The rule of a function is:
You CANNOT have one x-value with multiple different y values in the same function. You can however have different x values with the same y value.
Also for reference: independent means x value and dependent means y- value.
The first answer is not a function because as you can see there is one x-value with multiple y values.
second answer IS a function because as I said before you can have different x values with the same y value
third answer is a function again because you can have different x values with same y value
number four isn't a function bc again the -2 x value has 2 different y Values.
Answer: Because the graphs of the two equations overlap each other
Step-by-step explanation:
Every point on the first line also satisfies the second equation.
This is the same as equivalent fractions
where 1/2 = 2/4 = 3/6 = 4/8
Graphing these on a number line would only show one dot.
Answer:
13 cm × 12 cm
Step-by-step explanation:
The diagonal of the top or bottom faces of the box is the hypotenuse of a triangle with legs 12 cm and 5 cm. The Pythagorean theorem tells you that diagonal length is ...
d = √(12² +5²) = √(144 +25) = √169 = 13 . . . cm
The width of the divider is 13 cm.
The height of the divider is shown as 12 cm.
The dimensions of the dividing rectangle are 13 cm by 12 cm.
Answer:
its C
Step-by-step explanation:
f(x) = |(-5)+1|
f(x)=|4|
absolute value of 4 is 4
Step-by-step explanation:
(a) Fₙ₋₁ > 0, so Fₙ₊₁ > Fₙ. Each term is bigger than the one before it, so the function is increasing, meaning the series will diverge to infinity.
(b) Fₙ₊₁ / Fₙ = (Fₙ + Fₙ₋₁) / Fₙ
Divide.
Fₙ₊₁ / Fₙ = 1 + (Fₙ₋₁ / Fₙ)
Rewrite the second fraction using negative exponent.
Fₙ₊₁ / Fₙ = 1 + (Fₙ / Fₙ₋₁)⁻¹
Take the limit of both sides as n approaches infinity.
lim(n→∞) Fₙ₊₁ / Fₙ = 1 + lim(n→∞) (Fₙ / Fₙ₋₁)⁻¹
Substitute with φ.
φ = 1 + φ⁻¹
Solve.
φ² = φ + 1
φ² − φ − 1 = 0
φ = [ -(-1) ± √((-1)² − 4(1)(-1)) ] / 2(1)
φ = (1 ± √5) / 2
Since the ratio can't be negative:
φ = (1 + √5) / 2
