Simplify the following inequality 3x + 12 ≥2(4x + 3) −21 Help I need the answer ASAP

Explain the steps to finding the vertex of g(x) = 3x2 + 12x + 15

RUDIKE [14]

Answer:

The vertex of this parabola, $(-2, 3)$ , can be found by completing the square.

Step-by-step explanation:

The goal is to express this parabola in its vertex form:

$g(x) = a\, (x - h)^2 + k$ ,

where $a$ , $h$ , and $k$ are constants. Once these three constants were found, it can be concluded that the vertex of this parabola is at $(h,\, k)$ .

The vertex form can be expanded to obtain:

$\begin{aligned}g(x)&= a\, (x - h)^2 + k \\ &= a\, \left(x^2 - 2\, x\, h + h^2\right) + k = a\, x^2 - 2\, a\, h\, x + \left(a\,h^2 + k\right)\end{aligned}$ .

Compare that expression with the given equation of this parabola. The constant term, the coefficient for $x$ , and the coefficient for $x^2$ should all match accordingly. That is:

$\left\lbrace\begin{aligned}& a = 3 \\ & -2\,a\, h = 12 \\& a\, h^2 + k = 15\end{aligned}\right.$ .

The first equation implies that $a$ is equal to $3$ . Hence, replace the " $a\!$ " in the second equation with $3\!$ to eliminate $\! a$ :

$(-2\times 3)\, h = 12$ .

$h = -2$ .

Similarly, replace the " $a$ " and the " $h$ " in the third equation with $3$ and $(-2)$ , respectively:

$3 \times (-2)^2 + k = 15$ .

$k = 3$ .

Therefore, $g(x) = 3\, x^2 + 12\, x + 15$ would be equivalent to $g(x) = 3\, (x - (-2))^2 + 3$ . The vertex of this parabola would thus be:

$\begin{aligned}&(-2, \, 3)\\ &\phantom{(}\uparrow \phantom{,\,} \uparrow \phantom{)} \\ &\phantom{(}\; h \phantom{,\,} \;\;k\end{aligned}$ .

8 0

3 years ago

The simplest form of StartRoot 80 EndRoot can be written as a StartRoot b EndRoot, where a = and b =

Elden [556K]

Answer:

4√5

Step-by-step explanation:

√80 = √16 times √5

√16 = 4

4 times √5

4√5

6 0

3 years ago

Read 2 more answers

How do you work this problem

ankoles [38]

An easy way is to do it, if you get confused by multiplying fractions, is by turning the fractions into decimals. Since you are trying to find N you want to multiply the 1/5 by the 1/3.

1/5 = 0.2

1/3 = 0.33333333333333333333333333333333

if you multiply those you get 0.06666666666666666666666666666667 which when put into a fraction it equals 1/15

but if you don't want to do that just try to remember that you want to get by itself. and when multiplying fractions in this situation the bottom numbers only matter.. so 5 x 3 = 15 1/15

would you like me to put it in a document to show you?

7 0

3 years ago

Find the sine of ∠U. A)48/55 B)48/73 C)55/48 D)55/73

charle [14.2K]

Answer:

D) 55/73

Step-by-step explanation:

The question is on trigonometry. Sine of an angle is obtained using the SOH of SOHCAHTOA formula of trigonometry. SOH is an acronym for sine, opposite and hypotenuse. Sine of an angle is obtained from the ratio of opposite and hypotenuse of a given triangle. Thus, SOH

is denoted as stated below.

$sine \: \beta = \frac{opposite}{hypotenuse}$