Answer:
w≅8.46ft
Step-by-step explanation:
Data
focus=8
vertex=(0,0)
width=?
depth (y)=3ft
parabola equation: 
; then for V=(0,0), 
, be focus(f)=8in; 
→ 
we have that y=3ft then 
; but 1in≅0.083ft so 
→ x=±2.82, finally w=3*2.82≅8.46ft
Answer:
The first question:
x = -1
Step-by-step explanation:
Step 1 :
Pulling out like terms :
1.1 Pull out like factors :
-x - 1 = -1 • (x + 1)
Equation at the end of step 1 :
Step 2 :
Solving a Single Variable Equation :
2.1 Solve : -x-1 = 0
Add 1 to both sides of the equation :
-x = 1
Multiply both sides of the equation by (-1) : x = -1
One solution was found :
x = -1
Processing ends successfully
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Hey there!
To solve this, we need to plug each of our answer options into the inequality and see if it is true. Which ever one doesn't make the inequality true when plugged in is the answer.
OPTION A
(x,y)=(-3,0)
We plug our values into the inequality.
0≥ I-3I+3
You may have noticed the bars surrounding the negative three.. If you didn't know, this is called absolute value. Absolute value is how far the number is from 0 on the number line. -7 is 7 away from 0 on a number line, so the absolute value of -7 is 7. The absolute value of 7 is 7. The absolute value of 0 is 0. Absolute value is signified by these bars. Le'ts finish evaluating.
0≥6
As you can see, zero is not greater than or equal to six. So, option A is false.
Since A is not a solution, we already know that that is the answer, so we don't even need to check B and C. But, we can still evaluate them if you want.
OPTION B
6≥I-3I+3
6≥6
This is true.
OPTION C
4≥I0I+3
4≥3
This is also true.
Therefore, the answer is A. (-3,0)
Have a wonderful day!
Answer:
Step-by-step explanation:
Use law of cosines
c² = a² + b² - 2abcosθ
cosθ = (c² - a² - b²) / -2ab
c = length of AC = √(8 - 5)² + (4 - (-5))² = √90
b = length of AB = √(8 - 6)² + (4 - 3)² = √5
a = length of BC = √(6 - 5)² + (3 - (-5))² = √65
cosθ = (√90² - √65² - √5²) / -2√65√5
cosθ = 20 / -36.05551...
cosθ = - 0.5547001
θ = 123.69°
The GCF will be 3 because it is the greatest
