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natali 33 [55]
3 years ago
7

The graph of the function

Mathematics
1 answer:
OLEGan [10]3 years ago
5 0
F(x)=|x+3|-5 is the transformed function.
Take 3 values of x, -4, -3, -2 original f(x) for these are 1, 0, 1.
The same values for the transformed function are -4, -5, -4.
If we try to bring the -5 into the modulus, we get |x-2|. Now putting the values of x in we get: 6, 5, 4 and the graph is also displaced sideways so the solution is the transformed f(x)=|x+3|-5.
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alina1380 [7]

Answer: no lol

Step-by-step explanation:

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2 years ago
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Solve the following 3 × 3 system. Enter the coordinates of the solution below.
ICE Princess25 [194]

Step-by-step explanation:

2x - 3y - 2z = 4

[2] x + 3y + 2z = -7

[3] -4x - 4y - 2z = 10

Solve by Substitution :

// Solve equation [2] for the variable x

[2] x = -3y - 2z - 7

// Plug this in for variable x in equation [1]

[1] 2•(-3y-2z-7) - 3y - 2z = 4

[1] - 9y - 6z = 18

// Plug this in for variable x in equation [3]

[3] -4•(-3y-2z-7) - 4y - 2z = 10

[3] 8y + 6z = -18

// Solve equation [3] for the variable z

[3] 6z = -8y - 18

[3] z = -4y/3 - 3

// Plug this in for variable z in equation [1]

[1] - 9y - 6•(-4y/3-3) = 18

[1] - y = 0

// Solve equation [1] for the variable y

[1] y = 0

// By now we know this much :

x = -3y-2z-7

y = 0

z = -4y/3-3

// Use the y value to solve for z

z = -(4/3)(0)-3 = -3

// Use the y and z values to solve for x

x = -3(0)-2(-3)-7 = -1

Solution :

{x,y,z} = {-1,0,-3}

6 0
2 years ago
Restrict the domain of the quadratic function and find its inverse. Confirm the inverse relationship using composition. f(x) = 0
ANTONII [103]

The given function is

f(x)= 0.2 x²

Since f(x) will be defined for all real values of x.

So, Domain of f(x) will be ( x| x is a real number.)→This is set builder notation.

Finding the inverse of f(x):

y = 0.2 x²

→ x²= 5 y

→x = \pm\sqrt{5 y}→ → Inverse of f(x)

Replacing x by y and y by x,we get inverse of the given function

y = \pm\sqrt{5 x}→ →Domain x ≥ 0, x∈[0,∞]

Graph of function and its inverse are shown below.

8 0
2 years ago
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A firework is launched at the rate of 10 feet per second from a point on the ground 50 feet from an observer. to 2 decimal place
Kazeer [188]

The rate of change of the angle of elevation when the firework is 40 feet above the ground is 0.12 radians/second.

First we will draw a right angle triangle ΔABC, where ∠B = 90°

Lets, assume the height(AB) = h and base(BC)= x

If the angle of elevation, ∠ACB = α, then

tan(α) = \frac{AB}{BC} = \frac{h}{x}

Taking inverse trigonometric function, α = tan⁻¹ (\frac{h}{x}) .............(1)

As we need to find the rate of change of the angle of elevation, so we will differentiate both sides of equation (1) with respect to time (t) :

\frac{d\alpha}{dt}=[\frac{1}{1+ \frac{h^2}{x^2}}]*(\frac{1}{x})\frac{dh}{dt}

Here, the firework is launched from point B at the rate of 10 feet/second and when it is 40 feet above the ground it reaches point A,

that means h = 40 feet and \frac{dh}{dt} = 10 feet/second.

C is the observer's position which is 50 feet away from the point B, so x = 50 feet.

\frac{d\alpha}{dt}= [\frac{1}{1+ \frac{40^2}{50^2}}] *\frac{1}{50} *10\\ \\ \frac{d\alpha}{dt} = [\frac{1}{1+\frac{16}{25}}] *\frac{1}{5}\\ \\ \frac{d\alpha}{dt} = [\frac{25}{41}] *\frac{1}{5}\\   \\ \frac{d\alpha}{dt}= \frac{5}{41} =0.1219512

= 0.12 (Rounding up to two decimal places)

So, the rate of change of the angle of elevation is 0.12 radians/second.

5 0
3 years ago
How much would $200 invested at 7% interest compounded annually be worth after 5 years? Round your answer to the nearest cent. D
viktelen [127]
The future worth (F) of the investment at present (P) with a compound interest i after n years is calculated through the equation,
                                      F = P x (1 + i)^n
Substituting the known values,
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Thus, the future worth of the investment is approximately $280.51. 
6 0
2 years ago
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