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4 years ago

What is the common ratio for the geometric sequence?

Mathematics

1 answer:

Troyanec [42]4 years ago

8 0

Answer: Common ratio is $\frac{3}{5}.$

Step-by-step explanation: Given sequence −15,−9,−275,−8125,...

The general terms of a geometric sequence are:

$a, ar, ar^2, ar^3, ar^4 ......$ .

In common ratio is given by dividing next term from previous term

$\frac{ar}{a} = r$

Therefore, <em>in order to find the common ratio for the given geometric sequence, we need to divide second term by first term or third term by second term.</em>

Dividing second term by first term, we get

$\frac{-9}{-15}$

Dividing top and bottom by -3, we get

$\frac{3}{5}$ .

<h3>Therefore, common ratio is $\frac{3}{5}.$ </h3>

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What is the slope of the line that passes through the points (2, 3) and (8, 6)? 2/7 2 3/5 1/2

baherus [9]

Answer:

$\frac{1}{2}$

Step-by-step explanation:

THe slope of a straight line is given by the formula:

$m=\frac{y_2-y_1}{x_2-x_1}$

Where

m is the slope

x_1 and y_1 are the first coordinate pair points [(2,3)]

x_2 and y_2 are the second coordinate pair point [(8,6)]

So, we know that:

x_1 = 2

x_2 = 8

y_1 = 3

y_2 = 6

Now we substitute and find the value of slope to be:

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4 years ago

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KatRina [158]

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3 years ago

Item 15The entrance of a tunnel can be modeled by y=−11/50(x−4)(x−24), where x and y are measured in feet. The x-axis represents

Evgen [1.6K]

Answer:

The with of the tunnel at the ground level is 20 feet

Step-by-step explanation:

The equation that model the entrance of the tunnel is y = -11/50(x - 4)(x - 24)

Where the dimensions of 'x' and 'y' are in feet and the x-axis represent the ground level

The y-axis represent the height, and the equation is a quadratic equation with the shape of an upside down parabola to represent the shape of the entrance to the tunnel

The two coordinates of the parabola at the ground level (where y = 0)

of the tunnel entrance from which we can find the width by subtraction are given when y = 0 as follows;

y = 0 = -11/50(x - 4)·(x - 24)

∴ (x - 4)·(x - 24) = 0/(-11/50) = 0

When (x - 4)·(x - 24) = 0, x = 4, or x = 24

The coordinates at the ground corners of the tunnel entrance are therefore;

(4, 0), and (24, 0)

The with of the tunnel at the ground level is equal to the width of the parabola at the x-axis, which is given as follows;

The width of the parabola at the x-axis = Distance between points (4, 0), and (24, 0)

∴ The width of the parabola at the x-axis = √((0 - 0)² + (24 - 4)²) = √(24 - 4)² = 24 - 4 = 20 (distance between points having the same y-coordinates)

The width of the parabola at the x-axis = 20 ft. = The with of the tunnel at the ground level

∴ The with of the tunnel at the ground level = 20 feet.

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3 years ago

How to solve this <br>3 = (2x + 8)/3

seropon [69]

Answer:

x = 1/2

Step-by-step explanation:

First you want to get rid of the fraction, so you can multiply both sides of the equation by 3.

9 = 2x + 8

Then, subtract 8 from both sides to get x by itself.

1 = 2x

Finally, divide both sides by 2 so you only have one x

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This means that the answer is x = 1/2.

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belka [17]

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3 years ago

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