Determine if the triangle given is right, acute, or obtuse.

How many points do the graphs of the equations 6x - 3y = 7 and 12x - 6y = 14 have in common?

murzikaleks [220]

ALL of their points are common. If you multiply each side of the first equation by 2, you'll see that they're both the same line.

7 0

3 years ago

What is the sum of a 12-term arithmetic sequence where the last term is 13 and the common difference is -10?

Y_Kistochka [10]

$\bf n^{th}\textit{ term of an arithmetic sequence}\\\\
a_n=a_1+(n-1)d\qquad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
d=\textit{common difference}\\
----------\\
n=12\\
d=-10\\
a_{12}=13
\end{cases}
\\\\\\
a_{12}=a_1+(12-1)d\implies 13=a_1+(12-1)(-10)
\\\\\\
13=a_1-110\implies \boxed{123=a_1}$

$\bf \\\\
-------------------------------\\\\
\textit{sum of a finite arithmetic sequence}\\\\
S_n=\cfrac{n}{2}(a_1+a_n)\qquad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
a_n=\textit{value of the }n^{th}\ term\\
------------\\
n=12\\
a_1=123\\
a_{12}=13
\end{cases}
\\\\\\
S_{12}=\cfrac{12}{2}(a_1+a_{12})\implies S_{12}=\cfrac{12}{2}(123+13)$

and surely you know how much that is.

6 0

3 years ago

Without exponents logc (xy^6z^-4) what is the equivalent expression

Sever21 [200]

By eliminating exponents, the logarithmic expression $\log_{c} x\cdot y^{6}\cdot z^{-4}$ is equivalent to the logarithmic expression $\log_{c} x + 6\cdot \log_{c} y - 4\cdot \log_{c} z$ .

<h3>How to simplify logarithmic functions</h3>

In this problem we are supposed to eliminate all exponents of a logarithmic function by applying any of the following properties:

㏒ x · y = ㏒ x + ㏒ y
㏒ x/y = ㏒ x - ㏒ y
㏒ yˣ = x · ㏒ y

Now, we proceed to simplify the function:

$\log_{c} x\cdot y^{6}\cdot z^{-4}$

$\log_{c} x + \log_{c} y^{6} + \log_{c} z^{-4}$

$\log_{c} x + 6\cdot \log_{c} y - 4\cdot \log_{c} z$

By eliminating exponents, the logarithmic expression $\log_{c} x\cdot y^{6}\cdot z^{-4}$ is equivalent to the logarithmic expression $\log_{c} x + 6\cdot \log_{c} y - 4\cdot \log_{c} z$ .

To learn more on logarithms: brainly.com/question/24211708

#SPJ1

5 0

2 years ago

1178 × 125 = show work

zlopas [31]

1178x100=117800

1178x20=23560

1178x5=5890

117800+23560+5890=147250

7 0

3 years ago

Read 2 more answers

Anitra has 12 hair ribbons. One fourth of the ribbons are pink. Three are purple, and the rest are red. What fraction of Anitra'

Hatshy [7]