Which rule describes the composition of transformations that maps ABC to A”B’C”

Answer:

33.51 cm

Step-by-step explanation:

240/360 = 2/3 (Arc length is 2/3 of the total circumference)

C = 2[tex]\pi[/tex]r             ( Calculate the total circumference)    

C = 2(8)[tex]\pi[/tex]

C = 50.265

2/3(50.265)      (Take 2/3 of the circumference. times 2 divide by 3)

33.51

Use a calculator and leave the answer to C and then multiply and divide. You get a more precise answer.

The exact arc length is [tex]\frac{32\pi}{3}[/tex] radians.

The arc length in approximate form is 33.49 radians.

[tex]s = r\times \theta[/tex]

where r is the radius of the circle and [tex]\theta[/tex] is the central angle in radians.

Radians = Degrees ×[tex]\frac{\pi}{180^{\circ}}[/tex]

For given question,

We have been given a circle with a 8-cm radius associated with a central angle of 240 degrees.

[tex]r=8~cm,~\theta=240^{\circ}[/tex]

First we convert angle in radians.

[tex]\theta=240^{\circ}\\\\\theta=240^{\circ} \times \frac{\pi}{180^{\circ}}\\\\ \theta=\frac{4\pi}{3}[/tex]

Using the formula of the arc length,

[tex]s=8\times \frac{4\pi}{3} \\\\s=\frac{32\pi}{3}[/tex]

The exact answer of the arc length is [tex]s=\frac{32\pi}{3}[/tex]

Substitute the value of [tex]\pi = 3.14[/tex]

So, the arc length would be,

[tex]\Rightarrow s=\frac{32\times \pi}{3}\\\\\Rightarrow s=\frac{32\times 3.14}{3}\\\\\Rightarrow s=33.49[/tex]radians

Therefore, the exact arc length is [tex]\frac{32\pi}{3}[/tex] radians.

the arc length in approximate form is 33.49 radians.

Learn more about the arc length here:

https://brainly.com/question/16403495

#SPJ2

Answer:

To solve for x, you must multiply by the reciprocal.

In this case, multiply both sides by [tex]\frac{3}{2}[/tex] .

When doing this the result will be x = 3

9514 1404 393

Answer:

  1/3; geometric

Step-by-step explanation:

Apparently, your sequence is ...

  81, 27, 9, 3, 1, ...

The differences between these numbers vary, but the ratio of each to the one before is a constant:

  27/81 = 9/27 = 3/9 = 1/3

The sequence is geometric with a common ratio of 1/3. The next number in the sequence is (1)(1/3) = 1/3.

Answer:

It should be 8.6 yards, as 238.64÷3.14 = 74.

√74 = 8.60, or 8.6 :)

Answer:

mark me as brinalist if answers are correct

Answer:

Step-by-step explanation:

commission = 0.7% of $12,500

= 0.007×$12,500

= $87.5

Answer:

Kindly check explanation

Step-by-step explanation:

A.)

H0 : μ = 5000

H0 : μ > 5000

xbar = 6671 ; s = 8185.21 ; n = 52 ; α = 0.05

The test statistic :

T = (xbar - μ) ÷ (s/√(n))

T = (6671 - 5000) ÷ (8185.21/√52)

T = 3.814

Pvalue from Test statistic : ; df = n - 1 = 52-1= 51

Pvalue at 3.814; 51 = 0.000185

Pvalue < α ; Reject H0 and conclude that average birth is greater than 5000

B)

H0 : μ = 6000

H0 : μ < 6000

xbar = 4187 ; s = 4386 ; n = 52 ; α = 0.01

The test statistic :

T = (xbar - μ) ÷ (s/√(n))

T = (4187 - 6000) ÷ (4386/√52)

T = - 2.981

Pvalue from Test statistic : ; df = n - 1 = 52-1= 51

Pvalue at - 2.981; 51 = 0.0022

Pvalue < α ; Reject H0 and conclude that average death is less than 6000

C.)

H0 : μ < 2500

H0 : μ ≥ 2500

xbar = 2744 ; s = 3134.41 ; n = 52 ; α = 0.05

The test statistic :

T = (xbar - μ) ÷ (s/√(n))

T = (2744 - 2500) ÷ (3134.41/√52)

T = 0.561

Pvalue from Test statistic : ; df = n - 1 = 52-1= 51

Pvalue at 0.561; 51 = 0.289

Pvalue > α ; Fail to Reject H0 and conclude that average marriage is not greater Tha or equal to 2500

D.)

H0 : μ = 4000

H0 : μ ≤ 4000

xbar = 1451 ; s = 1217 ; n = 52 ; α = 0.01

The test statistic :

T = (xbar - μ) ÷ (s/√(n))

T = (1451 - 4000) ÷ (1217/√52)

T = - 15.10

Pvalue from Test statistic : ; df = n - 1 = 52-1= 51

Pvalue at - 15.10; 51 = 0.000001

Pvalue < α ; Reject H0 and conclude that average divorce is less eqaul to 4000

Answer:

C.

Step-by-step explanation:

For an angle to be supplementary to another angle, they must be equal to 180. Angles 6, 10, 13, and 9 are all supplementary to angle 16. Although there are more choices in different answers it wouldn't work with question, so C is the right answer.

Angle 16 is supplementary to angle 9 by the Same Side Interior Angles Theorem, which makes it supplementary to angle 10 by the Alternate Exterior Angles Theorem, which is also congruent to angle 13 by the Vertical Angles Theorem, which is also supplementary to angle 6 by the Alternate Exterior Angles Theorem.

Answer: (a) and (d)

Step-by-step explanation:

From the graph, vertex is at

Graph is same about the point [tex]x=2[/tex] . Therefore, axis of symmetry is the line [tex]x=2[/tex]

Y intercept is the place where curve intersect the Y-axis that is [tex](0,2)[/tex]

Option (a) and (d) are correct.

Answer:

Plastic is 22.5 pounds and aluminum is 32.5 pounds.

Step-by-step explanation:

total junk = 55 pounds

Value of plastic = $ 1.60 per pound

Value of aluminum = $ 1.28 per pound

Total value= $ 77.60

Let the plastic is p and the aluminum is 55 - p.

Total cost

77.60 = 1.6 p + (55 - p) x 1.28

77.60 =  1.6 p + 70.4 - 1.28 p

7.2 = 0.32 p

p = 22.5 pounds

So, plastic is 22.5 pounds and aluminum is 32.5 pounds.

Answer:

remember the chain rule:

h(x) = f(g(x))

h'(x) = f'(g(x))*g'(x)

or:

dh/dx = (df/dg)*(dg/dx)

we know that:

z = 4*e^x*ln(y)

where:

y = u*sin(v)

x = ln(u*cos(v))

We want to find:

dz/du

because y and x are functions of u, we can write this as:

dz/du = (dz/dx)*(dx/du) + (dz/dy)*(dy/du)

where:

(dz/dx)  = 4*e^x*ln(y)

(dz/dy) = 4*e^x*(1/y)

(dx/du) = 1/(u*cos(v))*cos(v) = 1/u

(dy/du) = sin(v)

Replacing all of these we get:

dz/du = (4*e^x*ln(y))*( 1/u) + 4*e^x*(1/y)*sin(v)

          = 4*e^x*( ln(y)/u + sin(v)/y)

replacing x and y we get:

dz/du = 4*e^(ln (u cos v))*( ln(u sin v)/u + sin(v)/(u*sin(v))

dz/du = 4*(u*cos(v))*(ln(u*sin(v))/u + 1/u)

Now let's do the same for dz/dv

dz/dv = (dz/dx)*(dx/dv) + (dz/dy)*(dy/dv)

where:

(dz/dx)  = 4*e^x*ln(y)

(dz/dy) = 4*e^x*(1/y)

(dx/dv) = 1/(cos(v))*-sin(v) = -tan(v)

(dy/dv) = u*cos(v)

then:

dz/dv = 4*e^x*[ -ln(y)*tan(v) + u*cos(v)/y]

replacing the values of x and y we get:

dz/dv = 4*e^(ln(u*cos(v)))*[ -ln(u*sin(v))*tan(v) + u*cos(v)/(u*sin(v))]

dz/dv = 4*(u*cos(v))*[ -ln(u*sin(v))*tan(v) + 1/tan(v)]

Answer:

[tex]\displaystyle f(3x) = \frac{6x + 5}{3x + 4}[/tex]

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle f(x) = \frac{2x + 5}{x + 4}[/tex]

Step 2: Find

Answer: The graph moved left 3 units.

(x, y) = (x - 3, y)

Answer:

3

Step-by-step explanation:

start with the ending answer and go backwards

Answer:

3.

Step-by-step explanation:

.

Answer:

1d = -3

2b = 2

2c = 1

3a = 3

3d = 4

Step-by-step explanation:

Polynomial 1: [tex]x^2-8x+15[/tex]

Multiply the leading coefficient, 1, and the last term, 15. You get: 15.

Then, list out the factors of 15 and the addends of -8 until you get two of numbers that are the same:

Factors of 15: -5 * -3

Addends of -8: -5 + -3

Replace the -8x with -5x - 3x:

[tex]x^2-5x-3x+15[/tex]

Put parentheses around the first 2 terms & last 2 terms and factor like so:

[tex](x^2-5x)-(3x+15)[/tex]

[tex]x(x-5)-3(x-5)[/tex]

[tex](x-5)(x-3)[/tex]

Looking at the answer (ax + b)(cx + d), d would correspond with -3.

