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2 years ago

How do you work out perimeter?

Mathematics

1 answer:

Harman [31]2 years ago

5 0

You need to add up all the sides to find the perimeter.

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Can someone please help me I'm confused as to what I'm supposed to do.

kobusy [5.1K]

I hope this helps you

(fog)(5)=f (g (5))=?

x= 5 g (5)=-4.5+3=-20+3=-17

f (g(5))=f (-17)=-2. (-17)-7

f (-17)=34-7

f (-17)=27

4 0

2 years ago

Prove 2√(x) + 1/√(x + 1) <= 2√(x+1) for all x in [0,inf)

EleoNora [17]

Start by multiplying each side of the inequality by $\sqrt{x + 1}$ and simplifying:

$2 \sqrt x + \frac{1}{\sqrt{x+1}} \leq 2 \sqrt{x + 1}$
$(2 \sqrt x + \frac{1}{\sqrt{x+1}})(\sqrt{x + 1}) \leq (2 \sqrt{x + 1})(\sqrt{x + 1})$
$2 \sqrt{x(x + 1)} + 1 \leq 2(x + 1)$
$2 \sqrt{x^2 + x} + 1 \leq 2x + 2$
$2 \sqrt{x^2 + x} \leq 2x + 1$
$\sqrt{x^2 + x} \leq x + \frac{1}{2}$

From here, we can square both sides to get

$x^2 + x \leq (x + \frac{1}{2})^2$
$x^2 + x \leq x^2 + x + \frac{1}{4}$
$0 \leq \frac{1}{4}$ , which is always true.

3 0

2 years ago

What is the value of the discriminant of the quadratic equation −1 = 5x2 −2x, and what does its value mean about the number of r

Zepler [3.9K]

For the equation:
-1=5 x^2 - 2 x
5 x^2 - 2 x + 1 = 0, then we substitute: a=5, b=-2, c =1
to discriminant formula: D= b^2 - 4 a c = (-2)^2 - 4 * 5 * 1 = 4 - 20 = - 16
Answer:
The discriminant is equal to -16 which means the equation has no real number solutions.

7 0

3 years ago

Read 2 more answers

Factoring Trinomials

alexandr402 [8]

25 a² + 20 ab + 4 b²

for formula $a^x+bx^ky^k+cy ^{2k }$ find u,v such that: u.v = a

and u+v = b then group according to $(ax ^{2k} +ux^ky^k)+(vx^ky^k+cy ^{2k} )$

= $(25a^2+10ab)+(10ab+4b^2)$

factor out 5a from : $25a^2+10ab : 5a(2b+5a)$

factor out 2b from : $10ab+4b^2: 2b(2b+5a)$

= $5a(2b+5a) + 2b(2b+5a)$

factor out : $(5a+2b)$

= $(5a+2b)(5a+2b)$

Refine:

$(2b+5a)^2$

hope this helps!.

3 0

3 years ago

Determine the greatest common divisor of the elements of the set \[ s = \{ n^{13} - n \mid n \in \mathbb{z} \}. \]

Kay [80]

Answer:

2730

Step-by-step explanation:

We want to determine the greatest common divisor of the elements of the set $S = \{ n^{13} - n \mid n \in \mathbb{Z} \}.$

We apply the Fermat's little theorem which states that if p is a prime number, then for any integer a, the number aᵖ − a is an integer multiple of p.

Now, $n^{13} \equiv n \mod p$ if p-1 divides 12.

Since the of 12 are 1,2,3,4, 6, 12, the corresponding primes are 2, 3, 5, 7, 13.

Therefore, the gcd of the elements in $2^{13}-2$ and $3^{13}-3$ is 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13.$

2*3*5*7*13=2730

Therefore, the gcd of the elements in set S is 2730.

5 0

2 years ago