30)
a)
We have to calculate the highest common factor (HCF) of 21 and 36.
21=3*7
36=2² * 3²
HCF (21,36)=3.
Therefore: the length of the side of the largest pieces into which Juanita and Samuel can cut the pizza must be 3 inches.
Answer:3 inches.
b)
Area (pizza)=21 in * 36 in=756 in²
Area (0ne piece of pizza)=3 in * 3 in=9 in².
number of pieces of pizza=Area pizza / area of one piece of pizza.
number of pieces of pizzas=756 in²/ 9 (in²/piece)=84 pieces.
answer=84 pieces.
31)
x=number
-x=opposite of number "x"
The opposite of a number sometimes will be greater than the number itself.
if we have a negative number, the opposite of this number will be greater than the negative number.
Example:
x=-10
the opposite of -10 is 10
therefore: 10>-10
If we have a positive number, the opposite of this number will not be greater than the positive number.
Example:
x=10
the opposite of 10 is -10
Therefore: -10<10
Interest earned=principle×interest rate×time
I=prt
I=1,000×0.0525×1
I=52.5
1). Since you have -2y and 4y, elimination is easy to do for solving for x..
Keep the first equation and multiply the second equation by 2. Then add.
5x - 2y = -1
8x + 4y = 56
10x - 4y = -2
8x + 4y = 56
-----------------
18x = 54
x = 3
Now we can use substitution to solve for y.
Substitute 3 for x in the first original equation and solve for y.
5x - 2y = -1
5(3) - 2y = -1
15 - 2y = -1
-2y = -16
y = 8
(3, 8)
2.)
3x - y = =16
-4x - y = 21
Multiply both sides of the first equation by -1 to change all signs. Then when you add the equations, you eliminate y and solve for x.
-3x + y = 16
-4x - y = 21
-----------------
-7x = 37
x = -37/7
Now multiply the first original equation by 4 and the second original by 3 to eliminate x and solve for y.
12x - 4y = -64
-12x - 3y = 63
---------------------
-7y = -1
y = 1/7
Solution: (-37/7, 1/7)
First, use the distance formula to find in the distance. Then use 1/2bh (formula for area of a triangle) to find the triangle’s area.
