SELECT TWO reasonable first steps for solving the equation 2(4x-11)=10.

8-35. Use your knowledge of polygons to answer the questions below, if possible.

Nataliya [291]

Answer:

(a)I. 13 Sides II. 7 Sides

(b) 4 Sides, Square

(c)x=52 degrees

(d)x=107 degrees

(e)1620 degrees

Step-by-step explanation:

(a)The Sum of the Interior angle of polygon with n sides is derived using the formula: (n-2)180.

I. If the Interior angle is $1980^0$

Then:

$(n-2)180^0=1980^0\\$Divide both sides by 180^0 $ to isolate n$\\n-2=11\\$Add 2 to both sides of the equation\\n-2+2=11+2\\n=13$

The polygon has 13 sides.

II. If the Interior angle is $900^0$

Then:

$(n-2)180^0=900^0\\$Divide both sides by 180^0 $ to isolate n$\\n-2=5\\$Add 2 to both sides of the equation\\n-2+2=5+2\\n=7$

The polygon has 7 sides.

(b)The sum of the exterior angle of a polygon is 360 degrees,

Each exterior angle of a n-sided regular polygon is: $\frac{360^0}{n}$

If the exterior angle of a regular polygon is 90°

Then:

$90\°=\frac{360^0}{n}\\ 90n=360\\n=4$

The regular polygon has 4 sides and it is called a Square.

(c)The Sum of the Interior angle of polygon with n sides is derived using the formula: (n-2)180.

Each Interior angle of a regular n-sided polygon is: $\frac{(n-2)180^0}{n}$

For a pentagon, n=5

Then:

$\frac{(5-2)180^0}{5}=2x+4\\108=2x+4\\108-4=2x\\104=2x\\x=52^0$

(d)The sum of the exterior angle of a polygon is 360 degrees.

If four of the exterior angles of a pentagon are 57, 74, 56, and 66.

Let the fifth angle=x

Then:

$57+74+56+66+x=360^0\\253+x=360\\x=107^0$

(e)The Sum of the Interior angle of polygon with n sides is derived using the formula: (n-2)180.

In an 11-gon., n=11

Therefore, the sum of the interior angle=(11-2)180= $1620^0$

The sum of the interior angle does not change either in a regular or irregular polygon.

3 0

2 years ago

2(4-8x)+6=-1 interpreting experiessions

Anestetic [448]

Answer:

X = $\frac{13}{16}$

Step-by-step explanation:

2 (4-8x) + 6 = 1

Multiply parentheses by 2

8 - 16x + 6 = 1

add (8 + 6)

14 - 16x = 1

Move constant to right and change its sign

-16x = 1 -14

Calcualte te difference

-16x = -13

divide bot sides by -16

x = $\frac{13}{16}$

8 0

3 years ago

Evaluate the integral by interpreting it in terms of areas Draw a picture of the region the integral

denis23 [38]

Answer:

Step-by-step explanation:

The picture is below of how to separate this into 2 different regions, which you have to because it's not continuous over the whole function. It "breaks" at x = 2. So the way to separate this is to take the integral from x = 0 to x = 2 and then add it to the integral for x = 2 to x = 3. In order to integrate each one of those "parts" of that absolute value function we have to determine the equation for each line that makes up that part.

For the integral from [0, 2], the equation of the line is -3x + 6;

For the integral from [2, 3], the equation of the line is 3x - 6.

We integrate then:

$\int\limits^2_0 {-3x+6} \, dx+\int\limits^3_2 {3x-6} \, dx$ and

$-\frac{3x^2}{2}+6x\left \} {{2} \atop {0}} \right. +\frac{3x^2}{2}-6x\left \} {{3} \atop {2}} \right.$ sorry for the odd representation; that's as good as it gets here!

Using the First Fundamental Theorem of Calculus, we get:

(6 - 0) + (-4.5 - (-6)) = 6 + 1.5 = 7.5

5 0

2 years ago

write an equation that describes the proportional relationship between the number of days in the number of weeks in a given leng

KatRina [158]

Answer:

Week 1 Day 7

Week 2 Day 14

Week 4 Day 28

Week 8 Day 56

Week 10 Day 70

Let x represent the number of weeks

Let y represent the number of days

Use the ratio of the constant of proportionally in the equation y =kx

y = 14/7x

y = 2x

Step-by-step explanation:

6 0

3 years ago

Remi invests ?600 for 5 years in a saving account. By the end of the 5 years he has received a total of ?75 simple interest. Wor

Allushta [10]

Answer:

2.5 %

Step-by-step explanation:

The simple interest formula is

I = Prt

Data:

I = $75

P = $600

t = 5 yr

Calculation:

75 = 600 × r × 5

75 = 3000 r

Divide each side by 3000

r = 75/3000 = 0.025 = 2.5 % APR

The annual percentage rate is 2.5 %.

4 0

3 years ago