13 + w/7 = -8 please solve

matrenka [14]

10×6 tens in unit form is written

10×6 tens= 60 tens= 600 units

4 0

4 years ago

The sum of the interior angles of a hexagon is equal to the sum of six consecutive integers. What is the measure of the smallest

kipiarov [429]

Answer:

Look to the explanation

Step-by-step explanation:

* Lets explain how to solve the problem

- The consecutive integers are the integers after each other like

1 , 2 , 3 , ......

- The rule of the sum of the interior angles of any polygon is:

(n - 2) × 180° , where n is the number of the sides of the polygon

- The sum of the interior angles of a hexagon is equal to the sum of

six consecutive integers

* Lets find the sum of the interior angle of the hexagon

∵ The hexagon has 6 sides

∴ n = 6

∴ The sum of its interior angles = (6 - 2) × 180° = 720°

* Lets find the sum of six consecutive integers

- Assume that the smallest integer is x

∴ The numbers are x , x + 1 , x + 2 , x + 3 , x + 4 , x + 5

∵ Their sum = x + (x + 1) + (x + 2) + (x + 3) + (x + 4) + (x + 5)

- Add like terms

∴ Their sum = 6x + 15

- Equate the sum of the 6 numbers by the sum of the angles of

the hexagon

∴ 6x + 15 = 720

- Subtract 15 from both sides

∴ 6x = 705

- Divide both sides by 6

∴ x = 117.5

- But 117 .5 not integer

∴ The sum of the interior angles of a hexagon can not equal the

sum of six consecutive integers

- But it can be if the numbers are consecutive odd integers

because the consecutive odd numbers are

x , x + 2 , x + 4 , x + 6 , x + 8 , x + 10

∴ Their sum = 6x + 30

∵ 6x + 30 = 720

- Subtract 30 from both sides

∴ 6x = 690

- Divide both sides by 6

∵ x = 115

∵ x represents the measure of the smallest angle

∴ The measure of the smallest interior angle of the hexagon is 115°

7 0

4 years ago

Write the expression in factored form s^2-20s-100

KatRina [158]

Answer:

The factors of given expression are 10+10√2 and 10-10√2.

Step-by-step explanation:

We have given a quadratic expression.

s²-20s-100

We have to find factors of given expression.

We use quadratic formula to find factors.

x = (-b±√b²-4ac) / 2a

From given expression, a = 1 , b = -20 and c = -100

Putting values in above formula, we have

x = (-(-20)±√(-20)²-4(1)(-100) ) / 2(1)

x = (20±√400+400 ) / 2

x = (20±√800) / 2

x = (20± √400×2) / 2

x = (20±20√2) / 2

x = 10±10√2

Hence, the factors of given expression are 10+10√2 and 10-10√2.

3 0

3 years ago

Lexi has already jarred 19 liters of jam and will jar an additional 9 liters of jam every day. How many days does lexi need to s

Marysya12 [62]

Answer:

Lexi need to spend 6 days to fill the jar with 73 liters of jam.

Step-by-step explanation:

Given:

amount of jam already had in jar =19 liters

amount of jam added each day in jar = 9 liters.

Total number of jam to be needed in jar = 73 liters.

We need to find the number of days required to jar 73 liters.

Solution:

To find the number of days required to jar 73 liters will be equal to amount of jam already had in jar plus amount of jam added each day in jar multiplied by number of days.

framing in equation form we get;

$19+9x= 73$

Subtracting both side by 19 we get;

$19+9x-19=73-19\\\\9x = 54$

Dividing both side by 9 we get;

$\frac{9x}{9}=\frac{54}{9}\\\\x=6\ days$

Hence Lexi need to spend 6 days to fill the jar with 73 liters of jam.

5 0

3 years ago

A triangle with angle measures of 20° and 30° is a (FILL IN THE BLANK) triangle.

White raven [17]

Obtuse triangle, if the two angles add up to 50 degrees and a whole triangle equals 180 degrees. That means the third angle is greater than 90 degrees and only obtuse angles are greater than 90 degrees

7 0

3 years ago