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3 years ago

-4(-3x - 8) - 4x + 8 = -8x + 40

1 answer:

3 0

First we expand and combine the terms on the left side. This gives us

12x + 32 -4x + 8 = -8x + 40

8x + 40 = -8x + 40. Because the two sides cancel each other out when you try and bring all the x to one side, the answer is x = 0.

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DanielleElmas [232]

The answer should be $40

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3 years ago

The Goodsmell perfume company has a new line of perfume and is designing a new bottle for it. Because of

Alex777 [14]

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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

Which value of x makes the following equation true?

Vlad [161]

3(x-3) = -3x + 39
3x - 9 = -3x + 39
3x + 3x = 39 + 9
6x = 48
x = 48/6
x = 8

In short, Your Answer would be Option C) 8

Hope this helps!

8 0

3 years ago

PLEASE HELP

laila [671]

<h3><u>Option A</u></h3>

$4 x^{2}+32 x-80=0$ is the required equation to calculate width of rectangular frame that has a total area of 140 square inches.

<h3><u>Solution:</u></h3>

Given that,

Length of a rectangular frame is given as 2x + 10

Width of the rectangular frame is given as 2x + 6

Total area = 140 square inches

<em><u>The area of rectangular frame is given as:</u></em>

$\text {area of rectangle}=\text {length } \times \text {width}$

Plugging in values, we get

$\begin{array}{l}{(2 x+10)(2 x+6)=140} \\\\ {4 x^{2}+12 x+20 x=80} \\\\ {4 x^{2}+32 x-80=0}\end{array}$

This is the required equation to calculate width of rectangular frame

Solve the above quadratic equation to get the value of "x"

$4 x^{2}+32 x-80=0$

<em><u>Use the quadratic equation formula:</u></em>

$x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

Here a = 4 ; b = 32 ; c = -80

$x=\frac{-32 \pm \sqrt{32^{2}-4(4)(-80)}}{2(4)}$

$x=\frac{-32 \pm \sqrt{2304}}{8}$

x = 2 or x = -10

Now measurement cannot be negative, so taking the positve value of "x", we can calculate the width

So put "x" = 2

Width of the rectangular frame = 2x + 6 = 2(2) + 6 = 10

Thus the width of frame is 10 inches

4 0

3 years ago