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2 years ago

If you apply the changes below to the absolute value parent function, f(x) = [X],

Mathematics

1 answer:

son4ous [18]2 years ago

6 0

Answer:

Step-by-step explanation:

Given f(x) then f(x + a) is a horizontal translation of f(x)

• If a > 0 then a shift to the left of a units

• If a < 0 then a shift to the right of a units

Here f(x) is shifted 4 units to the right , so

g(x) = | x - 4 |

Given f(x) then f(x) + c is a vertical translation of f(x)

• If c > 0 then a shift up of c units

• If c < 0 then a shift down of c units

Here f(x) is shifted 6 units up , so

g(x) = | x - 4 | + 6 → B

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Show that sinx/1+cosx=tanx/2

hammer [34]

Answer:

See proof below

Step-by-step explanation:

show that

sinx/1+cosx=tanx/2

From LHS

sinx/1+cosx

According to half angle

sinx = 2sinx/2 cosx/2

cosx = cos²x/2 - sin²x/2

cosx = cos²x/2 - (1- cos²x/2)

cosx = 2cos²x/2 - 1

cos x + 1 = 2cos²x/2

Substitute into the expression;

sinx/1+cosx

= (2sinx/2 cosx/2)/2cos²x/2

= sinx.2/cos x/2

Since tan x = sinx/cosx

Hence sinx/2/cos x/2 = tan x/2 (RHS)

This shows that sinx/1+cosx=tanx/2

7 0

2 years ago

Hepppppppplppppppplppppppppp

antoniya [11.8K]

Answer:

A = 3 ft, B = 7 ft, C = 4 ft, D = 5 ft, Surface Area = 96 ft^2

Step-by-step explanation:

Step 1: Determine the sides

A → 3 ft

B → 7 ft

C → 4 ft

D → 5 ft

Step 2: Determine the surface area

Area of the sides

$A= 4\ ft * 7\ ft = 28\ ft^2$

$A= 5\ ft * 7\ ft = 35\ ft^2$

$A= 3\ ft * 7\ ft = 21\ ft^2$

Area of the top and bottom triangles

$A= \frac{h\ *\ b}{2} = \frac{3\ ft\ *\ 4\ ft}{2} = \frac{12\ ft^2}{2} = 6\ ft^2 = 2(6\ ft^2) = 12\ ft^2$

Total Area

$28\ ft^2 + 35\ ft^2 + 21\ ft^2 + 12\ ft^2$

$96\ ft^2$

Answer: A = 3 ft, B = 7 ft, C = 4 ft, D = 5 ft, Surface Area = 96 ft^2

5 0

1 year ago

Read 2 more answers

Graph f(x)=−0.5x+3. Use the line tool and select two points to graph the line.

NikAS [45]

Answer: These are some points of the grahp:

(-2,4)

(0, 3)

(2, 2)

Explanation:

1) f(x) = -0.5x + 3, is the equation of the form y = mx + b

2) y = mx + b is slope-intercept equation of a line where the slope is m and the y-intercept is b, so, f(x) = - 0.5x + b has slope m = -0.5 and y-intercept b = 3.

3) To graph f(x) = -0.5x + 3, follow these steps:

draw two perpedicular axis: vertical axis, labeled y, and horizontal axis, labeled x.
draw marks on each axis, each mark equivalent to one unit.
the intersection point of the vertical and horizontal axis is the origin, i.e. point (0,0).
you can make a table with two or more points:

x f(x) = - 0.5x + 3

-2 4

0 3

2 2

4 1

6 0

4) You can see the graph in the figure attached, and select any of the points on the line either by using the table or by using the equation f(x) = -0.5x + 3.