A skating rink charges $6.25 for skate rentals for people of all age groups. If C
represents the total number of children who rented skates and A represents the
total number of adults who rented skates, which expression best represents the
total money earned by the skating rink for the rental of skates?
a. 6.25 + a + c
b. 6.25a + 6.250
c. 6.25 (a + c)
d. 6.25a X 6.250

Answer:

Simplify the numerator with the sine expression by taking A = B = x and simplify the denominator using A = x and B = 2x. The resulting denominator will have sin (2x) and cos (2x) which you can write in terms of sin (x) and cos (x) using the expressions above.

Step-by-step explanation:

Hello!

[tex]\large\boxed{a = -1}[/tex]

y = 2x³ + ax² - x + 3

Find the derivative using the power rule:

y' = 6x² + 2ax - 1

Substitute in the given slope and x value to solve for a:

3 = 6(1)² + 2(1)a - 1

3 = 6 + 2a - 1

4 = 6 + 2a

-2 = 2a

a = -1

Answer:

a = -1

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Calculus

The definition of a derivative is the slope of the tangent line.

The derivative of a constant is equal to 0.

Basic Power Rule:

Step-by-step explanation:

Step 1: Define

y = 2x³ + ax² - x + 3

y'(1) = 3

Step 2: Differentiate

Step 3: Solve for a

Answer:

(3p + 5)^2

Step-by-step explanation:

9p^2 + 30p + 25

9p^2 is the square of 3p = a

25 is the square of 5 = b

This may be the square of a binomial.

We need to check the middle term.

(a + b)^2 = a^2 + 2ab + b^2

2ab = 2(3p)(5) = 30p

This is the square of a binomial.

9p^2 + 30p + 25 = (3p + 5)^2

The car is at 60ft from you 5 seconds after it starts moving and 7.5 seconds after it starts moving.

The 48*t part means the number of feet that the car moves in t seconds

We know that the absolute value equation that models the distance is:

d(t) = |300 - 48*t|

Then what we need to solve is d(t) = 60, this is:

d(t) = 60 = |300 - 48*t|

That absolute value equation can be represented in two forms:

300 - 48*t = 60

300 - 48*t = -60

Solving these two we get the two times at which the car is at 60ft from you.

-48*t = 60 - 300

t = (60 - 300)/(-48)  = 5

t = (-60 - 300)/(-48) = 7.5

So the car is at 60ft from you 5 seconds after it starts moving and 7.5 seconds after it starts moving.

The 48*t part means the number of feet that the car moves in t seconds.

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Answer:

I think it c=4p

Step-by-step explanation:

I’m sorry if it wrong

Answer:11

Step-by-step explanation:

18*1/3+5=11

Answer:

11

Step-by-step explanation:

To find the number that is 5 more than [tex]\frac{1}{3}[/tex] of 18, we can start by evaluating what [tex]\frac{1}{3}[/tex]  is:

[tex]\frac{1}{3}[/tex]  of 18

⇒ [tex]\frac{1}{3} \times 18[/tex]

To multiply a whole number by a fraction, we can convert the whole number into a fraction by giving it a denominator of 1:

⇒ [tex]\frac{1}{3} \times \frac{18}{1}[/tex]

⇒ [tex]\frac{18}{3}[/tex]   [This is the same as 18 ÷ 3]

⇒ [tex]\bf 6[/tex]

Now that we have the value of [tex]\frac{1}{3}[/tex] of 18, we can simply add to it to find the number that is 5 more than [tex]\frac{1}{3}[/tex] of 18:

[tex](\frac{1}{3} \times 18) + 5[/tex]

⇒ [tex]6 + 5[/tex]

⇒ [tex]\bf 11[/tex]

∴ The number we are looking for is 11.

Answer:

choice A: john is correct

Answer:

51 is not compostite

Step-by-step explanation:

51 is an odd number and it is not able to be divided by other numbers so it is a prime number

Answer:

What are yu askin

Step-by-step explanation:

Answer:

64 Ounces

Step-by-step explanation:

Answer:

3:2

Step-by-step explanation:

can also be written as 3/2 as a fraction!

Answer:

Blue paint to red paint - 3:2

Red paint to blue paint 2:3

Step-by-step explanation:

For every 3 cups of blue paint there is 2 cups of red paint

For every 2 cups of red paint there is 3 cups of blue paint

Fraction Mode: 3/2 or 2/3

The function (5n² - 9) / (n + 3) is a natural number for n = 3 and n = 15.

A function is given which is (5n² - 9) / (2n + 6).

We have to find the value of natural number n for which the given function is also natural number.

What do you mean by natural numbers ?

Natural numbers are known as the counting numbers which starts from 1 and end at infinity and also includes the whole numbers excluding 0.

As per the question ;

(5n² - 9) / (2n + 6) is a natural number for the value of n which is also a natural number.

