Answer:
173
Step-by-step explanation:
Original coordinates of the points:
A (8,15) ; B (12,13) ; C (8,10)
Dilated scale factor of 3.
A ⇒ 3x = 3(8) = 24 ; 3y = 3(15) = 45 ⇒ A' (24,45)
B ⇒ 3x = 3(12) = 36 ; 3y = 3(13) = 39 ⇒ B' (36, 39)
C ⇒ 3x = 3(8) = 24 ; 3y = 3(10) = 30 ⇒ C' (24, 30)
The given image forms a right triangle. So, I'll get the short leg and long leg of the right triangle to solve for the hypotenuse, length of CB.
Short leg: y value of B and C
39 - 30 = 9
Long leg: x value of B and C
36 - 24 = 12
a² + b² = c²
9² + 12² = c²
81 + 144 = c²
225 = c²
√225 = √c²
15 = c
The length of CB is 15 units.
Answer:
x = 15
Step-by-step explanation:
let me know if you want an explanation
Answer: 0.65
Step-by-step explanation: To write a percent as a decimal, first remember that a percent is a ratio that compares a number to 100. We can think of 65% as the ratio 65 to 100 or 65 divided by 100. Remember that dividing by 100 moves the decimal point 2 places to the left.
<h2>
65% → .65 or 0.65</h2><h2 /><h3>
Therefore, 65% can be written as the decimal 0.65.</h3>
Answer:
The population for the first year is 75.35.
Step-by-step explanation:
Solution:
Given Data;
Carrying capacity (K) = 100
Growth rate (r) = 1.8% = 0.018
Initial population (Po) = 75
time = first year
Population at any given time (pt) = ?
Using the population growth rate formula, we have
<h2>
dp/dt = rp (1-p/t)---------------------------1</h2>
Where r is the growth rate, t is the given time and p is the population growth
Equation 1 is differentiated and is obtained as;
<h2>Pt = K/ [1 + (K-Po/Po)e^-rt]------------2</h2>
Substituting into equation 2, we have
Pt = 100/[ 1+ (100-75/75) *e^-0.018*1]
Pt = 100/[1+ (0.333 * e^-0.018]
= 100/[1 +(0.333*0.982)]
= 100/[1 + 0.327]
= 100/1.327
=75.35
