In the diagram below, Θ is measured in radians. Which equation represents the relationship between the radius, r, and arc length, s?

Circle O is shown. Line segments A O and B O are radii with length r. Angle A O B has a measure of theta. Arc A B has a measure of s.

s = Θ · r
r = Θ · s
s = Θ + r
r = Θ + s

An equation is formed of two equal expressions. The given equation can be solved for 'a' as a = K/(4+9b). Thus, the correct option is D.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The given equation, K = 4a + 9ab can be solved for a as shown below,

K = 4a + 9ab

K = a(4+9b)

a = K/(4+9b)

Hence, the given equation can be solved for 'a' as a = K/(4+9b). Thus, the correct option is D.

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Answer:

[tex]\huge\boxed{\sf 20z\³ + 24z\² - 5z - 6}[/tex]

Step-by-step explanation:

= (5z + 6)(2z + 1)(2x - 1)

= (5z + 6)[(2z)² - (1)²]

= (5z + 6)(4z² - 1)

Distributing

= 5z (4z² - 1) + 6(4z² - 1)

= 20z³ - 5z + 24z² - 6

Arrange

= 20z³ + 24z² - 5z - 6

[tex]\rule[225]{225}{2}[/tex]

Answer:

60

Step-by-step explanation:

1. parallel angle = 85

2. 180 - 85 = 95

3. 180 - (95+25) = 60

A polygon is a planar figure characterized by a limited number of straight-line segments joined to create a closed polygonal chain in geometry.

A polygon is a planar figure characterized by a limited number of straight-line segments joined to create a closed polygonal chain in geometry. A polygon is defined as a bounded planar region, a bounding circuit, or both.

2. Find the value of the supplementary angle of y for each polygon.

A.) For an isosceles triangle, using the base angle theorem we can write that the measure of the angle opposite to the congruent side will be equal. Therefore, the sum of the angles of the triangle can be written as,

y + y + 26° = 180°

2y = 154°

y = 77°

B.) The sum of the interior angles of a regular polygon is given as (n-2)180°, where n is the number of sides, also for a regular polygon the measure of each interior angle is equal. Since in a pentagon the number of sides is 5. Therefore, the measure of an interior angle can be written as,

y = [(n-2)180°]/n

y = [(5-2)180°]/5

y = 108°

3. The sum of the exterior angle of all the polygons is equal to 360°. Therefore, the sum of the exterior angles of the triangle and the pentagon will be the same, 360°

4. The formula to find the sum of the interior angles of a polygon, we can use the formula.

Sum of interior angles of an n-sided polygon = (n-2)180°

Where n is the number of sides.

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Answer:

c.) -3x + 6 = -9

Original question answer:

2x - 4 = 6

2x = 6 + 4

2x = 10

x = 10/2 = 5

===========

a) 5x - 6 = -11

5x = -11 + 6

5x = -5

x = -1

b) -4x - 2 = 10

-4x = 10 + 2

-4x = 12

x = 12/-4 = -3

c) -3x + 6 = -9

-3x = -9 - 6

-3x = -15

x = -15/-3 = 5

d) 2x + 3 = 7

2x = 7 - 3

2x = 4

x = 4/2 = 2

Answer:

Step-by-step explanation:

2x - 4 = 6    |add 4 to both sides

2x = 10    |divide both sides by 2

x = 5

a)

5x - 6 = -11   |add 6 to both sides

5x = -5    |divide both sides by 5

x = -1 ≠ 5

b)

-4x - 2 = 10   |add 2 to both sides

-4x = 12    |divide both sides by  (-4)

x = -3 ≠ 5

c)

-3x + 6 = -9     |subtract 6 from both sides

-3x = -15     |divide both sides by (-3)

x = 5 √

d)

2x + 3 = 7    |subtract 3 from both sides

2x = 4    |divide both sides by 2

x = 2 ≠ 5

The object moves 2 units to the left and then 3 units up.

Translation is a transformation technique used to change the position of an object on the xy-plane.

Given the translation vector (-2, 3), this translation shows a movement of an object to the left by 2units and 3 units in the upward direction

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Answer:

-31/30, -32/30, -33/30, -45/30, -49/30.

Step-by-step explanation:

-2/3 and -1 make denominators 30

-60/30 and -30/30

put any five

answer:

set 4

Step-by-step explanation:

because when you divide the numbers 12,16 and 20 by 2 you'll get 6,8 and 10 which is a Pythagoras family....and it will form a right angle triangle

Step-by-step explanation:

2/5 oz. for 1 cup

40 oz for x cups

2/5x = 40

x = 100 cups

Answer:

(2,-3) (3,-3)

Step-by-step explanation:

f(x) is y

x² - 5x + 3 = -3

x² - 5x + 6 = 0

ask yourself

which 2 numbers when multiplied give you

+6 and when added give you -5

they are -3 and -2

(x-3)(x-2)

x=3 x=2

when you put x=3 and x=2

in x² - 5x + 3 it's gives -3 which is y

(3,-3) (2,-3)

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Answer:

c

Step-by-step explanation:

