Given the functions:
1. You need to substitute the function g(x) into the function f(x), in order to find:
Then:
2. You need to substitute this value of "x into the function:
And then evaluate, in order to find:
You get:
Hence, the answer is:
Lets width od field is x , x>0 (if x<0 it is no sense) yards and length is (x+40)yards
So square of field is x(x+40)=6000
x²+40x=6000
x²+40x-6000=0
(x+100)(x-60)=0
x₁=-100 no sense
x₂=60 yards - width of field
x+40=x+60=100 yards - length of field
Answer: 60 yards - width of field, 100 yards - length of field
Answer:
y = (-5/2)x + 1
Step-by-step explanation:
We can see that the line intersects (0,1) and (2, -4). We use these points to find the slope: m = (-4-1)/(2-0) = -5/2. Also, the y-intercept is (0,1), so b = 1. Substituting these values into y=mx +b, we get y = (-5/2)x + 1.
I hope this helps! :)
<h3>
Answer: 16 cm</h3>
===================================================
Explanation:
The drawing is shown below.
- Point A = center of circle
- Points B,C,E = points on the circle's edge
- Point D = midpoint of chord CE
The goal is to find the length of CE based on these facts
- BC = 34 = diameter
- AD = 15 = distance from center to chord
- x = length of segment CD = length of segment DE
Notice how AB = AC = AE = 17 because they are all radii of the same circle. We cut the diameter in half to get the radius.
Focus on triangle CAD. We'll use the pythagorean theorem to find x.
a^2 + b^2 = c^2
(AD)^2 + (DC)^2 = (AC)^2
15^2 + x^2 = 17^2
225 + x^2 = 289
x^2 = 289 - 225
x^2 = 64
x = sqrt(64)
x = 8
Segment CD is 8 cm long, and so is segment DE.
To wrap things up, we then say:
CE = CD + DE
CE = 8 + 8
CE = 16
Chord CE is 16 cm long.
X^3 + 3x^2...factor out x^2
x^2 (x + 3) <==