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Olenka [21]
3 years ago
7

Can u guys solve all this

Mathematics
1 answer:
scZoUnD [109]3 years ago
8 0
Answer:

1) y = - 5/3x

2) y = - 4/3x

3) slope = - 1/17

4) slope = 6

6) y = -x - 1

7) y = -3/5x - 1/5

8) y = -x - 7

Step-by-step explanation:

5x + 3y = 0

3y = 0 - 5x

y = 0/3 - 5/3x or…

y = - 5/3x
- - - - - - - - - - - - - - - - -
4x + 3y = 0

3y = 0 - 4x

y = 0/3 - 4/3x or…

y = - 4/3x
- - - - - - - - - - - - - - - - -
(4, -9) , (-13, -8)

m = slope

m = change in y/change in x

m = (y2 - y1)/(x2 - x1)

m = (-8 - -9)/(-13 - 4)

m = 1/-17 or…

m = - 1/17
- - - - - - - - - - - - - - - - -
(8, 12) , (5, -6)

m = slope

m = change in y/change in x

m = (y2 - y1)/(x2 - x1)

m = (-6 - 12)/(5 - 8)

m = -18/-3

m = 18/3 or…

m = 6
- - - - - - - - - - - - - - - - -
6)

y = -x - 1

- - - - - - - - - - - - - - - - -
through (3, -2), parallel
to y = -3/5x

y = -3/5x + b

-2 = -3/5(3) + b

-2 = -9/5 + b

b = -2 - -9/5

b = - 1/5

The line would be y = -3/5x - 1/5
- - - - - - - - - - - - - - - - -
y = -x

(-5, -2)

-2 = 5 + b

b = -2 - 5

b = -7

The line would be y = -x - 7

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The function f(x) = x is translated using the rule (x, y) - (x - 6, y + 9) to create A(x).
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<em>It seems the correct function you need to mention is f(x) = sqrt x</em>

<em>so, I am assuming </em>f(x) = \sqrt{x}<em> and will solve the question based on it.</em>

Answer:

Check the explanation

Step-by-step explanation:

Given the function

f(x) = \sqrt{x}

As the function is translated according to the rule

  • (x, y) → (x - 6, y + 9)

Translation of the function f(x) = \sqrt{x} 6 units to the left will bring the function

g(x) = \sqrt{x+6}

Translation of the function  g(x) = \sqrt{x+6}  9 units up will bring the function

A\left(x\right)=\sqrt{x+6}+9

Determining the range of A\left(x\right)=\sqrt{x+6}+9

  • As we know that the range is the set of dependent values for which the function is defined.

\mathrm{The\:range\:of\:an\:radical\:function\:of\:the\:form}\:c\sqrt{ax+b}+k\:\mathrm{is}\:\:f\left(x\right)\ge \:k

k=9

f\left(x\right)\ge \:9

so

\mathrm{Range\:of\:}\sqrt{x+6}+9:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:f\left(x\right)\ge \:9\:\\ \:\mathrm{Interval\:Notation:}&\:[9,\:\infty \:)\end{bmatrix}

Therefore, the expression describes the range of A(x) will be:

f\left(x\right)\ge \:\:9\:or\:y\:\ge \:\:\:9

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