3 years ago

Please help What is the value of x show work

Mathematics

1 answer:

kondor19780726 [428]3 years ago

4 0

Answer:

$\boxed{x = 7}$

Step-by-step explanation:

ΔJKL ~ ΔMNP

So, the sides of both of the triangles are proportional.

Taking proportionality of their sides.

$\frac{JL}{JK} = \frac{MP}{MN}$

=> $\frac{20}{25} = \frac{4x-4}{30}$

Cross Multiplying

20 * 30 = 25(4x-4)

600 = 100x - 100

Adding 100 to both sides

600+100 = 120x

700 = 100x

Dividing both sides by 100

700/100 = x

x = 7

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What’s the equation in vertex form?

pshichka [43]

Answer:

$\large\boxed{y=(x+5)^2-64}$

Step-by-step explanation:

$\text{The vertex form of equation}\ y=ax^2+bx+c:\\\\y=a(x-h)^2+k\\\\h=\dfrac{-b}{2a},\ k=f(h)\\\\\text{We have the equation:}\ y=x^2+10x-39\to x=1,\ b=10,\ c=-39.\\\\\text{Substitute:}\\\\h=\dfrac{-10}{2(1)}=\dfrac{-10}{2}=-5\\\\k=f(-5)=(-5)^2+10(-5)-39=25-50-39=-64\\\\\text{Finally:}\\\\y=1(x-(-5))^2-64=(x+5)^2-64$