What’s the equation for the translation of y=|x|?

[tex]What’s the equation for the translation of y=|x|?[/tex]

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What’s the equation for the translation of y=|x|?

[tex]What’s the equation for the translation of y=|x|?[/tex]

3. tan(α) = height/distance

distance = height/tan(α)

distance = (648 m)/tan(13°) ≈ 1399.5 m

6. when y = |x| is translated 6 units down, 6 is subtracted from the y-value:

.. y = |x| -6

10. In point-slope form, the line through point (h, k) with slope m is

.. y -k = m(x -h)

For (h, k) = (10, -9) and m = -2, you have

.. y +9 = -2(x -10)

The solution to this exercise has been attached below. The problem has been solved in this way:

1. Different forms of linear equations. Point slope-intercept equation of the line that passes through two points.2. Inverse Function. 3. Average Rate of Change.4. Comparison of linear equations and inequalities5. Real-life problems6. Imaginary Number7. Radicals8. Rational exponent and radical form9. Radical expressions10. Quadratic equation11. Trinomial12. Factoring expressions13. Quadratic and linear graph14. A problem of height

1. y=2x-9

5. y = | x | + 6.5

6. y = | x – 5.5 |

7. y = | x + 8|

Step-by-step explanation:

There is not enough given information for some of the problems. Here are the solutions and reasons for those that area solvable:

Write a perpendicular line to the equation -3x-6y=17 by finding its slope and then flipping it to the negative reciprocal:

So -3x-6y=17 becomes y=-1/2x-17/6 where m = -1/2. The perpendicular slope is 2.

Using the point given, write the equation in point slope form and simplify to the slope intercept form:

[tex]y-y_1=m(x-x_1)\\y-3=2(x-6)\\y-3=2x-12\\y=2x-9[/tex]

When translating functions, remember:

Shifting left or right is addition and subtraction respectfully inside the function.Shifting up and down is addition and subtraction respectfully outside the function.

5. A translation of 6.5 units up is +6.5 outside the function y=|x| so equation y=|x|+6.5 is the translation.

6. A translation of 5.5 units to the right is - 5.5 inside the function y=|x| so equation y=|x-5.5| is the translation.

7. A translation of 8 units to the left is +8 inside the function y=|x| so equation y=|x+8| is the translation.

[tex]y=\cos x + 6[/tex]

Step-by-step explanation:

We are given a cos x function. We need to find the function shift 6 units up.

Graph will shift 6 units up. So, all y value of function shift vertically up.

y=f(x)

If shift h and k horizontally and vertically respectively then y=f(x+h)+k

y=cos x

Shift h and k unit then new function

y=cos(x+h)+k <=> cos x + 6

Thus, C is correct option.

5. When the dome is 50 feet high, the distance from the center is 5 feet

6. The equation that model the price y of an x-mile long ride is given as follows;

y = 0.1×x + $3.00

7. The discriminant is < 0; The equation has no real root

8. f(3) = 68

9. The equation representing the translation of the line f(x) = 7·x + 3 down 4 units is f(x) = 7·x + 7

Step-by-step explanation:

5. The given equation for the shape of the dome is presented as follows;

h = -2·d² + 100

Where;

h = The height of the dome (in feet)

d = The distance from the center

Therefore, we have;

When h = 50, d is found as follows;

h = -2·d² + 100

50 = -2·d² + 100

50 - 100 = -2·d²

-50 = -2·d²

∴ 2·d² = 50

d² = 50/2 = 25

d = √25 = 5 feet

Therefore when the dome is 50 feet high, the distance from the center is 5 feet

6. The given rate the cab charges per mile, x = $0.10

The rate the cab charges as flat fee = $3.00

Therefore, the price, y a person traveling by cab for x miles is given by the straight lie equation as y = m·x + c,

Where;

m = the slope or rate which in this case = $0.1/hour

c = A constant term which in this case = $3.00

Therefore

y = 0.1×x + $3.00

The equation that model the price y of an x-mile long ride is y = 0.1×x + $3.00

7. The discriminant, b² - 4·a·c of the quadratic equation is (-4)² - 4×3×6 = -56

which is < 0, the equation has no real root

8. Given f(x) = 7·x² + 5

f(3) = 7 × (3)² + 5 = 68

f(3) = 68

9. The equation representing the translation of the line f(x) = 7·x + 3 down 4 units is given as follows;

Down 4 units is equivalent to subtracting 4 from the y-coordinate value, therefore, we have;

f(x) - 4= 7·x + 3

f(x) = 7·x + 3 + 4

f(x) = 7·x + 7

The equation representing the translation of the line f(x) = 7·x + 3 down 4 units is f(x) = 7·x + 7

B: y=cos(x-5). I'm sorry I can't really explain.

1.

[tex]y = m(x - 4) + 7[/tex]

Explanation:

as we know that equation of straight line passing through a fixed point and having undefined slope is given as

[tex]y - y_1 = m(x - x_1)[/tex]

here we have

[tex](x_1, y_1) = (4, 7)[/tex]

so we will have

[tex]y - 7 = m(x - 4)[/tex]

[tex]y = m(x - 4) + 7[/tex]

2.

slope = ZERO

Explanation:

Slope of the straight line is defined as the tangent of the angle made by the line with respect to x axis

here we need to find the slope of a straight line parallel to x axis so the angle is ZERO degree

hence the slope will be given as

[tex]m = tan 0[/tex]

[tex]m = 0[/tex]

3.

[tex]m = 0.5[/tex]

Explanation:

Slope of a straight line passing through two different points is given as

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

here we will have

[tex]m = \frac{7 - 5}{1 + 3}[/tex]

[tex]m = \frac{2}{4}[/tex]

[tex]m = 0.5[/tex]

4.

[tex]y = |x - x'|[/tex]

here x' = any positive number

Explanation:

If we translate the graph 2 units left of the given position so we can say that we have shifted the graph above from its given position.

So we will have

[tex]y = |x - x'|[/tex]

here x' = any positive number

D.y-4=f(x+3)

Step-by-step explanation:

The correct translation would be y-4 because the y-coordinate moves down 4 units and f(x+3) because the x-coordinate would move 3 spaces to the right.

Hope this helps

1.

[tex]y = m(x - 4) + 7[/tex]

Explanation:

as we know that equation of straight line passing through a fixed point and having undefined slope is given as

[tex]y - y_1 = m(x - x_1)[/tex]

here we have

[tex](x_1, y_1) = (4, 7)[/tex]

so we will have

[tex]y - 7 = m(x - 4)[/tex]

[tex]y = m(x - 4) + 7[/tex]

2.

slope = ZERO

Explanation:

Slope of the straight line is defined as the tangent of the angle made by the line with respect to x axis

here we need to find the slope of a straight line parallel to x axis so the angle is ZERO degree

hence the slope will be given as

[tex]m = tan 0[/tex]

[tex]m = 0[/tex]

3.

[tex]m = 0.5[/tex]

Explanation:

Slope of a straight line passing through two different points is given as

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

here we will have

[tex]m = \frac{7 - 5}{1 + 3}[/tex]

[tex]m = \frac{2}{4}[/tex]

[tex]m = 0.5[/tex]

4.

[tex]y = |x - x'|[/tex]

here x' = any positive number

Explanation:

If we translate the graph 2 units left of the given position so we can say that we have shifted the graph above from its given position.

So we will have

[tex]y = |x - x'|[/tex]

here x' = any positive number

Everything he said was correct!

Step-by-step explanation:

I hope this helps!

- sincerelynini