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3 years ago

Find the common ratio of the geometric sequence: 4,3,9/4

Mathematics

1 answer:

Inessa05 [86]3 years ago

4 0

Answer:

The common ratio is

$\frac{3}{4}$

Step-by-step explanation:

To find the common ratio in a geometric sequence divide the next term by the previous term

That's

The first term is 3 and the next term is 4

so the common ratio will be

Hope this helps you.

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Write an equation in standard form for the line that passes through the point (2,-3) and is perpendicular to the line y + 4 = -2

sineoko [7]

For this case we have that by definition, the standard form of a linear equation is given by:

$ax + by = c$

By definition, if two lines are perpendicular then the product of their slopes is -1. That is to say:

$m_ {1} * m_ {2} = - 1$

We have the following point-slope equation of a line:

$y+4 = -\frac {2} {3}(x-12)$

The slope is:

$m_ {1} = - \frac {2} {3}$

We find the slope $m_ {2}$ of a perpendicular line:

$m_ {2} = \frac {-1}{m_ {1}}\\m_ {2} = \frac {-1} {-\frac {2} {3}}\\m_ {2} = \frac{3} {2}$

Thus, the equation is of the form:

$y-y_ {0} = \frac {3} {2} (x-x_ {0})$

We have the point through which the line passes:

$(x_ {0}, y_ {0}) :( 2, -3)$

Thus, the equation is:

$y - (- 3) = \frac {3} {2} (x-2)\\y + 3 = \frac {3} {2} (x-2)$

We manipulate algebraically:

$y + 3 = \frac{3} {2} x- \frac {3} {2} (2)\\y + 3 = \frac{3} {2} x-3$

We add 3 to both sides of the equation:

$y + 3 + 3 = \frac {3} {2} x\\y + 6 = \frac {3} {2} x$

We multiply by 2 on both sides of the equation:

$2(y + 6) = 3x\\2y + 12 = 3x$

We subtract 3x on both sides:

$2y-3x + 12 = 0$

We subtract 12 from both sides:

$2y-3x = -12$

ANswer:

$-3x + 2y = -12$

5 0

2 years ago

Factor 3/4 out of 3/4z + 6

Alenkasestr [34]

ANSWER

$\frac{3}{4} z + 6 = \frac{3}{4} (z + 8 )$

EXPLANATION

We want to factor
$\frac{3}{4}$
out of

$\frac{3}{4} z + 6$

The first term is already having a factor of
$\frac{3}{4}$
The constant term which is the second term is not having a factor of
$\frac{3}{4}$
so we need to use a trick of multiplying and dividing by the same factor to obtain,

$\frac{3}{4} z + 6 = \frac{3}{4} z + \frac{3}{4} \times \frac{6}{ \frac{3}{4} }$

We can now factor
$\frac{3}{4}$
out of the right hand side to obtain,

$\frac{3}{4} z + 6 = \frac{3}{4} (z + \frac{6}{ \frac{3}{4} } )$
Let us rewrite the right most fraction using the normal division symbol.

$\frac{3}{4} z + 6 = \frac{3}{4} (z + 6 \div \frac{3}{4} )$

We simplify to obtain,

$\frac{3}{4} z + 6 = \frac{3}{4} (z + 6 \times \frac{4}{3} )$

This further gives us,

$\frac{3}{4} z + 6 = \frac{3}{4} (z + 2 \times 4 )$

$\frac{3}{4} z + 6 = \frac{3}{4} (z + 8 )$

5 0

3 years ago

Read 2 more answers

Suppose y = 2x + 1 , where x and y are functions of t. (a) if dx/dt = 3, find dy/dt when x = 4. dy dt = (b) if dy/dt = 2, find d

qwelly [4]

Answer:

Step-by-step explanation:

If y = 2x + 1, then dy/dt = 2(dx/dt).

If y = 2x + 1, then y = 2(40) + 1 when 40 is substituted for x. y = 81.

(a) if dx/dt = 3, find dy/dt when x = 4:

Replacing dx/dt with 3 in dy/dt = 2(dx/dt) yields dy/dt = 2(3) = 6.

(b) if dy/dt = 2, find dx/dt when x = 40:

Replacing dy/dt with 2 in dy/dt = 2(dx/dt) results in 2 = 2(dx/dt), so dx/dt must be 1.

3 0

2 years ago

bonufazy [111]

A paln1 charges $0.35 per minute with no monthly fee (not sure )

4 0

2 years ago

Help

Korvikt [17]

Answer: No, it fails the vertical line test.

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers