Answer:
= 8n - 11
Step-by-step explanation:
There is a common difference between consecutive terms in the sequence, that is
5 - (- 3) = 13 - 5 = 21 - 13 = 8
This indicates the sequence is arithmetic with n th term
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = - 3 and d = 8 , thus
= - 3 + 8(n - 1) = - 3 + 8n - 8 = 8n - 11 ← note this is the second option, that is
f(n) = - 3 + 8(n - 1)
Answer: 91. I find the easiest method for questions like this about ratios is to multiply the side of the ratio you are given a value for, in this case the right hand side (children), by a number so it equals the value given. This was 2x13 to equal 26. Then, to find the value of the other side, the adults, you must multiply the left hand side by the same number used on the right hand side. 7x13 equals 91.
distance = 500 feet
Since Δ VWX and Δ YZX are similar then the ratios of corresponding sides are equal, that is
=
= 
completing the required values gives
=
( cross- multiply )
60l = 30 × 100 = 3000 ( divide both sides by 60 )
l = 500
distance across the swamp is 500 feet
Answer:
Jake has <em>$11.29 </em>dollars left.
Step-by-step explanation:
To find the answer, we will add up<em> $5 + $6.50 + $7.21</em> and we get<em> $18.71</em>. Now <em>subtract $30 from 18.71</em>, which is <em>$11.29</em>. Therefore, <em>Jake has $11.29 dollars left.</em>
Answer:
cos(x) = square root 2 over 2; tan(x) = 1
Step-by-step explanation:

was, before it was rationalized,

Therefore,

The side opposite the reference angle measures 1, the hypotenuse measures square root 2. That makes the reference angle a 45 degree angle. From there we can determine that the side adjacent to the reference angle also has a measure of 1. Therefore,
and
since tangent is side opposite (1) over side adjacent (1),
tan(x) = 1