Answer:

Step-by-step explanation:
You know how subtraction is the <em>opposite of addition </em>and division is the <em>opposite of multiplication</em>? A logarithm is the <em>opposite of an exponent</em>. You know how you can rewrite the equation 3 + 2 = 5 as 5 - 3 = 2, or the equation 3 × 2 = 6 as 6 ÷ 3 = 2? This is really useful when one of those numbers on the left is unknown. 3 + _ = 8 can be rewritten as 8 - 3 = _, 4 × _ = 12 can be rewritten as 12 ÷ 4 = _. We get all our knowns on one side and our unknown by itself on the other, and the rest is computation.
We know that
; as a logarithm, the <em>exponent</em> gets moved to its own side of the equation, and we write the equation like this:
, which you read as "the logarithm base 3 of 9 is 2." You could also read it as "the power you need to raise 3 to to get 9 is 2."
One historical quirk: because we use the decimal system, it's assumed that an expression like
uses <em>base 10</em>, and you'd interpret it as "What power do I raise 10 to to get 1000?"
The expression
means "the power you need to raise 10 to to get 100 is x," or, rearranging: "10 to the x is equal to 100," which in symbols is
.
(If we wanted to, we could also solve this:
, so
)
B
given f(x) in factored form, equate to zero for x-intercepts
(x - 8)(x - 4) = 0, hence
x = 4, x = 8 ← x- intercepts
The vertex lies on the axis of symmetry which is situated at the midpoint of the x- intercepts
x- coordinate of vertex =
= 6
f(6) = (6 - 8 )(6 - 4 ) = -2 × 2 = - 4 ← y-coordinate
vertex = (6, - 4 ) → B
1/2 + 1/2 + 2/3 + 3/4 + 47/48 + 48/49 +49/50 = 5.35542517007
This decimal form is ≈ to 5 2/5
Answer:
the answer should be x= -7 hope this helps!
Answer:
a = √11 and b = 6
Step-by-step explanation:
Refer to attached picture for reference
for an right triangle with angle θ
we are given
cos θ = 5/6 = length of adjacent side / length of hypotenuse
hence
adjacent length = 5 units
hypotenuse length = 6 units
the missing side is the "opposite" length which we can find with the Pythagorean equation. in our case:
hypotenuse ² = adjacent ² + opposite² (rearrange)
opposite ² = hypotenuse ² - adjacent ²
opposite ² = 6² - 5²
opposite = √ (6²-5²) = √11
sin θ = opposite length / hypotenuse (substitute values above)
sin θ = √11 / 6
hence a = √11 and b = 6