Find the radius of a circle that has an arc whose central angle measures 17 degrees and has a length of 12 degrees.

Answer:

the answer is XY = 24 units.

Step-by-step explanation:

Given:

XY is tangent to the circles with center P and O respectively.

OX=16 units

PY=6 units

OP=26 units

To find:

Side XY = ?

Solution:

As per given statement, the diagram of two circles and their tangent is shown in the diagram.

We need to do one construction here,

Draw a line parallel to tangent XY from P towards OX such that it meets OX at A .

Now, let us consider triangle [tex]\triangle OAP[/tex]. It is a right angled triangle.

With sides Hypotenuse, OP = 26 units  

Perpendicular, OA = 16 -6  = 10 units

Base AP is equal to XY.

If we find the value of Base AP, the value of XY is calculated automatically.

Let us use pythagorean theorem in [tex]\triangle OAP[/tex]:

According to pythagorean theorem:

[tex]\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Perpendicular}^{2}\\\Rightarrow OP^{2} = AP^{2} + OA^{2} \\\Rightarrow 26^2=XY^2+10^2\\\Rightarrow XY^2 = 676- 100\\\Rightarrow XY = \sqrt{576}\\\Rightarrow XY = 24\ units[/tex]

Hence, the answer is XY = 24 units.

Answer:

The error was made when they factored out the i, so this would be the distributive property they did not do correctly.

Factoring out the i was never needed.

Answer:

She shouldn't have factored out the i.

Step-by-step explanation:

In both parentheses, only one of the two additives had an "i" in it, so only one of them could have i factored out of it. If she wanted to factor out the i, the equation would look like this:

(4/i + 5)i + (-3/i + 7)i.

If anything, she should have done:

5i+7i + 4-3=

12i + 1.

Factoring out the i was unnecessary.

Hope this helps!

Answer:

Step-by-step explanation:

to solve an equation by completing the square in a quadratic formula

f(x)=ax²+bx+c

example :x²-6x-16=0

first rearrange if necessary, move the constant to one side .

x²-6x=16

second you find a new term to complete the square which is (b/2)², and add the term to both sides.(6/2)²=3²=9

x²-6x+9=16+9

x²-6x+9=25

third  factorize : find the common factor between 6 and 9 which is 3

x²-6x+9=25

(x-3)²=25

last solve for x: (x-3)²=25

x-3=√25

x=3±5

x=3+5=8 or 3-5=-2

Answer:

nine added to seven times a number.

Step-by-step explanation:

''x'' is the unknown number which is being multiplied by 7. Than 9 is added to it.

Answer:

4,500 Codes

Step-by-step explanation:

Given that, the access code consists of 4 digits.

Since, the First digit cannot be zero, and the last digit has to be even.

Therefore, Locks can only use numbers (0-9), which means the first digit has 9 possible outcomes ( 1-9),

the 2nd has 10 possible outcomes (0-10),

the same with the 3rd (0-10) and

finally the 4th has only 5 possible outcomes (0,2,4,6,8),

which we assume that zero is not excluded.

Finally, Mulitply 9 x 10 x 10 x 5 = 4,500.

The length of the arc s is 6.283 inches.

The length of an arc is given by the formula,

[tex]\rm{ Length\ of\ an\ Arc = 2\times \pi \times(radius)\times\dfrac{\theta}{360}[/tex]

where

θ is the angle, which arc creates at the center of the circle in degrees.

Radius, r = 8 in.

Angle, θ = 45°,

[tex]\rm{ Length\ of\ an\ Arc = 2\times \pi \times(radius)\times\dfrac{\theta}{360}[/tex]

[tex]\rm{ Length\ of\ the\ Arc\ s = 2\times \pi \times(8)\times\dfrac{45}{360}[/tex]

[tex]\rm{ Length\ of\ the\ Arc\ s =6.283\ inches.[/tex]

Hence, the length of the arc s is 6.283 inches.

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The approximate length of arc s on the given circle is; 6.28inches

The length of an arc is given by the formula;

Therefore,

Length, L = (45/360) × 2 × 3.14 × 8

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Answer:

Step-by-step explanation: wjbsgstexrczlkcidgxtftwdcwdkfmw,d,f

Answer:

Options (2), (3) and (4) are correct.

