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4 years ago

Transformation from function

Mathematics

1 answer:

tankabanditka [31]4 years ago

6 0

f(x) = (x - 1)² + 2

g(x) = (x-1)²

f(x) function is a g(x) function that was moved 2 units up, or

g(x) is f(x) that was moved 2 units down.

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What's 21/9 in the simplest form the answer

allsm [11]

2 2/9 is the answer to your question

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3 years ago

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Using synthetic division, find (2x4 + 4x3 + 2x2 + 8x + 8) ÷ (x + 2).

creativ13 [48]

The answer is 32x+8
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4 years ago

Please help I really need help on this I would really appreciate it anything helps !

andreev551 [17]

Answer:

AXE and CXD are vertical angles

AXF and FXD are supplementary angles

DXC and BXC are complementary angles

EXA and AXB are adjacent angles

AXC and CXD are supplementary angles

EXD and AXC are vertical angles

Step-by-step explanation:

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3 years ago

Give an example of a 2x2 matrix without any real eigenvalues:___________

9966 [12]

Answer:

Step-by-step explanation:

An eigenvalue of n × n is a function of a scalar $\lambda$ considering that there is a solution (i.e. nontrivial) to an eigenvector x of Ax =

Suppose the matrix $A = \left[\begin{array}{cc}-1&-1\\2&1\\ \end{array}\right]$

Thus, the equation of the determinant (A - $\lambda$ 1) = 0

This implies that:

$\left[\begin{array}{cc}-1-\lambda &-1\\2&1- \lambda\\ \end{array}\right] =0$

$-(1 - \lambda^2 ) + 2 = 0$

$-1 + \lambda ^2 + 2= 0$

$\lambda^2 +1 =0$

Hence, the eigenvalues of the equation are $\mathtt{\lambda = i , -i}$

Also, the eigenvalues can be said to be complex numbers.

3 0

3 years ago

. A fruit company recently released a new applesauce. By the end of its first year, profits on this product amounted to $24,700

lozanna [386]

Answer:

1) P(x) =14400x+10300 2)y=-4x+19 3) $y=\frac{-2x}{3} -14$ 4) x=-11

(Please check the pictures for better understanding)

Step-by-step explanation:

1) Firstly, let's organize the data. Let the dependent variable x be the years, and the Range P(x) the Profit. So arranging these linear functions y=ax+b and plugging the coordinates for each point (1, 24700) and (4, 67900). Goes:

24,700=x+b

67,900=4x +b

1.1)Solving for b, this Linear System of Equation by the Addition Method goes:

$24,700=x+b*(-4)\\67,900=4x+b\\----------\\-98,800=-4x-4b\\67,900=4x+b\\ -----------\\-30900=-3b\\\frac{3b}{3} =\frac{30900}{3}\\ b=10300$

1.2) Now, let's find the slope based on those two points (1, 24700) and (4, 67900) and using the formula to find the slope:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$m=\frac{67900-24700}{4-1}\\ m=\frac{43200}{3}\\ m=14400$

So now we can write this Linear Equation for the Profit:

P(x) =14400x+10300

2) An equation of the line perpendicular to 4y=x-8 has a slope equal to $m_{2}$ =- $\frac{-1}{m_{1}}$ the line. In this case, an equation perpendicular to 4y=x-8 .

Rearranging the given equation of the line 4y=x-8 goes:

$y=\frac{x}{4} -\frac{8}{4} \\ y=\frac{x}{4}-2$

2.1) The slope of this new line is equivalent to m=-4 since -4 is opposite inverse value for the slope of its perpendicular line (1/4).

If the line passes through the point (6,-5), then this point already belongs to this line.

Then, we can write.

-5=-4(6)+b

-5=-24+b

-5+24=-24+24+b

b=19

Now we can write the function:

y=-4x+19

3) Firstly, let's rearrange the equation. Into a General Equation of the Line y=ax+b

2x+3y=5

-2x+2x+3y=5-2x

3y=5-2x

$\frac{3y}{3} =\frac{5}{3} -\frac{2x}{3}$

$y=\frac{-2x}{3}+\frac{5}{3}$

3.2) Let's find out b, the linear coefficient by plugging the coordinates of the point (-3,-8).

Also, Parallel lines have the same value for the slope such as $m_{1}=m_{2}$

-8=-3(-2/3)+b

-8=2+b

-8-2=2-2+b

b=-10

Then the equation of this parallel line is:

$y=\frac{-2x}{3} -10$

4) Now on this last question, we have to find an equation of the line through the point (-11,-4) perpendicular to another line y=15

Suppose the slope of the first line is $m_{1}$ and the value of the slope of its perpendicular is $m_{2}=\frac{-1}{m_{1}}$

y=15 is a horizontal line with slope equals zero, we can rewrite it as y=0x+15.

Then the slope is zero for horizontal lines.

A perpendicular line to a horizontal line is a vertical one.

In addition to this, a vertical line passes through only one point in the x-axis. Then, there is no horizontal variation. This leads the formula of a slope to an undefinition for Real Set.

$m=\frac{y_{2}-y_{1}}{0}$

The only perpendicular line which passes through the point (-11,-4) to y=15 is the line x=-11.

7 0

3 years ago