Answer:
Catherine>Herb>Amy
Step-by-step explanation:
Amy's set range is 7, Herb is 8, and Catherine is 12.
Answer:
The number is -4.
Step-by-step explanation:
Let the number be n.
Given:
Max adds 7 to a number.
hence it is given as n+7
Multiply's the sum by -4 the result is 3 times the same number.
Hence the equation can be written as;
![-4(n+7)=3n](https://tex.z-dn.net/?f=-4%28n%2B7%29%3D3n)
Now Solving the above equation to find value of n we get;
![-4(n+7)=3n\\-4n-28=3n\\-4n-3n=28\\-7n=28\\n=\frac{28}{7}=-4](https://tex.z-dn.net/?f=-4%28n%2B7%29%3D3n%5C%5C-4n-28%3D3n%5C%5C-4n-3n%3D28%5C%5C-7n%3D28%5C%5Cn%3D%5Cfrac%7B28%7D%7B7%7D%3D-4)
The value of n is -4.
Now when we add 7 to number -4 we get answer as 3.
And when the sum is multiplied by -4 we get answer -12.
Also 3 times of number is equal to 3 multiplied by -4 we get answer as -12.
Hence when the sum is multiplied by -4 it is equal to 3 times of same number.
Hence from above we can say that the number is -4.
Answer:
a) x = 2 b) y = 5
Step-by-step explanation:
For a)
NOTE: Since line EC bisects angle FEG, it will be divided into 2 equal parts
angle FEG = 58
angle FEC = 11x + 7
angle CEG = 11x + 7
So:
58 = (11x + 7) + (11x + 7)
58 - 7 - 7 = 11x + 11x
44 = 22x
x = 2
For b)
angle AED = 16y + 10
angle AED = 90°
90 = 16y + 10
90-10 = 16y
y = 80/16
y = 5
Answer:
B. {x| x > 2 or x < -4}
<em></em>
Step-by-step explanation:
Given
![5(x - 2)(x + 4) > 0](https://tex.z-dn.net/?f=5%28x%20-%202%29%28x%20%2B%204%29%20%3E%200)
Required
Solve
![5(x - 2)(x + 4) > 0](https://tex.z-dn.net/?f=5%28x%20-%202%29%28x%20%2B%204%29%20%3E%200)
Start by dividing both sides by 5
![\frac{1}{5} * 5(x - 2)(x + 4) > \frac{0}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B5%7D%20%2A%205%28x%20-%202%29%28x%20%2B%204%29%20%3E%20%5Cfrac%7B0%7D%7B5%7D)
![(x - 2)(x + 4) > 0](https://tex.z-dn.net/?f=%28x%20-%202%29%28x%20%2B%204%29%20%3E%200)
Find critical point of the inequality by changing the inequality to equality
![(x - 2)(x + 4) = 0](https://tex.z-dn.net/?f=%28x%20-%202%29%28x%20%2B%204%29%20%3D%200)
Split the above expression
![x - 2= 0\ or\ x + 4= 0](https://tex.z-dn.net/?f=x%20-%202%3D%200%5C%20or%5C%20x%20%2B%204%3D%200)
Make x the subject of formula in both
![x - 2+2= 0+2\ or\ x + 4-4= 0-4](https://tex.z-dn.net/?f=x%20-%202%2B2%3D%200%2B2%5C%20or%5C%20x%20%2B%204-4%3D%200-4)
![x = 0+2\ or\ x = 0-4](https://tex.z-dn.net/?f=x%20%3D%200%2B2%5C%20or%5C%20x%20%3D%200-4)
![x = 2\ or\ x = -4](https://tex.z-dn.net/?f=x%20%3D%202%5C%20or%5C%20x%20%3D%20-4)
Check the intervals in between the critical points
Set:
--- This works in the inequality
Set:
--- This doesn't work in the inequality
Set:
--- This doesn't works in the inequality
Set:
--- This works in the inequality
<em>Hence, the solution is: {x| x > 2 or x < -4}</em>
A) 31 degrees
b) 118 degrees