Solomon needs to justify the formula for the arc length of a sector. Which expression best completes this argument?The circumference of a circle is given by the formula , where d is the diameter.Because the diameter is twice the radius, .If equally sized central angles, each with a measure of , are drawn, the number of sectors that are formed will be equal to _____.The arc length of each sector is the circumference divided by the number of sectors, or .Therefore, the arc length of a sector of a circle with a central angle of is given by or ... help please

Answer:

1 1/2 mile.

Step-by-step explanation:

There is 60 minutes in an hour, 60/20 is 3. 1/2*3=1.5

Answer:

1 1/2 miles or 3/2 miles

Step-by-step explanation:

We can represent the person's walking rate as the ratio 1/2 mile : 20 minutes. Since we can multiply both sides of a ratio without changing the rate, we can rewrite it as ---> 3*(1/2) miles : 3*20 minutes = 3/2 miles : 60 minutes =

1 1/2 miles : 1 hour

An alternative way would be to convert 20 minutes into 1/3 of an hour. We can set up an equation:

mph * 1/3 hour = 1/2 mile

Therefore, the mph must be 1/2 divided by 1/3, because we are multiplying by 1/3, and division is the opposite of multiplication.

mph = (1/2)/(1/3) = (1/2) * 3 = 3/2 or 1 1/2

Answer:

Yes, it is an exponential function. The base is 2.

Step-by-step explanation:

As you can see, the function is f(x) = 2^(2x).

Since there is an exponent, the function is exponential. Graphing functions is another way to make sure if it's exponential or not.

The base is 2 because 2x, the exponent, is applied to it.

---

I hope this helps, let me know if you have any questions.

Answer:

A

Step-by-step explanation:

Answer:

B

You do not have enough information to solve the question.

Answer:

c)  x² + 3x + 1

Step-by-step explanation:

-3 /  1         6          10         3

                 -3          -9         -3          

      1         3             1          0

Answer:  x² + 3x + 1

Step 1: Carry down the first number 1 as it is

Step 2:  Multiply 1 by -3 (1 * -3 = -3) and write this -3 under the next number 6 and then add. 6 + (-3) = 3

Step 3: Multiply this 3 by -3 (3 * -3 = -9) and write this -9 under the next number 10 and then add.10 +[-9] = 1

Step 4: Multiply 1  by -3 (1 * -3 = -3) and write this -3 under the next number 3 and then add. -3 +[-3] = 0

Answer:

[tex]\boxed{35\°}[/tex]

Step-by-step explanation:

Angle 1 is 55 degrees.

The whole angle of the upward left corner is 90 degrees.

[tex]90-55=35[/tex]

Corresponding angles are equal. The 35 degrees angle and angle 2 are corresponding angles.

Angle 2 is 35 degrees.

Answer:

C

Step-by-step explanation:

24.75

Answer:

x=7

Step-by-step explanation:

15+14+14+11=54

75-54=21

21/3=7

Answer:

x = 7ft

Step-by-step explanation:

Turn it into an equation:

x + 15 + 14 + 14 + 2x + 11 = 75

3x + 54 = 75

3x = 21

x = 7ft

Answer: 109.1 degrees

Step-by-step explanation:

To find the angle between the given vectors, we will use the formula below:

Cos(θ) = (U.V)/ |U|.|V|

Where

U = 13i - 8j

V = 2i + 9j

U.V = (2x13) + (-8×9)

U.V = 26 - 72

U.V = - 46

|U| = sqrt ( 13^2 + 8^2)

= sqrt ( 233) = 15.264

|V| = sqrt( 2^2 + 9^2)

= sqrt ( 85 ) = 9.22

Substitute all the value of the parameters into the formula

Cos ø = -46 / (15.3 × 9.2)

Cos ø = - 46 / 140.72

Cos Ø = - 32687

Find the cos inverse of the value

Ø = cos^-1( -32687)

Ø = 109.079 degrees

Therefore, the angle between the given vectors to the nearest tenth of a degree is 109.1 degrees

Answer: 0.4693877

Step-by-step explanation:

Given that:

cos x=−6/7,

From trigonometry :

Cosx + sinx = 1

Cos2x = cos(x + x)

Recall the double angle identity:

Cos2x = 2cos^2x - 1

Sin2x = 1 - 2sin^2x

Since cosx = - 6/7

Then

Cos2x = 2cos^2x - 1

Cos2x = 2cosx^2 - 1

Cos2x = 2(-6/7)^2 - 1

Cos2x = 2(36/49) - 1

Cos2x = 2 * (72/98) - 1

Cos2x = (2 * 0.7346938) - 1

Cos 2x = ( 1.4693877 - 1)

Cos2x = 0.4693877

Answer:

the 2 equations are on top of each other, they are the same line

which means it is consistent, dependent, infinite

Step-by-step explanation:

the second equation is just 4 times the first equations.

Answer: 360 degrees

Step-by-step explanation:

You are given a convex polygon that has 7 sides and one angle at each vertex.

The sum of the measure of external angle of a polygon Inrespective of the number of sides of the polygon will always be equal to 360 degree.

Therefore, the sum of the measure of its exterior angles is 360 degrees

Answer:

Jordan weighs 120 pounds, Sam weighs 60 pounds

Step-by-step explanation:

We can create an equation 2s=J. Our second equation is S+J=180. We can substitute J for 2s and our new equation will be 3s=180. We can divide 3 from both sides and we get s= 60. And we know that Jordan weighs two times as sam, then Jordan weighs 120 pounds.

Answer: Jordan=120. Sam=60

Step-by-step explanation: Together they weigh 180 pounds Jordan weighs twice as much as sam. We can write their values as Sam=x and Jordan=2x then we can make a equation

2x+x=180

3x=180

x=60

Then we can substitute x in Jordan and sams values to get our final answe;

Jordan=120. Sam=60

Answer:

Jenny has 50 marbles

Step-by-step explanation:

I find it easiest to right down the numbers as I read the question,

(9+10-4) x3 +7-2

Answer:

10 s'mores

Step-by-step explanation:

20 ÷ 2 = 10

but only if she has enough of the other ingredients too :)

Answer:

10 smore's

Step-by-step explanation:

If 2 graham crackers is required to make 1 smore

then 20 graham crackers will make 10 smore's

2 x 10 = 20

Answer:

1) There are 26 letters in the alphabet.  Thus, 27 people must be chosen because otherwise there could be 1 person per initial.

2) There are 7 days in a week.  Thus, if the first 7 had their birthdays on every day of the week, the 8th person must share a birthday on the same day of the week as another.

3) A phone number can contain 0,1,2,3,4,5,6,7,8,9.  Thus, if the first 10 people have a phone number that ends with each digit, the 11th must share it, as there are no unique options.

4)  100/2 = 50.  Thus, the minimum each bag could have is 50.

5) 19/3 > 6.  The maximum number you could get with numbers less than seven is 6,6,6 = 18.  18<19.  Thus, you need a number 7 or greater.

6) The worst scenario that could happen here is that you grab 8 German books, 10 French books, and 12 Spanish, Russian and Italian books.  This would be 54 books.  Thus, with the 55th book, you must have gotten 12 of at least one subject.  Thus, the answer is 55 books.

7) This is vague.  If she cannot repeat any of the three jokes in the triplet, then she must have 36 jokes for this to be possible, because 12*3=36

8) Each of the remaining 29 students made less than 12 mistakes.  Even if 2 students made 11,10,9,8,7,6,5,4,3,2,1 mistakes, there would still be multiple students left that would have made 11,10,9,8,7,6,5,4,3,2, or 1 mistake(s), meaning that at least 3 students made the same amount of mistakes.

9) 465/95 = about 4.9.  Thus, each table could have less than 6 seats, so we cannot be sure.

Hope it helps <3

Step-by-step explanation:

4.

Bags contain x and y numbers of marbles.

x + y > 100

The least number that is more than 100 is 101.

If x and y are both less than 51, then you have at most a total of 100 marbles.

To have 101 marbles, you must have one bag with at least 51 marbles, and the other bag with the rest. Neither bag must have at least 50 marbles. You can have 1 and 100, but that is still more than 50 marbles in one bag.

6.

You are looking for 12 books in the same language. Let's say you start by picking all 10 French books and all 8 German books. You are up to 18 books. There are no more French or German books, so you can't get to 12 books in one language with those. Now you pick 11 Spanish books, 11 Russian books, and 11 Italian books. That is another 33 books, and still no 12 books in one language. You already picked 18 books + 33 books = 51 books. The very next book must be a Spanish book or a Russian book or an Italian book, and it will make the 12th book of that language. You need to pick 52 books to be sure you have 12 of the a single language.

Answer: 52 books

7.

You need enough jokes to have 12 different combinations of 3. This is a case in which order does not matter.

If you have 3 jokes, named A, B, and C, you only have enough for 1 year, since ABC, ACB, BAC, BCA, CAB, and CBA are all the same triple of jokes.

This is a combination problem.

nCk = (n!)/[k!(n - k)!]

We know we need more than 3 jokes. Let's try 4.

n = 4

nCk = (4!)/[3!(4 - 3)!]

nCk = 4

We need 12, so 4 is not enogh.

n = 5

nCk = (5!)/[3!(5 - 3)!]

= 5 * 4/2

= 10

Now enough.

Try n = 6

nCk = (6!)/[3!(6 - 3)!]

= 20

With 6 different jokes, you can make 20 different triplets, so there is no need to repeat any triplet in 12 years.

Answer: 6 jokes

Answer:

Step-by-step explanation:

B=3x-2

C=12x+2

D=B=3x-2 (Vertically opposite angles)

A=?

Now; we know, A+B+C+D=360 deg.

=>A=360-(B+C+D)

  =360-(3x-2+12x+2+3x-2)

  =360-(18x-2) ----[1]

B+C=180 deg. (linear pair)

=> 3x-2+12x+2=180

=> 15x=180

=> x=180/15

   =12 ---[2]

subsitute [2] in [1];

=> A= 360-(18x-2)

   = 360-(18*12-2)

   = 360-(116-2)

   = 360-214

   = 146 deg.

So, the correct answer is (D).

Hope the answer is useful.  

Answer:

Step-by-step explanation:

Given,

< B = 3x - 2

<C = 12x + 2

Let's find the value of X

<B + < C = 180° ( sum of angle in straight line)

plug the values

[tex]3x - 2 + 12x + 2 = 180[/tex]

Collect like terms

[tex]15x - 2 + 2= 180[/tex]

Since, two opposites add up to zero, remove them from the equation

[tex]15x = 80[/tex]

Divide both sides of the equation by 15

[tex] \frac{15x}{15} = \frac{80}{15} [/tex]

Calculate

[tex]x = 12[/tex]

Replacing value,

<C = 12x + 2

plug the value of X

[tex] = 12 \times 12 - 2[/tex]

Multiply the numbers

[tex] = 144 + 2[/tex]

Calculate the difference

[tex] = 146[/tex]

The measure of <C is 146°

Here,

<A = < C ( being vertically opposite angles)

Vertically opposite angles are always equal.

<A = 146

Hence, Option D is the correct answer.

Hope this helps...

Best regards!!

Answer:

  A) True

Step-by-step explanation:

The ordered pair for the first expression is ...

  y = f(x)

  -3 = f(1)

  (x, y) = (1, -3)

The ordered pair for the second expression is ...

  y = f^-1(x)

  1 = f^-1(-3)

  (x, y) = (-3, 1)

The second ordered pair is the reverse of the first, so represents a point described by the inverse function. The statement is True.

Answer:

$936

Step-by-step explanation:

We have to take the interest, 4%, and multiply it by 150 which equals 6. Since there are 6 months left in the year, we multiply this number by 6 which gets us 36. Next, we have to take the amount that Zachary puts in the account each month, $150, and multiply it by 6 months which equals to $900. Finally, we add the total amount of interest, $36, and the total amount of money he puts in during the year, $900.

Answer:

C, 16

Explanation:

A rectangle has 4 sides, two of which have equal side lengths (the ones across from each other.) BC is equal to AD because of this rule. Hope this helps!

The measure of length BC of the rectangle will be 16 units. Then the correct option is C.

It is a polygon with four sides. The total interior angle is 360 degrees. A rectangle's opposite sides are parallel and equal, and each angle is 90 degrees.

From the diagram, we have

AD = BC = 16 units

Then the correct option is C.

More about the rectangle link is given below.

https://brainly.com/question/10046743

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Answer:

Step-by-step explanation:

Pythagorean Theorem: a^2+b^2=c^2.

15^2+ b^2=25^2

225+b^2= 625

b^2=400

b= 20 or x=20

Answer:

x = 20

Step-by-step explanation:

This is a right triangle and we know 2 of the points so we can use the Pythagorean Theorem to solve.  The formula for the Pythagoreom Theroem is a^2 + b^2 = c^2. Side a is 15 and Side b is x. Side c or the hypotenuse is 25. Let's solve for side b:

a^2 + b^2 = c^2

15^2 + b^2 = 25^2

225 + b^2 = 625

Subtract 225 from both sides to get b^2 alone.

b^2 = 625 - 225

b^2 = 400

Find the square root of both sides.

b = 20 or x =  20

Would appreciate it if you gave me brainliest answer :)

Answer:

x=8

Step-by-step explanation:

x2=x*x

Plug in 8

8*8=64

64=16(8)-64

64=128-64

64=64

Answer:

6*108>3*106

Step-by-step explanation:

If you multiply 6, and 108, you would get 648.

And if you were to multiply 3 and 106 you would get 318. And 648>318.

Therefore, 6*108>3*106

Answer:

tan (30°) = b/5

Step-by-step explanation:

this is the answer

Answer:

y=MX+b

Step-by-step explanation:

b is your y intercept

m is your slope

Answer:

so first start at the origin which is point (0,0). Go up the y-axis 7 points if the graph is scaled by 1s-- do this because the y intercept is point (0,7). Next count 3 points up and one point to the left since the slope of the graph is negative 3. Continue to go up three points and one point to the left until you cannot do so. To go the other way and finish the graph go back to your y intercept (0,7) and go three points down and one point to the right. Continue to do so until there's no more points on the graph and you're done!

================================================

Explanation:

x = time it takes for the bell to ring, time is in minutes

d = distance from his house to the school, in meters

distance = rate*time

If Andrew walks at a speed of 50 meters per minute, then he'll be 3 minutes late. This means he took x+3 minutes to get to class. The x represents the amount of time it takes if he arrived on time, then the +3 is those 3 minutes he is late. We then write

d = 50(x+3)

d = 50x+150

If he runs to school, then he's 3 minutes early. So he took (x-3) minutes to get to class. His rate is 80 meters per minute

d = 80(x-3)

d = 80x-240

We're referring to the same distance (d) value, which allows us to perform substitution to solve the two equations we formed

80x-240 = 50x+150

80x-50x = 150+240

30x = 390

x = 390/30

x = 13

Andrew has 13 minutes to get to class.

-------------------

Checking the answer:

If he walks at a speed of 50 m per minute, then he'll be 3 minutes late. So he really took 13+3 = 16 minutes to arrive. His distance traveled is d = r*t = 50*16 = 800 meters.

If he ran 80 m per minute, and is 3 minutes early, then he took 13-3 = 10 minutes to get to class. His distance is the same as before d = r*t = 80*10 = 800 meters. The fact we get 800 both times helps confirm we have the right answer.

Andrew has 13 minutes to get to class.

Algebra is the part of mathematics that helps represent problems or situations in the form of mathematical expressions.

In algebra, we use numbers like 2, −7, 0.068 etc., which have a definite or fixed value. In algebra we use variables like x, y, and z along with numbers.

Now, let x be the time it takes for the bell to ring.

let d be the distance from his house to the school, in meters

distance = speed*time

If Andrew walks at a speed of 50 meters per minute, then he'll be 3 minutes late.

So, Andrew took x+3 minutes to get to class.

Here in the expression +3 shows that she is late.

So,

d = 50(x+3)

d = 50x+150

Now, If he runs to school, then he reached 3 minutes early.

So, toe get in class he will take (x-3) minutes

Here -3 show the child reached early

d = 80(x-3)

d = 80x-240

Since the distance is same.

So, the two equations are equal.

80x-240 = 50x+150

80x-50x = 150+240

30x = 390

x = 390/30

x = 13

Hence, Andrew has 13 minutes to get to class.

Learn more about algebra here:

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Answer:

3,5,7

Step-by-step explanation:

Answer:

7,8.15

Step-by-step explanation:

Answer:

Step-by-step explanation:

I

Area of a circle = PI x r^2

Area of sheet = 22/7 x 18^2 = 1,018.29 square cm.

Area of small circle = 22/7 x 4.5^2 = 63.64 square cm.

There are 2 small circles so total area of the circles are 63.64 x 2 = 127.28 square cm.

Area of rectangle = l x w = 4 x 1 = 4 square cm.

Total area of cutouts = 127.28 + 4 = 131.28 square cm.

Area of sheet left, subtract area of cutouts fro area of sheet:

1018.29 - 131.28 = 887.01 square cm.

Round everything as needed.

Answer:

$5.30

Step-by-step explanation:

2 hamburgers = 2 ( 1.75)  = 3.50

1 milkshake =   1.80

Add them together

3.50+1.80 = 5.30

Answer:

5.80

Step-by-step explanation:

Given:

Price of hamburger=1.75

"of Hot dog=1.25

"of French fries=0.95

"of Milkshake=1.80

"of Soda pop=0.75

Required:

The cost to order 2 hamburgers and a milkshake from the menu shown=?

Formula:

2(Hamburger)+1(Milkshake)=Cost

Solution:

2(1.75)+1(1.80)=5.30

3.5+1.80=5.30

Hope this helps ;) ❤❤❤