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3 years ago

What is an equation of the line that passes through the points (1,-7) and (-4,8)

Mathematics

1 answer:

Nonamiya [84]3 years ago

4 0

Equation of the line is 3x + y + 4 = 0

Step-by-step explanation:

Step 1: Given points are (1, -7) and (-4,8)

⇒ x1 = 1, x2 = -4, y1 = -7, y2 = 8

Step 2: Form equation for the line using (y-y1) = m(x-x1). Find slope m.

⇒ m = (y2 - y1)/(x2-x1) = (8 - -7)/(-4 - 1) = 15/-5 = -3

Step 3: Substitute the values and form the equation.

⇒ y - -7 = -3(x - 1)

⇒ y + 7 = -3x + 3

⇒ 3x + y + 4 = 0

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3 years ago

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2 years ago

What is the 6th term of the geometric sequence where a1 = -4096 and a4 = 64?

Akimi4 [234]

$\bf \begin{array}{llccll}
term&value\\
\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\
a_1&-4096\\
a_2&-4096r\\
a_3&-4096rr\\
a_4&-4096rrr\\
&-4096r^3\\
&64
\end{array}\implies -4096r^3=64
\\\\\\
r^3=\cfrac{64}{-4096}\implies r^3=-\cfrac{1}{64}\implies r=\sqrt[3]{-\cfrac{1}{64}}
\\\\\\
r=\cfrac{\sqrt[3]{-1}}{\sqrt[3]{64}}\implies \boxed{r=\cfrac{-1}{4}}\\\\
-------------------------------$

$\bf n^{th}\textit{ term of a geometric sequence}\\\\
a_n=a_1\cdot r^{n-1}\qquad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
r=\textit{common ratio}\\
----------\\
r=-\frac{1}{4}\\
a_1=-4096\\
n=6
\end{cases}
\\\\\\
a_6=-4096\left( -\frac{1}{4} \right)^{6-1}\implies a_6=-4^6\left( -\frac{1}{4} \right)^5$

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3 years ago

Read 2 more answers

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NikAS [45]

Your round it to 300 so the answer is 300

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4 years ago

I’ll give points + brainalist for answer / explanation

Fynjy0 [20]

Answer:

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Step-by-step explanation:

The perimeter of a square is the length of the outside, which is found by adding all the side lengths. The circumference of a circle is similar because it is also the length of the outside of the shape.

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