By applying algebra, radical and power properties, we find that the simplified form of (√2 + √3) · (√5 - √7) is equal to √10 + √15 - √14 - √21. (Correct choice: B)

Herein we need to apply algebra and radical and power properties to simplify the expression described in the statement, whose procedure is shown below:

By applying algebra, radical and power properties, we find that the simplified form of (√2 + √3) · (√5 - √7) is equal to √10 + √15 - √14 - √21. (Correct choice: B)

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Answer:

B is correct

Step-by-step explanation:

Cus I said so

[tex]\text{Let's factor this quadratic.}\\\text{ We can start by thinking of two numbers such that,}\\\text{ if they are multiplied together, the product is 9}\\\text{if they're added together, the sum is -10, the middle term.}[/tex]

[tex]\rule{300}{1.7}[/tex]

[tex]\text{These numbers are -9 and -1.}\\\text{Checkup::}\\\text{-9*(-1)=9 and -9+(-1)=-10. The answer is good}[/tex]

[tex]\rule{300}{1.7}[/tex]

[tex]\text{Now, write these numbers as factors::}\\\text{(x-9)(x-1)=0 (make sure that the equation is \textbf{set to zero})}[/tex]

[tex]\rule{300}{1.7}[/tex]

[tex]\text{Now we can solve these mini equations in terms of x::}\\\text{x-9=0; \, x=9}\\\text{x-1=0; x=1}[/tex]

[tex]\rule{300}{1.7}[/tex]

[tex]\text{Our factors are:: \textsl{9 and 1}}[/tex]

Answer:

x=1

Step-by-step explanation:

Answer:

This is impossible.

Step-by-step explanation:

The interior angle of a regular polygon is equal to

[tex] \frac{180(n - 2)}{n} [/tex]

where n is the number of sides.

Setting this equal to 180°,

[tex] \frac{180(n - 2)}{n} = 180 \\ \\ \frac{n - 2}{n} = 1 \\ \\ n = n - 2 \\ \\ 0 = - 2[/tex]

which is false.

A rise of 8 and a run of 6. Then the correct option is B.

Coordinate geometry is the study of geometry using the points in space.

On a coordinate plane, a right triangle has points A (-5, -6), B (-5, -2), and C (-2, -2).

The distance between AB will be

AB² = (-5 + 5)² + (-2 + 4)²

AB² = 4²

AB = 4

The distance between BC will be

BC² = (-2 + 5)² + (-2 + 2)²

BC² = 3²

 BC = 3

Then the rise and run will be

rise / run = 4 / 3

Then this can be written as

rise / run = 8 / 6

Then the correct option is B.

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Answer:

think of each T in the original equation as an empty box, like this:

P(   ) = 2(   )² + (   ) - 7

when it says p(some number), it means replace all Ts in the equation with that number.

P( 0 ) = 2( 0 )² + ( 0 ) - 7 = 0 + 0 - 7 = -7

do the same for the rest <:)

for the second part, it's the same concept: every T is replaced with what's inside the parentheses.

so P( -t ) = 2( -t )² + ( -t ) - 7 = 2t² - t - 7

and so on and so forth.

Answer:

8 feet

Step-by-step explanation:

you have to calculate :(19+2x)(6+2x)=770

you will get X1=8,X2= negetive some value but measurement cant be negative .if you put X=8 you'll find LHS=RHS

Answer:

[tex]x= \frac{-25}{4}+\frac{1}{4} \sqrt{3705}[/tex]  or  [tex]x= \frac{-25}{4} + \frac{-1}{4}\sqrt{3705}[/tex]

Step-by-step explanation:

So first you need to find the area of the swimming pool:

19*6 = 114

Next you add the area of the swimming pool and the area of the walkway:

114 + 770 = 884

After this you solve for x using this equation:

(19 +2x) * (6 + 2x) = 884

This would normally find the area of the whole swimming pool area and the walkway but because we know that we can use it to solve for x.

The step-by-step is this:

[tex]4x^{2} +50x+114=884[/tex]

[tex]4x^2+50x+114-884=884-884[/tex]

 [tex]4x^2+50x+114-884=0[/tex]

Now we'll use the quadratic formula to simplify it farther:

[tex]x= \frac{-(50) + \sqrt{(50)^2-4(4)(-770)} }{2(4)}[/tex]

[tex]x=\frac{-50 + or - \sqrt{14820} }{8}[/tex]

[tex]x= \frac{-25}{4}+\frac{1}{4} \sqrt{3705}[/tex] or [tex]x= \frac{-25}{4} + \frac{-1}{4}\sqrt{3705}[/tex]

The value of x is 77 cm which will make the triangles similar by SSS similarity theorem

Given length of the three sides of one triangle are  35 , 20 and 20

and length of the three sides of another triangle are  x, 44,44

We need to find the values of x by using SSS Similarity theorem

We know that triangles are are similar by side - side - side similarity creation and hence the sides are in the same ratio

As both the triangles are isosceles triangles

Therefore ,

x/35 = 44/20=44/20 (Using ratio)

Solving the equation we get

x=44*35/20

x= 77

Hence the value of x is 77cm

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Answer:

6

Step-by-step explanation:

21 - 15 = 6

Hello!

