determine if the triangles are similar by side-side-side similarity

Answer:

See below for all answers and explanations

Step-by-step explanation:

1st Problem

[tex]F(s)=\frac{1}{s^4}+\frac{3s}{s^2+9}\\\\f(t)=\frac{t^3}{6}+3cos(3t)[/tex]

2nd Problem

[tex]F(s)=\frac{7}{s}+\frac{6}{s+4}-\frac{5}{s^2+16}\\ \\f(t)=7+6e^{-4t}-\frac{5}{4}sin(4t)[/tex]

3rd Problem

[tex]F(s)=\frac{1}{(s-2)(s+1)(s-3)}\\\\\frac{1}{(s-2)(s+1)(s-3)}=\frac{A}{s-2}+\frac{B}{s+1}+\frac{C}{s-3}\\ \\1=(s+1)(s-3)A+(s-2)(s-3)B+(s-2)(s+1)C[/tex]

[tex]1=(-1+1)(-1-3)A+(-1-2)(-1-3)B+(-1-2)(-1+1)C\\1=12B\\\frac{1}{12}=B[/tex]

[tex]1=(3+1)(3-3)+(3-2)(3-3)B+(3-2)(3+1)C\\1=4C\\\frac{1}{4}=C[/tex]

[tex]1=(2+1)(2-3)A+(2-2)(2-3)B+(2-2)(2+1)C\\1=-3A\\-\frac{1}{3}=A[/tex]

[tex]F(s)=\frac{-\frac{1}{3}}{s-2}+\frac{\frac{1}{12}}{s+1}+\frac{\frac{1}{4}}{s-3}\\ \\f(t)=-\frac{1}{3}e^{2t}+\frac{1}{12}e^{-t}+\frac{1}{4}e^{3t}[/tex]

4th Problem

[tex]F(s)=\frac{s+2}{s^2(s+1)(s-1)}\\ \\\frac{s+2}{s^2(s+1)(s-1)}=\frac{A}{s}+\frac{B}{s^2}+\frac{C}{s+1}+\frac{D}{s-1}\\\\s+2=s(s+1)(s-1)A+(s+1)(s-1)B+s^2(s-1)C+s^2(s+1)D\\ \\s+2=s^3A-sA+s^2B-B+s^3C-s^2C+s^3D+s^2D\\\\s+2=s^3(A+C+D)+s^2(B-C+D)-sA-B[/tex]

[tex]\begin{cases} A + C + D = 0\\B - C + D = 0\\- A = 1\\- B = 2 \end{cases}[/tex]

[tex]A+C+D=0\\(A+C+D=0)+(B-C+D)=0\\A+B+2D=0\\-1-2+2D=0\\-3+2D=0\\2D=3\\D=\frac{3}{2}[/tex]

[tex]A+C+D=0\\-1+C+\frac{3}{2}=0\\ \frac{1}{2}+C=0\\ C=-\frac{1}{2}[/tex]

[tex]F(s)=\frac{-1}{s}+\frac{-2}{s^2}+\frac{-\frac{1}{2}}{s+1}+\frac{\frac{3}{2}}{s-1}\\ \\f(t)=-1-2t-\frac{1}{2}e^{-t}+\frac{3}{2}e^{t}[/tex]

5th Problem

[tex]F(s)=\frac{s+1}{s(s^2+1)}\\\\\frac{s+1}{s(s^2+1)}=\frac{A}{s}+\frac{Bs+C}{s^2+1}\\\\s+1=(s^2+1)A+s(Bs+C)\\\\s+1=s^2A+A+s^2B+sC\\\\s+1=s^2(A+B)+sC+A[/tex]

[tex]\begin{cases} A + B = 0\\C = 1\\A = 1 \end{cases}[/tex]

[tex]A+B=0\\1+B=0\\B=-1[/tex]

[tex]F(s)=\frac{1}{s}+\frac{-s+1}{s^2+1}\\ \\F(s)=\frac{1}{s}+\frac{1-s}{s^2+1}\\\\F(s)=\frac{1}{s}+\frac{1}{s^2+1}+\frac{-s}{s^2+1}\\\\f(t)=1+sin(t)-cos(t)[/tex]

Answer:

Area of a regular polygon formulas

Step-by-step explanation:

area = n * a * ri / 2 , having ri - incircle radius (it's also an apothem - a line segment from the center to the midpoint of one of its sides)

area = perimeter * ri / 2 , given ri and polygon perimeter.

area = n * (ri)² * tan(π/n) , given ri.

Answer:

A) The page indictor shows 1/4

Step-by-step explanation:

Because 1 is out of a multiple 4 pages.

Hope it helps.

Answer:

39 sq.in

Step-by-step explanation:

find area of circle then subtract

Answer:

3.9 in²

Step-by-step explanation:

The shape is constructed of 2 semicircles (with diameter of 6 in) inside a square.  Therefore, to calculate the yellow region, subtract the area of the semicircles (which form a circle) from the area of the square, then halve the answer.

Area of a square = [tex]x^2[/tex]  ([tex]x[/tex] is the length of one side)

Given:

⇒ area of the square = 6² = 36 in ²

Area of a circle = [tex]\pi r^2[/tex]

Diameter of a circle = 2r

(where r is the radius)

Given:

⇒ area of the circle = [tex]\pi[/tex] × 3² = 9[tex]\pi[/tex] in²

Area of yellow region = (area of square - area of circle) ÷ 2

                                    = (36 - 9[tex]\pi[/tex]) ÷ 2

                                    = 3.9 in² (nearest tenth)

Answer:

Step-by-step explanation: just write from 2 to 11 one by one

Answer:358800

Number of dispositions of 4 letters without repetitions of the alphabet (26 letters): 26*25*24*23=358800

Step-by-step explanation:

Answer:

D. $2304.70

Step-by-step explanation:

a typical 2000 square foot house may cost anything from $200000 to $300000

Step-by-step explanation:

How much of a premium do you pay for a steel house worth $190,000 with $49,000 worth of content in a suburban area?

B. $1372.70

The graph of [tex]g(x)[/tex] opens downward and is shifted to the right 6 and up 3 units.

Let be [tex]f(x) = x^{2}[/tex], we need to apply the following three rigid transformations on [tex]f(x)[/tex] to obtain [tex]g(x)[/tex]:

Hence, the graph of [tex]g(x)[/tex] opens downward and is shifted to the right 6 and up 3 units. [tex]\blacksquare[/tex]

To learn more on rigid transformations, we kindly invite to check this verified question: https://brainly.com/question/1761538

Answer:

The graph of  opens downward and is shifted to the right 6 and up 3 units.

decimal system is the name of our number system.

Answer:

Our Number System is Hindu Arabic Number System.

The digits are: 0,1,2,3,4,5,6,7,8,9

Answer:

x = 10

y = 5√3

Step-by-step explanation:

SOLVE FOR X :

ABC = 90°

ABC + ACB + BAC = 180°

90° + ACB + 30° = 180°

ACB = 60°

cos(ACB) = BC/AC

cos(60°) = 5/x

x = 10

SOLVE FOR Y:

tan(BAC) = BC/AB

tan (30°) = 5/y

y = 5√3

PLEASE MARK ME AS BRAINLIEST AND HAVE A NICE DAY :)

The due date of the promissory note is May 24th 2013.

Data;

To calculate the due date of the note, we can use the formula of future value of the note.

[tex]FV = PV (1 + \frac{r}{n})^d\\ 3970 = 3600 (1 + \frac{9.6}{12})^d\\3970 = 3600(1+0.008)^d\\\frac{3970}{3600} =(1.008)^n[/tex]

Let's take the natural log of both sides

[tex](1.008)^n = (\frac{3970}{3600})\\ n\ln(1.008) = \ln(\frac{397}{360})\\ n = 12.28[/tex]

This is approximately 12 months and 9 days.

The due date of the promissory note is May 24th 2013.

Learn more on promissory note here;

https://brainly.com/question/25793394

https://brainly.com/question/4267195

Answer: 13 and 9

Step-by-step explanation:

because since there are two people 38-(8x2)=22

The only numbers that add up to 22 that have a difference of 4 are 13 and 9

Another way:

T=C+4

T+8+C+8=38

C+4+C+8=

Answer:

3y + 3 or 3(y+1)

Step-by-step explanation:

y + y + 1 + y + 2

= 3y + 3

= 3(y+1)

Answer:

3

Step-by-step explanation:

If x=11 then the top line would equal 11+4, which is 15

If y=3 then the bottom line would equal 3+2, which is 5

So, you end up with 15/5, which equals 3

Answer:

i think it's 22500 deep down to the ocean

Answer:

8( b - 4 )

Step-by-step explanation:

8 x ( b - 4 )

8( b - 4 )

I hope this helps!

Answer: 20 Pounds

Step-by-step explanation:

1/4 X 5 = 1/20 then reverse it

20/1 = 20 Pounds

(may not be correct!!!)

Answer:

The answer is A!

