AC=23 AB=2x+2 and BC=3x +6 find BC

I need to find the least common denominator of x+2/x^2+2x-3 , x-7/x^2+5x+6

grin007 [14]

Answer:

(x + 3)(x - 1)(x + 2)

Step-by-step explanation:

The fractions are:

$\dfrac{x + 2}{x^{2} + 2x - 3} \text{ and } \dfrac{x - 7}{x^{2} + 5x + 6}$

Factor each denominator

$x^{2} + 2x - 3 = (x + 3)(x - 1)\\x^{2} + 5x + 6 = (x + 3)(x + 2)$

We must find the least common multiple of the denominators. We take the maximum power of each separate factor.

Factors of first fraction = (x + 3) × (x - 1)

Factors of second fraction = (x + 3) × (x + 2)

LCM = (x + 3)(x - 1)(x + 2)

The lowest common denominator of the two fractions is (x + 3)(x - 1) (x + 2).

4 0

3 years ago

A boat can travel with a speed of 13 km/hr in still water. If the speed of the stream is 4 km/hr, find the time taken by the boa

ser-zykov [4K]

Answer:

t=4h

Steps below

Step-by-step explanation:

We know:

speed of boat with respect to earth: 13 km

speed of stream with respect to earth: 4 km

13 km/h + 4 km/h = 17 km/h The time to travel 68 km with this speed is thus t = 68 km 17 km h = 4 h

<em><u>Hope this helps.</u></em>

4 0

3 years ago

A vendor sells hot dogs, bags of potato chips, and soft drinks. A customer buys 4 hot dogs, 3 bags of potato chips, and 4 soft d

GuDViN [60]

The price of chips is $ 0.75, the price of a hot dog is $ 2 and the price of a soft drink is $ 1.25.

Step-by-step explanation:

Given,

A customer buys 4 hot dogs, 3 bags of potato chips, and 4 soft drinks for $15.25.

The price of a hot dog is $1.25 more than the price of a bag of potato chips.

The cost of a soft drink is $2.75 less than the price of two hot dogs.

To find the cost of each item.

Let,

The price of chips = x

The price of a hot dog = x+1.25

Price of two hot dog = 2(x+1.25) = 2x+2.5

The price of a soft drink = 2x+2.5-2.75 = 2x-0.25

Now,

According to the problem,

4(x+1.25)+3x+4(2x-0.25) = 15.25

or, 15x+5-1 = 15.25

or, 15x = 11.25

or, x = 0.75

Hence,

The price of chips = $ 0.75

The price of a hot dog = $ 0.75+1.25 = $ 2

The price of a soft drink = $ 2×0.75-0.25 = $ 1.25

5 0

3 years ago

The Lewis family and the Perry family each used their sprinklers last summer. The water output rate for the Lewis family's sprin

Rashid [163]

The Lewis family and the Perry family each used their sprinklers last summer. The water output rate for the Lewis family's sprinkler was 15 L per hour. The water output rate for the Perry family's sprinkler was 40 L per hour. The families used their sprinklers for a combined total of 65 hours, resulting in a total water output of 1850 L . How long was each sprinkler used

Answer:

Hours of use of sprinkler by Lewis family is 30 hours.

Hours of use of sprinkler by Perry family is 35 hours.

Step-by-step explanation:

Let W = hours of use by Lewis family

65 - W = hours of use by Perry family

Then;

15W + 40*(65 - W) = 1850

15W + 2600 - 40W = 1850

(15 - 40)W = 1850 - 2600

-25W = −750

W = 750/25 = 30

Therefore;

W = 30

65 - W = 65 - 30 = 35

Hence,

Hours of use by Lewis family is 30 hours.

Hours of use by Perry family is 35 hours.

3 0

3 years ago

A certain bookstore chain has two stores, one in San Francisco and one in Los Angeles. It stocks three kinds of books: hardcover

victus00 [196]

Answer:

Answer:

a. Sales from January to June: Matrix B6

Hard Soft Plastic

San Francisco 4,200 7,200 12,000

Los Angeles 2,400 1,200 3,000

b) Ending Inventory: Matrix D:

Hard Soft Plastic

San Francisco 400 4,800 3,000

Los Angeles 1,600 7,800 3,000

Step-by-step explanation:

a) Data and Calculations:

Stock on January 1: Matrix A

Hard Soft Plastic

San Francisco 1,000 3,000 6,000

Los Angeles 1,000 6,000 3,000

Sales in January: Matrix B

Hard Soft Plastic

San Francisco 700 1,200 2,000

Los Angeles 400 200 500

Restocking: Matrix C

Hard Soft Plastic

San Francisco 600 1,500 1,500

Los Angeles 500 500 500

Total Sales over the first 6 months =

Matrix B * 6 = Matrix B6

Sales in January: Matrix B

Hard Soft Plastic

San Francisco 700 1,200 2,000

Los Angeles 400 200 500

* 6

=

Sales from January to June: Matrix B6

Hard Soft Plastic

San Francisco 4,200 7,200 12,000

Los Angeles 2,400 1,200 3,000

Matrix C6 = Matrix C * 6

=

Restocking: Matrix C6

Hard Soft Plastic

San Francisco 3,600 9,000 9,000

Los Angeles 3,000 3,000 3,000

Inventory at the end of June =

Matrix A + Matrix C6 - Matrix B6

= Matrix D

Stock on January 1: Matrix A

Hard Soft Plastic

San Francisco 1,000 3,000 6,000

Los Angeles 1,000 6,000 3,000

+

Restocking: Matrix C6

Hard Soft Plastic

San Francisco 3,600 9,000 9,000

Los Angeles 3,000 3,000 3,000

-

Sales from January to June: Matrix B6

Hard Soft Plastic

San Francisco 4,200 7,200 12,000

Los Angeles 2,400 1,200 3,000

Ending Inventory: Matrix D:

Hard Soft Plastic

San Francisco 400 4,800 3,000

Los Angeles 1,600 7,800 3,000

3 0

2 years ago