Answer:

[tex]\Large \boxed{\sf A. -7}[/tex]

Step-by-step explanation:

We have this inequality:

[tex]\sf -5x - 7 \geq 28[/tex]

Let's solve this inequality:

◼ Add 7 to both sides:

[tex]\sf -5x - 7+7 \geq 28+7[/tex]

◼ Simplify both sides:

[tex]\sf -5x \geq 35[/tex]

◼ Divide both sides by -5, so also change the sign of the inequality

[tex]\sf \dfrac{-5x}{-5} \leq \dfrac{35}{-5}[/tex]

◼ Simplify both sides:

[tex]\boxed{\sf x \leq -7}[/tex]

So the correct answer is A. -7

Step-by-step explanation:

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The expected value of the winnings from the game is $4

The payout probability distribution is given as:

Payout ($) 2 4 6 8 10

Probability 0.5 0.2 0.15 0.1 0.05

The expected value is then calculated as:

[tex]E(x) = \sum x * P(x)[/tex]

This gives

E(x) = 2 * 0.5 + 4 * 0.2 + 6 * 0.15 + 8 * 0.1 + 10 * 0.05

Evaluate the expression

E(x) = 4

Hence, the expected value of the winnings from the game is $4

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Answer:

I have $550; my sister has $300.

Step-by-step explanation:

Let the amount I have be x.

Let the amount my sister has be y.

We have a total of $850, so

x + y = 850

50% of my amount plus 75% of my sister's amount equals $500.

0.5x + 0.75y = 500

We have a system of two equations:

x + y = 850

0.5x + 0.75y = 500

Multiply the second equation by 2 and subtract the first equation from it.

0.5y = 150

y = 300

x + y = 850

x + 300 = 850

x = 550

Answer: I have $550; my sister has $300.

The number of pieces that Marco places is given as follows:

30 pieces.

The number of pieces that Marco places is obtained applying the proportions in the context of the problem.

The fractions of each person are given as follows:

Hence the fraction composed by these three people is given as follows:

1/2 + 1/5 = (5 + 2)/10 = 7/10 = 0.7.

Hence Michele's fraction is given as follows:

1 - 0.7 = 0.3.

As Michele arranges 90 pieces, the total number of pieces is given as follows:

0.3x = 90

x = 90/0.3

x = 300.

Marco arranged one tenth, hence the number is:

0.1 x 300 = 30.

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Using the normal distribution, it is found that the probability that the sample mean is above 80 is of 0.1056 = 10.56%.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters are given as follows:

[tex]\mu = 75, \sigma = 24, n = 36, s = \frac{24}{\sqrt{36}} = 4[/tex].

The probability that the sample mean is above 80 is one subtracted by the p-value of Z when X = 80, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{80 - 75}{4}[/tex]

Z = 1.25

Z = 1.25 has a p-value of 0.8944.

1 - 0.8944 = 0.1056.

0.1056 = 10.56% probability that the sample mean is greater than 80.

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The number of rounds of bingo when the two costs would be the same is 3.

The equation that represents the total cost for adults is : 13 +2r

The equation that represents the total cost for children: 10 + 3r

where r is the number of rounds

When the two costs are the same, the two above equations would be equal: 13 + 2r = 10 + 3r

13 - 10 = 3r - 2r

r = 3

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STEP 1 : Rearrange this Absolute Value Inequality

Absolute value inequalitiy entered

|2x-1| < 11

STEP 2 : Clear the Absolute Value Bars

Clear the absolute-value bars by splitting the equation into its two cases, one for the Positive case and the other for the Negative case.

The Absolute Value term is |2x-1|

For the Negative case we'll use -(2x-1)

For the Positive case we'll use (2x-1)

STEP 3 : Solve the Negative Case

-(2x-1) < 11

Multiply

-2x+1 < 11

Rearrange and Add up

-2x < 10

Divide both sides by 2

-x < 5

Multiply both sides by (-1)

Remember to flip the inequality sign

x > -5

Which is the solution for the Negative Case

STEP 4 : Solve the Positive Case

(2x-1) < 11

Rearrange and Add up

2x < 12

Divide both sides by 2

x < 6

Which is the solution for the Positive Case

STEP 5 : Wrap up the solution

-5 < x < 6

Solution in Interval Notation

(-5,6) .

The length of lake is 4500 feet.

A triangle is a closed shape with 3 angles, 3 sides, and 3 vertices. A triangle with three vertices P, Q, and R is represented as △PQR.

Here, In ΔABE and ΔDCE

          ∠ABE = ∠DCE         { each 90⁰ }

          ∠AEB = ∠CED         { vertically opposite angle}

By AA similarity, we get

          ΔABE ≈ ΔDCE

Now, AB/CD = BE/CE

       AB/500 = 1800/200

       AB/500 = 9

        AB = 9 X 500

       AB = 4500 feet.

Thus, the length of lake is 4500 feet.

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