Two squares is sometimes similar.
A square can be any size, as long as all four of it's sides are equal.
A square would be a rectangle if two of the sides were different than the rest.
A square would be a trapezoid if only one of it's sides were different.
For a square to be always similar, the ratio of it's sides must be equal to the ratio of the second square.
For example:
All of a square's sides are 5 across.
In order for another square to be ALWAYS similar, it's sides must be a multiple of (The length of the original square's sides) 5 (10,15,20,25,30...)
This is called a ratio. (5/10 = 1/2, 5/15 = 1/3, 5/20 = 1/4 etc...)
Answer:
81
Step-by-step explanation:
The formula for calculating the sum of geometric series varies depending on the value of its common ratio.
Given the common ratio to be 2/3 which is less than 1, the formula to be used is given as;
Sn = a(1-rⁿ)/1-r
n is the number of terms of the series
a is the first term
r is the common ratio.
Sn is the sum of the series
Given n = 3, r = 2/3 and Sn = 171,
a= ?
Substituting this values in the formula we have;
171 = a{1-(2/3)³}/1-2/3
171 = a{1-8/27}/(1/3)
171 = a(19/27)/(1/3)
171 = 19a/27 × 3/1
171 = 57a/27
57a = 171×27
57a = 4,617
a = 4,617/57
a = 81
The first term of the series is 81
Answer:
x>-1
Step-by-step explanation:
We will assume that here the question prompt us to solve the Inequality given and find the value of x for which is true and valid.
To begin with, let us re write our inequality clear as:
Eqn(1).
Now, since this is an Inequality it must be noted that <em><u>for any operation of multiplication/devision</u></em> with a<u> </u><u><em>Negative number</em></u>, the order of the Inequality will change from ≤ to ≥ and vice versa.
So having said that, let us solve Eqn(1) and obtain a value for
as follow:
Remove Negative sign from both signs and change order of inequality from < to >.
Factor Out Bracket on Left Hand Side
Make Common Denominator on Both Sides
Eliminate denominator to simplify and remove fractions
Gather equal terms on each side
Simplify
Solve for 
<em>Thus solving the inequality gives that x is greater than -1:</em>
<em> i.e. </em>
Hi there! The answer is x = 8.

Let's solve this equation step by step!
First we use the following rule.

which basically means that an exponential equation with the same base on both sides of the equation must also have the same exponents.
We get the following.

Now we use the following rule for logarithms.

When we apply this rule in our eqiation, we end up with the following.

Now we only need to do some basic math, work out the exponents first.

Subtract 8.

~ Hope this helps you!
9514 1404 393
Answer:
p(x) = 3(x -2)^4(x +2) . . . in factored form
p(x) = 3x^5 -18x^4 +24x^3 +48x^2 -144x +96 . . . in standard form
Step-by-step explanation:
When a polynomial has a zero at x=p, it has a factor of (x -p). The exponent of the factor is the multiplicity of the zero. The product of factors can be multiplied by 3 to make the leading coefficient be 3.
p(x) = 3(x -2)^4(x -(-2))
= 3(x^4 +4(-2)x^3 +6(-2)^2x^2 +4(-2)^3x +(-2)^4)·(x +2)
= 3(x^4 -8x^3 +24x^2 -32x +16)(x +2)
= 3(x^5 -6x^4 +8x^3 +16x^2 -48x +32)
p(x) = 3x^5 -18x^4 +24x^3 +48x^2 -144x +96