Let f(x)+x^2+3x+2<br> What is the average rate of change of f(x) from 3 to 6?

PLS HELP ASAP I WILL IVE BRAINLIST ANSWER!!!!!Leon verified that the side lengths 21, 28, 35 form a Pythagorean triple using thi

Juliette [100K]

Answer:

Leon is correct. (Option 1)

Step-by-step explanation:

Given that Leon verified that the side lengths 21, 28, 35 form a Pythagorean triple using this procedure.

Step 1: Find the greatest common factor of the given lengths: 7

Step 2: Divide the given lengths by the greatest common factor: 3, 4, 5

Step 3: Verify that the lengths found in step 2 form a Pythagorean triple.

we have to explain whether or not Leon is correct.

As, 3,4,5 forms a Pythagorean triplet i.e satisfies the Pythagoras theorem

$Hypotenuse^2=Base^2+Perpendicular^2$

⇒ $5^2=3^2+4^2$

Let a, b, c forms a Pythagorean triplet

$a^2+b^2=c^2$

Multiplied by 4 on both sides

⇒ $4a^2+4b^2=4c^2$

⇒ ${2a}^2+{2b}^2={2c}^2$

Hence, we say 4a, 4b and 4c also forms a Pythagorean triplet.

∴ multiplying every length of a Pythagorean triple by the same whole number results in a Pythagorean triple.

Hence, Leon is correct.

4 0

3 years ago

Read 2 more answers

Identify this sequence: 5, 15, 45, 135, …<br> Arithmetic<br> Geometric<br> Neither

user100 [1]

Answer:

5 * 2 is 10 + 5 and then 15 * 2 + 15 45 * 2 + 45

Step-by-step explanation:

times it by to add that number

3 0

3 years ago

Read 2 more answers

The population of Collin County, which follows the exponential growth model,

Anestetic [448]

Answer:

(a) k=0.06217

(b) $P=264036e^{0.06217t}$

(c) 556,755 is the population in 2012

Step-by-step explanation:

Population increased from 264,036 in 1990 to 491,675 in 2000.

Let assume , year 1990 as t=0

When t=0, population P = 264,036

When t=10, population P = 491,675

Exponential growth equation is P=P_0e^(kt)

$P_0$ is the initial population when t=0

So $P_0= 264,036$

When t=10, population P = 491,675

Plug in all the values and find out k

$491675 = 264036 e^{k*10}$

Divide both sides by 264036

$\frac{491675}{264036}=e^{k*10}$

To remove 'e' we take ln on both sides

$ln(\frac{491675}{264036})=lne^{10k}$

$ln(\frac{491675}{264036})=10kln(e)$

The value of ln(e) = 1

$ln(\frac{491675}{264036})=10k$

Divide both sides by 10

k=0.06217

Exponential growth equation is $P=P_0e^{kt}$

We know $P_0= 264,036$

Replace the value of k

$P=264036e^{0.06217t}$

Now , we find the population in 2012

For year 2012 , t= 12

So we plug on 12 for t and solve for P

$P=264036e^{0.06217*12}$

P = 556755.09504

556,755 is the population in 2012

4 0

3 years ago

A pet shop had 8 identical fish tanks in the shape of rectangular prisms. The width and height of each tank was (x - 7) inches a

kipiarov [429]

The area of rectangular base of each tank

7 0

3 years ago

5)Find two square numbers that add up to 20

Wittaler [7]

The square of 4 and 2 adds up to 20!
4 square is 16.
2 square is 4
So 16+4=20

8 0

3 years ago

Let f(x)+x^2+3x+2 What is the average rate of change of f(x) from 3 to 6?