Write the equation y= x^2-6x+16 in vertex form

The children from a football club are put into rows in the sports hall. When put into rows of 9 children, there are 2 children l

g100num [7]

We are told that the children from a football club are put into rows in the sports hall. When put into rows of 9 children there are 2 children left over. When put into rows of 12 children there are 2 children left over.

We will find least number of children in football club by finding LCM of 9 and 12.

Multiples of 9 are: 9, 18, 27, 36, 45, 54, 63,...

Multiples of 12 are: 12, 24, 36, 48, 60, 72, 84,...

We can see that least common multiple of 9 and 12 is 36.

We are told that 2 children left over from putting them into 9 and 12 children per row. To find least number we will add 2 to 36.

$9\cdot4+2=36+2=38$

$12\cdot3+2=36+2=38$

$\text{Least number of children in football club}=36+2=38$

Therefore, the least number of children in the football club is 38.

5 0

3 years ago

For each of the following functions, determine if they are injective. Also determine if theyare surjective. Also determine if th

timurjin [86]

Answer:

Check below

Step-by-step explanation:

1. Definition for intervals

$(a,b)=\left \{ x\in\Re : a$

2. Functions

1) $\Re \rightarrow \Re \\ f(x)=x$

Let's perform graph tests.

That's an one to one, injective function. Look how any horizontal line touches that only once. Also, It's a surjective and a bijective one.

2) $\Re\geq0\rightarrow\Re , f(x)=x+1\\$

Injective, surjective and bijective.

Injective: a horizontal line crosses the graph in one point.

3) $f:\Re\geq 0\rightarrow\Re, f(x) = cos(x)$

The cosine function is not injective, bijective nor surjective.

4) $f:\Re\rightarrow\Re \:f(x)=ex$

Since e, is euler number it's a constant. It's also injective, surjective and bijective.

5) Quite unclear format

$6) \:f:\Re\rightarrow(0,\infty), f(x) =ex$

Despite the Restriction for the CoDomain, the function remains injective, surjective and therefore bijective.

$7) f:\Re\geq 0 \rightarrow \Re\geq0, f(x) =x^{4}$

Not injective nor surjective therefore not bijective too.

$8).f:\{-1,2,-3\}}\rightarrow \{1,4,9\}, f(x) =x^{2}$

$f(-1)=1, f(2)=4, f(-3)=9$

Injective (one to one), Surjective, and Bijective.

$10) f:\Re\geq 0\rightarrow [-1,1], f(x)= cos(x)\\-1=cos(x) \therefore x=\pi,3\pi,5\pi,etc.$

Surjective.

$11.f:R\geq 0[-1,1], f(x) = 0\\$

Surjective

12.f: US Citizens→Z, f(x) = the SSN of x.

General function

13.f: US Zip Codes→US States, f(x) = The state that x belongs to.

Surjective

7 0

3 years ago

Does a triangle with side lengths 7, StartRoot 80 EndRoot, and StartRoot 31 EndRoot from a right triangle?

AlladinOne [14]

Answer and Step-by-step explanation:

The sides we have are 7, $\sqrt{80}$ , and $\sqrt{31}$ .

The square root of 80 is less than 9 but greater than 8 (because $8^2$ is 64, $9^2$ is 81, and 80 is in between those two values), and the square root of 31 is definitely less than the square root of 80.

So, $\sqrt{80}$ is the longest side.

1) The square of $\sqrt{80}$ is: $(\sqrt{80} )^2=80$

2) The sum of the squares of the two shorter sides is:

$7^2+(\sqrt{31} )^2=49+31=80$

3) Since the square of the longest side is equal to the sum of the squares of the two shorter sides, by the Pythagorean Theorem, the triangle is a right triangles.

Hope this helps!

4 0

3 years ago

Read 2 more answers

A preliminary study of hourly wages paid to unskilled employees in three metropolitan areas was conducted. Included in the sampl

andriy [413]

There is a system glitch during the process of adding my answer here so i create a document file for the answer, you find it in the attachment below.

Download docx

5 0

3 years ago

Write an equation that models the sequence 200, 500, 1250

Vsevolod [243]

Answer:

1200

Step-by-step explanation:500-200=300

1250-500=750

750-300=450

750+450=1200

5 0

3 years ago