Step-by-step explanation:

The given function is f(x) = [tex]-\sqrt[3]{x}[/tex]

1). First derivative of the function = f'(x) = [tex]\frac{d}{dx}(-\sqrt[3]{x} )[/tex]

  f'(x) = [tex]-\frac{1}{3}(x)^{-\frac{2}{3}}[/tex]

  Since derivative is negative, function will be decreasing everywhere.

  Therefore, Option (1) is incorrect.

2). Since value of the function is true for every value of all real values of x.

  Domain of the function is (-∞, ∞).

  Therefore, Option (2) is correct.

3). For the given domain, range of the function will be all real values of y Or (-∞, ∞)

  Therefore, Option (3) is correct.

4). Function 'f' when reflected across x axis, equation of the reflected function will be g(x) = [tex]\sqrt[3]{x}[/tex].

 Therefore, Option (4) is correct.

5). For a point (3, -27),

  -27 = [tex]-\sqrt[3]{3}[/tex]

  Therefore, Option (5) is incorrect.

Answer:

The answer is B, C, and D

Step-by-step explanation:

Hope this helps. :)

Answer:

135.5

hope this helps :)

Answer:

Yes, the ordered pair is correct.

Explanation:

You can check the if the ordered pair by substituting the values into the equation. If you substitute the ordered pair (1, 3), then you can make sure the ordered pair is correct. The equation with the substitution will be 3 = 1 + 2, which results in the true equation 3 = 3, therefore the ordered pair is correct.

Answer:

Pretty Simple!

Step-by-step explanation:

So, according to similar triangles, all the measures of their corresponding angles are equal.

According to the picture, <A corresponds to <D. Thus:

m<D=32 degrees

Hope this helps!

Answer:

C. 32°  

Step-by-step explanation:

If two triangles are similar, their corresponding angles must be equal.

∠D corresponds to ∠A, so

  ∠D = ∠A

  ∠A = 32°

∴ ∠D = 32°

Answer:

[tex]\boxed{-i}[/tex]

Step-by-step explanation:

[tex]-i^5[/tex]

Use identity : [tex]i^5 =i[/tex]

[tex]-(i)[/tex]

Answer: 1320; 495

Step-by-step explanation:

Explanation is in the attachment file

Answer:

The correct option is;

B. The robot filters the expected amount of air and water, but it doesn't use the expected amount of energy

Step-by-step explanation:

The given requirements are;

Volume of air and water to be filtered by the robot = 343 liters

The amount of energy consumed by the robot < 49 joules

The number of minutes the robot filters air and water to filter more than 343 liters = 12A + 8W > 343

The number of minutes the robot filters air and with less than 49 Joule of energy = 3A + 4W < 49

Given that filtering air takes 20 minutes, filtering water takes 15 minutes, we have;

To filter more than 343 liters, we have

12*20 + 8*15 = 360 > 343

The robot meets the amount of air and water requirement

To filter with less than 49 joules we have

3*20 + 4*15 = 120 > 49

Therefore, the robot does not meet the energy requirement

The correct option is the robot filters the expected amount of air and water, but it doesn't use the expected amount of energy.

Answer:

2 pi

Step-by-step explanation:

The radius is 2

The area of a circle is

A = pi r^2

We have 1/2 of a circle so

1/2 A = 1/2 pi r^2

         =1/2 pi ( 2)^2

         =1/2 pi *4

      = 2 pi

Answer:

[tex]y = 2g - 2[/tex]

[tex]y + g = 16[/tex]

Step-by-step explanation:

Given

Let g represent the green marbles

Let y represent the y marbles

Required

Determine the relationship between both marbles

The question says that y is 2 less than twice of g

This implies that: [tex]y = 2g - 2[/tex]

The question further states that, Sarah has a total of 16 marbles;

This implies that [tex]y + g = 16[/tex]

So, the system of equation that defines the relationship between y and g are:

y = 2g - 2

y + g = 16

Answer:

edge 2021

Step-by-step explanation:

If you let g be the variable for the green marbles and y be the variable for the yellow marbles, which equation represents the relationship between yellow and green marbles?

✔ y = 2g - 2

Sarah has a total of 16 marbles. Which equation represents the total number of marbles she has?

