All categories

4 years ago

5(x+4)+10-2x+3(2x+9)

Mathematics

1 answer:

qwelly [4]4 years ago

4 0

Answer:

x = (-19)/3

Step-by-step explanation:

Solve for x:

10 - 2 x + 5 (x + 4) + 3 (2 x + 9) = 0

5 (x + 4) = 5 x + 20:

10 - 2 x + 5 x + 20 + 3 (2 x + 9) = 0

3 (2 x + 9) = 6 x + 27:

6 x + 27 + 5 x - 2 x + 10 + 20 = 0

Grouping like terms, 6 x + 5 x - 2 x + 10 + 20 + 27 = (-2 x + 5 x + 6 x) + (10 + 20 + 27):

(-2 x + 5 x + 6 x) + (10 + 20 + 27) = 0

-2 x + 5 x + 6 x = 9 x:

9 x + (10 + 20 + 27) = 0

10 + 20 + 27 = 57:

9 x + 57 = 0

Subtract 57 from both sides:

9 x + (57 - 57) = -57

57 - 57 = 0:

9 x = -57

Divide both sides of 9 x = -57 by 9:

(9 x)/9 = (-57)/9

9/9 = 1:

x = (-57)/9

The gcd of 57 and 9 is 3, so (-57)/9 = (-(3×19))/(3×3) = 3/3×(-19)/3 = (-19)/3:

Answer: x = (-19)/3

Read more about right triangles at:

brainly.com/question/2437195

3 0

2 years ago

Write 44/3 as a whole or mixed number in simplest form.

stealth61 [152]

14 2/3 is the answer

7 0

3 years ago

Read 2 more answers

For 5 points and brainliest to the best correct answer, find the missing measures.<br> Thank you

zzz [600]

Answer:

x = 7
y = 97°
z = 19

Step-by-step explanation:

The markings on the figure show this to be a parallelogram. That means opposite sides are congruent. Because the sides are parallel, "alternate interior" angles are also congruent.

Angle y forms a linear pair with the one marked 83°, so is supplementary to it:

y = 180°-83° = 97°

The angle marked y is an exterior angle to the triangle containing the angle marked (7x -5)°. As such, it is equal to the sum of the remote interior angles, the one marked (7x -5)° and the unmarked one that is congruent to (3x +32)°.

(7x -5) +(3x +32) = 97 . . . . . angle relations in the left-side triangle

10x +27 = 97 . . . . . . . collect terms

10x = 70 . . . . . . . . subtract 27

x = 7 . . . . . . . . divide by 10

The side marked Z is congruent to the opposite parallel side, so ...

z = 19

The missing measures are ...

x = 7
y = 97°
z = 19

_____

<em>Additional comment</em>

You can also find the value of y by adding up the interior angles of the right-side triangle. The one not shown there is "alternate interior" to the one marked (7x -5)°, hence has the same measure. This gives ...

(7x -5) +(3x +32) +83 = 180

Subtracting 83° from both sides gives the equation we used above.

4 0

3 years ago

Listed below are the numbers of hurricanes that occurred in each year in a certain region. The data are listed in order by year.

Drupady [299]

Answer:

Range = 13

Variance = 10.22

Standard deviation = 3.20

Since this data is time-series therefore, the measures of variation do not reveal anything about the pattern of hurricanes over time.

Step-by-step explanation:

We are given the number of hurricanes that occurred in each year in a certain region.

8 9 8 7 9 15 5 6 8 4 12 7 8 2

Range:

The range of the data set is found by

Range = Maximum value - minimum value

The maximum value in the data set is 15

The minimum value in the data set is 2

Range = 15 - 2

Range = 13

Variance:

To find the variance, first compute the mean of the data set.

Mean = Sum/n

Mean = (8+9+8+7+9+15+5+6+8+4+12+7+8+2)/14

Mean = 108/14

Mean = 7.714

The variance is given by

σ² = (x - mean)²/(n - 1)

σ² = (8 - 7.714)² + (9 - 7.714)²+ (8 - 7.714)² + (7 - 7.714)² + (9 - 7.714)² + (15 - 7.714)² + (5 - 7.714)² + (6 - 7.714)² + (8 - 7.714)² + (4 - 7.714)² + (12 - 7.714)² + (7 - 7.714)² + (8 - 7.714)² + (2 - 7.714)²/(14 - 1)

σ² = 10.22

Standard deviation:

The standard deviation of the data set is given by

σ² = √σ

σ² = √10.22

σ² = 3.20

Since this data is time-series therefore, the measures of variation do not reveal anything about the pattern of hurricanes over time.

7 0

3 years ago