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3 years ago

Find the value of Q in the following system so that the solution to the system is {(x,y) : x-3y=4}

Mathematics

1 answer:

Assoli18 [71]3 years ago

3 0

Answer:

Q=2

Step-by-step explanation:

hello :

the solution to the system is

{(x,y) : x-3y=4} means infinty solution

X-3y=4 ....(*)

Qx-6y=8....(**)

multiply (*) by -2

-2x+6y = -8 (***)

add (*) and (***) : (Q-2)x =0

this ie true for reals x when Q=2

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fgiga [73]

Answer:

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Step-by-step explanation:

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3 years ago

Determine formula of the nth term 2, 6, 12 20 30,42

nalin [4]

Check the forward differences of the sequence.

If $\{a_n\} = \{2,6,12,20,30,42,\ldots\}$ , then let $\{b_n\}$ be the sequence of first-order differences of $\{a_n\}$ . That is, for n ≥ 1,

$b_n = a_{n+1} - a_n$

so that $\{b_n\} = \{4, 6, 8, 10, 12, \ldots\}$ .

Let $\{c_n\}$ be the sequence of differences of $\{b_n\}$ ,

$c_n = b_{n+1} - b_n$

and we see that this is a constant sequence, $\{c_n\} = \{2, 2, 2, 2, \ldots\}$ . In other words, $\{b_n\}$ is an arithmetic sequence with common difference between terms of 2. That is,

$2 = b_{n+1} - b_n \implies b_{n+1} = b_n + 2$

and we can solve for $b_n$ in terms of $b_1=4$ :

$b_{n+1} = b_n + 2$

$b_{n+1} = (b_{n-1}+2) + 2 = b_{n-1} + 2\times2$

$b_{n+1} = (b_{n-2}+2) + 2\times2 = b_{n-2} + 3\times2$

and so on down to

$b_{n+1} = b_1 + 2n \implies b_{n+1} = 2n + 4 \implies b_n = 2(n-1)+4 = 2(n + 1)$

We solve for $a_n$ in the same way.

$2(n+1) = a_{n+1} - a_n \implies a_{n+1} = a_n + 2(n + 1)$

Then

$a_{n+1} = (a_{n-1} + 2n) + 2(n+1) \\ ~~~~~~~= a_{n-1} + 2 ((n+1) + n)$

$a_{n+1} = (a_{n-2} + 2(n-1)) + 2((n+1)+n) \\ ~~~~~~~ = a_{n-2} + 2 ((n+1) + n + (n-1))$

$a_{n+1} = (a_{n-3} + 2(n-2)) + 2((n+1)+n+(n-1)) \\ ~~~~~~~= a_{n-3} + 2 ((n+1) + n + (n-1) + (n-2))$

and so on down to

$a_{n+1} = a_1 + 2 \displaystyle \sum_{k=2}^{n+1} k = 2 + 2 \times \frac{n(n+3)}2$

$\implies a_{n+1} = n^2 + 3n + 2 \implies \boxed{a_n = n^2 + n}$

6 0

2 years ago

Solve the quadratic equation by factoring. 9x^2+24x+20=4

const2013 [10]

D. -4/3

Let's solve your equation step-by-step.

9x2+24x+20=4

Step 1: Subtract 4 from both sides.

9x2+24x+20−4=4−4

9x2+24x+16=0

Step 2: Factor left side of equation.

(3x+4)(3x+4)=0

Step 3: Set factors equal to 0.

3x+4=0 or 3x+4=0

x= −4 /3

Hope This helps

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3 years ago

1 pol

BigorU [14]

In 3 hours, they could bake 87 birthday cupcakes. If you divid 145 by 5 this gives you 29, and you multiply this by 3 to find how many can be made in 3 hours, which gives you 87:) hope this helps!

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3 years ago

The function f(x) = square root -x is shown on the graph. Which statement is correct?

EastWind [94]

Answer:

The Domain of the graph is all real numbers less than or equal to 0.

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3 years ago

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