✔ y + g = 16

Answer:

0.431 inches

Step-by-step explanation:

We were given the following values:

Height the tennis ball was dropped = 100in

Rebound height = 58in

We have to find the rebound ratio

= 58in/100in = 0.58

The formula to be used

Height on nth bounce = Initial height × (Rebound ratio)ⁿ

Where n = number of bounce

Height on the 10th bounce = 100 × (0.58)^10

Height on the 10th bounce = 0.4308042069inches

Approximately, the height on the 10th bounce = 0.431 inches.

Answer:

a) Multiplica la variable independiente por -7 y luego resta 7

Step-by-step explanation:

Sea [tex]f(x) = -7\cdot x - 7[/tex], las acciones realizadas por la función sobre la variable independiente, esto es, [tex]x[/tex], son:

1) Multiplica la variable por 7.

2) Refleja el resultado anterior con eje de simetría en el eje x. (Multiplicación por -1).

3) Traslada vertical el resultado de 2) siete unidades en la dirección -y.

Por ende, la opción correcta es a).

Answer: 75 u²

Step-by-step explanation:

1/2(5)((14)+(16))

Add in parenthesis

1/2(5)(30)

Multiply

1/2(150)

Multiply

75

Hope it helps <3

Answer:

a. True, because they are corresponding angles.

b. False, because angles 1 and 2 are supplementary, meaning that they add up to 180 degrees, but 125 + 65 = 190 degrees.

c. True, because they are corresponding angles.

d. True, becuase they are two angles that add up to 180 degrees.

e. True, because they are both interior angles on opposite sides of the transversal.

Answer:

a. True.

b. False.

c. True.

d. True.

e. True.

Step-by-step explanation:

a. This statement is true because angles 6 and 8 are vertical angles. That means they are congruent.

b. This statement is false because Elm Street is a straight line, which means that angles 1 and 2 are supplementary angles and their measures will add up to be 180 degrees. 65 + 125 = 190, which is not equal to 180.

c. This statement is true because angles 5 and 1 correspond to each other.

d. This statement is true because angles 7 and 8 form a straight line.

e. This statement is true because they are interior angles that are alternate.

Hope this helps!

Answer:

See explanation

Step-by-step explanation:

if multiply the 3 factors together you get

(x² - x - 2)(x - 3) - trinomial x binomial

x³ - 3x²- x² + 3x - 2x + 6 - polynomial

x³ - 4x² + x + 6, this is the polynomial with those factors.

Poly means many so it could be a bigger polynomial with more factors but if it is limited to only these factors than there is just the one polynomial.

The polynomial is x³ - 4x² + x + 6 with factors (x-2), (x+1), and (x-3)

A polynomial is the defined as mathematical expression that have a minimum of two terms containing variables or numbers. A polynomial can have more than one term.

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.

Operators which let do a basic mathematical calculation

+ Addition operation: Adds values on either side of the operator.

For example 12 + 2 = 14

- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.

for example 12 -2 = 10

* Multiplication operation: Multiplies values on either side of the operator

For example 12*2 = 24

Given that ,

P(x) has three factors (x-2), (x+1), and (x-3).

Multiplying the 3 factors together, we get

⇒ (x-2)(x+1)(x-3)

⇒ [x(x-3) - 2(x+1)](x-3)

⇒ (x² - x - 2)(x - 3)

⇒ x³ - 3x²- x² + 3x - 2x + 6

Rearrange the terms likewise and apply arithmetic operations

⇒ x³ - 4x² + x + 6

Hence, the polynomial is x³ - 4x² + x + 6 with factors (x-2), (x+1), and (x-3).

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Answer:

4/ 3 = 7

Step-by-step explanation:

Answer: x=3

Step-by-step explanation:

first add two to each side

Simplify  7+2 to 9

3x=9

divide both sides by 3.

x=9/3

simplify 9/3 to 3

​

k = b + 13

k - 19 = b - 6

k = b + 19 - 6

k = b + 13

Answer:

[tex]\boxed{k=b+13}[/tex]

Step-by-step explanation:

[tex]k-19=b-6[/tex]

Add 19 on both sides.

