfrac{2}{3} \\\\P(x > 16) = 0.6667\\\\ P(x > 16) = 66.67\ \%[/tex]

The probability of the complement of event A is 66.67%.

More about the probability link is given below.

https://brainly.com/question/795909

Answer:

Step-by-step explanation:

4x2−y2−24x+4y+28=0⇒(4x2−24x)−(y2−4y)+28=0

Answer:

18

Step-by-step explanation:

you take away -9 from both sides

27-9=18

Answer:

9

Step-by-step explanation:

so first you send +9 to the right , it will become -9

2p + 9 = 27

2p = 27 - 9

you substract -9 from 27

2p = 18

next step you send 2 to the other side... since it multiply on the left side...it will become divide on the right side, so that p can be alone

2×p = 18

p = 18 ÷2

p = 9

i rewrote it without explication

full step is : 2p = 27 - 9

2p = 18

p = 18 ÷ 2

p = 9

Answer:

Step-by-step explanation:

Answer:

6 divided by 3 would come first

Step-by-step explanation:

follow pemdas which stands for parenthesis, exponents, multiplication, division, adadditiaddition, then subtraction

Answer:

I think it might be this one

Answer:

3

Step-by-step explanation:

6x (horizontal totals) + 12 x(vertical totals) = 54

18x = 54

x = 3

HOPE THIS HELPS!!!

[tex]17.00906 < 17.00936 < 17.00963 < 17.09360 < 17.09361[/tex]

Hope that helps!

Answer:

C

Step-by-step explanation:

a linear equation has the form

y = ax + b

y = - [tex]\frac{6}{7}[/tex] x - 11 ← is in this form and is a linear equation

Answer:

C: Linear

Step-by-step explanation:

Linear equations are also called first-order equations. An equation in which the unknowns are all primary so, it’s linear.

Answer:

Solve using the supplement of the angles.

Step-by-step explanation:

For the first page, you should use the supplement of the angles. This means, on a straight line, you can subtract the known angle from 180 degrees to find the missing angle. The top angle, for example, will be 180 - 46 resulting in the interior angle being 134 degrees.

You can do this until you find all of the known interior angles, then using the sum of interior angles and the current known interior angles you can find the last known interior angle. If they are asking you to solve for an exterior angle, you can once again subtract the known interior angle from 180 degrees to find the exterior angle.

For the second page, you can refer to exterior angles again. Knowing that all exterior angles add to 360 degrees, and since we are given all of them, we can set the sum of the exterior angles to 360 degrees.

9x + 4x + (5x + 10) + (5x + 25) = 360

Simplify.

23x = 325.

Solve for x.

Step-by-step explanation:

Given:

We know that:

Considering all the info we can make below chart:

Nikolas' car trip                                                                    

                        |    at 100 km/h  | at 80 km/h |  Total       |

Distance            |         x              |      y            |   500 km  |

Time                   |      x/100         |     y/80       |     5 1/2 h   |

Answer:

Lin=48 seconds Diego=30 seconds

Step-by-step explanation:

Answer:

Lin   48 seconds      Diego 30 seconds

Step-by-step explanation:

Lin ----- 48 seconds  

Diego---------30 seconds  

Lin ---------- 12 ounces ÷ (1/4) ounces/second = 12 ÷ (1/4) = 48 seconds  

Diego --------- 20 ounces ÷ (2/3) ounces/second = 20 ÷  (2/3) = 30 seconds  

Answer:

3/5

Step-by-step explanation:

Answer:

[tex]\frac{3}{5}[/tex] would be your answer

Step-by-step explanation:

Since you have [tex]\frac{15}{25}[/tex] and the denominator for the answer is 5. You will be dividing 15 and 25 by 5. Making it look like:

15 ÷ 5 = 3

25 ÷ 5 = 5

so your answer will be

[tex]\frac{3}{5}[/tex]

Answer:

The answer is 22 point 62 degrees.

Answer:

When we add 23°, 145°, 23° and 69° we get 260°

And 260° does not have defined number of sides

Step-by-step explanation:

These are the polygons with the number of sides and angles

Polygon Name  |  Number of Interior Angles  |  Sum of Interior Angles

Triangle                                     3                                    180°

Quadrilateral                            4                                    360°

Pentagon                                  5                                    540°

Hexagon                                   6                                    720°

Septagon                                  7                                    900°

Octagon                                    8                                   1080°

Nonagon                                   9                                   1260°

Decagon                                   10                                  1440°

Explanation:

6 = number of games the first friend won

x = number of games the other friend won

6+x = x+6 = total number of games

x+6 = 13 total games

Solving for x leads to x = 7

Answer:

-6

Step-by-step explanation:

if you put all on a number line negitive six is the furthest to the left. meaning its the lowest number

Answer:

Coordinates on a graph cannot be larger or smaller than each other. They are just locations. If you are asking which number has the lowest value, it would be the negative with the highest number. In this case, -6 is the smallest value.

Step-by-step explanation:

Step-by-step explanation:

we start with the point-slope form

y - y1 = a(x - x1)

where "a" is the slope, (x1, y1) is a point on the line, and then we simplify that equation giving us the slope-intercept form

y = ax + b

so,

y - -9 = -9(x - 1)

y + 9 = -9(x - 1)

and now simplifying this

y + 9 = -9x + 9

y = -9x