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3 years ago

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Lamps sell for $50 each and coffee tables sell for $200. Two times as many lamps were sold than tables. Total sales were $3,000.

How many of each were sold? What were the total sales in dollars for each?

1 answer:

pav-90 [236]3 years ago

7 0

There were 20 lamps sold and 10 tables sold with the lamps having a total sale of $1,000 and the tables having a total sale of $2,000.

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The sum of 5 consecutive even numbers is 180 what is the first number in the sequence

Anit [1.1K]

First, a even number in general could be written as 2k for any k ( k is any integer number).

Let x_1, x_2, x_3, x_4, x_5 the 5 consecutive even numbers, then,

x_1 + x_2 + x_3 + x_4 + x_5 = 180. But for the first commentary, any of the x_i's are even numbers, so, are of the form 2k_i, but, they are consecutive, think about the sequence: 2,4,6,8,10, we could written as 2(1) + 2 (2) + 2(3) + 2(4) + 2(5), the numbers between (), are the k's and are consecutive, and we could write consecutive numbers as x, x+1, x+1 +1 = x+2, (x+2)+1, etc.

So, for the previous commentary, we rewrite

x_1 + x_2 + x_3 + x_4 + x_5 = 180

as

2k + 2(k+1) + 2(k+2) + 2(k+3) + 2(k+4) = 180

is equivalent to (factorizing 2)

2 [k + k+1 + k+2 +k+3 +k+4 ] = 180

(divide both sides by 2)

[k + k+1 + k+2 +k+3 +k+4 ] = 90

(simplifyng the expression)

5k+10 = 90

(substracting 10 in both sides)

5k = 80

(divide both sides by 5)

k = 16

then, the first number is x_1 = 2k = 2(16) = 32

Now, we can check, the corresponding sequence was

32 + 34 +36 +38 +40 = 180.

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3 years ago

Complete the table of values below so that it represents a line with a constant rate of change of `-\frac{3}{4}.`

Nady [450]

To find values of the table, plug in the given corresponding values of x or y, and constant rate of change (m) = -3/4 into y = mx.

<h3>What is the Constant Rate of Change?</h3>

Constant rate of change of any table or function is a comparison of how two variables are changing, which can be determined using the formula, m = change in y/change in x = $\frac{y_2 - y_1}{x_2 - x_1}$ .

Where x and y are the coordinates of a table or functions, and m is the constant rate of change, the equation that models the relationship would be, y = mx.

The image of the table is missing, however, to complete the given table, plug in any of the given values of x or y, and constant rate of change (m) = -3/4 into y = mx.

Learn more about constant rate of change on:

brainly.com/question/10866779

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