Answer:
AB = 2*sqrt(5) or
AB = 4.47
Step-by-step explanation:
AB is the hypotenuse of a right triangle A and B and the corner where 2 and 4 meet.
The length of AB is governed by the Pythagorean Theorem.
AB^2 = x^2 + y^2 Substitute 2 and 4 for x and y
AB^2 = 2^2 + 4^2 Expand the right side
AB^2 = 4 + 16 Add the right side
AB^2 = 20 Take the square root of both sides
sqrt(AB^2) = sqrt(20)
Factor 20 = 2*2 *5
Rule: when taking the square root of a number the pairs can take 1 member of the pair outside the root sign and throw the other one a way.
AB = 2 * sqrt(5) One of the roots has been thrown away.
Answer:
Explanation:
The table that shows the pattern for this question is:
Time (year) Population
0 40
1 62
2 96
3 149
4 231
A growing exponentially pattern may be modeled by a function of the form P(x) = P₀(r)ˣ.
Where P₀ represents the initial population (year = 0), r represents the multiplicative growing rate, and P(x0 represents the population at the year x.
Thus you must find both P₀ and r.
<u>1) P₀ </u>
Using the first term of the sequence (0, 40) you get:
P(0) = 40 = P₀ (r)⁰ = P₀ (1) = P₀
Then, P₀ = 40
<u> 2) r</u>
Take two consecutive terms of the sequence:
- P(1) / P(0) = 40r / 40 = 62/40
You can verify that, for any other two consecutive terms you get the same result: 96/62 ≈ 149/96 ≈ 231/149 ≈ 1.55
<u>3) Model</u>
Thus, your model is P(x) = 40(1.55)ˣ
<u> 4) Population of moose after 12 years</u>
- P(12) = 40 (1.55)¹² ≈ 7,692.019 ≈ 7,692, which is round to the nearest whole number.
Answer:
<u>Step-by-step explanation:</u>
5x + 2y = 7 ⇒ 2(5x + 2y = 7) ⇒ 10x + 4y = 14
-2x + 6y = 9 ⇒ 5(-2x + 6y = 9) ⇒ -10x + 30y = 45
34y = 59
<u>÷34 </u> <u>÷34 </u>
y = 59/34
Solution:
We know that:
The wheel was invented about 2500 Before Christ.
The gasoline automobile was invented in AD 1885.
Therefore the number of years passed between the invention of the wheel and the invention of the automobile is:
years
Answer:
(5/24) gallons of gas to mow the side yard
Step-by-step explanation:
We can easily solve this proble by applying a rule of three
5/16 gallons of gas --------------------------------- for 1 backyard
x gallons of gas ------------------------------------- 2/3 backyard
x = ((2/3)/1)*(5/16) gallons of gas
x = ((2/3))*(5/16) gallons of gas
x = ((10/48) gallons of gas
x = (5/24) gallons of gas