[tex]k-19+19=b-6+19[/tex]

[tex]k=b+13[/tex]

Answer:

The solution is

Step-by-step explanation:

x - 3y = 6 ............ Equation 1

2x + 2y = 4 ............ Equation 2

Make x the subject in equation 1 and substitute it into equation 2

That's

x = 6 + 3y

2( 6 + 3y ) + 2y = 4

Expand and simplify

12 + 6y + 2y = 4

8y = - 8

Divide both sides by 8

y = - 1

Substitute y = - 1 into x = 6 + 3y

That's

x = 6 + 3(-1)

x = 6 - 3

x = 3

x = 3 y = - 1

( 3 , - 1)

Hope this helps you

Answer:

B. ( 3 , - 1)  

Step-by-step explanation:

x - 3y = 6 Equation 1

2x + 2y = 4  Equation 2

x = 6 + 3y

2( 6 + 3y ) + 2y = 4

12 + 6y + 2y = 4

8y = - 8

y = - 1

x = 6 + 3(-1)

x = 6 - 3

x = 3

x = 3 y = - 1

( 3 , - 1)

Answer:

Step-by-step explanation:

A term, loosely defined, is a product of numbers and variables. Terms are separated from one another with a + or a - sign. So we have 2 terms here.

The degree of the polynomial, because it is just in terms of x and no other variable, is the highest degree'd term.  Our highest degree of x is 3, so this is a third degree polynomial.

It is classified by its number of terms:

1 term is a monomial, 2 terms is a binomial, 3 is a trinomial, and anything higher is just called a "polynomial". This has 2 terms so it is a binomial.

The answer is:

Work/explanation:

Here's how we classify polynomials based on the number of terms:

monomial - has only one term

binomial - has two terms

trinomial - has three terms

polynomial - has four terms or more

As for degrees, those are the highest exponents the polynomial.

Now, [tex]\sf{14x^3+x^2}[/tex] has 2 terms so it's a binomial; the highest exponent is 3.

Answer:

La máquina llenó:

6 baldes

Step-by-step explanation:

Por regla de tres:

4 baldes son a 30 minutos

M baldes son a 45 minutos

M = 45*4/30

M = 180/30

M = 6

Answer:

9.16

Step-by-step explanation:

We know that

Total expense = price of sugar * consumption

let price of sugar was 100

So total expense = 100*10=1000

But now new expense =1100 (I,e.10% more than 1000)

and new price =120(i,e. 20% more than 100)

So new consumption = new expense/ new price=

1100/120

=110/12

=9.16

HOPE IT HELPS :)

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Answer:

16 2/3 %   or approx. 16.67%

Step-by-step explanation:

Original price = 100%

New price = 100+20% = 120%

To reduce back to 100%

we need to reduce 20% from 120 % = 20/120 = 1/6 = 16 2/3 % = 16.7% approx.

Answer:

1. [tex]\bold{S=f(P) = 0.07P}[/tex]

2. x = 16

3. Part 1: P is the independent variable and S is the dependent variable.

Part 2: x is the independent variable and y is the dependent variable.

Step-by-step explanation:

1. To write the function notation for:

Sales tax is 7% of the total price.

Let the total price be [tex]P[/tex].

And sales tax be [tex]S[/tex].

As per the given statement:

[tex]S = 7\% \ of\ P\\\Rightarrow S =\dfrac{7}{100}P\\\Rightarrow S=0.07P[/tex]

Writing it in the function notation:

[tex]\bold{S=f(P) = 0.07P}[/tex]

2. To find the value of x such that [tex]f(x) = 14[/tex] and

[tex]f(x) = \dfrac{1}4x + 10[/tex]

Putting the value of [tex]f(x) = 14[/tex]

[tex]14 = \dfrac{1}4x + 10\\\Rightarrow \dfrac{1}4x =14-10\\\Rightarrow \dfrac{1}4x =4\\\Rightarrow x =4\times 4\\\Rightarrow \bold{x =16}[/tex]

3. To find the dependent and independent variable.

Independent variables are those whose value is not dependent on the other variable's values.

Dependent variables are dependent on the value of other variables.

In question 1:

[tex]\bold{S=f(P) = 0.07P}[/tex]

P is the independent variable.

S is the dependent variable.

In question 2:

If we write it as follows:

[tex]y=f(x) = \dfrac{1}4x + 10[/tex]

x is the independent variable and y is the dependent variable.

Answer:

1/6

Step-by-step explanation:

using this formula

[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

You get 0.1666666666666666666666666666666666666666

which is 1/6

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