Which number is irrational
1 answer:
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Answer:
Intercept form is y= (x+5)(x+3)
vertex is (-4,1)
y intercept is (0,15)
x intercepts are (-5,0) (-3,0)
Step-by-step explanation:
Given quadratic function
To rewrite it in standard form we need to expand (x+4)^2
Intercept form is y=a(x-p)(x-q)
Factor x^2 + 8x + 15
product is 15 and sum is 8, 5*3= 15 and 5+3=8
(x+5)(x+3)
Intercept form is y= (x+5)(x+3)
Vertex form of equation is y=(x-h)^2+k
where (h,k) is the vertex
, here h = -4 and k =1 so vertex is (-4,1)
To find y intercept plug in 0 for x
y= (x+5)(x+3)
y= (0+5)(0+3) = 15, so y intercept is (0,15)
to find x intercept plug in 0 for y
y= (x+5)(x+3)
0= (x+5)(x+3), x+5 =0 and x+3=0
x=-5 and x= -3
So x intercepts are (-5,0) (-3,0)
Answer:
a. y = 4,200
b. 9.2%
Step-by-step explanation:
Given the information:
- The intinital value: 4,200
- The population is decreasing at a rate of 2.4% per year
=> the base number of the exponential function is:
100% - 2.4% = 97.6% = 0.976
Let t is quarter
Let y is the population
=> the following shows an exponential decay function to find the quarterly decay rate is:
y (t)= 4,200
b. The population is decreasing by how much percent per quarter?
Let t = 0 we have: y(0) = 4,200
Let t = 1 we have: y(1) = 4,200
=> the decreasing percentage is:
= (y(0) - y(1)) / y(0)*100%
= (4200 - 3811) / 4200 *100%
= 389/4200*100%
= 9.2%