If y varies directly with x, that means they change at proportion rates. We can define their relationship using a constant k.
y = kx
Plug in what we know to find k.
-3 = 5k
k = -3/5
So:
y = -1 * (-3/5)
y = 3/5
9514 1404 393
Answer:
- The graph has an open circle at 7.
- The arrow points left.
Step-by-step explanation:
Adding 10 and dividing by 4, we have ...
4x < 28
x < 7
The comparison does not include the "equal to" case, so the circle at x=7 is open. Values of x less than 7 are in the solution set. Those values are found to the left of 7 on the number line.
- The graph has an open circle at 7.
- The arrow points left.
Answer:
Solution
p = {-3, 1}
Step-by-step explanation:
Simplifying
p2 + 2p + -3 = 0
Reorder the terms:
-3 + 2p + p2 = 0
Solving
-3 + 2p + p2 = 0
Solving for variable 'p'.
Factor a trinomial.
(-3 + -1p)(1 + -1p) = 0
Subproblem 1
Set the factor '(-3 + -1p)' equal to zero and attempt to solve:
Simplifying
-3 + -1p = 0
Solving
-3 + -1p = 0
Move all terms containing p to the left, all other terms to the right.
Add '3' to each side of the equation.
-3 + 3 + -1p = 0 + 3
Combine like terms: -3 + 3 = 0
0 + -1p = 0 + 3
-1p = 0 + 3
Combine like terms: 0 + 3 = 3
-1p = 3
Divide each side by '-1'.
p = -3
Simplifying
p = -3
Subproblem 2
Set the factor '(1 + -1p)' equal to zero and attempt to solve:
Simplifying
1 + -1p = 0
Solving
1 + -1p = 0
Move all terms containing p to the left, all other terms to the right.
Add '-1' to each side of the equation.
1 + -1 + -1p = 0 + -1
Combine like terms: 1 + -1 = 0
0 + -1p = 0 + -1
-1p = 0 + -1
Combine like terms: 0 + -1 = -1
-1p = -1
Divide each side by '-1'.
p = 1
Simplifying
p = 1
Solution
p = {-3, 1}
Answer:
In 3 hours Henry can write 5 pages. So, In 1 hour Henry can write pages. Now, In 8 hours Henry can write pages. In 8 hours Henry can write 13.3 pages.
Step-by-step explanation:
Subtract 2/3 from 4 and 1/2
first turn 4 and 1/2 into a fraction
2/2 = 1 so 4 = 8/2 + 1/2 = 9/2
now you have 9/2-2/3
now find lowest common denominator ( 2*3 =6)
9/2 becomes 27/6
2/3 becomes 4/6
now you have 27/6 - 4/6 = 23/6
6/6 = 1
6*3=18, 23-18 = 5
so she needs 3 and 5/6 yards of fabric
