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3 years ago

10

Dan bought x pounds of potatoes for $0. 85 per pound and y pounds of grapes for $1. 29 per pound. The total cost was less than $

5. Which inequality represents his purchase? 1. 29x 0. 85y < 5 1. 29x 0. 85y > 5 0. 85x 1. 29y > 5 0. 85x 1. 29y < 5.

1 answer:

Grace [21]3 years ago

5 0

Answer:

0.85x + 1.29y < 5

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Applying the formula for the sum of the first n integers? a-Evaluate 2+4+6+......+500

hammer [34]

Answer:

$S_{250} = 62750$

Explanation:

Given

$Sequence: 2 + 4 + 6 + ..... + 500$

Required

Evaluate the sequence

The sequence shows an arithmetic progression and will be solved using the sum of n terms of an Arithmetic Sequence as follows:

$S_n = \frac{n}{2}(a + L)$

But first, we need to determine the value of n as follows:

$L = a + (n - 1)d$

Where

$L = Last\ Term = 500$

$a = First\ Term = 2$

$d = Common\ Difference = 4 - 2 = 2$

So:

$L = a + (n - 1)d$

$500 = 2 + (n - 1) * 2$

Open bracket

$500 = 2 + 2n - 2$

Collect Like Terms

$2n = 500 + 2 - 2$

$2n = 500$

Divide through by 2

$n = 250$

So:

$S_n = \frac{n}{2}(a + L)$ becomes

$S_{250} = \frac{250}{2}(2 + 500)$

$S_{250} = 125(2 + 500)$

$S_{250} = 125(502)$

$S_{250} = 125 * 502$

$S_{250} = 62750$

<em>Hence, the sum of the sequence is 62750</em>

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The width of a rectangle is to third the length. When each dimension is decreased by 2 cm, the area is decreased by 32 cm period

mario62 [17]

Hey there!!

Basic formula :

Area of a rectangle = Length × breadth

Given :

Width = two third of the length

......................................................

Let's take the dimension of the length as ' x '

Then the breadth would be = 2x / 3

Area = ( x ) × ( 2x / 3 )

Area = 2x² / 3

........................................................

Each dimension is decreased by 2

This states that we will need to add 2 to both length and breadth

.......................................................

Length = x - 2

Breadth = 2x / 3 - 2

= 2x - 6 / 3

Area = ( x - 2 ) × ( 2x - 6 / 3 )

Area = 2x² - 10x + 12 / 3

.................................................

What they say?

Area is decreased by 32 cm

Which means..

If we add 32 to the new rectangles area , the areas would be equal to the new and the old rectangle

2x² / 3 = ( 2x² - 10x + 12 / 3 ) + ( 32 )

2x² / 3 = 2x² - 10x + 108 / 3

Multiplying by 3 on both sides

2x² = 2x² - 10x + 108

Adding 10x on both sides

2x² + 10x = 2x² + 108

subtracting by 2x² on both sides

10x = 108

Dividing by 10 on bot sides

x = 10.8

Length of the original rectangle = 10.8 cm

Breadth = 2 ( 10.8 ) / 3

= 7.2 cm

Hope my answer helps!

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