As you may already be familiar, these functions f(x) and g(x) are piecewise. They consist of multiple functions with different domains.
1. For #1, the given input is f(0). Since 0≤1, you should use the first equation to solve. f(0)=3(0)-1 ➞ f(0)=-1
2. Continue to evaluate the given input for the domains given. 1≤1, therefore f(1)=3(1)-1➞f(1)=2
3. 5>1, therefore f(5)=1-2(5)➞f(5)=-9
4. -4≤1; f(-4)=3(-4)-1➞f(-4)=-13
5. -3<0<1; g(0)=2
6. -3≤-3; g(-3)=3(-3)-1➞g(-3)=-10
7. 1≥1; g(1)=-3(1)➞g(1)=-3
8. 3≥1; g(3)=-3(3)➞g(3)=-9
9. -5≤-3; g(-5)=3(-5)-1➞g(-5)=-16
Hope this helps! Good luck!
Answer:
b = -5/2
Step-by-step explanation:
- 6 (b + 3)= - 8 + 5
- 6b - 18= - 3
- 6b= - 3 + 18
- 6b= 15
b= - 15/6
b= - 5/2
Answer:
#15) B. 30 mn^5
#17) B. 1/2
Step-by-step explanation:
<h2>#15:</h2>
The area of a trapezoid is given in the formula: 1/2(a + b) * h, where a is the length of the top of the trapezoid, b is the length of the bottom of the trapezoid, and h is the height of the trapezoid.
All of these measurements are given so all that you need to do is to substitute these values into the formula.
Substitute 3 for a, 9 for b, and 5 for h.
Solve inside the parentheses first. Add 3 and 9.
Multiply 12 and 1/2 together.
Multiply 6 and 5.
We need to figure out if the area is to the 5th or 6th power. When we added 3 and 9 together, we combined like terms so the exponent stayed to the 3rd power.
After multiplying this ^3 by the 5mn^2, the exponent becomes to the 5th power because you add exponents when multiplying.
Therefore the final answer is B. 30 mn^5.
<h2>#17:</h2>
When going down from 32 to 8 to 2, you can see that each number is being divided by 4.
32 / 4 = 8...
8 / 4 = 2...
So to find the next number in this sequence you would divide 2 by 4.
The answer is B. 1/2.
Answer:
a) 301.59 cubic centimeters
b) 235.87 square centimeters
Step-by-step explanation:
a)
Volume of ice cream cone is volume of hemisphere PLUS volume of cone.
Volume of Hemisphere = 
radius is given as 4, so,
Volume of Hemisphere = 
Now, Volume of Cone = 
Where radius is 4 and height is 10, so,
Volume of Cone = 
Volume of Ice Cream Cone = 134.04 + 167.55 = 301.59 cubic centimeters
b)
Surface area of ice cream cone is surface area of hemisphere PLUS surface area of cone.
Surface Area of Hemisphere = 
Surface Area of Cone = 
We dont need to use the first part, 
since it is "inside". We need to find l, slant height, by using pythagorean theorem on a triangle we can make (bottom right).
4^2 + 10^ 2 = l^2
16 + 100 = l^2
116 = l^2
l = 10.77
Now to find the surface area of cone = 
Surface area of ice cream cone = 100.53 + 135.34 = 235.87 square centimeters
Answer:
Answer is B 84ft
Step-by-step explanation:
It is this because this is a rectangle with an area of 112 with a triangle shape cut out of it. The area of that missing piece is 28 so do 112-28 and you get the answer of 84
