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3 years ago

11

This system of equations has infinitely many solutions which of the following statements is not true

1 answer:

Leno4ka [110]3 years ago

4 0

Answer: The graphs of the equations are parallel lines.

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80,40,20,_,5<br><br> What’s the pattern?

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Half.
the missing number is 10
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Use a graph to how the relationship of the number of bacteria over a 6 day period.

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4 years ago

Hi, can you help to find (all the roots/zeros), please!!!

OLga [1]

Solution

Given the quadratic equation

$x^2-2x-38=0$

we need to find the zeros of the equation

To do that, we use the completing the square method

Step 1. Add 38 to both sides

$\begin{gathered} \Rightarrow x^2-2x-38+38=38 \\ \\ \Rightarrow x^2-2x=38 \end{gathered}$

Step 2: add the square of half of the coefficient of x to both sides

That is;

$\begin{gathered} \Rightarrow x^2-2x+(\frac{1}{2}\cdot(-2))^2=38+(\frac{1}{2}\cdot(-2))^2 \\ \\ \Rightarrow x^2-2x+1=38+1 \\ \\ \Rightarrow x^2-2x+1=39 \\ \\ \Rightarrow(x-1)^2=39 \end{gathered}$

Step 3: Simplify the above expression;

$\begin{gathered} \Rightarrow x-1=\pm\sqrt[]{39} \\ \\ \Rightarrow x=1\pm\sqrt[]{39} \end{gathered}$

4 0

1 year ago

Help please! any1 know this

ra1l [238]

Answer:

C, 3

Step-by-step explanation:

By creating a best line of fit you can get the sets of points (16,50) and (12,40)

Using these to find the slope we can get $\frac{40-50}{12-16} =\frac{-10}{-4}$

-10/-4 is 2.5 The best approximation would be C, because if you round it up to the nearest number you would get 3.

3 0

3 years ago

Do the points (−1,9) and (2,4) represent the vertex and a sample point, respectively, of y=−2(x+1)2+9? Explain

Reil [10]

Answer:

Vertex: (-1,9) is true

Sample Points: (2,4) is not true

Step-by-step explanation:

Given

$Vertex: (-1,9)$

$Sample\ Points: (2,4)$

Required

Determine if the vertex and sample points exist for $y= -2(x+1)\²+9$

Solving for the vertex:

$y= -2(x+1)\²+9$

Writing the given equation in the form:

$y = ax^2 + bx + c$

Expand the bracket

$y= -2(x+1)(x+1)+9$

Open Bracket

$y= -2(x+1)(x+1)+9$

$y = -2(x^2 + 2x + 1) + 9$

Open bracket

$y = -2x^2 - 4x -2 + 9$

$y = -2x^2 - 4x +7$

Solve for x using:

$x = \frac{-b}{2a}$

Where $a = -2$ ; $b = -4;$

<em>So:</em>

$x = \frac{-(-4)}{2 * (-2)}$

$x = \frac{4}{-4}$

$x = -1$

Substitute -1 for x in $y = -2x^2 - 4x +7$

$y = -2(-1)^2 -4(-1) + 7$

Simplify all brackets

$y = -2(1) + 4 + 7$

$y = -2 + 4 + 7$

$y = 9$

Hence;

<em>The vertex (x,y) is (-1,9)</em>

<em>This is true</em>

Checking sample points: $(2,4)$

In this case; $x = 2$ and $y = 4$

Substitute $x = 2$ and $y = 4$ in $y= -2(x+1)\²+9$

$4 = -2(2 + 1)^2 + 9$

$4 = -2(3)^2 + 9$

$4 = -2 * 9 + 9$

$4 = -18 + 9$

$4 \neq -9$

<em>Hence;</em>

<em>This sample points </em> $(2,4)$ <em> does not exist</em>

8 0

3 years ago