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Mathematics

1 answer:

Greeley [361]3 years ago

5 0

Answer:

Step-by-step explanation:

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To solve this system of equations by elimination, what operation could be used to eliminate the x-variable and find the value of

babymother [125]

Answer:

The value of y is $y=\frac{42}{17}$

Step-by-step explanation:

we have

$4x+3y=6$ -----> equation A

$18x+5y=6$ -----> equation B

To eliminate the x-variable and find the value of y Multiply the equation A by -18/4 both sides or multiply the equation B by -4/18 both sides

I choice

Multiply the equation A by -18/4 both sides

$(-18/4)[4x+3y]=6*(-18/4)$

$-18x-13.5y=-27$ ------> equation C

Adds equation B and equation C

$18x+5y=6\\-18x-13.5y=-27\\-------\\5y-13.5y=6-27\\-8.5y=-21\\\\ y=\frac{42}{17}$

7 0

3 years ago

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: