A circle has a radius of 5 inches and a central angle that intercepts an arc with a length of 30 in. What is the measure, in radians, of this central angle

Answer:

Roots:  -7, 2

Step-by-step explanation:

-x² = 5x - 14

-x² -5x +14 = 0

x² + 5x - 14 = 0

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

x = -7 or x = 2

A statement which is known as tautology is a type of compound statement in whose result is always the truth value. We don't take in consideration the other individual values in consideration , the result in tautology is always true.

It is one of the most significant part in logical mathematics if we need to find the most accurate answers or findings among a given group of answers.

In mathematics, tautology is used so as to ensure that the results which is obtained are true and exact and not false . A tautology is a compound statement and it will always returns true value. The result in tautology is always true, regardless of what the constituent parts are.

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Answer:

Infinite many solutions

Step-by-step explanation:

9d − 8 = –8 + 9d

* add 8 to each side *

-8 + 8 cancels out

-8 + 8 cancels out

we're left with 9d = 9d

When the same number/variable is on each side of the equal sign there is an infinite amount of solutions

Answer:

c.3 got a 100

Step-by-step explanation:

C

Step-by-step explanation:

"If p then q" is a conditional statement, and its contrapositive is If ~q then ~p.

Knowing about the inverse statement makes it simple to comprehend how to build a contrapositive statement. Take the negation of the hypothesis and the conclusion to produce the conditional statement's opposite.

Create the inverted statement first, then swap the hypothesis and conclusion to create the contrapositive of the conditional statement. Adding "not" to both component statements and switching the order of the provided conditional statements will result in contrapositive assertions, in other words.

If a number n is even, then n2 is even, and vice versa, is the contrapositive statement to "If a number n is even, then n2 is even."

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The area of the pool increasing at the rate of 753.98 cm²/min when the radius is 5 cm

Given:

radius of the pool increases at a rate of 24 cm/min

To Find:

How quickly does the pool's area grow when the radius is 5 cm?

Solution:

we are given with the circular pool

hence the area of the circular pool =

A = πr²-----------------------------(1)

The area of the pool os increasing at the rate of 24 cm/min, meaning that the area of the pool is changing with respect to time t

so differentiating eq (1)  with respect to t , we have

dA/dt =π 2r dr/dt

we have to find  dA/dt    with  dr/dt  = 24 cm/min and  r =  5cm

substituting the values

dA/dt = π 2(5)24

dA/dt =  π 26*8

dA/dt =  π 240

dA/dt =240π

dA/dt = 753.98

The area of the pool increasing at the rate of 753.98 cm²/min when the radius is 5 cm

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After solving, the length of the trains in meters is 60 meters.

In the given question, it takes a train of a certain length 15 seconds to pass under a sign, and it takes the same train 40 seconds to pass under a bridge that is 100 meters wide.

We have to find the length (in meters) of the train.

Let the length of the train is x.

The length of the bridge is 100 meters.

As we know that the formula of the speed is the ratio of distance that he traveled in the certain duration of time.

So Speed = Distance/Time

So according to the question;

(x + 100)/40 = x/15

Now solving the expression using the cross multiplication

15x + 1500 = 40x

Subtract 15x on both side, we get

25x = 1500

Divide by 25 on both side, we get

x = 60 meters

Hence, the length of the trains in meters is 60 meters.

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It is 10

I REALLY HOPE THIS HELPS :D

Answer:

7.96 centimeters squared

Step-by-step explanation:

In the photo.

Answer:

B. 10

Step-by-step explanation:

To find the answer we would plug each given number into x to see if it makes the equation true

A. 2(5) = 20

    10 [tex]\neq[/tex] 20

B. 2(10) = 20

    20 = 20

C. 2(20) = 20

    40 [tex]\neq[/tex]20

As you can see, the only answer that makes the equation 2x=20 true, is answer B

Answer:

The volume of the largest cylinder is 3.14(10)^2(30) = 9424.78cm^3

The volume of the smallest cylinder is 3141.59cm^3

The volume of the medium cylinder is 6282.67 cm^3

Step-by-step explanation:

the equation for a cylinder's volume is pi(r)^2(height)

The volume of the largest cylinder is 3.14(10)^2(30) = 9424.78cm^3 (remember the units!)

The volume of t he smallest cylinder is 1/3 the largest or: 9424.78/3 = 3141.59cm^3 (remember the units!)

The volume of the medium cylinder is 2/3 the largest or 9424.78(2/3) = 6282.67 cm^3

Answer:

C)  x = 28

Step-by-step explanation:

35 + 40 + 5x+5 + 5x = 360

10x + 80 = 360

10x = 280

x = 28

Answer:

1,705 elk

Step-by-step explanation:

7,750 / 50 =  155 groups of elk

155 groups x 11 per group = 1,705 elk.

Answer:

Alex deleted 37.5 selfies

Step-by-step explanation:

Let X be the number of selfies that Vic deleted.

Alex deleted 3X selfies.

After deleting selfies, Alex has 90-3X selfies left.

Vic has 75-X selfies left.

Since Alex has half as many selfies as Vic, we can set up the equation: 90-3X = (75-X)/2

Multiplying through the parentheses on the right side, we get: 90-3X = 75-X/2

Combining like terms, we get: 2X = 15

Dividing both sides by 2, we get: X = 7.5

Since X represents the number of selfies that Vic deleted, Vic deleted 7.5 selfies.

