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3 years ago

What is the vertex of the quadratic function: y=-3(x+5)^2-4

1 answer:

6 0

V=(-5,-4)
to find the vertex you use V=-b/2a
y=-3(x+5)^2-4
which then turns to
y=-3x^2-30x-79
a=-3
b=-30 x=30/2(-3)
x=30/-6
x=-5
plug x into the equation and solve for y =-3(-5)^2-30(-5)-79
y=-4
x=-5 y=-4 Vertex=(-5,-4)

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In what form is the following linear equation written?

krok68 [10]

Answer:

<h2>B. Standard</h2>

Step-by-step explanation:

The point-slope form of an equation of a line:

$y-y_1=m(x-x_1)$

m - slope

(x₁, y₁) - point

The slope-intercept form of an equation of a line:

$y=mx+b$

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$Ax+By=C$

The general fom of an equation of a line:

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We have the equation 3x - 2y = 4 in standard form.

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3 years ago

How do i solve this quadratic equation x²+6x+c

Anuta_ua [19.1K]

recall in a perfect square trinomial, the middle term is the tale-tell guy, we know the middle term is the product of 2 and the two other guys without the exponent, so in this case 6x = 2*√x² * √c.

$\bf 6x=2\cdot \sqrt{x^2}\cdot \sqrt{c}\implies 6x=2\sqrt{x^2c}\implies 6x=2x\sqrt{c}\\\\\\\cfrac{6x}{2x}=\sqrt{c}\implies 3=\sqrt{c}\implies 3^2=c\implies 9=c$

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3 years ago

What is the solution to the following system?<br> -4y=8 <br> x+3y-3z=-26<br> 2x-5y+z=19

Viktor [21]

⓵
-4ỿ = 8

Simplify the left side in order to isolate the ỿ!

-4ỿ = 8
+4 +4

Ỿ = 12

⓶
× + 3y - 3z = -26

Simplify the left side in order to isolate the ×, ỿ and z!

× + 3y - 3z = -26
÷3 ÷3

× + ỿ - 3z = -8,66 periodic
÷-3 ÷-3

× + ỿ + z = 2,88 periodic

⓷
2× - 5ỿ + z = 19

Simplify the left side in order to isolate the ×, ỿ and z!

2× - 5ỿ + z = 19
÷2 ÷2

× - 5ỿ + z = 9,5
÷-5 ÷-5

× + ỿ + z = -1,9

3 0

3 years ago

Read 2 more answers

HELP ME OUT PLS!!!!!

pantera1 [17]

The Answer Is C. 64, hope I helped

4 0

2 years ago

Read 2 more answers

A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. An industrial tank of this shape must h

mestny [16]

Answer:

Radius =6.518 feet

Height = 26.074 feet

Step-by-step explanation:

The Volume of the Solid formed = Volume of the two Hemisphere + Volume of the Cylinder

Volume of a Hemisphere $=\frac{2}{3}\pi r^3$

Volume of a Cylinder $=\pi r^2 h$

Therefore:

The Volume of the Solid formed

$=2(\frac{2}{3}\pi r^3)+\pi r^2 h\\\frac{4}{3}\pi r^3+\pi r^2 h=4640\\\pi r^2(\frac{4r}{3}+ h)=4640\\\frac{4r}{3}+ h =\frac{4640}{\pi r^2} \\h=\frac{4640}{\pi r^2}-\frac{4r}{3}$

Area of the Hemisphere = $2\pi r^2$

Curved Surface Area of the Cylinder = $2\pi rh$

Total Surface Area=

$2\pi r^2+2\pi r^2+2\pi rh\\=4\pi r^2+2\pi rh$

Cost of the Hemispherical Ends = 2 X Cost of the surface area of the sides.

Therefore total Cost, C

$=2(4\pi r^2)+2\pi rh\\C=8\pi r^2+2\pi rh$

Recall: $h=\frac{4640}{\pi r^2}-\frac{4r}{3}$

Therefore:

$C=8\pi r^2+2\pi r(\frac{4640}{\pi r^2}-\frac{4r}{3})\\C=8\pi r^2+\frac{9280}{r}-\frac{8\pi r^2}{3}\\C=\frac{9280}{r}+\frac{24\pi r^2-8\pi r^2}{3}\\C=\frac{9280}{r}+\frac{16\pi r^2}{3}\\C=\frac{27840+16\pi r^3}{3r}$