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Amiraneli [1.4K]
2 years ago
8

(7•8) + 1/2 (3•3) 1/2(7•8)+1/2(3•3) (7•8)+(3•3) 1/2(7•8)+(3•3)

Mathematics
1 answer:
AfilCa [17]2 years ago
8 0

Answer:4.5 for triangle + 56= 60.5 squuare units

Step-by-step explanation:

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What are the roots of the polynomial equation x^3-5x+5=2x^2-5? Use a graphing calculator and a system of equations. Round nonint
leonid [27]

The right answer is c. –2.24, 2, 2.24


This question needs to be solved in two ways. First, using a graphing calculator. Next, using a system of equations.


1. Using a graphing calculator.


We have the following polynomial equation:

x^3-5x+5=2x^2-5


By ordering this equation we have:

x^3-2x^2-5x+10=0


So, we can say that this equation comes from a function given by:

f(x)=x^3-2x^2-5x+10


Thus, by plotting this function, we have that the graph of this function is indicated in Figure 1. By zooming, we can see, in Figure 2, that the roots of the polynomial equation are the x-intercepts of f(x) which are:


x_{1}=-2.236 \\ \\ x_{2}=2 \\ \\ x_{3}=2.236


Finally, rounding noninteger roots to the nearest hundredth we have:


\boxed{Root_{1}=-2.24} \\ \\ \boxed{Root_{2}=2} \\ \\ \boxed{Root_{3}=2.24}


2. Using a system of equations.


The ordered equation is:

x^3-2x^2-5x+10=0


By arranging to factor out we have:

x^3-5x-2x^2+10=0


Then, by factoring:

x(x^2-5)-2(x^2-5)=0


Term (x^2-5) is a common factor, thus:


(x-2)(x^2-5)=0 \\ \\ (x-2)(x-\sqrt{5})(x+\sqrt{5})=0 \\ \\ Finally: \\ \\ \boxed{Root_{1}=-\sqrt{5}=-2.24} \\ \\ \boxed{Root_{2}=2} \\ \\ \boxed{Root_{3}=\sqrt{5}=2.24}

6 0
3 years ago
Read 2 more answers
7n-4=31<br> So what does n represent?
Lorico [155]

Answer:

n=5

Step-by-step explanation:

7n-4   =     31

    +4        +4

7n  =  35

/7        /7

n=5

6 0
3 years ago
Soooo Hard<br> Please someone help me
Alisiya [41]

\frac{1}{2} ( \frac{2}{3}  +  \frac{3}{4}) \\  =  \frac{1}{2}  ( \frac{2 \times 4}{3 \times 4}  +  \frac{3 \times 3}{4 \times 3} ) \\  =  \frac{1}{2} ( \frac{8}{12}  +  \frac{9}{12} ) \\  =  \frac{1}{2} ( \frac{8 + 9}{12} ) \\   = \frac{1}{2} ( \frac{17}{12} ) \\  =  \frac{1 \times 17}{2 \times 12}  \\  =  \frac{17}{24}
The answer is 17/24
8 0
3 years ago
How would you solve this problem?
klio [65]

Answer:

a) 6x²/2x³-4

b)  2ln (2x^3-4)+ C

Step-by-step explanation:

a) Given the ln(2x³-4). We will use the chain rule in differentiating the function

If y = ln(2x³-4);

u = 2x³-4; du/dx = 3(2)x³⁻¹

du/dx = 6x²

y = ln u; dy/du = 1/u

According to chain rule, dy/dx = dy/dy*du/dx

dy/dx = 1/u * 6x²

dy/dx = 1/2x³-4 * 6x²

dy/dx = 6x²/2x³-4

Hence, the derivative of the given function is 6x²/2x³-4

b) Given an integral function \int\limits {\frac{12x^2}{2x^3-4} } \, dx, the integral problem can be solved using integration by substitution method as shown below;

From the question, let y = 2x³-4... 1, dy/dx = 6x²

dx = dy/6x² ... 2

Substituting equation 1 and 2 into the question given;

\int\limits {\frac{12x^2}{y} } \,\frac{dy}{6x^2} \\\\= \int\limits {\frac{2dy}{y} } \\\\= 2 \int\limits {\frac{dy}{y} }\\\\= 2lny + C\\substituting\ y = 2x^3-4\ into\ the \ resulting\ function\\\\= 2ln (2x^3-4)+ C

3 0
3 years ago
Encontrar X..................
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X is 51
Because I did this a few days bakc
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