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3 years ago

Raymoon sold an article at a loss of 5%. If he had sold it for 270 more, he would have gained 7% find the cost prize of article

Mathematics

1 answer:

mote1985 [20]3 years ago

7 0

IᑎᔕEᑕTIOᑎ ᑭEᒍᗩY✓ hahahaha

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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

Whats the slope on the graph?

oee [108]

Answer:

-9/5 is the slope

Step-by-step explanation:

Please give brainliest :)

6 0

2 years ago

a 9 pound bag of sugar is being split into containers that hold 2/3 of a pound. how many containers of sugar will the 9 pound ba

LUCKY_DIMON [66]

Namely, how many times does 2/3 go into 9?

well

$\bf 9 \div \frac{2}{3}\implies \cfrac{9}{\frac{2}{3}}\implies \cfrac{\quad \frac{9}{1}\quad }{\frac{2}{3}}\implies \cfrac{9}{1}\cdot \cfrac{3}{2}\implies \cfrac{27}{2}
\\\\\\
\textit{2 goes \underline{13 times} into 27, with a \underline{remainder of 1}}\implies 13\frac{1}{2}$

3 0

3 years ago

Use any method to add or subtract (1 point) <br> 5/7 - (3/14 + 3/14)

Ray Of Light [21]

Answer: