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3 years ago

Convert this quadratic function to vertex form.

1 answer:

3 0

Y=x² +14x +48
y-48 = x² +14x
y-48+7² = x² +2*7*x +7²
y-48+49 = (x+7)²
y+1= (x+7)²
y=(x+7)² - 1

Vertex of the function is (-7,-1). Minimum value of this function is a vertex value , because parabola directed up.

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$290, 12.5%, 6 months

Veronika [31]

The information shown here only shows a principal sum, a rate of interest and a period or time. There is no question as to what is needed. But suppose the need is for simple interest, then we calculate using the given information and the formula: I = PRT where I is simple interest, P is the principal, R is the rate per year, and T is time P = 290, T is 6 months which is 0.5 years, R = 12.5 % which is written as 0.125 in decimal fraction. I = 290 × 0.125 x 0.5 → I = 18.125 Therefore after 6 months , the interest earned will be 18. 125 dollars

3 0

3 years ago

(show your work please) There are 3 green balls, 5 red balls, and 2 blue balls in a box. One ball is randomly drawn, replaced an

JulsSmile [24]

B is the answer, because the half of the balls added

7 0

3 years ago

Read 2 more answers

Which is the axis of symmetry of a parabola with y^2=-8x^2

yawa3891 [41]

It would be y^8 = 12^5

5 0

3 years ago

A block of ice has a square top and bottom and rectangular sides. At a certain point in

Lilit [14]

Answer:

$\frac{dV}{dt} = 360 \ cm^3/h$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Geometry

Volume of a Rectangular Prism: V = lwh

Calculus

Derivatives

Derivative Notation

Differentiating with respect to time

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Step-by-step explanation:

Step 1: Define

$l = 30 \ cm\\w = l\\\frac{dl}{dt} = 2 \ cm/h\\h = 20 \ cm\\\frac{dh}{dt} = 3 \ cm/h$

Step 2: Differentiate

Rewrite [VRP]: $V = l^2h$
Differentiate [Basic Power Rule]: $\frac{dV}{dt} = 2l\frac{dl}{dt} \frac{dh}{dt}$

Step 3: Solve for Rate

Substitute: $\frac{dV}{dt} = 2(30 \ cm)(2 \ cm/h)(3 \ cm/h)$
Multiply: $\frac{dV}{dt} = 360 \ cm^3/h$

Here this tells us that our volume is decreasing (ice melting) at a rate of 360 cm³ per hour.

3 0

3 years ago

A rectangular box which is open at the top can be made from an12-by-18-inch piece of metal by cutting a square from each corner

algol [13]

Answer:

h=2.35in, l=13.3in and w=7.3in

Step-by-step explanation:

In order to solve this problem, we must start by drawing a diagram that will represent the prolem. (Look at attached picture)

From the diagram we can see that the length ad the width of the box are found by using the following expressions:

L=18-2x

W= 12-2x

H=x

next, we can make use of the volume formula of a rectangular prism, which is the following:

V=WLH

so we can substitute the expressions we got before on the formula:

V=x(12-2x)(18-2x)

and for ease of calculation, we can multiply the terms, so we get:

$V=x(216-24x-36x+4x^{2})$

$V=x(4x^{2}-60x+216)$

$V=4x^{3}-60x^{2}+216x$

So now we can find the derivative of the volume:

$V'=12x^{2}-120x+216$

and set it equal to zero, so we get:

$12x^{2}-120x+216=0$

and now we can solve. We can start by factoring the left side of the equation, so we get:

$12(x^{2}-10x+18)=0$

which yields:

x^{2}-10x+18=0

This one can only be solved by using the quadratic formula:

$x=\frac{-b\pm \sqrt{-b^{2}-4ac}}{2a}$

so we substitute the corresponding values:

$x=\frac{-(-10)\pm \sqrt{-(-10)^{2}-4(1)(18)}}{2(1)}$

which yields:

x=7.65in or x=2.35in

we keep the 2.35in only, because the 7.65in returns an impossible box, since that would make the width a negative width.

So the 2.35in height would give us the greatest box. Now we can use it to find the height, the width and the length of the box.

Height=x=2.35

W=12-2x=12-2*2.35=7.3in

L=18-2x=18-2(2.35)=13.3in

5 0

3 years ago