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1 year ago

A car traveled at a constant speed. The graph shows how far the car traveled, in miles, during a given amount of time, in hours.

Mathematics

1 answer:

snow_tiger [21]1 year ago

8 0

Answer:

Step-by-step explanation:

A car traveled at a constant speed as shown in the graph.

Distance traveled is on the y-axis and duration of travel on the x-axis.

Point A(3.5, 210) shows,

Distance traveled = 210 miles

Time to travel = 3.5 hours

So the point (3.5, 210) shows the distance traveled by the car in 3.5 hours is 210 miles.

Slope of the line = speed of the car = $\frac{\text{Distance traveled}}{\text{Time}}$

= $\frac{210}{3.5}$

= 60 mph

Now we will find the speed of the car at another point B(1, 60).

If the speed of car is same as the point B as of point A, point B will lie on the graph.

Speed of the car at B(1, 60) = $\frac{\text{Distance traveled}}{\text{Time}}$

= $\frac{60}{1}$

= 60 mph

Hence, we can say that point B(1, 60) lies on the graph.

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Which polynomial function could be represented by the graph below?

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Note that

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The x-intercepts are at points x=-3, x=0, x=2. The graph should be increasing - decreasing - increasing.

$f(x)=x^3-x^2-6x=x(x^2-x-6)=x(x+2)(x-3)$

The x-intercepts are at points x=-2, x=0, x=3. The graph should be increasing - decreasing - increasing.

$f(x)=-2x^3-2x^2+12x=-2x(x^2+x-6)=-2x(x-2)(x+3)$

The x-intercepts are at points x=-3, x=0, x=2. The graph should be decreasing - increasing - decreasing.

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From the diagram you can see that x-intercepts are at points x=-3, x=0, x=2 and the graph is decreasing-increasing-decreasing.

Answer: correct choice is 3.

7 0

2 years ago

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How many solutions does the equation sin(5x) = 1/2 have on the interval (0, 2PI]

Darina [25.2K]

Answer:

Step-by-step explanation:

Given the equation

Sin(5x) = ½

5x = arcSin(½)

5x = 30°

Then,

The general formula for sin is

5θ = n180 + (-1)ⁿθ

Divide through by 5

θ = n•36 + (-1)ⁿ30/5

θ = 36n + (-1)ⁿ6

The range of the solution is

0<θ<2π I.e 0<θ<360

First solution

When n = 0

θ = 36n + (-1)ⁿθ

θ = 0×36 + (-1)^0×6

θ = 6°

When n = 1

θ = 36n + (-1)ⁿ6

θ = 36-6

θ = 30°

When n = 2

θ = 36n + (-1)ⁿ6

θ = 36×2 + 6

θ = 78°

When n =3

θ = 36n + (-1)ⁿ6

θ = 36×3 - 6

θ = 102°

When n=4

θ = 36n + (-1)ⁿ6

θ = 36×4 + 6

θ = 150

When n =5

θ = 36n + (-1)ⁿ6

θ = 36×5 - 6

θ = 174°

When n = 6

θ = 36n+ (-1)ⁿ6

θ = 36×6 + 6

θ = 222°

When n = 7

θ = 36n + (-1)ⁿ6

θ = 36×7 - 6

θ = 246°

When n =8

θ = 36n + (-1)ⁿ6

θ = 36×8 + 6

θ = 294°

When n =9

θ = 36n + (-1)ⁿ6

θ = 36×9 - 6

θ = 318°

When n =10

θ = 36n + (-1)ⁿ6

θ = 36×10 + 6

θ = 366°

When n = 10 is out of range of θ

Then, the solution is from n =0 to n=9

So the equation have 10 solutions in the range 0<θ<2π

4 0

1 year ago

Let the sample space be S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Suppose the outcomes are equally likely. Compute the probability of

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Answer:

The probability is 3/5

Step-by-step explanation:

Given,

Sample space, S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10},

⇒ n(S) = 10,

Odd numbers less than 7 = 1, 2, 3, 4, 5 and 6

i.e. E = {1, 2, 3, 4, 5, 6}

⇒ n(E) = 6,

$\because \text{Probability}=\frac{\text{Favourable outcomes}}{\text{Total outcomes}}$

So, the probability of the event E,

$P(E) =\frac{n(E)}{n(S)}$

$=\frac{6}{10}$

$=\frac{3}{5}$

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1 year ago

What is 10 × 7 thousands in unit form

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Answer:

ten thousands/thousands/hundreds/tens/ones

7 / 0 / 0 / 0 / 0

Explanation:

10 x 7,000 = 70, 000

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Answer:

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Step-by-step explanation:

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1 year ago