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3 years ago

1. In 2005, there were 100 rabbits in Polygon Park. The population increased by

Mathematics

1 answer:

Olegator [25]3 years ago

6 0

The exponential growth formula is y = a(1+r)^x

y = 100(1+.11)^t

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Ben went to the hardware store and bought 7 pieces of rope of equal length. The total length of the ropes was 56 meters. How lon

Harman [31]

Answer:

8 meters

Step-by-step explanation:

56 / 7 = 8

6 0

3 years ago

Which of the following are solutions to the equation below 3x^2+27x+54=0

VikaD [51]

Answer:x=6

Step-by-step explanation:Step-1 : Multiply the coefficient of the first term by the constant 1 • 18 = 18

Step-2 : Find two factors of 18 whose sum equals the coefficient of the middle term, which is -9 .

-18 + -1 = -19

-9 + -2 = -11

-6 + -3 = -9 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -6 and -3

x2 - 6x - 3x - 18

Step-4 : Add up the first 2 terms, pulling out like factors :

x • (x-6)

Add up the last 2 terms, pulling out common factors :

3 • (x-6)

Step-5 : Add up the four terms of step 4 :

(x-3) • (x-6)

Which is the desired factorization

7 0

3 years ago

Read 2 more answers

X^2 + 5x - 24 = 0 How do I solve by factoring

tiny-mole [99]

Answer:

x = -8 or x = 3

Step-by-step explanation:

To factor ax² + bx + c, use AC method.

a times c is 1 × -24 = -24.

Factors of ac (-24) that add up to b (5) are 8 and -3.

Divide by a and reduce: 8/1 and -3/1.

Therefore, the factors are x + 8 and x − 3.

x² + 5x − 24 = 0

(x + 8) (x − 3) = 0

x = -8 or 3

7 0

3 years ago

What is it tell me please

leva [86]

Answer:

19.995

Step-by-step explanation:

7 0

2 years ago

Let f(x) = cx^k be a power function such that f(13) is four times the size of f(1). What is the power k?

Ivenika [448]

Answer:

0.540

Step-by-step explanation:

Hi there,

To get started in order to solve this, please recall the property of logarithms.

This question is a bit tricky, but doable. Best way to solve this is first compare the two functions:

$f(x) = cx^{k} \\ f(13)=4f(1)$

Now, let's see what the function gives at 13 and 1:

$f(13)=c13^{k}\\f(1)=c1^{k}$

Something to recognize is that 1 to the power of <em>anything</em> is just 1, so f(1) is reduced to:

$f(1)=c$ We are making progress!

Next, we can set both f(13) forms equivalent to each other, watch this:

$f(13)=f(13) = 4f(1)$ but we know what f(1) is equal to, and let's substitute our knowns:

$c13^{k}=4c1^{k} = 4c$ the c constant on both left and right side cancel out:

$13^{k}=4$ Now, take the logarithm form of both side of the equation. I used natural log, but you can also use common logs:

$ln(13^{k})=ln(4)$ ⇒ $k*ln(13)=ln(4)$ this was performed using <em>the power log rule. </em>

Isolate k:

$k=\frac{ln(4)}{ln(13)} =0.540$ using a calculator.

If you liked this solution, hit Thanks or give a rating!

thanks,

8 0

2 years ago