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3 years ago

The length of two complementary angles are x and 2x+12. Find the measures of the angles.

1 answer:

4 0

There's no such thing as the "length"of an angle.
But we know what you're getting at.

You have said that the angles are complementary. If two angles are
complementary, then their sum is 90 degrees, so we can take your
two angles and write:

 x (one angle) plus (2x + 12) (the other one) = 90 degrees

 x + 2x + 12 = 90

Subtract 12 from each side: x + 2x = 78

Add the x's on the left side: 3x = 78

Divide each side by 3 : x = 26 degrees

One angle is 'x' = 26 degrees

The other one is (2x + 12) = 52+12 = 64 degrees

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3 years ago

Consider a data set containing the following values: 70 65 71 78 89 68 50 75 The mean of the preceding values is 70.75. The devi

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Answer:

If this is the sample data, the sample variance is 125.07 and the sample standard deviation is 11.18

If this is a population data, the population variance is 109.44 and the population standard deviation is 10.46

Step-by-step explanation:

We are given the following data-set:

70, 65, 71, 78, 89, 68, 50, 75

Deviations from the mean

–0.75, –5.75 , 0.25, 7.25, 18.25, –2.75, –20.75, 4.2

Sample size, n = 8

Sample:

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

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

Sum of squares of differences =

0.5625 + 33.0625 + 0.0625 + 52.5625 + 333.0625 + 7.5625 + 430.5625 + 18.0625 = 875.5

$s = \sqrt{\dfrac{875.5}{7}} = 11.18$

$\text{ Sample variance} = s^2 = 125.07$

Population:

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

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

Sum of squares of differences =

0.5625 + 33.0625 + 0.0625 + 52.5625 + 333.0625 + 7.5625 + 430.5625 + 18.0625 = 875.5

$\sigma = \sqrt{\dfrac{875.5}{8}} = 10.46$

$\text{ Population variance} = \sigma^2 = 109.44$

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3 years ago

Nancy sells handcrafted bracelets at a flea market for $6. If her monthly fixed costs are $625 and each bracelet cost her $1.75

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148, 6-1.75=5.25, then.... 625/5.25& round up.... its 148.

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2 years ago

Find the area if the composite shape

soldi70 [24.7K]

Answer:

111 m²

Step-by-step explanation:

A rectangle is a quadrilateral (has four sides and four angle) with two pairs of parallel sides. Opposite sides of a rectangle are equal to each other. Also all the angles of a rectangle are 90° each.

The area of a rectangle = length * width

For rectangle 1, length = 12 m, width = 3 m

Therefore area of rectangle 1 = length * width = 12 m * 3 m = 36 m²

For rectangle 2, length =(12 m - 3 m - 3 m) = 6 m, width =(15 m - 10 m) =5 m

Therefore area of rectangle 2 = length * width = 6 m * 5 m = 30 m²

For rectangle 3, length = 15 m, width = 3 m

Therefore area of rectangle 3 = length * width = 15 m * 3 m = 45 m²

Area of composite shape = Area of rectangle 1 + Area of rectangle 2 + Area of rectangle 3

Area of composite shape = 36 m² + 30 m² + 45 m² = 111 m²

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3 years ago

A trapezoid is a polygon that has exactly one pair of parallel sides.

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3 years ago

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