Polynomial 2: [tex]2x^3-8x^2-24x[/tex]

First factor out the x:

[tex]x(2x^{2}-8x-24)[/tex]

Divide the polynomial inside by 2 and place the 2 outside with the x:

[tex]2x(x^2-4x-12)[/tex]

Then find the factors of 1*-12 and the addends of -4 and see which two numbers match:

Factors of -12: -6 * 2

Addends of -4: -6 + 2

Replace the -8x with -6x + 2x:

[tex]2x(x^2-6x+2x-12)[/tex]

Put parentheses around the first 2 terms & last 2 terms and factor like so:

[tex]2x((x^2-6x)+(2x-12))[/tex]

[tex]2x(x(x-6)+2(x-6))[/tex]

[tex]2x((x+2)(x-6))[/tex]

[tex]2x(x+2)(x-6)[/tex]

Looking at the answer (2x)(ax + b)(cx + d), b & c would correspond with 2 & 1.

Polynomial 3: [tex]6x^2+14x+4[/tex]

Divide the polynomial by 2:

[tex](2)(3x^2+7x+2)[/tex]

Find the factors of 3*2 and the addends of 7 and see which two numbers match:

Factors of 6: 6 * 1

Addends of 7: 6 + 1

Replace the 7x with 6x + x:

[tex](2)(3x^2+6x+x+2)[/tex]

Put parentheses around the first 2 terms & last 2 terms and factor like so:

[tex](2)((3x^2+6x)+(x+2))[/tex]

[tex](2)(3x(x+2)+(x+2))[/tex]

[tex](2)((3x+1)(x+2))[/tex]

[tex](2)(3x+1)(x+2)[/tex]

Then multiply the 2 with the (x+2) and here's your final answer:

[tex](3x+1)(2x+4))[/tex]

Looking at the answer (ax + b)(cx + d), a & d correspond with 3 & 4.

Hope that helps (●'◡'●)

(This took a while to write, sorry about that)

Answer:

Answer:Amy used 4 41-cent stamps and 8 6-cent stamps.

Step-by-step explanation:

Let x represent the number of 41-cent stamps that Amy used. Let y represent the number of 6-cent stamps that Amy used.

41 cents = 41/100 = $0.41

6 cents = 6/100 = $0.06

She uses 41-cent stamps and 6-cent stamps to pay $2.12 in postage. It means that

0.41x + 0.06y = 2.12

Multiplying through by 100, it becomes

41x + 6y = 212

6y = 212 -41x

We would test for corresponding values of x and y that satisfies the equation and they must be whole numbers.

If x = 3,

6y = 212 - 41 × 3 = 89

y = 89/6 = 14.8333

If x = 4,

6y = 212 - 41 × 4 = 48

y = 48/6 = 8

Answer:Amy used 4 41-cent stamps and 8 6-cent stamps.

Step-by-step explanation:

Let x represent the number of 41-cent stamps that Amy used. Let y represent the number of 6-cent stamps that Amy used.

41 cents = 41/100 = $0.41

6 cents = 6/100 = $0.06

She uses 41-cent stamps and 6-cent stamps to pay $2.12 in postage. It means that

0.41x + 0.06y = 2.12

Multiplying through by 100, it becomes

41x + 6y = 212

6y = 212 -41x

We would test for corresponding values of x and y that satisfies the equation and they must be whole numbers.

If x = 3,

6y = 212 - 41 × 3 = 89

y = 89/6 = 14.8333

If x = 4,

6y = 212 - 41 × 4 = 48

y = 48/6 = 8

Answer:

C

Step-by-step explanation:

p=20+1

Without any extra conditions, the answer could be 3, and the simplest polynomial with the given roots would be

(x + 5) (x - (1 + 4i )) (x + 4i )

= x ³ + 4x ² + (11 - 4i ) x + 80 - 2i

If the polynomial is supposed to have only real coefficients, then any complex roots must occur along with their complex conjugates:

(x + 5) (x - (1 + 4i )) (x - (1 - 4i )) (x + 4i ) (x - 4i )

= x ⁵ + 3x ⁴ + 23x ³ + 133x ² + 112x + 1360

and then the degree would be 5.

Answer:

Step-by-step explanation:

P=R3000.00

T=3 years

SI=R905

SI=P\times R\times T\\R905=R3000\times \frac{r}{100}\times 3SI=P×R×T

R905=R3000×  

100

r

​

×3

R905=\frac{R9000r}{100}R905=  

100

R9000r

​

R905=\frac{R905}{R90}R905=  

R90

R905

​

r=\frac{R905}{R90.}r=  

R90.

R905

​

r=10.06\%r=10.06%

Step-by-step explanation:

each point should be at a 2. the center is 0,0

Answer:

2√14 prob I'm not 100% sure

Answer:

i put in 3 to make 23436 because 36 is divisible by 6

Answer:

1 hour

Step-by-step explanation:

J = 50 mph by 2 hours

S = 50 mph by 1 hour

2-1 = 1

Answer/Step-by-step explanation:

✔️-72 ÷ (-2)

The division of two negative numbers will give us a positive number. i.e. - ÷ - = +

Therefore:

-72 ÷ (-2) = 36

✔️-72 ÷ 2

The division of a negative number and a positive number will give us a negative number. i.e. - ÷ + = -

Therefore:

-72 ÷ 2 = -36

✔️72 ÷ (-2)

The division of a positive number and a negative number will give us a negative number. i.e. + ÷ - = -

Therefore:

72 ÷ (-2) = -36

Step-by-step explanation:

2x-1 - (4/(2x-1)) + 5

2x^2 -4x -2 -4 + 10x - 5

2x^2 +6x -11

Step-by-step explanation:

Hey there!

Here;

f(x) = 5x + 1

g(x) = (√x)

Now;

fog(X) = f(g(x))

= f(√x)

= 5√x + 1

Therefore, fog(X) = 5√x + 1.

Hope it helps!

Answer:

a) The expression for the number of bacteria is [tex]P(t) = 100\cdot e^{1.131\cdot t}[/tex].

b) There are 2975 bacteria after 3 hours.

c) The rate of growth after 3 hours is about 3365.3 bacteria per hour.

d) A population of 10,000 will be reached after 4.072 hours.

Step-by-step explanation:

a) The population growth of the bacteria culture is described by this ordinary differential equation:

[tex]\frac{dP}{dt} = k\cdot P[/tex] (1)

Where:

[tex]k[/tex] - Rate of proportionality, in [tex]\frac{1}{h}[/tex].

[tex]P[/tex] - Population of the bacteria culture, no unit.

[tex]t[/tex] - Time, in hours.

The solution of this differential equation is:

[tex]P(t) = P_{o}\cdot e^{k\cdot t}[/tex] (2)

Where:

[tex]P_{o}[/tex] - Initial population, no unit.

[tex]P(t)[/tex] - Current population, no unit.

If we know that [tex]P_{o} = 100[/tex], [tex]t = 1\,h[/tex] and [tex]P(t) = 310[/tex], then the rate of proportionality is:

[tex]P(t) = P_{o}\cdot e^{k\cdot t}[/tex]

[tex]\frac{P(t)}{P_{o}} = e^{k\cdot t}[/tex]

[tex]k\cdot t = \ln \frac{P(t)}{P_{o}}[/tex]

[tex]k = \frac{1}{t}\cdot \ln \frac{P(t)}{P_{o}}[/tex]

[tex]k = \frac{1}{1}\cdot \ln \frac{310}{100}[/tex]

[tex]k\approx 1.131\,\frac{1}{h}[/tex]

Hence, the expression for the number of bacteria is [tex]P(t) = 100\cdot e^{1.131\cdot t}[/tex].

b) If we know that [tex]t = 3\,h[/tex], then the number of bacteria is:

[tex]P(t) = 100\cdot e^{1.131\cdot t}[/tex]

[tex]P(3) = 100\cdot e^{1.131\cdot (3)}[/tex]

[tex]P(3) \approx 2975.508[/tex]

There are 2975 bacteria after 3 hours.

c) The rate of growth of the population is represented by (1):

[tex]\frac{dP}{dt} = k\cdot P[/tex]

If we know that [tex]k\approx 1.131\,\frac{1}{h}[/tex] and [tex]P \approx 2975.508[/tex], then the rate of growth after 3 hours:

[tex]\frac{dP}{dt} = \left(1.131\,\frac{1}{h} \right)\cdot (2975.508)[/tex]

[tex]\frac{dP}{dt} = 3365.3\,\frac{1}{h}[/tex]

The rate of growth after 3 hours is about 3365.3 bacteria per hour.

d) If we know that [tex]P(t) = 10000[/tex], then the time associated with the size of the bacteria culture is:

[tex]P(t) = 100\cdot e^{1.131\cdot t}[/tex]

[tex]10000 = 100\cdot e^{1.131\cdot t}[/tex]

[tex]100 = e^{1.131\cdot t}[/tex]

[tex]\ln 100 = 1.131\cdot t[/tex]

[tex]t = \frac{\ln 100}{1.131}[/tex]

[tex]t \approx 4.072\,h[/tex]

A population of 10,000 will be reached after 4.072 hours.