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3 years ago

How do I find the vertex and the standard form? Plz explain

Mathematics

1 answer:

xenn [34]3 years ago

7 0

Answer:

Vertex form

y = -4(x + 3)^2 + 10

Standard form;

y = -4x^2-24x - 26

Step-by-step explanation:

Mathematically, we have the vertex form as

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

(h,k) represents the vertex

We have h as -3 and k as 10

y = a(x+3)^2 + 10

To get a, we substitute any of the points

Let us use (-1,-6)

-6 = a(-1+3)^2 + 10

-6-10 = 4a

4a = -16

a = -16/4

a = -4

So we have the equation as;

y = -4(x+3)^2 + 10

For the standard form;

We expand the vertex form;

y = -4(x + 3)(x + 3) + 10

y = -4(x^2 + 6x + 9) + 10

y = -4x^2 - 24x -36 + 10

y = -4x^2 -24x -26

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A cable car starts off with n riders. The times between successive stops of the car are independent exponential random variables

nikitadnepr [17]

Answer:

The distribution is $\frac{\lambda^{n}e^{- \lambda t}t^{n - 1}}{(n - 1)!}$

Solution:

As per the question:

Total no. of riders = n

Now, suppose the $T_{i}$ is the time between the departure of the rider i - 1 and i from the cable car.

where

$T_{i}$ = independent exponential random variable whose rate is $\lambda$

The general form is given by:

$T_{i} = \lambda e^{- lambda}$

(a) Now, the time distribution of the last rider is given as the sum total of the time of each rider:

$S_{n} = T_{1} + T_{2} + ........ + T_{n}$

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Now, the sum of the exponential random variable with $\lambda$ with rate $\lambda$ is given by:

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5 0

3 years ago

Beyonce went to the mall and saw a

svetoff [14.1K]

The answer is $9,100

6,500 x .08 = 520
520 x 5 = 2,600
2,600 + 6,500 = 9,100

Hope this helps!

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3 years ago

C equals 2 pi r; Cequals62.8 (Circumference of a circle)

tatuchka [14]

Answer:

about 10

Step-by-step explanation:

62.8 = 2 pi r/2

62.8/2 = pi r

31.4/pi = pi r/pi

about 10 = r

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3 years ago

A cylindrical specimen of cold-worked copper has a ductility (%el) of 25%. if its cold-worked radius is 10 mm, what was its radi

loris [4]

The radius of the cylinder before deformation is 7.5mm

<h3>Deformation of an object</h3>

From the given question, we are given that;

cold work radius of the cylinder is 10mm

Ductility = 25%

Determine the radius before deformation

Radius before deformation = (1- 0.5) + 10

Radius before deformation = 0.75 * 10

Radius before deformation = 7.5mm

Hence the radius of the cylinder before deformation is 7.5mm

Learn more on deformation here: brainly.com/question/6417346

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2 years ago

The vertices of a triangle are A(0,0),B(3,8) and C(9,0). What is the area of this triangle?

Svetradugi [14.3K]

Answer:

Step-by-step explanation:

To find the area of a triangle where you know the x and y coordinates of the three vertices, you'll need to use the coordinate geometry formula: area = the absolute value of Ax(By - Cy) + Bx(Cy - Ay) + Cx(Ay - By) divided by 2. Ax and Ay are the x and y coordinates for the vertex of A. The same applies for the x and y notations of the B and C vertices.

Fill in the numbers for each corresponding letter combination within the formula.

Fill in your formula like this: 0(8-10) + 3(0-0) + 9(0-8).

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0 from 8 = 8, 0 from 0 = 0 and 8 from 10 = 2.

Multiply that result by the number to the left of the parentheses.

0 by 8 = 0, 3 by 0 = 0 and 9 by 2 = 18.

Add the three products together.

0 + 0 + 18 = 18

Divide the sum of the three products by 2.

18 ÷ 2 = 9

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2 years ago