Estimate the amount of the tip by rounding the bill to the nearest ten dollars before calculating.

20% tip on a bill of $945.41

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:

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

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: 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:

Step-by-step explanation:

here,

base=28 ft

height=24 ft

are of parallelogram=base*height

=28*24

=672 ft^2

Answer:

672 ft²

Step-by-step explanation:

Area of parallelogram is the same as the area of a rectangle.

28 × 24 = 672 ft²

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

Answer:

sinA=sin(90-B)

sinA=90_B

now,A+B

=90

Answer:

Wikipedia says:

"In geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles)."

https://en.wikipedia.org/wiki/Square

Step-by-step explanation:

[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]

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:

[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:

They are all squares similar to the base.

Step-by-step explanation:

They are not congruent to the base but are similar.

Answer:

I think it's a

I'm not that sure tho

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:

10  1/5 pi

Step-by-step explanation:

First find the area of the circle

A = pi r^2 = pi *6^2 = 36 pi

Then find the fraction of the circle that is shaded

A circle is 360 degrees

102/360 =17/60

Multiply the fraction by the area

17/60 * 36 pi

51/5 pi

10  1/5 pi

Answer:

32.04

Step-by-step explanation:

firstly area of a sector is angle/360 multiplied by pi *r squared

so in this case it is going to be 102/360 *pi *6^2

6 squared is 36 all multiplied by pi and 106/360

it is advisable that you enter them all at once in your calculator

the final answer will be32.0444507

which is rounded to 32.04

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:

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:

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:

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:

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:

(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:

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.

https://brainly.com/question/7558603

#SPJ2

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:

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

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.