Answer:
The equation of the line that is perpendicular to the line that passes through the point (-4, 2) is y = -9·x/5 + 18
Step-by-step explanation:
The coordinates of the point of intersection of the two lines = (5, 9)
The coordinates of a point on one of the two lines, line 1 = (-4, 4)
The slope of a line perpendicular to another line with slope, m = -1/m
Therefore, we have;
The slope, m₁, of the line 1 with the known point = (9 - 4)/(5 - (-4)) = 5/9
Therefore, the slope, m₂, of the line 2 perpendicular to the line that passes through the point (-4, 4) = -9/5
The equation of the line 2 is given as follows;
y - 9 = -9/5×(x - 5)
y - 9 = -9·x/5 + 9
y = -9·x/5 + 9 + 9
y = -9·x/5 + 18
Therefore, the equation of the line that is perpendicular to the line that passes through the point (-4, 2) is y = -9·x/5 + 18.
Answer:
Find out the what function equation represents the population of the city after t years .
To prove
The population of a city is 451,400. The population is expected to decrease at a rate of 3.2% each year.
This can be represented by exponential decreasing function.
Where a is the initial value.
r is the rate in decimal form
t is the time.
Here
a = 451,400
3.2 % is written in the decimal form.
= 0.032
Put in the formula
Therefore the decrease in the population of the city after t years is represented by
Answer:
The set of numbers that could not represent the three sides of a right triangle are;
{9, 24, 26}
Step-by-step explanation:
According to Pythagoras's theorem, when the lengths of the three sides of a right triangle includes two legs, 'x', and 'y', and the hypotenuse side 'r', we have;
r² = x² + y²
Where;
r > x, r > y
Therefore, analyzing the options using the relationship between the numbers forming the three sides of a right triangle, we have;
Set 1;
95² = 76² + 57², therefore, set 1 represents the three sides of a right triangle
Set 2;
82² = 80² + 18², therefore, set 2 represents the three sides of a right triangle
Set 3;
26² = 24² + 9², therefore, set 3 could not represent the three sides of a right triangle
Set 4;
39² = 36² + 15², therefore, set 4 represents the three sides of a right triangle
Answer:
The enrollment after 5 years is 10,724
Step-by-step explanation:
Generally, we can have the depreciation formula written as follows;
A = P(1 - r)^t
A is the number of enrollment in after a certain number of years t
P is the initial population which is 13,500
r is the rate of depreciation which is 4.5% = 4.5/100 = 0.045
t = 5 years
Substituting these values, we have it that;
A = 13,500(1-0.045)^5
A = 10,723.84
