Ellie made an octagon and used a ruler so each side is the same length. Her octagon has a perimeter of 80 inches. What is the length of each side? ___ (your answer) inches

Answer:

[tex]p(x) = k(x -1)^{3} * (x -4)^{2} * (x +3)[/tex] --- General polynomial

The degree is 6

[tex]p(x) = -\frac{1}{3}(x -1)^{3} * (x -4)^{2} * (x +3)[/tex] --- The polynomial precisely

Step-by-step explanation:

Given

[tex](a,b,c)= (1,4,-3)[/tex] --- zeros

[tex](m_1,m_2,m_3) =(3,2,1)[/tex] --- multiplicities

Solving (a): The polynomial

The polynomial is represented as:

[tex]p(x) = (x -a)^{m_1} * (x -b)^{m_2} * (x -c)^{m_3}[/tex]

So, we have:

[tex]p(x) = (x -1)^{3} * (x -4)^{2} * (x +3)^{1}[/tex]

[tex]p(x) = (x -1)^{3} * (x -4)^{2} * (x +3)[/tex]

Include constant k; So, the polynomial becomes

[tex]p(x) = k(x -1)^{3} * (x -4)^{2} * (x +3)[/tex]

Solving (b): The degree (d)

To do this, add up the multiplicities

[tex]d = m_1 +m_2 +m_3[/tex]

[tex]d = 3+2+1[/tex]

[tex]d = 6[/tex]

The degree is 6

Solving (c): The actual polynomial

In (a), we have:

[tex]p(x) = k(x -1)^{3} * (x -4)^{2} * (x +3)[/tex]

[tex]p(0)=16[/tex] means:

[tex](x,p(x)) = (0,16)[/tex]

This gives:

[tex]16 = k(0 -1)^{3} * (0 -4)^{2} * (0 +3)[/tex]

[tex]16 = k(-1)^{3} * (-4)^{2} * (3)[/tex]

[tex]16 = k*-48[/tex]

Solve for k

[tex]k = \frac{16}{-48}[/tex]

[tex]k = -\frac{1}{3}[/tex]

So:

[tex]p(x) = k(x -1)^{3} * (x -4)^{2} * (x +3)[/tex]

[tex]p(x) = -\frac{1}{3}(x -1)^{3} * (x -4)^{2} * (x +3)[/tex]

Answer: 3

Step-by-step explanation:

Distribute the 5: 15x-5=40

Add 5 from both sides: 15x=45

Divide 15 by both sides: 3

Answer:

a-3

Step-by-step explanation:

5(3x-1)=40

15x-5=40

15x=40+5

15x=45

x=45/15

x=3

Answer:

570 meters

Step-by-step explanation:

[tex]\frac{8}{152} :\frac{30}{y}[/tex]

y × 8 = 152 × 30

8y = 4560

8y ÷ 8 = 4560 ÷ 8

y = 570

Answer:

They are all squares similar to the base.

Step-by-step explanation:

They are not congruent to the base but are similar.

Answer:

BC = 24

Step-by-step explanation:

We know that triangles CAB and CED are similar because all three of their angles are the same. Thus, we know that the side lengths of these triangles have to be proportional to each other. You would match side BC with side DC and sides AC with EC.

AC/EC = BC/DC

30/10 = (32-x)/x

3 = (32-x)/x

Then using algebraic properties, solve for x.

3x = 32 - x

4x = 32

x = 8.

Lastly, plug in 8 for the x in BC, 32 - 8, so the length of BC is 24

Answer:

B

Step-by-step explanation:

Δ CBA and Δ CDE are similar triangles, then the ratios of corresponding sides are equal, that is

[tex]\frac{CB}{CD}[/tex] = [tex]\frac{CA}{CE}[/tex] , substitute values

[tex]\frac{32-x}{x}[/tex] = [tex]\frac{30}{10}[/tex] = 3 ( multiply both sides by x )

32 - x = 3x ( add x to both sides )

32 = 4x ( divide both sides by 4 )

8 = x

Then

BC = 32 - x = 32 - 8 = 24 → B

Answer:

Step-by-step explanation:

x = 7

Symbolically, this equation is:

 x        7

----- = -----

90       9

Cross multiplying yields 9x = 9(7), and so x must be 7.

