F(x) = 3x^2+6x-2
= 3(x^2+2x-2/3)
= 3(x^2 +2x + 1 - 1 - 2/3)
= 3((x+1)^2 - 1 - 2/3)
= 3((x+1)^2 -5/3))
= 3(x+1)^2 - 5
So our function is in the form:
f(x) = 3(x+1)^2 - 5
where a = 3, h = -1, k = -5
Yes, i<span>n mathematics, a </span>rational number<span> is any </span>number<span>that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q.</span>
To find the volume of this one we need to break it down
now i see half of a cylinder and rectangle:)
but first lets find the volume of the rectangle...
In order to find the Volume of a rectangle we need to use this formula...
Length x width x height
in this case...
length = 10in
width = 6 in
height = 8in
lets solve:)
10 x 6 x 8 = 480
or we write it like this
480in³
now time to find the volume of the half cylinder:)
But first lets remember the volume for a cylinder
Volume =

So lets find our measurements

= 3.14
r² = 5² or 25
h = 6
so lets plug in our values just like our formula said:)
3.14 x 25 x 6
now lets easily solve
<span>3.14 x 25 x 6 = 471
</span>now since we found an entire cylinder and we only want half of a cylinder lets divide our answer in half
471 ÷ 2 = 235.5
so we write it like this 235.5units³
But we have to add both of our multiples together so lets do that
Volume of rectangle = <span>480in³
</span>volume of half sphere = 235.5units³
480 + 235.5 = 715.5
answer = 715.5units³
I hope this helped and everyone learned something new
anyways don't forget to
MARK ME BRAINLIEST! :D
Answer:
a. False
b. True
Step-by-step explanation:
Given that:
The sample size of the college student n = 100
The population of student that participated p = 38
We are to identify from the following statement if it is true or false.
From part a;
It is false since the random samples not indicate the population perfectly. As such we can't conclude that the proportion of students at this college who participate in intramural sports is 0.38.
The statement in part b is true because the sampling variation, random samples also do not indicate the population perfectly but it is close to be 0.38. Thus, it is suitable to conclude that the proportion of students at this college who participate in intramural sports is likely to be close to 0.38, but not equal to 0.38.
Answer:
The correct answer is 2 inches.
Step-by-step explanation:
Let l inches and w inches be the length and width of a rectangle respectively.
According to the given problem, l - 8 =
.
Area of the rectangle is given to be, according to the question, 18 square inches.
Thus l × w = 18
⇒ l × (2l - 16) = 18
⇒ 2
- 16l - 18 = 0
⇒
- 8l - 9 = 0
⇒ ( l - 9) ( l + 1) = 0
The possible values of l are 9 and -1. As the length cannot be equal to -1, thus the value of the length is 9 inches.
Width of the rectangle is 2 inches.