Let $x$ be the unknown number. Its square is $x^2$ . The product of 6 and the square of the number is $6x^2$ . Increase this by 5 and you get $6x^2+5$ .

If this has to equal 4, you have $6x^2+5=4$

4 0

2 years ago

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A a) Is (x + 4) a factor of (x^ 2 +9x+20)? In other words , does x + 4 divide evenly into x ^ 2 + 9x + 20 ?

liubo4ka [24]

Answer:

Yes

Step-by-step explanation:

the factors of (x^ 2 +9x+20) are (x+4)(x+5)

3 0

2 years ago

Which is an equation of a direct proportion? a.y=1/6x+6 b.y=6/x c.y=6x-6 d.y=6x

Amanda [17]

Answer:

Option D. y=6x

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form $y/x=k$ or $y=kx$

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

Verify each case

case a) y=(1/6)x+6

Is a linear equation, but is not a direct variation. The line not passes through the origin

case b) y=6/x

The equation represent an inverse variation

case c) y=6x-6

Is a linear equation, but is not a direct variation. The line not passes through the origin

case d) y=6x

The equation represent a direct variation

6 0

2 years ago

The recursive rule for a sequence is shown.an=an−1+9a1=21 what is the explicit rule for this sequence?

bixtya [17]

Answer:

Meaning of Explicit rule , is the general rule for a sequence.

The given sequence is defined as,

$a_{n}=a_{n-1}+9a_{1}-21$ ----(1)

Common Difference(d) of an airthmetic Sequence= N th term - (N-1) th term

$=a_{n}-a_{n-1}\\\\=a_{n-1}-a_{n-2}$

Equation 1 can be written as,

$a_{n}-a_{n-1}=9 a_{1}-21\\\\ d =9a_{1}-21$

General rule or explicit rule for this sequence is given as:

$a_{n}=a_{1} +(n-1)d\\\\a_{n}=a_{1}+(n-1)(9a_{1}-21)\\\\a_{n}=a_{1}+9na_{1}-21 n-9a_{1}+21\\\\a_{n}=-8a_{1}+21+n(9a_{1}-21)$

6 0

2 years ago