Answer:

its b!!

Step-by-step explanation:

Answer:

4.55

Step-by-step explanation:

step 1.     6.5 / 500 =  .013

step 2.    .013 X 350  = 4.55

Hope this helps

Answer:

49ft^2

Step-by-step explanation:

3.5ft X 4= 14ft

Area of parallelogram formula:

(perpendicular height)(base)= area

(14ft)(3.5ft)=49ft^2

Answer:

RO = 17.9

Step-by-step explanation:

If they're similar, the fraction between their sides need to be equal, so do this:

NK/NM = RO/RQ

71.6/64 = RO/16

71.6•16/64 = RO

RO = 17.9

Answer:

a)    x= 34°

b)    x = 51°

Step-by-step explanation:

Points to keep in mind when solving  triangle problems.

An isosceles triangle has two equal sides and the angles opposite to those sides are also equal angles.

A triangle with all sides equal is called an equilateral triangle, which is also called equiangular triangle.  

Answer:

y+2x-5= 0

Step-by-step explanation:

Applying,

(y-y₁) = m(x-x₁)............... Equation 1

Where m = slope

But,

m = (y₂-y₁)/(x₂-x₁)

Given: y₁ = -3, y₂ = 1, x₁ = 4, x₂ = 2

m = (1+3)/(2-4)

m = 4/-2

m = -2

Substituting into equation 1

(y+3) = -2(x-4)

y+3 = -2x+8

y = -2x+8-3

y = -2x+5

y = 5-2x

y+2x-5 = 0

Answer:

1) -5

2) 5

3) -4

4) 7

5) 3

Step-by-step explanation:

1) -20 divided by -4

2) -2 plus 7

3) 20 divided by 5

4) -2 plus 9

5) 20 minus 17

Step-by-step explanation:

Given equation :-

Slope intercept form :-

→ 4x + 3y - 8 = 0

→ 3y = -4x + 8

→ y = (-4x + 8)/3

→ y = -4/3x + 8/3

Answer:

y = -4/3x + 8/3.

Step-by-step explanation:

4x + 3y - 8 = 0

3y  - 8 = -4x

3y = -4x + 8

Divide through by 3:

y = -4/3x + 8/3.

Answer:

(p+u)(y+9)

Step-by-step explanation:

p(y+9)+u(y+9)

Multiply them out

py+uy+9p+9u

y(p+u)+9(p+u)

=(p+u)(y+9)

Answer:

3.2 , Edgar , Liam

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

Answer:

Nope, this is because the angles in a triangle add up to 180, whereas these values added are equal to 200 degrees

No, the angles with measures 80°, 55°, and 65° cannot form angles on a line.

In geometry, angles on a line are also known as "linear angles" or "straight angles." A straight angle measures 180°, and it is formed by two rays that point in opposite directions and share a common endpoint, creating a straight line. To determine if the given angles can form a straight angle, we need to add their measures.

Let's calculate the sum of the given angles:

Sum = 80° + 55° + 65°

       = 200°

Since the sum of the given angles (200°) is not equal to 180°, it means that the angles cannot form a straight line. Instead, they form a shape that is not a straight angle, such as a triangle or a polygon.

In this case, the given angles form a triangle since they satisfy the triangle inequality theorem. The sum of any two sides of a triangle is always greater than the third side. Mathematically, for a triangle with sides of lengths a, b, and c, the inequality holds: a + b > c, b + c > a, and c + a > b.

Therefore, the angles with measures 80°, 55°, and 65° cannot form angles on a line but rather form a triangle with a sum of 180°, satisfying the triangle inequality.

To know more about Linear Angles here

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[tex]\huge\textsf{Hey there!}[/tex]

[tex]\large\textsf{Monomial means an algebraic expression that consists of using ONE term}[/tex]

[tex]\mathsf{39n^3: 1, 3, 13, 39, n, n, n}[/tex]

[tex]\mathsf{48n^2: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, n, n}[/tex]

[tex]\large\textsf{Like terms: 1, 2, 3, n, n}[/tex]

[tex]\boxed{\boxed{ \large\textsf{Answer: \bf The GCF (Greatest Common Factor): 3n}^2}}\huge\checkmark[/tex]

[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{aAmphitrite1040:)}[/tex]

