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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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Through how many radians do the minute hand and the hour hand move between 1:00 p.m. and 1:45 p.m. (on the same day)?

timofeeve [1]

Answer:

π/8 radians

Step-by-step explanation:

THIS IS THE COMPLETE QUESTION

In 1 h the minute hand on a clock moves through a complete circle, and the hour hand moves through 1 12 of a circle. Through how many radians do the minute hand and the hour hand move between 1:00 p.m. and 1:45 p.m. (on the same day)?

SOLUTION

✓If the minute hand on a clock moves through complete circle in 1 hour, then it means that it goes through a circle and angle of circle in radians is 2π.

Between 1:00 p.m. and 1:45pm in the same day we have 45 minutes i.e (1.45 pm -1pm)

Within the 1hour minutes, the hand can move with complete cycle of 2π radians

Then At time t= 45minutes

Angle through the circle at 45 minutes= 45/60 ×2π radians

= 3π/2 radians

And if the hour hand goes through a complete cycle 1/12 as told in the question we have 1/2 × 2π radians

For t=45 minutes

Then 1/12 × 2π ×45/60

= π/8 radians

Hence, the minute hand and the hour hand move π/8 radians between 1:00 p.m. and 1:45 p.m.

5 0

3 years ago

Suppose 100 people all toss a hat into a box and then proceed to randomly pick out a hat. what is the expected number of people

tatuchka [14]

1 person because there is 1 in 100 chance that you get your hat back

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3 years ago

I need help on this hhhhhhhh

Anon25 [30]

$\huge\text{Hey there!}$

$\mathsf{\dfrac{10^{15}}{10^4}}$

$\mathsf{10^{15}}\\\mathsf{=10\times10\times10\times10\times10\times10\times10\times10\times10\times10\times 10\times10\times10\times10\times10}\\\mathsf{= \boxed{\bf 1,000,000,000,000,000}}$

$\mathsf{\dfrac{\bold{1,000,000,000,000,000}}{10^4}}$

$\mathsf{10^4}\\\mathsf{= 10\times10\times10\times10}\\\mathsf{10\times10=\bf 100}\\\mathsf{100\times100}\\\mathsf{= \boxed{\bf 10,000}}$

$\mathsf{\dfrac{1,000,000,000,000,000}{\bf 10,000}}$

$\mathsf{\dfrac{1,000,000,000,000,000}{10,000}}\\\\\mathsf{= 1,000,000,000,000,000\div 10,000}\\\\\mathsf{= \boxed{\bf 100,000,000,000}}$

$\mathsf{10^{11}}\\\mathsf{10\times10\times10\times10\times10\times10\times10\times10\times10\times10\times10}\\\mathsf{= \boxed{\bf 100,000,000,000}}$

$\mathsf{100,000,000,000= 100,000,000,000= 10^{11}}$

$\boxed{\boxed{\large\text{Answer: BASICALLY }\mathsf{\dfrac{10^1^5}{10^4}\large\text{ is EQUAL to or EQUIVALENT to}}}}\\\boxed{\boxed{\mathsf{10^{11}}\large\text{ because they both give you the result of \bf 100,000,000,000}}}\huge\checkmark$