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3 years ago

Solve the following system by substitution -3x+y=-5 and 3x+6y=0

Mathematics

1 answer:

Jobisdone [24]3 years ago

3 0

Answer:

$x=\frac{10}{7},\:y=-\frac{5}{7}$

Step-by-step explanation:

$\begin{bmatrix}-3x+y=-5\\ 3x+6y=0\end{bmatrix}\\\\\mathrm{Isolate}\:x\:\mathrm{for}\:-3x+y=-5:\quad x=-\frac{-5-y}{3}\\\\\mathrm{Subsititute\:}x=-\frac{-5-y}{3}\\\\\begin{bmatrix}3\left(-\frac{-5-y}{3}\right)+6y=0\end{bmatrix}\\\\Simplify\\\\\begin{bmatrix}5+7y=0\end{bmatrix}\\\\\mathrm{Isolate}\:y\:\mathrm{for}\:5+7y=0:\quad y=-\frac{5}{7}\\\\\mathrm{For\:}x=-\frac{-5-y}{3}\\\\\mathrm{Subsititute\:}y=-\frac{5}{7}\\\\x=-\frac{-5-\left(-\frac{5}{7}\right)}{3}$

$-\frac{-5-\left(-\frac{5}{7}\right)}{3}=\frac{10}{7}\\\\x=\frac{10}{7},\:y=-\frac{5}{7}\\\\$

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Answer:

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Step-by-step explanation:

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3 years ago

What is the inverse of this function? f(x)=-1/2 square root of x+3, x > -3

yuradex [85]

The inverse function of $f(x) = -\frac 12\sqrt{x + 3}$ is $f^{-1}(x) = 4x^2- 3$

<h3>How to determine the inverse function?</h3>

The function is given as:

$f(x) = -\frac 12\sqrt{x + 3}$

Rewrite as;

$y = -\frac 12\sqrt{x + 3}$

Swap the positions of x and y

$x = -\frac 12\sqrt{y + 3}$

Multiply through by -2

$-2x = \sqrt{y + 3}$

Square both sides

4x^2 = y + 3

Subtract 3 from both sides

y = 4x^2 - 3

Express as an inverse function

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Hence, the inverse function of $f(x) = -\frac 12\sqrt{x + 3}$ is $f^{-1}(x) = 4x^2- 3$

Read more about inverse function at:

brainly.com/question/2541698

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2 years ago

Find the vertex of y=-5x^2+10x+3

Sholpan [36]

Answer: (h,k) (-1, -8)

Step-by-step explanation:

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3 years ago

Read 2 more answers

9. Consider an experiment that consists of determing the type of job (either blue-collar or white-collar) and the political affi

kari74 [83]

Answer:

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Step-by-step explanation:

An outcome is a possible result of an event. Sample space is the set of all possible outcomes.

An event is a subset of the sample space.

Let B, W denotes blue-collar, white-collar respectively.

Let R, D and I denotes republican, democrat, or independent respectively.

Number of members of an adult soccer team = 15 members

To find:Number of outcomes

Sample space:

$S=\left \{ \left ( (x_1,y_1),(x_2,y_2),...,(x_{15},y_{15}) \right )|x_i\varepsilon \left \{ B,W \right \} \,,\,y_i\varepsilon \left \{ R, D, I \right \}\right \}$