Step-by-step explanation:

arc CAD = 2×63= 126°

< ADB = ½×180 = 90°

arc AD = 126-36 = 90°

< ABD = ½×90° = 45°

< BAD = 180-90-45 = 45°

arc BD = 2×45 = 90°

Answer:

216π sq ft

Step-by-step explanation:

given that :

d = 12 ft => r = 12/2 = 6ft

h(cyl) = 10 ft

h(cone) = 8 ft

the surface area = ?

the solution :

the slant of cone = √r²+h²

= √6²+8²= √100 = 10 ft

the surface area of silo =

the lateral area of cone + the lateral area of cylinder + the base area

= π×r×slant + 2×π×r×h(cyl) + π×r²

= π×6×10 + 2×π×6×10 + π×6²

= 60π + 120π + 36π

= 216π sq ft

The surface area of the silo will be 216π square feet. Then the correct option is C.

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

A silo consists of a cone stacked on top of a cylinder, where the radii of the cone and the cylinder are equal.

The surface area is the sum of the surface area of the cone and cylinder. Then we have

The diameter of the cylindrical base of the silo is 12 ft and the height of the cylinder is 10 ft, while the height of the cone is 8 ft.

Surface area = πrl + 2πrh + πr²

The length of the radius will be

r = d /2

r = 12 / 2

r = 6 ft

The length of slant height will be

l² = 6² + 8²

l² = 100

l = 10 ft

Then the surface area of the silo will be

SA = π × 6 × 10 + 2π × 6 × 10 + π6²

SA = 60π + 120π + 36π

SA = 216π square feet

The surface area of the silo will be 216π square feet.

Then the correct option is C.

More about the geometry link is given below.

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Answer:

10 litres

Step-by-step explanation:

50 litres - 100%

x litres - 30%

x=(50*30)/100=15 litres - that's 30% of the tank (this amount of water is already added)

50 litres - 100%

x litres - 50%

x=(50*50)/100=25 litres - that's 50% of the tank (this amount of water will be in the tank)

To find what amount of water should be added we must subtract the amount of water that is already added from the amount of water that will be in the tank.

25 - 15=10 litres should be added

Answer:

w equal to 9z

or z equals to w/9

Answer:

The percentage markdown is approximately 19%

Step-by-step explanation:

The cost at which the computer store bought the program = $40

The selling price at which the store sold the program = $32.5

The percentage markdown is given as follows;

Let CP represent the cost at which the computer store bought the program, and let SP represent the selling price of the program, we can find the percentage markdown as follows;

[tex]Percentage \ markdown = \dfrac{CP- SP}{CP } \times 100[/tex]

CP = $40, SP = 32.5

Therefore, we get;

[tex]Percentage \ markdown = \dfrac{40- 32.5}{40} \times 100 = 18.75\% \approx 19\%[/tex]

The percentage markdown ≈ 19%.

Answer:

[tex] \frac{194}{3} [/tex]

Step-by-step explanation:

[tex]64 \frac{2}{3} [/tex]

[tex]64 + \frac{2}{3} [/tex]

[tex]64 \times \frac{3}{3} + \frac{2}{3} [/tex]

[tex] \frac{64 \times 3}{3} + \frac{2}{3} [/tex]

[tex] \frac{64 \times 3 + 2}{3} [/tex]

[tex] \frac{192 + 2}{3} [/tex]

[tex] \frac{194}{3} [/tex]

Answer:

sinA=sin(90-B)

sinA=90_B

now,A+B

=90

Answer:

1. [tex]Area = 28.26[/tex]

2 and 3: See explanation

Step-by-step explanation:

Solving (1)

[tex]r = 3[/tex] --- radius

The area is:

[tex]Area = \pi r^2[/tex]

[tex]Area = 3.14* 3^2[/tex]

[tex]Area = 28.26[/tex]

There are no enough information to solve (2) and (3) as the radius and/or diameter are not provided.

However, the following formula will be used to calculate the required areas.

[tex]Area = \pi r^2[/tex] --- same process as (1)

Answer:

slope = -3/4

Step-by-step explanation:

y(1)-y(2)/x(1)-x(2)

Plug in coordinates (0,4) and (4,1)

1-4/4-0

-3/4 is the slope