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Dimas [21]
3 years ago
5

Which of the following is equivalent to the polynomial below?

Mathematics
1 answer:
Gnoma [55]3 years ago
6 0

Answer:

(x-(4+\sqrt{3}i))(x-(4-\sqrt{3}i))

Step-by-step explanation:

Consider the quadratic expression

x^2-8x+19

First, find its discriminant:

D=(-8)^2-4\cdot 1\cdot 19=64-76=-12

Note that i^2=-1, then D=12i^2.

Use quadratic formula to find the roots:

x_{1,2}=\dfrac{-(-8)\pm \sqrt{12i^2}}{2\cdot 1}=\dfrac{8\pm 2\sqrt{3} i}{2}=4\pm \sqrt{3}i

Now, given quadratic expression is equivalent to

(x-(4+\sqrt{3}i))(x-(4-\sqrt{3}i))\\ \\=(x-4-\sqrt{3}i)(x-4+\sqrt{3}i)

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Answer: 1/5

Step-by-step explanation:

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The pair of square pyramids are similar. Use the given information to find the scale factor of the smaller square pyramid to the
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\bf \qquad \qquad \textit{ratio relations}
\\\\
\begin{array}{ccccllll}
&\stackrel{ratio~of~the}{Sides}&\stackrel{ratio~of~the}{Areas}&\stackrel{ratio~of~the}{Volumes}\\
&-----&-----&-----\\
\cfrac{\textit{similar shape}}{\textit{similar shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3}
\end{array}\\\\
-----------------------------

\bf \cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{s}{s}=\cfrac{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\\\\
-------------------------------\\\\
\stackrel{\stackrel{pyramids}{scale~factor}}{\cfrac{small}{large}}\qquad \qquad \cfrac{s}{s}=\cfrac{\sqrt[3]{64}}{\sqrt[3]{343}}\implies \cfrac{s}{s}=\cfrac{4}{7}\implies 4:7
8 0
3 years ago
Step by step explanation
vodka [1.7K]

Answer: x = 4 and y = -3

Step-by-step explanation:

2x + 4y = -4

2x = -4 - 4y

x = -2 - 2y

Now that we have solved the first equation for x, we plug (-2 - 2y) into the other equation in place of x and then solve for y.

3(-2 -2y) + 5y = -3

-6 - 6y + 5y = -3

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y = -3

Now that we know y, we plug it into the original equation and solve for x.

2x + 4(-3) = -4

2x + -12 = -4

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You can check the answer by plugging both x and y into either of the original equations.

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3 years ago
a computer store bought a program at a cost of $20 and sold it at a selling price$26. what is the percent markup
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3 years ago
1. What is the solution of the equation<br> 3y-5y+10=36?<br> 1. -13<br> 2. 2<br> 3. 4.5<br> 4. 13
VikaD [51]

Answer:

1: -13

Step-by-step explanation:

First, simplify the equation to -2y+10=36

Subtract 10 from both sides

-2y=26

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y=-13

5 0
3 years ago
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