Let's assume ;

(5n² - 9) / (2n + 6) = k

or

(5n² - 9) / (n + 3) = 2k

So , we can say that (5n² - 9) / (n + 3) is an even number.

We know that ;

Dividend ÷ Divisor = Quotient

If we divide (5n² - 9) by (n + 3) we will get ;

Quotient = 5n - 15

and

Remainder = 36

We can write it as ;

(5n² - 9) ÷ (n + 3) = (5n - 15) + {36 / (n+ 3)}

Here ;

36 / (n+ 3) is a natural number and n is a natural number.

Assume ;

n = 1 , 3 , 6 , 9 , 15 , 33

Let's check ;

for n = 1 ;

(5n - 15) + {36 / (n+ 3)} will be ;

= (5 - 15) + {36 / (1+ 3)}

= -1

for n = 3 ;

(5n - 15) + {36 / (n+ 3)} will be ;

= (15 - 15) + {36 / (3+ 3)}

= 6

for n = 6 ;

(5n - 15) + {36 / (n+ 3)} will be ;

= (30 - 15) + {36 / (6+ 3)}

= 19

for n = 9 ;

(5n - 15) + {36 / (n+ 3)} will be ;

= (45 - 15) + {36 / (9+ 3)}

= 33

for n = 15 ;

(5n - 15) + {36 / (n+ 3)} will be ;

= (75 - 15) + {36 / (15+ 3)}

= 62

for n = 33 ;

(5n - 15) + {36 / (n+ 3)} will be ;

= (165 - 15) + {36 / (33+ 3)}

= 151

So , we found that only for values of n = 3 and n = 15 , the value of (5n - 15) + {36 / (n+ 3)} is also an even number.

Thus , the function (5n² - 9) / (n + 3) is a natural number for n = 3 and n = 15.

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he ran a mile in 8.4 minutes. Step-by-step explanation:

As per given data area of the top of the rectangular table 21 square feet ,

width [tex]3\frac{1}{2}[/tex] feet the length of the table is equal to 6 feet.

As given,

Area of the top of the rectangular table = 21square feet

Width of the table =  [tex]3\frac{1}{2}[/tex] feet

Let 'l' be the length of the rectangular table

Area = length × width

⇒ 21 =(7/2) × l

⇒l =(21 ×2)/7

⇒l=6feet

Therefore, as per given data area of the top of the rectangular table 21 square feet , width [tex]3\frac{1}{2}[/tex] feet the length of the table is equal to 6 feet.

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Answer:

11.5

Step-by-step explanation:

Answer:

1.Many pairs of triangles designed into a building, for example as roof ends, would be congruent, so the roof beam and the top edges of the walls are horizontal.

2.The congruent triangle is used in most of the building that are design to stay in bad conditions and Strong winds for Example the Sydney Bridge.

3.in real life two triangles are rarely exactly congruent. However they are crucial in the construction of large man-made structures. This is because a triangle is the most stable shape and the congruence is needed to create even surfaces.

Answer:

The store sold 4,400 video games all year.

Step-by-step explanation:

Percentages

The x percent of a number N is calculated as:

[tex]\displaystyle P=\frac{x}{100}*N[/tex]

If the value of P is known, then:

[tex]\displaystyle N=\frac{100}{x}*P[/tex]

We know the store sold P=550 video games during the month of December and it corresponds to the x=12% of its yearly games sales (N).

Let's calculate N:

[tex]\displaystyle N=\frac{100}{12.5}*550[/tex]

N = 4,400

The store sold 4,400 video games all year.

Answer:

A is the correct answer

Answer: I think the answer is A.

Sorry if I'm wrong.

Answer:

I‘m pretty sure its a special right triangle, basically a 30, 60, 90 triangle. I checked with the formula and it’s correct. So the angle W is wither a 60 Degree or 30 degree and I‘m on the side of 30 degrees.

So I’m pretty sure its 30 degree.

The formuda is the hypotenuse is 2x and the (a) (3 in this case) is x. The 5 would come out as the formula 3[tex]\sqrt{3}[/tex]. Now we know the sides, 3, 5 and 6 so we just plug it in and solve for the square root and it equals to ABOUT 5.

I’m not sure if I’m correct but I’m not confident.

Answer:

 svkjhpwheqigjufhwqieweho87qrf

Step-by-step explanation:

Answer:

65 ft

Step-by-step explanation:

in 7 second the rocket went 65 ft

Answer:

Step-by-step explanation:

1). Let the length of a marathon race = x miles

   Marathon runner runs this race in the sequence formed as,

   [tex]\frac{x}{2},\frac{x}{4},\frac{x}{8}.........[/tex]

  Common ratio = [tex]\frac{\frac{x}{4}}{\frac{x}{2}}[/tex]

                           = [tex]\frac{x}{4}\times \frac{2}{x}[/tex]

                           = [tex]\frac{1}{2}[/tex]

  Therefore, it's a geometric sequence.

