Answer:
4033
Step-by-step explanation:
An easy way to solve this problem is to notice the numerator, 2017^4-2016^4 resembles the special product a^2 - b^2. In this case, 2017^4 is a^2 and 2016^4 is b^2. We can set up equations to solve for a and b:
a^2 = 2017^4
a = 2017^2
b^2 = 2016^4
b = 2016^2
Now, the special product a^2 - b^2 factors to (a + b)(a - b), so we can substitute that for the numerator:
<h3>
</h3>
We can notice that both the numerator and denominator contain 2017^2 + 2016^2, so we can divide by 
which is just one, and will simplify the fraction to just:
2017^2 - 2016^2
This again is just the special product a^2 - b^2, but in this case a is 2017 and b is 2016. Using this we can factor it:
(2017 + 2016)(2017 - 2016)
And, without using a calculator, this is easy to simplify:
(4033)(1)
4033
Answer:
The annual growth rate between 1985 and 2005 is 0.95%
The value of the house in the year 2010 is $152,018
Step-by-step explanation:
Let the annual growth rate = r
Value of the house in year 1985 = $120,000
Value of the house in year 2005 = $145,000
Time (t) = 2005 - 1985
= 20 years
A = P (1 + r)^t
145000 = 120000 (1 + r) ^20
(1 +r)^20 = 145000 / 120000
(1 +r)^20= 1.2083
(1 +r)^20= (1.2083)^1/20
(1 +r)^20= 1.0095
r = 1.0095 - 1
r = 0.0095
r% = 0.0095 x 100
= 0.95%
Value of the house in year 2010
=145000(1 + r)^5
=145000 (1 + 0.0095)^5
= 145000 x 1.0484
=$152,018
Answer:
Step-by-step explanation:
<u>Solve left to right →:</u>
- 10 - 19 + 5
- = (10 - 19) + 5
- = -9 + 5
- = -4.
Nothing else to say.
<h2>
Your answer is -4.</h2>
For this case we have to define root properties:
![\sqrt [n] {a ^ n} = a ^ {\frac {n} {n}} = a](https://tex.z-dn.net/?f=%5Csqrt%20%5Bn%5D%20%7Ba%20%5E%20n%7D%20%3D%20a%20%5E%20%7B%5Cfrac%20%7Bn%7D%20%7Bn%7D%7D%20%3D%20a)
In addition, we know that:
On the other hand:
Thus, we can rewrite the given expression as:
ANswer:
Option B
<h2>
Explanation:</h2>
In every rectangle, the two diagonals have the same length. If a quadrilateral's diagonals have the same length, that doesn't mean it has to be a rectangle, but if a parallelogram's diagonals have the same length, then it's definitely a rectangle.
So first of all, let's prove this is a parallelogram. The basic definition of a parallelogram is that it is a quadrilateral where both pairs of opposite sides are parallel.
So let's name the vertices as:
First pair of opposite sides:
<u>Slope:</u>
Second pair of opposite sides:
<u>Slope:</u>
So in fact this is a parallelogram. The other thing we need to prove is that the diagonals measure the same. Using distance formula:
So the diagonals measure the same, therefore this is a rectangle.
