—4 and 4 are ____________ because they have the same absolute value but different signs.

Mathematics

1 answer:

sergij07 [2.7K]3 years ago

3 0

Opposites. Their sum is zero so they are called opposites.

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Consider lines An and CD

vichka [17]

Answer:

slope of AB = 2

slope CD = 2

Step-by-step explanation:

the equation of a line is y = ax+ b where a is the slope, b is the y-intercept

let us take yB - yA

→ yB - yA = axB <u>+ b</u> - axA <u>- b</u>

→ yB - yA = a(xB - xA)

→ a = (yB - yA) / (xB = xA) = (6 - 2) / (-5 - (-7)) = 2

same goes for line CD

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3 years ago

What is the first term in a geometric sequence if the common ratio is − 2 and the sum of the first six terms is −105?

Serggg [28]

$\bf \qquad \qquad \textit{sum of a finite geometric sequence}
\\\\
S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
r=\textit{common ratio}\\
----------\\
r=-2\\
n=6\\
S_6=-105
\end{cases}$

$\bf -105=a_1\left( \cfrac{1-(-2)^6}{1-(-2)} \right)\implies -105=a_1\left( \cfrac{1-(64)}{1+2} \right)
\\\\\\
-105=a_1\left( \cfrac{-63}{3} \right)\implies -105=a_1(-21)
\\\\\\
\cfrac{-105}{-21}=a_1\implies 5=a_1$

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3 years ago

Please help guys

Andrej [43]

X = 35, because the angles on top and bottom are equal, so its 60 - 25=35

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4 years ago

Evaluate f(-2) if f(x)=-3x^2-1

Pani-rosa [81]

f(x)=-3x^2-1

f(-2)= -3(-2)²-1=-3·4-1= - 13

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