A system of equations with infinitely many solutions is a system where the two equations are identical. The lines coincide. Anything that is equal to
will work. You could try multiply the entire equation by some number, or moving terms around, or adding terms to both sides, or any combination of operations that you apply to the entire equation.
You could multiply the whole thing by 4.5 to get
. If you want, you could mix things up and write it in slope-intercept form:
. The point is, anything that is equivalent to the original equation will give infinitely many solutions x and y. You can test this by plugging in values x and y and seeing the answers!
The attached graph shows that four different equations are really the same.
There should be 1,400 pages in an order that costs the same for both companies.
Let x be the unknown number of pages.
1st Company = 42 + 0.05x
2nd Company = 0.08x
0.08x = 42 + 0.05x
0.08x - 0.05x = 42
0.03x = 42
0.03x / 0.03 = 42 / 0.03
x = 1400 pages
To check
0.08x = 42 + 0.05x
0.08 (1400) = 42 + (0.05 * 1400)
112 = 42 + 70
112 = 112
Lucia can make 8 invisibility potions total!
she has 16 newt eyes overall and only two are required for one option
sooo
she can make 8 potions.
hope this helps!
Answer:
y - 5 = 2(x + 2)
General Formulas and Concepts:
Point-Slope Form: y - y₁ = m(x - x₁)
x₁ - x coordinate
y₁ - y coordinate
m - slope
Step-by-step explanation:
<u>Step 1: Define</u>
Slope <em>m</em> = 2
Point (-2, 5)
<u>Step 2: Create equation</u>
y - 5 = 2(x + 2)
Answer:
a=21.1
Step-by-step explanation:
You can use the given (incorrect) equation and fill in the value of t to find h:
h = 12.5 +9sin(750(3.5)) = 3.68 . . . . feet
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Or, you can use the correct equation, or just your knowledge of revolutions:
h = 12.5 +9sin(750(2π·3.5)) = 12.5 . . . . feet
in 3.5 minutes at 750 revolutions per minute, the propeller makes 2625 full revolutions, so is back where it started — at 12.5 feet above the ground.
