Answer:
Option C. 3√3
Step-by-step explanation:
Please see attached photo for brief explanation.
In the attached photo, we obtained the following:
Opposite = a
Adjacent = 3
Hypothenus = 6
Angle θ = 60°
We can obtain the value of 'a' as follow:
Tan θ = Opposite /Adjacent
Tan 60° = a/3
Cross multiply
a = 3 x Tan 60°
But: Tan 60° = √3
a = 3 x Tan 60°
a = 3 x √3
a = 3√3
Therefore, the length of the altitude of the equilateral triangle is 3√3.
Answer:
see explanation
Step-by-step explanation:
The equation of a parabola in vertex form is
y = (x - h)² + k (h, k) are the coordinates of the vertex
Given y = x² + 7x - 5
To express in vertex form use the method of completing the square
add/subtract ( half the coefficient of the x- term )²
y = x² + 2(
)x +
-
- 5
y = (x +
)² -
- 
y = (x +
)² - 
Hence
a =
and b = - 
Convert to an equation:
50^2=2+25^2=2*5=10
Simplify:
2500=625=10=10
What is wrong is that 2500 does not equal 625 which does not equal 10.
Answer:
Recursive:

Explicit:

And the 20th term is 225.
Step-by-step explanation:
We have the sequence:
35, 45, 55, 65.
Notice that each subsequent term is 10 more than the previous term.
Therefore, our common difference is (+)10.
Recursive Rule:
The standard format for the recursive rule is:

Where a is the initial term and d is the common difference.
From our sequence, we know that a the initial term is 35.
And as determined, our common difference d is 10.
Substitute. Hence, our recursive rule is:

Explicit Rule:
The standard format for the explicit rule is:

Where a is the initial term and d is the common difference. So, let’s substitute 35 for a and 10 for d. Hence, our explicit formula is:

Now, let’s find the 20th term. We will utilize the explicit rule since the recursive rule can get tedious. Substitute 20 for n because we would like to 20th term. Thus:

Evaluate:

Hence, the 20th term is 225.
Answer:
2:1
Step-by-step explanation:
well we show ratio by the sign ' : '
ratio of iced tea to lemonade= 12:6
now we reduce it to minimum by dividing it with same number.
12 is divisible by 6
so,
the reduced form is = 2:1
therefore,
ratio of the number of students who want iced tea to the number of students who want lemonade = 2:1.