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Find the common difference for the sequence below. 1/4, 5/16, 3/8,..

vredina [299]

Answer:

the common difference of the sequence is $(\frac{1}{16})$

Step-by-step explanation:

A sequence of numbers is said to be in arithmetic progression of each term of the sequence has same common difference.

Now, here first term a1 = 1/4

Second term a2 = 5/16

Third term a3 = 3/8

Now, Common difference (d) = a2 - a1 = a3 - a2

Now, a2 - a1 = $\frac{5}{16} - \frac{1}{4} = \frac{5 - 4}{16} = \frac{1}{16}$

Now, a3 - a2 = $\frac{3}{8} - \frac{5}{16} = \frac{6 - 5}{16} = \frac{1}{16}$

Hence, the common difference of the sequence is $(\frac{1}{16})$

5 0

3 years ago

PLEASE HELP ME If this rectangle is dilated using a scale factor of One-half through point B, what is the result? Point B is the

elixir [45]

Answer:

It is B just took the unit quiz

4 0

3 years ago

Read 2 more answers

A company mixes two kinds of cleansers to get a blend they sell for 59 cents a liter. One of the cleansers costs 50 cents per li

Lilit [14]

Answer:

Cleanser that costs 50 cents is 1400 liters, Cleanser that costs 80 cents is 600 liters.

Step-by-step explanation:

We can solve this by using <em>simultaneous equations</em>:

Let us express the question in terms of equations

Let a be cleanser at 50 cents and let b be the cleanser at 80 cents.

Equation 1: 0.5a + 0.8b = 0.59(a+b)

Equation 2: a + b = 2000

From equation 2, a = 2000 - b (Let's call this equation 3)

2. Substituting equations 2 and 3 in Equation 1:

0.5a + 0.8b = 0.59(a+b)

0.5(2000 - b) + 0.8b = 0.59(2000)

1000 - 0.5b + 0.8b = 1180

0.3b = 180

b = 600

Substitute in equation 3:

a = 2000 - 600

a = 1400

As a note, I formed equation 1 because I know for a fact the cost per liter of a and b. I also know it is sold at 0.59 cents per liter. We are selling 2000 liters in this instance, therefore 0.59(2000) = 1180, which in this case is the selling price.

4 0

4 years ago

Choose the equation below that represents the line passing through the point (1, -4) with a slope of 1/2

tatiyna

For this case we have that by definition, the line equation of the slope-intersection form is given by:

$y = mx + b$

Where:

m: It's the slope

b: It is the cut-off point with the y axis

According to the statement we have:

$m = \frac {1} {2}$

Thus, the equation is of the form:

$y = \frac {1} {2} x + b$

We substitute the given point and find "b":

$-4 = \frac {1} {2} (1) + b\\-4 = \frac {1} {2} + b\\-4- \frac {1} {2} = b\\b = - \frac {9} {2}$

Finally, the equation is of the form:

$y = \frac {1} {2} x- \frac {9} {2}$

Answer:

$y = \frac {1} {2} x- \frac {9} {2}$

6 0

3 years ago

Lorene plans to make several open-topped boxes in which to carry plants. She makes the boxes from rectangular sheets of cardboar

Katen [24]

Answer:

29 feet in length, 5 feet in width and 12 feet in height

Step-by-step explanation:

We have that for the volume of a quadrangular prism is:

V = l * w * h

Ie length times width times height

In this case, the height is determined by the squares that you put in each corner, taking into account that a square has all the same sides, the height is 12 inches. h = 12

they tell us that the length is 24 inches more than the width, that is, l = 24 + w

replacing we have:

1740 = (24 + w) * w * 12

1740 = 12 * w ^ 2 + 288 * w

12 * w ^ 2 + 288 * w - 1740 = 0

if we calculate the root, we have w = 5 or w = -29

only works when w = 5

Thus:

l = 24 + 5

l = 29

which means that the dimensions are:

29 feet in length, 5 feet in width and 12 feet in height

5 0

3 years ago