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natulia [17]
3 years ago
14

Suppose that a cyclist began a 476

Mathematics
1 answer:
mojhsa [17]3 years ago
6 0
Well, we know the cyclist left the western part going eastwards, at the same time the car left the eastern part going westwards

the distance between them is 476 miles, and they met 8.5hrs later

let's say after 8.5hrs, the cyclist has travelled "d" miles, whilst the car has travelled the slack, or 476-d, in the same 8.5hrs

we know the rate of the car is faster... so if the cyclist rate is say "r", then the car's rate is r+33.2

thus    \bf \begin{array}{lccclll}
&distance&rate&time\\
&-----&-----&-----\\
\textit{eastbound cyclist}&d&r&8.5\\
\textit{westbound car}&476-d&r+33.2&8.5
\end{array}\\\\
-----------------------------\\\\
\begin{cases}
\boxed{d}=8.5r\\\\
476-d=(r+33.2)8.5\\
----------\\
476-\boxed{8.5r}=(r+33.2)8.5
\end{cases}

solve for "r", to see how fast the cyclist was going

what about the car? well, the car's rate is r + 33.2
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F(x)=12x2-4x-8. G(x)=11x-6
AlekseyPX

Answer: Second option.

Step-by-step explanation:

Given the functions f(x) and g(x):

f(x)=12x^2-4x-8\\\\g(x)=11x-6

You need to divide them in order to find (\frac{f}{g})(x) asked in the exercise. Then:

(\frac{f}{g})(x) =\frac{12x^2-4x-8}{11x-6}

Now, it is important to remember that, by definition, the division by zero is not defined. Therefore, the denominator of the function cannot be zero.

Let's find the value of "x" for which the denominator of the function would be zero:

1. You need to make the denominator equal to zero:

11x-6=0

2. Finally, you must solve for "x":

11x=6\\\\x=\frac{6}{11}

Therefore, as you can see, the answer is:

 (\frac{f}{g})(x) =\frac{12x^2-4x-8}{11x-6}, x=\frac{6}{11}

4 0
3 years ago
Choose the correct numbers from the box below to complete the subtraction sentence that follows
maw [93]

Answer:

umm there isn't a subtraction sentence

Step-by-step explanation:

7 0
2 years ago
Andy has a stamp collection with 343 stamps, Of these 296 are from Germany. Is 40,50 or 60 a more reasonable estimate for how ma
mariarad [96]

Answer:

40 Stamps

Step-by-step explanation:

According to the scenario, given data are as follows,

Total stamp collected = 343

Stamps from Germany = 296

To estimate the stamps from other contact, we first round off the given number of stamps.

So, Total stamp collected = 340 ( Rounded off)

Stamps from Germany = 300 ( Rounded off)

So, Stamps from other contact = 340 - 300 = 40 stamps

3 0
3 years ago
Eight times the difference of a number and seventeen is thirty"?
Y_Kistochka [10]
Difference of a number and 17:   x - 17
eight times that = 8(x - 17)
8(x - 17) = 30

divide both sides by 8
x - 17 = 30/8

x = 30/8 + 17 which is 20.75
5 0
3 years ago
Read 2 more answers
a parabola contains the points (0,0),(-1,-2) and (1,6). what is the equation of the parabola in standard form?
tensa zangetsu [6.8K]

Let the equation be:

y = ax^2 + bx + c.

Then, substitue the three points into the equation.

First point: 0 = a0^2 + b0 + c.

So  c = 0.

Second point: -2 = a(-1)^2 + b(-1) + c.

So  a - b + c = -2.

Third point: 6 = a*1^2 + b*1 + c.

So  a + b + c = 6.

We know that c=0 already, so we substitute c=0 into the last two equations and we would get:

a - b = -2

a + b = 6

We add the two equations and we get:

2a = 4

a = 2

Then, we substitute a=2 into a-b=-2 and we get:

-b = -4

b = 4

Now we know a = 2, b = 4, and c = 0

Then, the equation of the parabola would be:

2x^2 + 4x

5 0
3 years ago
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