2). First movie rental cost = $2

  Followed by each additional movie rental cost = $1

  Therefore, rental of movies will be in the form of a linear equation,

  y = 2x + 1

  where x = number of movies

  And y = Rental of movies

  It's not a geometric sequence.

3). 10, 1, 0.1, 0.01.......

  Ratio in 2nd and 1st term = [tex]\frac{1}{10}=0.1[/tex]

  Ratio in 3rd and 2nd term = [tex]\frac{0.1}{1}=0.1[/tex]    

  Therefore, ratio in each term is common.

  Sequence formed will be a geometric sequence.

4). [tex]\sum_{k=1}^{7}4(0.2)^{k-1}[/tex]

   Expression represents a common ratio of 0.2,

  Therefore, expression given will represent a geometric sequence.

5). -4, 20, -100, 500, ...........

   Ratio of 2nd and 1st term = [tex]\frac{20}{-4}[/tex] = -5

   Ratio of 3rd and 2nd term = [tex]\frac{-100}{20}[/tex]

                                               = -5

   There is a common ratio = -5

   Therefore, it's a geometric sequence.

6). -1, 5, 11, 17.........

   Ratio of 2nd and 1st term = [tex]\frac{5}{-1}=-5[/tex]

   Ratio of 3rd and 2nd term = [tex]\frac{11}{5}=2.2[/tex]

   -5 ≠ 2.2

   Therefore, sequence is not a geometric sequence.

7). -500, 100, -20, 4........

   Ratio of 2nd and 1st term = [tex]\frac{100}{-500}=-\frac{1}{5}[/tex]

   Ratio of 3rd and 2nd term = [tex]\frac{-20}{100}=-\frac{1}{5}[/tex]  

Answer:

I agree with person above

Step-by-step explanation:

Answer: 0.3, 38%, 4%, 0.44, 25, 720?

Step-by-step explanation: I don't really know what the 25 and 720 are in this case it's a little complicated if you specify it more I can give you a more accurate answer sorry if this didn't help but if it did I'm glad to be helpful :)

Answer: 119°

∠C + 112° = 180°

⇔ ∠C = 180 - 112 = 68°

because ∠B is the outer angle of the triangle

=> ∠B = ∠C + 51° = 68° + 51° = 119°

=> ∠B = 119°

Step-by-step explanation:

Answer:

119

Step-by-step explanation:

The number of large frame bought by women are 5 and small frames are 9.

Let 'x' be the number of large frames.

Let 'y' be the number of small frames.

The concepts used is;

money + money = money  and

number of small frames + number of large frames = total number of frames.

Cost of each small frame is $7.

The cost of each large frame is $18.

Total cost is $153.

The system of equations are formed as;

$18y + $7x = $153   ........equation 1.

x + y = 14  

y = 14 - x   .....Put this in equation 1.

$18y + $7x = $153

18(14 - x) + 7x = $153

252 - 18x + 7x = 153

11x = 99

x = 9

y = 14 - 9 = 5

Thus, the number of large frame bought by women are 5 and small frames are 9.

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Answer:

the answer is Y

Step-by-step explanation:

The greatest common factor (GCF) of two polynomial expressions is y.

The greatest common factor (GCF) of two polynomial expressions is the polynomial with the largest set of factors that is a factor of both polynomials.

To find the GCF of y2(y + 1) and y(y + 2), we can factor each polynomial:

y2(y + 1) = y(y)(y + 1)

y(y + 2) = y(y + 2)

The only factor that both polynomials have in common is y, so the GCF is y.

Here is the solution in more detail:

Factor each polynomial.

y2(y + 1) = y(y)(y + 1)

y(y + 2) = y(y + 2)

Find the factors that are common to both polynomials.

The only factor that both polynomials have in common is y.

The GCF is the polynomial with the largest set of factors that is a factor of both polynomials.

The GCF is y.

Therefore, the GCF of y2(y + 1) and y(y + 2) is y.

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The angle by which turns counterclockwise about point P to coincide with is 180 degree angle

What is 180 degree angle?

The angle which forms a straight line is called the 180-degree angle. A 180-degree angle is a straight angle and it is exactly half of a revolution. The two arms of the angle which are making 180-degree are just opposite to each other from the common vertex.

The points D, P and C forms a straight line.

So, if it turns clockwise about Point P, it would make an angle of 180 degree.

as the point D and C are of equal lengths and opposite to each other, the angle from P turning clockwise makes 180 degree angle.

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Answer:

100

80

Step-by-step explanation:

plato

Answer:

the oeange will be there for u

Step-by-step explanation:

1 then 4 then 3 then 6 then 2