2

Mathematics

1 answer:

Daniel [21]2 years ago

4 0

Answer:

Step-by-step explanation:

P = (-4, 3)

Reflecting across the y axis negates the x value

P₁ = (4, 3)

Reflecting across the x axis negates the y value

P' = (4, -3)

option D

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Jimmy Neutron is building a skateboarding ramp that is 16 inches high. The angle formed by the ramp and the ground is 21 degrees

adell [148]

Answer:

44.65 inches

Step-by-step explanation:

Height of ramp = 16 inches

Length of ramp, l

Angle formed by ramp and ground = 21°

Using Pythagoras :

Sinθ = opposite / hypotenus

Sin21° = 16 / l

0.3583679 = 16 / l

0.3583679 * l = 16

l = 16 / 0.3583679

l = 44.646855 inches

Hence, length of ramp is 44.65 inches

5 0

2 years ago

The vertex of this parabola is at (2,-1) when the y value is 0 and then x value is 5 what is the coefficient of the squared term

Darina [25.2K]

$\bf ~~~~~~\textit{parabola vertex form} \\\\ \begin{array}{llll} \stackrel{\textit{we'll use this one}}{y=a(x- h)^2+ k}\\\\ x=a(y- k)^2+ h \end{array} \qquad\qquad vertex~~(\stackrel{2}{ h},\stackrel{-1}{ k}) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{cases} h=2\\ k=-1 \end{cases}\implies y=a(x-2)^2-1 \\\\\\ \textit{we also know that } \begin{cases} y=0\\ x=5 \end{cases}\implies 0=a(5-2)^2-1\implies 1=9a \\\\\\ \cfrac{1}{9}=a\qquad therefore\qquad \boxed{y=\cfrac{1}{9}(x-2)^2-1}$

now, let's expand the squared term to get the standard form of the quadratic.

$\bf y=\cfrac{1}{9}(x-2)^2-1\implies y=\cfrac{1}{9}(x^2-4x+4)-1 \\\\\\ y=\cfrac{1}{9}x^2-\cfrac{4}{9}x+\cfrac{4}{9}-1\implies \stackrel{its~coefficient}{y=\stackrel{\downarrow }{\cfrac{1}{9}}x^2-\cfrac{4}{9}x-\cfrac{5}{9}}$