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Aneli [31]
2 years ago
10

Write the equation of the parabola that has the vertex at point (2,-11) and passes through the point (0,5).

Mathematics
1 answer:
aleksandr82 [10.1K]2 years ago
7 0

~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}

\stackrel{vertex}{(\stackrel{h}{2}~~,~~\stackrel{k}{-11})}\qquad y=a(x-2)^2-11\qquad \qquad \textit{we also know that} \begin{cases} x=0\\ y=5 \end{cases} \\\\\\ 5=a(0-2)^2-11\implies 16=4a\implies \cfrac{16}{4}=a\implies 4=a \\\\[-0.35em] ~\dotfill\\\\ ~\hfill y=4(x-2)^2-11~\hfill

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BC = 36; D = 15. What is the value of BD - AC.<br> B<br> A<br> BD - AC =
Snezhnost [94]

Answer:

BD - AC = 0

Step-by-step explanation:

Given that:

BC = 36 , CD = 15 and BD = x

As these are forming right angled triangle,

Using Pythagorean theorem,

(BD)^2+(CD)^2=x^2\\(36)^2+(15)^2 = x^2\\1296 + 225 = x^2\\1521 = x^2\\

Taking square root on both sides

\sqrt{x^2}=\sqrt{1521}\\x=39

As the given shape is rectangular, the sides parallel to each other will have same values.

AB = 15 , AD = 36 and AC = x

(15)^2+(36)^2 = x^2 \\225 + 1296 = x^2 \\1521 = x^2 \\x = 39

Now,

BD - AC = 39 - 39 = 0

Hence,

BD - AC = 0

5 0
3 years ago
donna is a software saleswoman. her monthly salary is $1500 plus an additional $120 for every copy of English is fun she sells.
SSSSS [86.1K]

Answer:

S=1500+120N

Step-by-step explanation:

3 0
2 years ago
What is y=x+10 in Standard Form?<br><br> ASAP please, thanks!
Allushta [10]
The standard form is Ax + By = C

Given the linear equation, y = x + 10, we must transpose x to the left-hand side of the equation:

- x + y = x — x + 10

- x + y = 10

Next, we must multiply both sides by (-1) because A must be positive:

(-1) (- x + y) = 10 (-1)

This leads to:

x — y = -10 in standard form, Ax + By = C


4 0
2 years ago
How do you write 4 13/20 as a decimal
yaroslaw [1]
4.65

I hope I helped you 
5 0
3 years ago
Read 2 more answers
Find the sum and express it in the simplest form.(2y^2+9y+4)+(-3y^2-3y-9)
vampirchik [111]
Since the operation between the two sets of parentheses is addition, we don't have to do anything with it, and can remove the parentheses.
Our new expression is: 2y^2+9y+4-3y^2-3y-9

Now, we just add like terms together to solve for the simplest form of the expression.
2y^2+9y+4-3y^2-3y-9
(2-3)y^2+(9-3)y+(4-9)
-y^2+6y-5

Our final answer is -y^2+6y-5.
8 0
3 years ago
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