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3 years ago

9

What is the first term for an arithmetic sequence with a12 = 56 and a21=101?

1 answer:

Alenkinab [10]3 years ago

4 0

The first term is -43.

Explanation:

an = a + (n - 1)d

a12 = a + 11d = 56, first equation
a21 = a + 20d = 101, second equation

Subtract the second equation from the first equation, cancelling +a and -a
11d - 20d = 56 - 101
-9d = -45
d = 5

Subtitute d into the first equation
a + 99 = 56
a = -43

a refers to the first term, hence the first term is -43.

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Read 2 more answers

Find an equation of the line. Write the equation using function notation.

Gemiola [76]

The equation of line perpendicular to 4y = x-8 passing through (3,-3) is:

$y = -4x+9$

Step-by-step explanation:

Given equation of line is:

$4y=x-8$

We have to convert the given line in slope-intercept form to find the slope of the line

So,

Dividing both sides by 4

$\frac{4y}{4} =\frac{x-8}{4}\\y = \frac{1}{4}x-\frac{8}{4}\\y = \frac{1}{4}x-2$

Let m1 be the slope of given line

Then

$m_1 = \frac{1}{4}\\$

Let m2 be the slope of line perpendicular to given line

As we know that produt of slopes of two perpendicular lines is -1

$m_1.m_2 = -1\\\frac{1}{4} . m_2 = -1\\m_2 = -1*4\\m_2 = -4$

The slope intercept form of line is given by:

$y = m_2x+b$

Putting the value of slope

$y = -4x+b$

to find the value of b, putting (3,-3) in equation

$-3 = (-4)(3) + b\\-3 = -12 +b\\b = -3+12\\b = 9$

Putting the value of b in the equation

$y = -4x+9$

Hence,

The equation of line perpendicular to 4y = x-8 passing through (3,-3) is:

$y = -4x+9$

Keywords: Equation of line, slope

Learn more about equation of line at:

#LearnwithBrainly

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3 years ago

Ryan collects rainwater in a barrel for his garden. The barrel is filled with 12 gallons of water. Ryan used 7.4 gallons to wate

alekssr [168]

Answer:

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