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3 years ago

6

What is the point-slope form of a line with slope 3 that contains the point (2,1)?

1 answer:

Serjik [45]3 years ago

8 0

Answer:

A) $y-1=3(x-2)$

Step-by-step explanation:

Point-slope formula.

$y-y_1=m(x-x_1)$

Given.

Slope (m) = 3

Points (x, y) = (2, 1)

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Match each series with the equivalent series written in sigma notation

PIT_PIT [208]

Answer:

$3 + 12 + 48 + 192 + 768 = \sum\limits^4_{n=0} 3 * 4^n$

$4 + 32 + 256 + 2048 + 16384 = \sum\limits^4_{n=0} 4 * 8^n$

$2 + 6 + 18 + 54 + 162 = \sum\limits^4_{n=0} 2* 3^n$

$3 + 15 + 75 + 375 + 1875 = \sum\limits^4_{n=0} 3* 5^n$

Step-by-step explanation:

Given

See attachment for complete question

Required

Match equivalent expressions

Solving (a):

$3 + 12 + 48 + 192 + 768$

The expression can be written as:

$3 \to 3*4^{0$ --- 0

$12 \to 3 * 4^{1$ ---- 1

$48 \to 3 * 4^{2$ --- 2

$192 \to 3 * 4^{3$ ---- 3

$768 \to 3 * 4^{4$ ---- 4

For the nth term, the expression is:

$Term = 3 * 4^{n$ ---- n

So, the summation is:

$3 + 12 + 48 + 192 + 768 = \sum\limits^4_{n=0} 3 * 4^n$

Solving (b):

$4 + 32 + 256 + 2048 + 16384$

The expression can be written as:

$4 \to 4 * 8^0$ --- 0

$32 \to 4 * 8^1$ ---- 1

$256 \to 4 * 8^2$ --- 2

$2048 \to 4 * 8^3$ ---- 3

$16384 \to 4 * 8^4$ ---- 4

For the nth term, the expression is:

$Term \to 4 * 8^n$ ---- n

So, the summation is:

$4 + 32 + 256 + 2048 + 16384 = \sum\limits^4_{n=0} 4 * 8^n$

Solving (c):

$2 + 6 + 18 + 54 + 162$

The expression can be written as:

$2 \to 2 * 3^0$ --- 0

$6 \to 2 * 3^1$ ---- 1

$18 \to 2 * 3^2$ --- 2

$54 \to 2 * 3^3$ ---- 3

$162 \to 2 * 3^4$ ---- 4

For the nth term, the expression is:

$Term \to 2 * 3^n$ ---- n

So, the summation is:

$2 + 6 + 18 + 54 + 162 = \sum\limits^4_{n=0} 2* 3^n$

Solving (d):

$3 + 15 + 75 + 375 + 1875$

The expression can be written as:

$3 \to 3 * 5^0$ --- 0

$15 \to 3 * 5^1$ ---- 1

$75 \to 3 * 5^2$ --- 2

$375 \to 3 * 5^3$ ---- 3

$1875 \to 3 * 5^4$ ---- 4

For the nth term, the expression is:

$Term \to 3 * 5^n$ ---- n

So, the summation is:

$3 + 15 + 75 + 375 + 1875 = \sum\limits^4_{n=0} 3* 5^n$

5 0

3 years ago

What is the median of 36,14,21,39,11,2

Usimov [2.4K]

Answer: 30

Step-by-step explanation:

21+39/2

=30

4 0

3 years ago

Read 2 more answers

valkas [14]

Answer:

A

Step-by-step explanation:

=16x²-25

=(4x)²-(5)²

Using formula a²-b²=(a+b)(a-b)

=(4x+5)(4x-5)

6 0

3 years ago

Which function represents a quantity growing exponentially?

Lelechka [254]

Answer: c

Step-by-step explanation:

4 0

3 years ago

HEEEEEELPPPPPPPPPPPPPPPPPP PLSSSSSSSSSSSSSSSSSSSSS

Elza [17]

Answer:

g(n) = 18 - 4n

Step-by-step explanation:

Given the recursive formula

g(n) = g(n - 1) - 4 with common difference d = - 4 and g(1) = 14

The explicit formula for an arithmetic sequence is

g(n) = g(1) + (n - 1)d , then

g(n) = 14 - 4(n - 1)

= 14 - 4n + 4

= 18 - 4n

5 0

3 years ago