Since Alex deleted 3 times as many selfies as Vic, Alex deleted 37.5 = <<37.5=22.5>>22.5 selfies.

The number of selfies deleted by Alex is 51.

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that Alex took 90 selfies and Vic took 75 selfies. Today, they each decided that some of these selfies were not very good and deleted them. Alex deleted three times as many selfies as Vic. Now, Alex has half as many selfies as Vic.

Let Vic deleted x selfies and number of selfies deleted by Alex is 3x,

Therefore,

Since, Alex has half as many selfies as Vic, we can set up the equation: 90-3x = (75-x)/2

180 - 6x = 75 - x

5x = 105

x = 17

3x = 51

Hence, the number of selfies deleted by Alex is 51.

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The height of the equilateral triangle when its side length is given as 8 inches is calculated to be 6.93 inches.

The equilateral triangle has all sides and angles equal. The angles are always equal to 60 degrees.

Given that,

Side length of the equilateral triangle = 8 inches

Angles = 60 degrees

Height = ?

Therefore, let us find the height of the triangle using the Pythagoras theorem,

c² = a² + b²

8² - 4² = b²

b² = 64 - 16

b² = 48

b = 6.93 inches

Thus, the height of the equilateral triangle is calculated to be 6.93 inches.

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Answer:

The top looks like a trapezoid and so does the bottom so it's a prism.

lets find the area of the base!

15(base 1) + 7(base2) = 22

22 x 5(height) = 110

110 divided by 2( x 1/2) = 55

Now we multiply by the actual height of the TOTAL prism which is 11.

55 x 11 = 605 cubic feet, is your answer.

Formula for AREA of a trapezoid:

B1(base 1) + B2(base 2) x H(height) x 1/2 (basically just dividing by 2)

Answer:The sum of first angle second angle =150

⇒  The ratio of third and fourth angle is 2:3

⇒  Let third angle fourth angle be 2x and 3x.

Step-by-step explanation:

150 +2x+3x=360

⇒  5x=210

⇒  x=42

⇒  Now, 2x=2×42

=84

⇒  3x=3×42

=126  

⇒  The measure of two angles are 84

 and 126

PLEASE GIVE BRAINLIEST

Step-by-step explanation:

Sum of angles of quadrilateral = 360 degree

so 210+20+6x+7x = 360

230+13x= 360

13x= 360-230=130

x= 130/13=10

so third angle =6x= 6*10=60 degree

and 4th angle= 7x= 7*10=70 degree

50-3x<20

the answer is C. 11

Answer:

A

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

1 1/3

Step-by-step explanation:

Answer:

i dont know the answer i just need points im sorry

Step-by-step explanation:

Answer: C

Step-by-step explanation:

The HL Theorem states that if the hypotenuse and leg of a right triangle are congruent to the hypotenuse and leg of another right triangle, then the two triangles are congruent.

In this case, 16 is the hypotenuse (the longest side of a right triangle) and 13 is the leg.

Answer:

I think the answer is 3:1. found it by counting the no. of boxes

Answer:

76 degrees

Step-by-step explanation:

find angle 5 by subtracting 76 from 180 to get 104 degrees

the find angle 7 by subtracting 104 from 180 to get 76

180-76 =104

180-104=76

Answer:

8 free drinks

Step-by-step explanation:

80 ÷ 20 = 4

4 × 2 = 8

Answer:

Step-by-step explanation:

x = 1/2 ( arc(SF) + arc(RQ))

ARC SF = 50

Arc RQ (the large one ) = 200

Large Arc RQ = 200

Arc SF = 50

x = 1/2 (50 + 200)

x = 1/2 250

x = 125

f(x) =2(3ˣ) is an exponential function which has an initial value of 2.

Another word for "involving an exponent" in mathematics is exponential. For instance, an exponential rise in a number occurs when you raise it to the tenth power.

A mathematical function with the formula f(x) = aˣ is an exponential function. where an is a constant known as the function's base and x is a variable. The transcendental number e, or roughly 2.71828, is the exponential-function base that is most frequently seen. A variable is used as the exponent in exponential functions.

The exponential function that has an initial value of 2 is f(x) = 2ˣ.

f(x) = 2(3ˣ) can be written as f(x) = 2 × 3ˣ, so it starts at 2 × 3⁰ = 2 × 1 = 2.

f(x) = 3(2ˣ) can be written as f(x) = 3 × 2ˣ, so it starts at 3 × 2⁰ = 3 × 1 = 3

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Answer:

D.

Step-by-step explanation:

Polyhedron

Answer:

Polyhedron

Step-by-step explanation:

A solid that is bounded by polygons, called faces, that enclose a single region of space.

He must purchase 3 packages of hot dogs and 2 packages of hot dog buns for a total of 24 hot dogs with buns if he doesn't want to have any leftover hot dogs or buns. You should be aware that students might respond with 24, which is the least common multiple of 8 and 12.

The hot dog buns most frequently used in the American region of New England and its cuisine are New England-style hot dog buns, also referred to as New England hot dog buns or top-loading hot dog buns.

As you can see, "hot dog" is a versatile word that can be used as a noun, verb, adjective, or even as an exclamation.

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Answer:

79

Step-by-step explanation:

3x +16 + 5x - 4 = 180

8x +12 = 180

8x = 180 -12

8x = 168

x=21

3*21+16= 79