Step-by-step explanation:

area of the base = pi*(4x+2)^2 = pi*(16x^2 +16x +4)

volume of cylinder = pi*r^2 *h

V = pi *(16x^2 +16x +4)(5x+4) = pi*(80x^3 +80x^2 +20x +64x^2 +64x +16) =

= pi*(80x^3 +144x^2 +84x +16)

Answer:

Step-by-step explanation:

The volume of a cylinder can be thought of as the area of a circle, scaled by the height of the cylinder. The formula for the volume of a cylinder is:

[tex]V=\pi r^2h[/tex]

Plug in the radius, and the height:

[tex]V=\pi (4x+2)^2(5x+4)[/tex]

Use FOIL to expand the squared binomial:

[tex]V=\pi (16x^2+16x+4)(5x+4)[/tex]

Bring out the binomial to the front of the trinomial:

[tex]V=\pi [(5x+4)(16x^2+16x+4)][/tex]

The process to multiply a trinomial by a binomial involves multiplying the trinomial by each term of the binomial:

[tex]V=\pi [(5x+4)(16x^2+16x+4)]=\pi [5x(16x^2+16x+4)+4(16x^2+16x+4)][/tex]

The rest is just distributing and tedious algebra:

[tex]V=\pi [(80x^3+80x^2+20x)+(64x^2+64x+16)][/tex]

Combine like terms and order the terms from highest exponent to lowest exponent. That is the definition of standard form:

[tex]V=\pi [80x^3+144x^2+84x+16][/tex]

[tex]V=4\pi [20x^3+36x^2+21x+4][/tex]

Answer: $41000 Was the Smiths family budget last year.

Step-by-step explanation:

First you take $4620 and DIVIDE it by .11 you will get $42000 and since last year had $1000 less to spend you subtract $1000 from $42000 to get $41000 for the budget last year.

Answer:

9

Step-by-step explanation:

Follow PEMDAS

[tex]4-(-6)+(-4)+3x\\4+6-4+3x\\6+3x\\6+3=9[/tex]

Answer:

6

Step-by-step explanation: [tex]4-\left(-6\right)+\left(-4\right)+3\times0[/tex]

Apply the Inverse Property of Addition

[tex]-\left(-6\right)+3\times0[/tex]

Apply Zero Property of Multiplication

[tex]-\left(-6\right)[/tex]

Determine the sign

[tex]6=YOUR\ ANSWER[/tex]

I hope this helps you

:)

The answer is 21. Hope this Helps!

Answer:

p = 1.25x + 70

Step-by-step explanation:

We know she makes $70 each day and we know she makes $1.25 for each computer she sells.

With that we can add it into an equation because we can add 70 + 1.25, but the amount for each computer she sells in unknown so we give it an x which makes it 1.25x.

So, we do 1.25x + 70, but the amount total is missing so that is our p.

This finally completes our equation, p = 1.25x + 70 or  1.25x + 70 = p

Answer:

THE AWNSWER IS A≥3B

Step-by-step explanation:

A≥3B

Answer: 30

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Answer:

30 is the correct answer

Answer:

Step-by-step explanation:

Two distinct lines will always have a point of intersection, provided they are not parallel. That is, the system of equations {x +y = 1, y = mx} will have a unique solution as long as m ≠ -1.

The solution to the system can be found by substitution:

  x +mx = 1

  x(1 +m) = 1 . . . . factor out x

  x = 1/(1+m) . . . . . divide by the coefficient of x; we must have m ≠ -1

  y = m/(1+m) . . . . find the y-coordinate of the solution

The point of intersection is (1/(1+m), m/(1+m)).

__

The above solution is undefined when the denominator is zero: m = -1. There is no solution for m = -1.

Answer:

y=(-1/9)x-(10/3)

Step-by-step explanation:

Since the line is perpendicular to y=9x-5, the slope of that line would be the opposite of the reciprocal of the original slope value. In this case, the slope of the line would be -1/9. So we have y=(-1/9)x+? Since we know a point, (-3, -3), we can input this back into our original equation and we have: -3=(1/3)+? We simplify and we have ?=-10/3. Therefore the final equation of the line that is perpendicular to that line and passes through the point (-3,-3) is y=(-1/9)x-(10/3).  

Answer:

The formula that is used to calculate the surface area of a triangular prism is, Surface area = (Perimeter of the base × Length of the prism) + (2 × Base Area) = (S1 + S2+ S3)L + bh; where 'b' is the bottom edge of the base triangle, 'h' is the height of the base triangle, L is the length of the prism and S1, S2 and S3 are the edges of the base triangle.

Answer:

60

Step-by-step explanation:

10x = (21x - 3)/2

20x = 21x - 3

x = 3

measure of arc HF = 21x - 3 = 21(3) - 3 = 60