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pychu [463]
2 years ago
7

Determine the domain and range of F(x)=2(x+1)^2-3

Mathematics
2 answers:
alexdok [17]2 years ago
6 0
Domain is 0
range is -1
ollegr [7]2 years ago
3 0

Answer:  domain: all real numbers.  range: [-3, infinity)

Step-by-step explanation:

We've got f(x) = 2(x+1)^2 - 3.

You can plug in any number for x without a problem, so the domain is all real numbers, written \mathbb R.

If you graph the function, you can see it touches -3 but cannot go lower; however, it can reach anything higher than -3. Therefore the range is [-3, \infty).

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Janice's insurance costs $1,245 a year. How much should she budget for insurance each month? *
Phoenix [80]

Answer:

$103.75

Step-by-step explanation:

$1,245 devide by 12

5 0
2 years ago
78 correct answers out of 100 test questions and 39 correct answers out of 50 question are these equivalent
storchak [24]
78/100
= 39/50

39/50
= 39/50

yes these is equivalent
3 0
2 years ago
Read 2 more answers
If y= -7 when x= -28, find y when x=20​
weqwewe [10]
This question is imposible in the field of math because, you need two points in order to determine slope and you only have one which is (-28, -7) which isn’t enough
5 0
3 years ago
A rectangular piece of cardboard measuring
MariettaO [177]

Answer:

(a) x<8

(b) \displaystyle v=384x-80x^2+4x^3

(c) \displaystyle x=3.13

(d) \displaystyle 0.917

Step-by-step explanation:

<u>Optimization </u>

It is the procedure to find the set of values for the variables of a function such that it reaches a maximum or a minimum value. If equalities are given as relationships between the variables, then the derivative is a suitable method to find the critical points or candidates for extrema values.

The problem at hand is about a geometric maximization, given some dimensional conditions. First, we have a rectangular piece of cardboard measuring 24 x 16 inches. A box is to be made out of that cardboard by cutting equal size squares from each corner and folding up the sides of length x.  

(a)

\displaystyle w=24\ in

\displaystyle L=16\ in

When we do so, the base of the box will have dimensions

\displaystyle W'=24-2x

\displaystyle L'=16-2x

Since the new width of the base must be positive, then

\displaystyle 24-2x>0

which poses the restriction

\displaystyle x

The same situation happens with the length

\displaystyle 16-2x>0

x<8

Since this last condition is more restrictive than the first, we state that x must be less than 8

(b) The volume of the box is the product of the area of the base by the height x

\displaystyle v=L'.W'.x

\displaystyle v=(16-2x)(24-2x)\ x

Operating

\displaystyle v=(384-80x+4x^2)x

\displaystyle v=384x-80x^2+4x^3

(c)

To find the maximum volume, we take the first derivative of V:

\displaystyle v'=384-160x+12x^2

Equating to zero to find the critical points

\displaystyle v'=0

\displaystyle 12x^2-160x+384=0

Dividing by 4:

\displaystyle 3x^2-40x+96=0

The roots of the equation are:

\displaystyle x=10.19,x=3.13

Since x=10.19 is out of the restrictions found in part a, the only valid solution is

\displaystyle x=3.13

We must test if the critical point is a maximum or a minimum, by computing the second derivative

\displaystyle v''(x)=-160+24x

\displaystyle v''(3.13)

Since the second derivative is negative, the value is a maximum

(d) We must find all the values of x such as v>288:

\displaystyle 384x-80x^2+4x^3>288

Rearranging

\displaystyle 4x^3-80x^2+384x-288>0

Simplifying by 4

\displaystyle x^3-20x^2+96x-72>0

Factoring

\displaystyle (x-6)(x^2-14x+12)>0

\displaystyle (x-6)(x-13.083)(x-0.917)>0

We found three real and positive roots for the third-degree polynomial

x=6,\ x=0.917,\ x=13.083

The function is positive when

\displaystyle 0.917

or

\displaystyle x>13.083

The only interval lying into the valid values of x is

\displaystyle 0.917

5 0
3 years ago
UVWX is a parallelogram.<br> Given WV=x+8 and XU=2x+3, find the value of x.
Rudik [331]

Answer:

x = 5

Step-by-step explanation:

If you draw out the parallelogram UVWX, WV is across from XU, meaning they're congruent because opposite sides of a parallelogram are congruent.

So:

x + 8 = 2x + 3

8 = x + 3

5 = x

x = 5

3 0
3 years ago
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