Dominic is a landscape architect and is designing a garden with an area of up to 500 square feet. He will use two types of plants: zinnias and petunias. Each zinnia plant requires 1.6 square feet of ground and each petunia plant requires 1.8 square feet of ground. Each zinnia plant costs $4 and each petunia plant costs $3, and the architect must spend no more than $600. Let z represent the number of zinnia plants and p represent the number of petunia plants.

Three of the constraints for this situation are z≥0, p≥0, and 1.6z+1.8p≤500.

What is the other constraint for this situation?
Enter your answer in the boxes.

z + __
p≤ __

Marshall uses the polynomial identity (x−y)2=x2−2xy+y2 to show that 8² = 64.

What values can Marshall use for x and y?

x = 8 and y = 64

x = 10 and y = 2

x = 2 and y = 6

x = 64 and y = 0

b. 24 mm

step-by-step explanation:

use the pythagorean theorem.

a^2 + b^2 = c^2

a^2 + 7^2 = 25^2

a^2 + 49 = 625

a^2 = 576

a = 24

answer: b. 24 mm

all it means is function 3

8

step-by-step explanation:

to find the amount of gift bags to use all the supplies, find the gcf or greatest common factor. this is the largest number which multiplies evenly into each term.

48 has factors: 1, 2, 3, 4, 6, 8, 12. 16, 24, 48

80 has factors: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80

64 has factors: 1, 2, 4, 8, 8, 16, 32, 64

the highest number factor they all share in common is 8. this means there will be 8 bags with 6 pencils, 10 markers, and 8 stickers in each bag.

x = -3

y = -18

step-by-step explanation:

to solve by substitution, substitute one variable and solve for the other. then substitute again to find the remaining variable.

x-1/3(3x-9) = -3 since y=3x-9 substittute y.

x-1/3(3x-9)=-3

x + x +3 = -3

2x+3=-3

2x+3-3= -3-3

2x=-6

x=-3

substitute again into y=3x-9

y=3(-3)-9

y=-9-9

y=-18