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2 years ago

Help me out please I don’t understand

Mathematics

1 answer:

yulyashka [42]2 years ago

8 0

$\\ \sf\Rrightarrow y=-4(x+2)^2-1$

Compare to the vertex form of parabola

y=a(x-h)^2+k

h=-2
k=-1

So vertex should be at (h,k)=(-2,-1)

Graph attached

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Find the equilibrium quantity and equilibrium price for the commodity whose supply and demand functions are given.

expeople1 [14]

Rewriting the two equations:

[Supply] $p = q^2+20$
[Demand] $p=-4q^2+10q+18600$

Equilibrium price is when
Supply = Demand
$q^2+20 = -4q^2+10q+18600$
$q^2+4q^2+20-10q-18600 = 0$
$5q^2-10q-18580=0$ ⇒ Simplifying the equation by dividing each term by 5

$q^2-2q-3716=0$

The simplified equation is in quadratic form.
There are three main methods for solving a quadratic equation: factorizing, completing the square, or quadratic formula.

Using the formula, we need the value of a, b, and c which is the constant of the quadratic equation.
$q_1= \frac{-b+ \sqrt{(b)^2-4ac)} }{2a}$ , and $q_2= \frac{-b- \sqrt{(b)^2-4ac)} }{2a}$

We have a = 1, b = -2, and c = -3716
Substituting these values into the formula we have
$q_1= \frac{-(-2)+ \sqrt{(-2)^2-4(1*-3716)} }{2} =61.97$
$q_2= \frac{-(-2)- \sqrt{(-2)^2-4(1*-3716)} }{2} =-59.97$

Since 'q' represents a quantity, we can't have negative values, so we choose the value of 'q' to be 61.97 ≈ 62 (rounded to the nearest whole number)

Answer: Equilibrium quantity = 62

4 0

3 years ago

Pls help !!! I've already failed it twice this is my last try please help there's other questions on my account.

Gala2k [10]

It’s the third one

7 0

3 years ago

Read 2 more answers

Mallory and five of her friends bought a box of 36 cookies. together they ate 2/3 of the cookies

Rzqust [24]

Answer:

<em>24 cookies got eaten</em> <em>12 weren't eaten</em>

Step-by-step explanation:

36 divided by 3 = 12

12 x 2 = 24 ( since they ate 2/3)

36-24=12 (12 weren't eaten)

5 0

3 years ago

A rectangular cake has a length of 22 1/2 inches and a width of 10 inches. How many whole, square pieces of cake with side lengt

faltersainse [42]

Well, we need to find the area of the cake. 22.5 times 10 is 225. That is the area then we need to find the area of each piece of cake. 2.5 times 2.5 is 6.26.
so divide the area of the cake by the area of each piece to find how many pieces can be cut.
225/6.25=36 36 pieces of cake can be cut from the cake

5 0

4 years ago

I need a, b, and c. I don’t quite understand this.

Stels [109]

9514 1404 393

Answer:

a) y = (x -4)² -4

b) (4, -4)

c) translated 4 right, 4 down

Step-by-step explanation:

a) Apparently "graphing form" is a reference to "vertex form." That form is ...

y = a(x -h)² +k . . . . . . parabola with vertex (h, k) and vertical scale factor 'a'

The coefficient of x² in your given equation is 1, so a=1. The values of h and k can be found as follows.

'h' is the opposite of half the x-coefficient in your equation, so is h = -(-8/2) = 4. The value of k is the square of h, subtracted from the constant in your equation: k = 12 -h² = 12 -16 = -4. (This applies when a=1, as here.) These calculations are the "cut to the chase" version of "completing the square."

The method of "completing the square" has you consider the x-terms separately from the constant term:

y = (x² -8x) +12

To "complete the square", you want to make the terms in parentheses be a perfect square trinomial. You do that by adding the square of half the x-coefficient. In order to keep the same equation, you need to subtract an equivalent amount outside parentheses:

y = (x² -8x +(-8/2)²) +12 -(-8/2)² . . . . . add and subtract (-8/2)²

y = (x -4)² +(12 -16)

Then the vertex form is ...

y = (x -4)² -4 . . . . and the vertex is (h, k) = (4, -4).

The graphing calculator plot attached confirms this vertex value.

The problem statement tells you that you can also find this form by averaging the x-intercepts. If you factor your equation, you get ...

y = (x -6)(x -2)

The x-values that make these factors zero {6, 2} are the x-intercepts. Their average (6+2)/2 = 4 is the x-coordinate of the vertex (h). You can find the y-coordinate of the vertex by evaluating y when x=4: y = 4² -8·4 +12 = -4. So, the vertex by this method is (h, k) = (4, -4), and the equation in graphing form is ...

y = (x -4)² -4 . . . . as above.

b) As we saw above, the vertex coordinates are (h, k) = (4, -4).

c) The vertical scale factor 'a' is 1, so the only transformation done on the graph is to move the parent vertex (0, 0) to the location (4, -4). That is, the graph has been translated 4 units right and 4 units down. (In the attached, the parent function is shown with a dashed line.)

8 0

3 years ago