Q1. The answers are (–1, 8), (0, 7), (3, 18)
<span>–3x + y ≥ 7
</span>Let's go through all choices:
<span>(–2, –3)
</span>(-3) * (-2) + (-3) ≥ 7
6 - 3 ≥ 7
3 ≥ 7 INCORRECT
(–1, 8)
(-3) * (-1) + 8 ≥ 7
3 + 8 ≥ 7
11 ≥ 7 CORRECT
(0, 7)
(-3) * 0 + 7 ≥ 7
0 + 7 ≥ 7
7 ≥ 7 CORRECT
(1, 9)
(-3) * 1 + 9 ≥ 7
-3 + 9 ≥ 7
6 ≥ 7 INCORRECT
(3, 18)
(-3) * 3 + 18 ≥ 7
-9 + 18 ≥ 7
9 ≥ 7 CORRECT
Q2. The answers are:
5x + 12y ≤ 80
x ≥ 4
<span>y ≥ 0
</span>
<span>x - small boxes
</span><span>y - large boxes
</span>He has x small boxes that weigh 5 lb each and y large boxes that weigh 12 lb each <span>on a shelf that holds up to 80 lb:
5x + 12y </span>≤ 80
Jude needs at least 4 small boxes on the shelf: x ≥ 4
Let's check if y can be 0:
5x + 12y ≤ 80
5x + 12 * 0 ≤ 80
5x + 0 ≤ 80
5x ≤ 80
x ≤ 80 / 5
x ≤ 16
x ≥ 4 can include x ≤ 16
So, y can be 0: y ≥ 0
Answer:
y=3x
Step-by-step explanation:
The equation of a line can be written as 'y=mx+b', where 'm' is the slope, 'b' is a number, and 'x' and 'y' represent the 'x' and 'y' co-ordinates of any point on the line.
To find the slope m, take two points (x₁,y₁) and (x₂,y₂) and use the formula
m= (y₂-y₁)/(x₂-x₁)
Our points are (1,3) and (2,6):
(6-3)/(2-1)=3/1=3
Now that we have found the slope, we can write the equation as
y=3x+b
To find b, sub in a point:
9=3(3)+b
9=9+b
b=0
So our equation is y=3x
Expanded FormFind the Expanded Forms of:
Answer:
Standard Form:
7.362
Expanded forms can be written
like a sentence or stacked for
readability as they are here.
Expanded Numbers Form:
7 + 0.3+ 0.06+ 0.002
Expanded Factors Form:
7 ×1 +3 × 0.1+6 × 0.01+2 × 0.001
Expanded Exponential Form:
7 × 100+3 × 10-1+6 × 10-2+2 × 10-3
Word Form:
seven and
three hundred sixty-two thousandths
Answer:
15 oz/ 1 lb
Step-by-step explanation:
