Alex is 12 years older than George.
Carl is three times older than Alex
The sum of their ages is 68
Find the ratio of George's age to Carl's age to Alex's age.

The length of arc ABC with center O and radius of 9 units is 13π.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let r represent the radius of the circle. Hence:

arc ADC = (100 / 360) * 2πr

5π = (100 / 360) * 2πr

r = 9 units

arc ABC = (260 / 360) * 2π(9) = 13π

The length of arc ABC with center O and radius of 9 units is 13π.

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The representation, in polar coordinates, of the point (1 , 5pi/6) is (-1, 11pi/6).

It should be noted that polar coordinate simply means a coordinate system where the point on the plane is determined by a distance and reference point.

In this case, the representation, in polar coordinates, of the point (1 , 5pi/6) is (-1, 11pi/6). When graphing the polar coordinate, the pole should be moved in a direction opposite the given positive angle.

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Answer:

-1

Step-by-step explanation:

trust

Step-by-step explanation:

As it is given that, a cylinder has a height of 15 yards and the volume of the cylinder is 15,260.4 cubic yards and we are here to find the radius of the cylinder.

[tex] \: [/tex]

We know that,

[tex]{ \longrightarrow\qquad{\frak {\pmb{ \pi {r}^{2}h = Volume_{(cylinder) } }}}} \\ \\[/tex]

Where,

[tex] \: [/tex]

Now, we will substitute the given values in the formula :

[tex] \: [/tex]

[tex]{ \longrightarrow\qquad{\sf {\pmb{ 3.14 \times {r}^{2} \times 15 = 15260.4 }}}} \\ \\[/tex]

[tex]{ \longrightarrow\qquad{\sf {\pmb{ {r}^{2} \times 47.1 = 15260.4 }}}} \\ \\[/tex]

[tex]{ \longrightarrow\qquad{\sf {\pmb{ {r}^{2} = \dfrac{15260.4}{47.1} }}}} \\ \\[/tex]

[tex]{ \longrightarrow\qquad{\sf {\pmb{ {r}^{2} \ = 324 }}}} \\ \\[/tex]

[tex]{ \longrightarrow\qquad{\sf {\pmb{ r = \sqrt{324} }}}} \\ \\[/tex]

[tex]{ \longrightarrow\qquad{ \underline{ \boxed{\pmb {\frak{ r = 18 } }}}}} \: \: \: \bigstar\\ \\[/tex]

[tex] \: [/tex]

Therefore,

Answer:

Step-by-step explanation:

Given:

To Find:

Solution:

Here we are given height and volume of the cylinder. To find the radius of the cylinder We will substitute the value of height and volume in give formula:

Volume of cylinder = πr²h

➝ 15,260.4 = 22/7 × (r)² × 15

➝ 15,260.4 = (r)² × 330/7

➝ 15,260.4 = (r)² × 47.1

➝ 15,260.4/47.1 = (r)²

➝ 324 = (r)²

➝ √324 = r

➝ 18 = r

Hence,

Answer:

x = ± [tex]\sqrt{3}[/tex]

Step-by-step explanation:

3x² - 9 = 0 ( add 9 to both sides )

3x² = 9 ( divide both sides by 3 )

x² = 3 ( take square root of both sides )

x = ± [tex]\sqrt{3}[/tex]

or

3x² - 9 = 0 ← factor out 3 from each term

3(x² - 3) = 0

equate x² - 3 to zero and solve for x

x² - 3 = 0 ( add 3 to both sides )

x² = 3 ( take square root of both sides )

x = ± [tex]\sqrt{3}[/tex]

The pints of ice cream for the students is an illustration of metric units

Nadia needs 12 pints of ice cream for the 24 students

The given parameter is:

Students = 24

She needs one cup for each student in the class.

So, the number of cups needed is:

Cups = 24

1 cup makes 1/2 pint.

So, we have:

Pint = 1/2 * 24

Pint = 12

Hence, Nadia needs 12 pints of ice cream for the 24 students

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The values of y when x=5.7 will be 5. In the graphs, the function is represented as y=⌊x⌋

A diagram depicting the relationship between two or more variables, each measured along with one of a pair of axes at right angles.

In the graphs the function y=⌊x⌋

The value of the y obtaining will be the whole number of the left axis of the integers.5 is the nearest whole number to the 5.7.

The given value of the function is ;

y = [ 5.7 ] = 5

Hence the value of the y is 5.

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Answer:

Step-by-step explanation:

The answer will be t=-35Sin{[tex]\pi[/tex]/6m)+55 average daily temperature, t, in degrees Fahrenheit for a city as a function of the month of the year.

Temperature is the degree or intensity of heat present in a substance or object, especially as expressed according to a comparative scale and shown by a thermometer or perceived by touch.

For the equation: 35cos(pi/6(m+3)+55)

Simplify it by multiplying pi/6 in the bracket values:  

[tex]=35 Cos (\dfrac{\pi m}{6}+\dfrac{3\pi }{6}+55)[/tex]

[tex]=35 Cos(\dfrac{\pi m}{6}+55+\dfrac{\pi}{2})[/tex]

Now suppose x = m.pi/6+55, while pi/2 = 90⁰

As per law cos(x+90⁰)=-sin(x)

so,cos((m.pi/6)+55+90⁰=-sin((m.pi/6)+55)

Hence answer will be

[tex]=-35Sin(\dfrac{\pi m}{6}+55)[/tex]

The law cos(x+90⁰)=-sin(x) can be proved by putting y=90⁰ in the following formula,

cos(x+y)=cos(x).cos(y)-sin(x).sin(y)

Hence the answer will be t=-35Sin{[tex]\pi[/tex]/6m)+55 average daily temperature, t, in degrees Fahrenheit for a city as a function of the month of the year.

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Answer:

A

Step-by-step explanation:

t = negative 35 sine (StartFraction pi Over 6 EndFraction m) + 55

Answer:

Step-by-step explanation:

Answer:

hi, where's mt 20pts

Step-by-step explanation:

0.3

12+6+9+13=40

12/40 (or 3/10 simplified)

Thus, 0.3 as a decimal

Hope this helps!

Answer:

B

Step-by-step explanation:

yes, the angles are the same.

and the scale factor is

NS / GA = 15/12 = 5/4

The loan option that would allow Charles to pay the LEAST in interest is option A.

Compound Interest is a process where the interest is credited to the initial amount and interest, on the whole, is charged again. and this continues for t period of time.

It is given by the formula,

[tex]A=P(1+r\%)^n[/tex]

where A is the value after t period of time, P is the principal amount, and,

r is the rate of interest.

A.) Principle amount = $10,000

Time Period of loan = 2 years

Rate of Interest = 4.75% per annum

Now, the total amount can be written as

[tex]=P(1+r\%)^n\\\\= \$10,000 \times (1+0.0475)^2\\\\= \$10,972.56[/tex]

The interest will be = $10,972.56 - $10,000 = $972.56

B.)  Principle amount = $10,000

Time Period of loan = 3 years

Rate of Interest = 4.00% per annum

Now, the total amount can be written as

[tex]=P(1+r\%)^n\\\\= \$10,000 \times (1+0.04)^2\\\\= \$11,248.64[/tex]

The interest will be = $11,248.64 - $10,000 = $1,248.64

C.) Principle amount = $10,000

Time Period of loan = 4 years

Rate of Interest = 3.75% per annum

Now, the total amount can be written as

[tex]=P(1+r\%)^n\\\\= \$10,000 \times (1+0.0375)^2\\\\= \$11,586.5[/tex]

The interest will be = $11,586.5- $10,000 = $1,586.5

D.) Principle amount = $10,000

Time Period of loan = 5 years

Rate of Interest = 3.00% per annum

Now, the total amount can be written as

[tex]=P(1+r\%)^n\\\\= \$10,000 \times (1+0.03)^5\\\\= \$11,592.74[/tex]

The interest will be = $11,592.74 - $10,000 = $1,592.74

Hence, the loan option that would allow Charles to pay the LEAST in interest is option A.

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The algebraic expression that is a polynomial with a degree of 2 is

6x^2-6x+5.

The degree of a term of a polynomial is the total sum of the exponents of the variables in each term.

The highest degree of the polynomial is considered the degree of the polynomial.

For the first option,

[tex]4x^3-2x+10[/tex]

The highest degree is 3.

The second option is,

[tex]x^2-8x^3+3[/tex]

This polynomial also has a degree of 3.

The third option is,

[tex]6x^2-6x+5[/tex]

This last option has a degree of 2.

Therefore the correct answer is option C.

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Answer:The answer is C

Step-by-step explanation:Edge 2022 :)

31°

hope it helps......!!!!!

The sum of two polynomials is 8d^5 - 3c^3d2 +5c^2d^3 - 4cd^4 +9

2d^5 - c^3d^2 +8cd^4 +1 would be 6d^5 - 2c^3d^2+ 5c^2d^3 - 12cd^4 +8.

Polynomials are those algebraic expressions that consist of variables, coefficients, and constants. The standard form of polynomials has mathematical operations such as addition, subtraction, and multiplication.

Given that

[tex]8d^5 - 3c^3d2 +5c^2d^3 - 4cd^4 +9\\[/tex]

Now

if one is added i.e.

[tex]2d^5 - c^3d^2 +8cd^4 +1,[/tex]

Now let us assume the other polynomial be x

So,

[tex]8d^5 - 3c^3d2 +5c^2d^3 - 4cd^4 +9\\[/tex] = x + [tex]2d^5 - c^3d^2 +8cd^4 +1,[/tex]

x = [tex]8d^5 - 3c^3d2 +5c^2d^3 - 4cd^4 +9\\[/tex] - ( [tex]2d^5 - c^3d^2 +8cd^4 +1,[/tex])

x = [tex]6d^5 - 2c^3d^2+ 5c^2d^3 - 12cd^4 +8[/tex]

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Let's consider what the problem wants us to find:

Let's find the fractional part:

 ⇒ the fractional part is equal:

       [tex]\frac{degree-covered-by-angle}{total-angle} =\frac{280}{180} =\frac{2*2*7*10}{2*2*3*3*5} =\frac{7*10}{3*3*5} =\frac{70}{45}=\frac{14}{9}[/tex]

  Answer: The angle 280 degrees covers 14/9 of a semicircle.

Let's find the angle measure in radians:

 ⇒ we know that [tex]2\pi[/tex] radians are equal to 360 degrees

    ⇒ to convert any degree to radians, you must multiply [tex]\frac{\pi }{180}[/tex]

        so [tex]280*\frac{\pi }{180} =\frac{28}{18}*\pi =\frac{28\pi }{18}=\frac{2*14*\pi }{2*9} =\frac{14\pi }{9}[/tex]

 Answer: The angle 280 degrees in radians is [tex]\frac{14\pi} {9}[/tex] which in terms of [tex]\pi[/tex] is

14/9

Hope that helps!

Answer:

x = 27 units

Step-by-step explanation:

39 / ( 39+ 26) = x / (x+18)

x = 27

Volume of rectangle is

10 times 5 times 3

150 cm

3.14 times radius times 2 times height

So, 50.24 Cm

So its 200.24 Cm

The complex number z = 4(cos(5pi/6) + isin(5pi/6)) is given as z = -3.464 + 2i in standard form

Complex numbers are the numbers which is in the form of:

a + ib where, a,b are real numbers and 'i' is an imaginary number.

The complex number can also be represented in polar form as:

z = r(cosФ + isinФ)

Given the complex number:

z=4(cos(5pi/6) + isin(5pi/6)), hence converting to standard form gives:

z = -3.464 + 2i

The complex number z = 4(cos(5pi/6) + isin(5pi/6)) is given as z = -3.464 + 2i in standard form

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Answer:

-2 square root 3 + 2i

Step-by-step explanation:

Distance measure how far an object have gone. The length of the line segment that has the endpoints A (-3,2) and B (1,0) is 2√5.

The formula for calculating the distance between two coordinates is expressed as:

D = √(x2-x1)²+(y2-y1)²

Given the coordinate points A (-3,2) and B (1,0), the length of the line segment that has the endpoint is given as:

D = √(0-2)²+(1+3)²
D = √(2)²+(4)²
D = √16+4
D=√20
D = 2√5

Hence the length of the line segment that has the endpoints A (-3,2) and B (1,0) is 2√5

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Answer:

the answer 192(If Multiplied)

Answer:

9 is A 10 is D

not sure of the other two

Step-by-step explanation:

9 increases by 4 every time

10 increases by 7 every time

Answer:

9. A

10. D

11. D

12. A

Step-by-step explanation:

9. Look at the pattern; 6+4=10, 10+4=14, 14+4=18, 18+4=22.

10. Same thing for number nine.

11 & 12. Its just vocab

Answer:

  x = 13

Step-by-step explanation:

The relevant fact about vertical angles is that they are congruent, their measures are equal. This lets you write an equation relating the expressions for the measures of angles A and B.

__

  ∠A = ∠B

  (8x -12)° = (6x +14)° . . . . . substitute given expressions

  2x = 26 . . . . . . . . . . . divide by °, add 12-6x

  x = 13 . . . . . . . . . . divide by 2

Answer:

[tex] \red{ \rule{1pt}{500000pt}}[/tex] [tex] \red{ \rule{1pt}{500000pt}}[/tex]

Step-by-step explanation:

The Net profit margin is 22.41%

Rusty's Tool experienced $67550 in net sales, creating a gross profit of $50338.

If Rusty had a total operating expense of $35200 then we have to find the net profit margin.

Since profit $50338 includes the operating expense of $35300 then net profit will be

= $50338 - $33500

= $15138

Now the selling price is given as $67550.

Profit margin = (Net profit/selling price) 100

Profit margin =151.38/675.50=22.41 %

Therefore, the answer is profit margin = 22.41%.

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Answer:

x = a/7

Step-by-step explanation:

Area is length x width, so let's call our unknown, the length, x

So the total area is 7 (the width) times x

If the total area is a, then we can write the equation a = 7(x)

Next, we have to isolate the variable for the length, x

To do this, we divide both sides by 7, leaving a/7 = x, or x = a/7

The Bruce must include X and Z in his report.

We have given  the data on four electric circuits listed in the table

For w :

Voltage, V=18\ V

resistance, [tex]R=38\ \Omega[/tex]

The formula of Ohm's low is V=IR

[tex]I=\dfrac{V}{R}[/tex]

[tex]I=\dfrac{18\ V}{38\ \Omega}[/tex]

I=0.47

[tex]q=0.47\times8[/tex]

So charge,q=It

q=3.76\ C

For x :

Voltage, V=24\ V

[tex]resistance, R=34\ \Omega[/tex]

so, V=IR...(Ohm's low)

[tex]I=\dfrac{V}{R}[/tex]

[tex]I=\dfrac{24\ V}{34\ \Omega}[/tex]

I=0.705

[tex]q=0.705\times8[/tex]

So charge,q=It

q=5.64\ C

For y :

Voltage, V=34\ V

resistance, [tex]R=70\ \Omega[/tex]

so, V=IR.......(Ohm's low)

[tex]I=\dfrac{V}{R}[/tex]

[tex]I=\dfrac{34\ V}{70\ \Omega}[/tex]

I=0.485

[tex]q=0.485\times8[/tex]

So charge,q=It

q=3.88\ C

For z :

Voltage, V=12\ V

resistance, [tex]R=18\ \Omega[/tex]

so, V=IR......(Ohm's low)

[tex]I=\dfrac{V}{R}[/tex]

[tex]I=\dfrac{12\ V}{18\ \Omega}[/tex]

I=0.66

[tex]q=0.66\times8[/tex]

So charge,q=It

q=5.28\ C

Therefore, the circuits X and Z deliver 5.64 C and 5.28 C of charge.

Hence, Bruce must include X and Z in his report.

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Answer: A) X and Z

Step-by-step explanation:

Got it right on edge.