MATHEMATICS HIGH SCHOOL

What is the exact value of the trigonometric ratio of tan-240 degrees?

Answers

Answer 1
Answer: Tan240=1.732050808
Tan^-1(240)=89.76126897

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The graph of y=√x is shifted 2 units up and 5 units left, Which equation represents the new graph?A. y=-√x+5) +2

B. y=-√x-2) +5

C. y=-√x+2) -5

D. y=-√x-5) +2

Answers

y = √(x + 5) + 2

Further explanation

Given:

The graph of y = √(x) is

  • shifted 2 units up, and
  • 5 units left.

Question:

Which equation represents the new graph?

The Process:

The translation is a form of transformation geometry.

Translation (or shifting): moving a graph on an analytic plane without changing its shape.

In general, given the graph of y = f(x) and v > 0, we obtain the graph of:  

  • \boxed{ \ y = f(x) + v \ } by shifting the graph of \boxed{ \ y = f(x) \ } upward v units.  
  • \boxed{ \ y = f(x) - v \ } by shifting the graph of \boxed{ \ y = f(x) \ } downward v units.  

That's the vertical shift, nowthe horizontal one. Given the graph of y = f(x) and h > 0, we obtain the graph of:  

  • \boxed{ \ y = f(x + h) \ } by shifting the graph of \boxed{ \ y = f(x) \ } to the left h units.  
  • \boxed{ \ y = f(x - h) \ } by shifting the graph of \boxed{ \ y = f(x) \ } to the right h units.

Therefore, the combination of vertical and horizontal shifts is as follows:  

\boxed{\boxed{ \ y = f(x \pm h) \pm v \ }}  

The plus or minus sign follows the direction of the shift, i.e., up-down or left-right.

- - - - - - - - - -

Let's solve the problem.

Initially, the graph of y = √(x) is shifted 2 units up.

\boxed{y = √(x) \rightarrow is \ shifted \ 2 \ units \ up \rightarrow \boxed{ \ y = √(x) + 2 \ }}

Followed by shifting 5 units left.

\boxed{y = √(x) + 2 \rightarrow is \ shifted \ 5 \ units \ left \rightarrow \boxed{ \ y = √(x + 5) + 2 \ }}

Thus, the equation that represents the new graph is\boxed{\boxed{ \ y = √(x + 5) + 2 \ }}

The answer is A.

Learn more

  1. Which phrase best describes the translation from the graph y = 2(x – 15)² + 3 to the graph of y = 2(x – 11)² + 3? brainly.com/question/1369568
  2. The similar problem of shifting brainly.com/question/2488474  
  3. What transformations change the graph of (f)x to the graph of g(x)? brainly.com/question/2415963

Keywords: the graph of, y = √x, shifted 2 units up, 5 units left, which, the equation, represents, the new graph, horizontal, vertical, transformation geometry, translation

Answer:

A. y=√(x+5)+2.

Step-by-step explanation:

We are given the function y=√(x).

Now, the function is shifted 2 units up and 5 units to the left.

That is, the function is translated 2 units up and 5 units to the left.

Since, we know,

Translation of 'k' units up changes the function f(x) to f(x)+k.

So, the function translated 2 units up is y=√(x)+2.

Translation of 'k' units to the left changes the function f(x) to f(x+k).

So, the new function translated 5 units left is y=√(x+5)+2.

Hence, the equation representing the new function is y=√(x+5)+2.

On a map, 3 inches corresponds to 100 miles. Find the actual distance between two cities that are 7 1/2 inches apart on the map.

Answers

Check by using law of ratios and proportions:
3 is to 100 = 7.5 is to x
Rule: The product of the means equals the product of the extremes.
3•x = 7.5•(100)
3x = 750
x= 750 : 3
x = 250

What is 6:12 in simplest form?
A.2
B.21
C. 12
D. 12.6

Answers

Answer: 1:2 or 1/2

Step-by-step explanation:

6:12

Step 1: find a common divisible value, in this case, it is 6

Step2: divide through 6

1:2 or 1/2

Answer:

It’s B

Step-by-step explanation:

What is the equation of a horizontal line that passes through the point at
(-2,-3)????

Answers

Equation\ of\ a\ horizaontal\ line\ is:y=b\n\nLine\ passes\ through\ the\ point\ (-2;-3)\ then\ answer\ is\ y=-3
A horizontal line has the same y-value everywhere, no matter what the x-value is.

The equation of the line is [ y = -3 ].

A number changed to 193 after it was rounded. To what place was the number rounded?

Answers

The number was rounded to the nearest one.
Are there any answer choices?

Solve for x: |x − 2| 10 = 12 a.) x = 0 and x = 4
b.) x = −4 and x = 0
c.) x = −20 and x = 4
d.) no solution

Answers

|x - 2| + 10 = 12
|x - 2| = 12 - 10 = 2
x - 2 = 2 or x - 2 = -2
x = 2 + 2 or x = -2 + 2
x = 4 or x = 0
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