MATHEMATICS HIGH SCHOOL

Functions f(x) and g(x) are shown below:f(x) = x2
g(x) = x2 − 8x + 16

In which direction and by how many units should f(x) be shifted to obtain g(x)?

Left by 4 units
Right by 4 units
Left by 8 units
Right by 8 units

Answers

Answer 1
Answer:

Answer:  The answer is (B) Right by 4 units.

Step-by-step explanation:  The two functions f(x) and g(x) are defined as follows:

f(x)=x^2,\n\ng(x)=x^2-8x+16.

We are to check the correct transformation  of the graph of f(x) to the graph of g(x).

We can rewrite the graph of g(x) as follows:

g(x)=x^2-8x+16=x^2-2* x* 4+4^2=(x-4)^2.

Comparing this with the equation of f(x), we can say that f(x) is shifted right by 4 units to obtain g(x).

The graphs of both the functions are shown in the attached figure.
Answer 2
Answer:

Answer:

Left by 4 units

Step-by-step explanation:

I took it the first time and put Right 4 units and got it wrong. When i put left by 4 units i got it right.

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PLEASE HELP ASAP!!! I NEED CORRECT ANSWERS ONLY PLEASE!!!Find the tangent of ∠Y.

Write your answer as an integer or as a decimal rounded to the nearest hundredth.

tan(Y) =

Answers

Answer:

tan∠Y = 2,14

Step-by-step explanation:

First , we need to determine XY

in order to do that we use the Pythagorean theorem :

XY = √(85^2-77^2) = 36

tan∠Y = 77/36 = 77÷36 = 2,138888888889

Answer:

Step-by-step explanation:

Triangle WXY is a right angle triangle.

From the given right angle triangle

WY represents the hypotenuse of the right angle triangle.

With ∠Y as the reference angle,

XY represents the adjacent side of the right angle triangle.

WX represents the opposite side of the right angle triangle.

To determine XY, we would apply Pythagoras theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side²

85² = 77² + XY²

XY² = 85² - 77² = 7225 - 5929

XY = √1296 = 36

To determine tan Y, we would apply trigonometric ratio

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On average Exante Express trains are 50km/hr faster than Paral passenger trains. A Paral passenger train requires 60% more time then Exante train to travel 1800 km from Matsay to Rawindi. Calculate average speed of each train. Calculate time it takes for each train for the journey.

Answers

V- average\ speed\ of\ Exante\ Express\ train\nt-travel\ time\ of\ Exante\ Express\ train \n \nV= (S)/(t) \ \ \ \ and\ \ \ V-50= (S)/(t+60\%t) = (S)/(1.6t)\ \ \ \ and\ \ \ S=1800\n \nV= (1800)/(t) \ \ \ and\ \ \ V-50=(1800)/(1.6t)\ \ \ \Rightarrow\ \ \ (1800)/(t)-50= (1125)/(t) \ /\cdot t\n \n1800-50 t=1125\ \ \ \Rightarrow\ \ \ 50t=1800-1125\ \ \ \Rightarrow\ \ \ 50t=675\ /:50\n \nt=13.5\ [h]=13\ [h]\ 30\ [min]\n\n1.6t=21.6\ [h]=21\ [h]+ 0.6\cdot60\ [min]=21\ [h]\ 36\ [min]

V= (1800)/(t) =(1800)/(13,5) =133 (1)/(3) \ [km/h]\approx133.3\ [km/h]\n\nV-50\approx83.3\ [km/h]

Ans.\n average\ speed\ of\ Exante\ Express\ train\ is\ 133.3\ km/h,\ntravel\ time\ of\ Exante\ Express\ train\ is\ 13\ h\ 30\ min;\naverage\ speed\ of\ Paral \ passenger \ train\ is\ 83.3\ km/h,\ntravel\ time\ of\ Paral \ passenger\ train\ is\ 21\ h\ 36\ min

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Answers

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Answers

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