Find the sum or difference of this polynomial. (3x^3+10x+5)-(x^3-4x+6)

Mathematics

1 answer:

ehidna [41]3 years ago

4 0

Answer:

2x³ + 14x - 1

Step-by-step explanation:

3x³ + 10x + 5 - x³ + 4x - 6

= 2x³ + 14x - 1

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Find the vertex, focus, directrix, and focal width of the parabola. (5 points)

Anarel [89]

$\bf \textit{vertical parabola vertex form with focus point distance} \\\\ 4p(y- k)=(x- h)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h,k+p)}\qquad \stackrel{directrix}{y=k-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{"p"~is~negative}{op ens~\cap}\qquad \stackrel{"p"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}$

$\bf -\cfrac{1}{20}x^2=y\implies \cfrac{x^2}{-20}=y\implies x^2=-20y\implies (x-0)^2=-20(y-0) \\\\\\ (x-\stackrel{h}{0})^2=4(\stackrel{p}{-5})(y-\stackrel{k}{0})$

something noteworthy is that the squared variable is the "x", thus the parabola is a vertical one, the "p" value is negative, so is opening downwards, and the h,k is pretty much the origin,

vertex is at (0,0)

the focus point is "p" or 5 units down from there, namely at (0, -5)

the directrix is "p" units on the opposite direction, up, namely at y = 5

the focal width, well, |4p| is pretty much the focal width, in this case, is simply yeap, you guessed it, 20.

8 0

3 years ago

Lisa sold $75 worth of play tickets.Adult tickets cost $4 each and children’s ticket cost $4 each.How many children’s tickets co

Helga [31]

Yes, there are many possible answers. An equation that can model your situation is:
4a+4b=75, with a being the amount of adult tickets sold, and b being the amount of children’s tickets sold.
Because both tickets cost 4 dollars, you would multiply the amount of tickets sold, by the price (in dollars) of the ticket.
So, you can find possible answers by substituting the amount of adult tickets sold. Say, 4 adults bought tickets. You could then substitute a for 4. So the equation would look like this.
4(4)+4b=75
16 + 4b = 75
4b = 75 - 16
4b = 59
Divide each side by four
B = 14.75

The reason you got a decimal number is because 75 cannot be divided by 4 evenly. So, in this context, you could say that 15 children bought tickets. One child had an issue, and Lisa gave them a 25% discount. This would explain why there are only 75 dollars worth in tickets. I hope I helped, this is my first question I have ever answered so I’m not entirely sure if this was helpful or not. Hope you figure this out!

3 0

3 years ago

In a Parallelogram CARS , <C = 5x-20 and <A = 3x+20. Find the value of x ?

coldgirl [10]

Given that

In a Parallelogram CARS ,∠C = (5x-20)°

∠A = (3x+20)°

angle C and angle A are adjacent angles

We know that

In a Parallelogram the adjacent angles are supplementary.

⇛∠C + ∠A = 180°

⇛ (5x-20)°+(3x+20)° = 180°