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PtichkaEL [24]
1 year ago
9

State the domain of 1b, then determine the equation of any vertical asymptotes and/or coordinates of any holes in the graph of t

he function.

Mathematics
1 answer:
Katena32 [7]1 year ago
6 0

We have

f(x)=\frac{2x^2+x}{x^2-5x+6}

First we will factorize the function

f(x)=\frac{x(2x+1)}{\mleft(x-2\mright)(x-3)}

The domain is

\: \mleft(-\infty\: ,\: 2\mright)\cup\mleft(2,\: 3\mright)\cup\mleft(3,\: \infty\: \mright)

In this case, we have two vertical asymptotes

x-2=0

x=2

x-3=0

x=3

ANSWER

The domain is

\: \mleft(-\infty\: ,\: 2\mright)\cup\mleft(2,\: 3\mright)\cup\mleft(3,\: \infty\: \mright)

The vertical asymtotes

x-2=0

x=2

x-3=0

x=3

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Simplify the following without using a calculator<br>a)<br>- 4 x (8-(-3)) + 7​
bulgar [2K]
-4(8-(-3))+7

Remove the parentheses, negative with negative will equal a positive so the new equation will be -4(8+3)+7. So 8+3=11, -4(11)+7. -4(11)=-44 and then add -44+7 which will equal -37
3 0
3 years ago
Solve the system by using a matrix equation (Picture provided)
Katyanochek1 [597]

Answer:

Option b is correct (8,13).

Step-by-step explanation:

7x - 4y = 4

10x - 6y =2

it can be represented in matrix form as\left[\begin{array}{cc}7&-4\\10&-6\end{array}\right] \left[\begin{array}{c}x\\y\end{array}\right] = \left[\begin{array}{c}4\\2\end{array}\right]

A= \left[\begin{array}{cc}7&-4\\10&-6\end{array}\right]

X= \left[\begin{array}{c}x\\y\end{array}\right]

B= \left[\begin{array}{c}4\\2\end{array}\right]

i.e, AX=B

or X= A⁻¹ B

A⁻¹ = 1/|A| * Adj A

determinant of A = |A|= (7*-6) - (-4*10)

                                    = (-42)-(-40)

                                    = (-42) + 40 = -2

so, |A| = -2

Adj A=  \left[\begin{array}{cc}-6&4\\-10&7\end{array}\right]

A⁻¹ =  \left[\begin{array}{cc}-6&4\\-10&7\end{array}\right]/ -2

A⁻¹ =  \left[\begin{array}{cc}3&-2\\5&-7/2\end{array}\right]

X= A⁻¹ B

X=  \left[\begin{array}{cc}3&-2\\5&-7/2\end{array}\right] *\left[\begin{array}{c}4\\2\end{array}\right]

X= \left[\begin{array}{c}(3*4) + (-2*2)\\(5*4) + (-7/2*2)\end{array}\right]

X= \left[\begin{array}{c}12-4\\20-7\end{array}\right]

X= \left[\begin{array}{c}8\\13\end{array}\right]

x= 8, y= 13

solution set= (8,13).

Option b is correct.

3 0
3 years ago
Need the answer !!?’
Murrr4er [49]

....the answer is <CBA.

6 0
3 years ago
Read 2 more answers
What is the answer??
Alchen [17]

Answer: 7.8 ⋅ 10^{4}

Step-by-step explanation:

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7.8 ⋅ 10^{4}

4 0
3 years ago
(1CQ) Determine whether the series -8/5+32/25-128/125+... is convergent or divergent.
Ivan

Answer:

The series is convergent answer ⇒ (a)

Step-by-step explanation:

* The series is -8/5 + 32/25 + -128/125 + ........

- It is a geometric series with:

- first term a = -8/5 and common ratio r = 32/25 ÷ -8/5 = -4/5

* The difference between the convergent and divergent

  in the geometric series is :

- If the geometric series is given by  sum  = a + a r + a r² + a r³ + ...

* Where a is the first term and r is the common ratio

* If |r| < 1 then the following geometric series converges to a / (1 - r).  

- Where a/1 - r is the sum to infinity

* The proof is:

∵ S = a(1 - r^n)/(1 - r) ⇒ when IrI < 1 and n very large number

∴ r^n approach to zero

∴ S = a(1 - 0)/(1 - r) = a/(1 - r)

∴ S∞ = a/1 - r

* If |r| ≥ 1 then the above geometric series diverges

∵ r = -4/5

∴ IrI = 4/5

∴ IrI < 1

∴ The series is convergent

3 0
3 years ago
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