the area of a rectangular patio is 5 5/8 square yards it's length is 1 and 1/2 yards what is the patios with in yards answering

Mathematics

1 answer:

jeyben [28]3 years ago

7 0

Answer:

the width is 3.75

Step-by-step explanation:

you divide 5 5/8 by 1 1/2

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How many terms are there in a geometric series if the first term is 4, the common ration is 3 and the sum of the series is 160

Marina CMI [18]

$\bf \qquad \qquad \textit{sum of a finite geometric sequence}
\\\\
S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
r=\textit{common ratio}\\
----------\\
a_1=4\\
r=3\\
S_n=160
\end{cases}$

$\bf 160=4\left( \cfrac{1-3^n}{1-3} \right)\implies 160=4\left( \cfrac{1-3^n}{-2} \right)\implies 160=-2(1-3^n)
\\\\\\
160=2(3^n-1)\implies \cfrac{160}{2}=3^n-1\implies 80=3^n-1
\\\\\\
81=3^n~~
\begin{cases}
81=3\cdot 3\cdot 3\cdot 3\\
\qquad 3^4
\end{cases}\implies 3^4=3^n\implies 4=n$

3 0

3 years ago

This is a 30-60-90 triangle. a What is the measure of x? Х 43 X= = [ ?

kherson [118]

Answer:

See below:

Step-by-step explanation:

Hello! I hope you are having a nice day!

We can solve this problem in two steps; solving and theory.

I'll go and start off with the theory part!

Theory

We know that in geometry there are many types of triangles that have various different angles. With that, there are a few special triangles that people have made formulas for, one being a 30, 60, and 90 degree triangle.

The theorem states that the hypotenuse is $2x$ , the side opposite to 60 degrees is $x\sqrt{3}$ , and the bottom is $x$ .

Solving

We can solve this problem in a step, we just need to know what the theorem said and implement it here, since we know the values of the sides of the triangle, we can solve it by finding out the opposite side and applying the theorem rules.

If we look at the graph, we can see that the $x$ part of the side opp. of 60 degrees is 4, that means that $x$ would be double of 4, which is 8.

Therefore your answer would be: $x=8$