The difference of 9 and the quotient of a number t and 6 is 5

1 answer:

3 0

Assuming you are supposed to solve for the variable "t",

9 - (t ÷ 6) = 5

Subtract 9 from both sides.

9 - 9 - (t ÷ 6) = 5 - 9

Simplify.

- (t ÷ 6) = -4

Distribute -1 throughout the parenthesis.

-t ÷ -6 = -4

Multiply both sides by -6.

-t ÷ -6 × -6 = -4 × -6

Simplify.

-t = 24

Divide both sides by -1.

-t ÷ -1 = 24 ÷ -1

Simplify.

t = -24

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If g(x)=4x^2-16 we’re shifted 9 united to the right and 1 down, what would the new equation be?

Inessa05 [86]

Shown in the graph

<h2>Explanation:</h2>

Using graph tools we can graph the function:

$g(x)=4x^2-16$

which is the red graph shown below. As you can see, this is a parabola. The rule for vertical and horizontal shifts is as follows:

$Let \ c \ be \ a \ positive \ real \ number. \ \mathbf{Vertical \ and \ horizontal \ shifts} \\ in \ the \ graph \ of \ y=f(x) \ are \ represented \ as \ follows:$

$\bullet \ Vertical \ shift \ c \ units \ \mathbf{upward}: \\ h(x)=f(x)+c \\ \\ \bullet \ Vertical \ shift \ c \ units \ \mathbf{downward}: \\ h(x)=f(x)-c \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ right \ \mathbf{right}: \\ h(x)=f(x-c) \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ left \ \mathbf{left}: \\ h(x)=f(x+c)$