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2 years ago

Sanjit drives the 45 km distance between York and Leeds he then drives a further 42 km from Leeds to Blackpool

2 answers:

8 0

45 km at 54 km/hr

45 / 54 = 5/6 

It took him 5/6 of an hour, or 50 minute 

61.4117 km/hr

I am Lyosha [343]2 years ago

3 0

Answer: His average speed for his total journey from York to Blackpool is approximately 61.41 km/h.

Step-by-step explanation:

$\text{ The average speed}=\frac{\text{Total distance covered}}{\text{Total time taken}}$

Since, The distance covered by him from York to Leeds = 45 km,

The speed when he covered this distance = 54 km/ h

Thus, the time taken by him in travelling from York to Leeds = 45/54 hours (Because, Time = Distance/speed)

Now, The distance covered by him from Leeds to Blackpool = 42 km,

The time taken by him in travelling from Leeds to Blackpool = 35 minutes = 35/60 hours

Hence, the total time taken by him in this journey

$=\frac{45}{54}+\frac{35}{60}=\frac{450+315}{540}=\frac{765}{540}=\frac{17}{12}$ hours

And, the total distance he covered= 45 + 42 = 87 km

Thus, His average speed

$=\frac{87}{17/12}= \frac{12\times 87}{17}=\frac{1044}{17}=61.4117647\approx 61.41\text{ km per hour}$

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The triangles in the diagram are congruent. If mF = 40°, mA = 80°, and mG = 60°, what is mB?

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Answer:

The answer is 40 degrees.

Step-by-step explanation:

Since the two triangles are congruent, which means they are the same shape and size, they share the same angle measures. Since angle B is the same as angle F, it equals 40 degrees.

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If cos Θ = square root 2 over 2 and 3 pi over 2 < Θ < 2π, what are the values of sin Θ and tan Θ?

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Answer:

The answer is

$sin(\theta)=-\frac{\sqrt{2}}{2}$

$tan(\theta)=-1$

Step-by-step explanation:

we know that

$tan(\theta)=\frac{sin(\theta)}{cos(\theta)}$

$sin^{2}(\theta)+cos^{2}(\theta)=1$

In this problem we have

$cos(\theta)=\frac{\sqrt{2}}{2}$

$\frac{3\pi}{2}$

The angle $\theta$ belong to the third or fourth quadrant

The value of $sin(\theta)$ is negative

Step 1

Find the value of $sin(\theta)$

Remember

$sin^{2}(\theta)+cos^{2}(\theta)=1$

we have

$cos(\theta)=\frac{\sqrt{2}}{2}$

substitute

$sin^{2}(\theta)+(\frac{\sqrt{2}}{2})^{2}=1$

$sin^{2}(\theta)=1-\frac{1}{2}$

$sin^{2}(\theta)=\frac{1}{2}$

$sin(\theta)=-\frac{\sqrt{2}}{2}$ ------> remember that the value is negative

Step 2

Find the value of $tan(\theta)$

$tan(\theta)=\frac{sin(\theta)}{cos(\theta)}$

we have

$sin(\theta)=-\frac{\sqrt{2}}{2}$

$cos(\theta)=\frac{\sqrt{2}}{2}$

substitute

$tan(\theta)=\frac{-\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}}$

$tan(\theta)=-1$

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the garza family drives to a state park. the remaining distance, in miles, to reach the state park is 285−60x , where x represen

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285 - 60x ; where x represents the number of driving hours.

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Which translation maps the vertex of the graph of the function f(x) = x2 onto the vertex of the function g(x) = x2 – 10x +2?

zhuklara [117]

Answer:

The translation that maps the vertex of the graph of the function f(x) = x² onto the vertex of the function g(x) = x² - 10x + 2 is 5 units to the right and 23 units down.

Explanation:

1) Vertex form of the function that represents a parabola.

The general form of a quadratic equation is Ax² + Bx + C = 0, where A ≠ 0, and B and C may be any real number. And the graph of such equation is a parabola with a minimum or maximum value at its vertex.

The vertex form of the graph of such function is: A(x - h)² + k

Where, A a a stretching factor (in the case |A| > 1) or compression factor (in the case |A| < 1) factor.

2) Find the vertex of the first function, f(x) = x²

This is the parent function, for which, by simple inspection, you can tell h = 0 and k = 0, i.e. the vertex of f(x) = x² is (0,0).

3) Find teh vertex of the second function, g(x) = x² -10x + 2

The method is transforming the form of the function by completing squares:

Subtract 2 from both sides: g(x) - 2 = x² - 10x

Add the square of half of the coefficient of x (5² = 25) to both sides: g(x) - 2 + 25 = x² - 10x + 25

Simplify the left side and factor the right side: g(x) + 23 = (x - 5)²

Subtract 23 from both sides: g(x) = (x - 5)² - 23

That is the searched vertex form: g(x) = (x - 5)² - 23.

From that, using the rules of translation you can conclude immediately that the function f(x) was translated 5 units horizontally to the right and 23 units vertically downward.

Also, by comparison with the verex form A(x - h)² + k, you can conclude that the vertex of g(x) is (5, -23), and that means that the vertex (0,0) was translated 5 units to the right and 23 units downward.

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