-5(6y + 4) + 25 = 15(2y + 5) + 73

Svetllana [295]

The denominator of the first term is a difference of squares, such that

4a ² - b ² = (2a)² - b ² = (2a - b) (2a + b)

So you can write the fractions as

(4a ² + b ²)/((2a - b) (2a + b)) - (2a - b)/(2a + b)

Multiply through the second fraction by 2a - b to get a common denominator:

(4a ² + b ²)/((2a - b) (2a + b)) - (2a - b)²/((2a + b) (2a - b))

((4a ² + b ²) - (2a - b)²) / ((2a - b) (2a + b))

Expand the numerator:

(4a ² + b ²) - (2a - b)²

(4a ² + b ²) - (4a ² - 4ab + b ²)

4ab

So the original expression reduces to

4ab / ((2a - b) (2a + b))

or

4ab / (4a ² - b ²)

upon condensing the denominator again.

8 0

3 years ago

4. The Television Chocolate Room was painter

VashaNatasha [74]

Answer:

C

Step-by-step explanation:

5 0

3 years ago

Listed below are prices in dollars for one night at different hotels in a certain region. Find the range, variance, and standar

Artyom0805 [142]

Answer:

Range = 115$

Standard Deviation = 43.76$

Variance = 1915.142$

Option A) The measures of variation are not very useful because when searching for a room, low prices, location, and good accommodations are more important than the amount of variation in the area.

Step-by-step explanation:

We are given the data for prices in dollars for one night at different hotels in a certain region.

234, 160, 119, 131, 218, 207, 146, 141

Range:

Sorted data: 119, 131, 141, 146, 160, 207, 218, 234

$\text{Range} = 234-119 = 115\$$

Standard Deviation:

$\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}$

where $x_i$ are data points, $\bar{x}$ is the mean and n is the number of observations.

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

$Mean =\displaystyle\frac{1356}{8} = 169.5$

Sum of squares of differences = 4160.25 + 90.25 + 2550.25 + 1482.25 + 2352.25 + 1406.25 + 552.25 + 812.25 = 13406

$\sigma = \sqrt{\dfrac{13406}{7}} = 43.76\$$

Variance =

$\sigma^2 = 1915.142\$$

Measure of variance for someone searching for room:

Option A) The measures of variation are not very useful because when searching for a room, low prices, location, and good accommodations are more important than the amount of variation in the area.

5 0

3 years ago

Find the slope of the line passing through the points (6, -6) and (4, -4)

djyliett [7]

To find the slope (m), use the slope formula:

$m=\frac{y_2-y_1}{x_2-x_1}$ and plug in the two points

(4, -4) = (x₁, y₁)

(6, -6) = (x₂, y₂)

[lines usually go from left to right, so the point furthest to the left is the 1st point]

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

$m=\frac{-6-(-4)}{6-4}$ [two negative signs cancel each other out and become positive]

$m=\frac{-6+4}{6-4}$

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

m = -1

3 0

3 years ago

What are the numerical measures of each angle in the diagram? 1 and 3 measure degrees. 2 and 4 measure degrees. (3x - 1)º (2x +

Tanya [424]

Answer:

Step-by-step explanation:

In the diagram shown, the measure of angle 1 is oppositely directed to angle 2 and oppositely directed angles are equal.

Hence <1 = <3

Given < 1 = 3x-1 and <3 = 2x+9

Hence 3x-1 = 2x+9

collect like terms

3x-2x = 9+1

x = 10°

Since <1 = 3x-1

on substituting x = 10

<1 = 3(10)-1

<1 = 30-1

<1 = 29°

<1+<2 = 180 (angle on a straight line)

29+<2 = 180

<2 = 180-29

<2 = 151°

Similarly, on substituting x = 10 into <3

<3 = 2x+9

<3 = 2(10)+9

<3 = 20+9

<3 = 29°

<3+<4 = 180 (angle on a straight line)

29+<4 = 180

<4 = 180-29

<4 = 151°

3 0

3 years ago

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