can somebody help me with this problem ???

5n² can be expressed as, 5n² =  3² x 5⁵ x x⁶

Given that n can be written as the product of the primes as

n = 3 x 5² x x³

This expression for n is called the prime factorization of n.

We need to express 5n² as such a product of primes.

For that taking square of n, add the power 2 with the existing powers of 3,5 and x,

So, n² = ( 3 x 5² x x³)² = 3² x 5⁴ x x⁶

So 5n² = 5(3² x 5⁴ x x⁶)

Multiplying 5 with the existing power of 5, 5⁴,

⇒ 5n² = 3² x 5⁵ x x⁶

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Answer:The answer is -0.6

Step-by-step explanation: -15.4-10.4 is -25.8

                                             -25.8+25.2 is -0.6

                           So therefore the answer is -0.6

Answer: -2, 2

Step-by-step explanation:

The derivative of a function, f(x), at a point where f(x) has a sharp turn (or cusp) does not exist.

The derivative of a function, f(x), at a point where f(x) has a vertical tangent line does not exist.

Using this information, we can see that f(x) is not differentiable when x=3 since there is a vertical tangent line. We can also see that f(x) is not differentiable when x=-1 since there is a cusp.

Answer:

Step-by-step explanation:

See attachment

The following figures are Line, Ray, Line Segment, Parallelogram and Cuboid in the sequential order.

a) Line - A line is a two-dimensional figure. It is a group of points joining together to form a single entity which extends in both directions infinitely. It has no end points.

b) Ray - A ray is a two-dimensional figure. It is a group of points joining together to form a single entity, but it extends infinitely in only one direction. It has one end point.

c) Line segment - A line segment is a two-dimensional figure. It is a group of points joining together to form a single entity, but it does not extend infinitely in any direction. It has two end points and a finite length.

d) Parallelogram - A parallelogram is a two-dimensional figure having 4 sides whose opposite sides are equal in length and also parallel to each other. The diagonals of the parallelogram intersect each other at equal distance.

e) Cuboid - A cuboid is a three-dimensional figure made up of rectangular faces of varying length, breadth and height. The opposite faces of a cuboid are similar in dimensions. It has 12 edges, 12 vertices and 6 faces.

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[tex]\huge\boxed{y+2=-\dfrac{4}{3}(x-3)}[/tex]

Given a point and a slope, we want to write an equation in point-slope form.

The point-slope form is defined as:

[tex]y-y_1=m(x-x_1)[/tex]

In this equation, [tex](x_1, y_1)[/tex] is a known point on the line and [tex]m[/tex] is the line's slope.

Substitute in the values:

[tex]y-(-2)=-\dfrac{4}{3}(x-3)[/tex]

Finally, simplify. Subtracting a negative number is the same as adding a positive number:

[tex]\large\boxed{y+2=-\dfrac{4}{3}(x-3)}[/tex]

Answer:

Step-by-step explanation:

Let the speed of the private jet is p and commercial jet is c.

Find c:

The composed function for the surface area of the cube for any given volume of an inscribed sphere, A(V) =  24( [tex]\sqrt[3]{\frac{3V}{4\pi} }[/tex])²

The function used to find the radius r of a sphere given volume V,

r(V) = [tex]\sqrt[3]{\frac{3V}{4\pi} }[/tex]

The function used to find the length of the side s of the cube depending on the radius r of the sphere, s(r) = 2r

The function used to find the surface area A of the cube depending on the side of the cube s, A(s) = 6s²

We need to find the composed function for the surface area A of the cube for any given volume V of an inscribed sphere. i.e., A(V)

We have, A(s) = 6s²

Substituting function for s to A(s)

⇒ A(s(r)) = 6(2r)² = 24r²

Substituting function for r into A(s(r)),

⇒ A(s(r(V))) = 24( [tex]\sqrt[3]{\frac{3V}{4\pi} }[/tex])²

So the function for the surface area of the cube depending on the volume of the inscribed sphere, A(V) =  24( [tex]\sqrt[3]{\frac{3V}{4\pi} }[/tex])²

The question is incomplete. Find the complete question below:

Consider a cube with an inscribed sphere. The function  r(V) = [tex]\sqrt[3]{\frac{3V}{4\pi} }[/tex] can be used to find the radius, r, of a sphere given the volume, V . The function  s(r) = 2r can be used to find the side length of the cube, s , depending on the radius of the sphere. The function A(s) = 6s² can be used to find the surface area,  A , of the cube. Which is the composed function for the surface area of the cube for any given volume of an inscribed sphere?

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Answer:

Answer is D

Step-by-step explanation:

The function will become:

f ( x ) = 3 x ; 0 ≤ x ≤ 2

f ( x ) = 6 + 4 ( x - 2) for 2 < x ≤ 5

f ( x ) = 20 for x > 5

We are given that:

The parking garage charges $ 3 per hour if the car is parked there for less than 2 hours.

So, we get that:

Parking fees = 3 x for 0 ≤ x ≤ 2

Now, we get that, if the car is parked for more than 2 hours and less than 5 hours, then the parking fee is

6 + 4 ( x - 2) for 2 < x ≤ 5

Now, we are given that it charges a fixed fee of $ 20 if car is parked for more than 5 hours. So, the parking fee will be

20 for x > 5

So, the function becomes:

f ( x ) = 3 x ; 0 ≤ x ≤ 2

f ( x ) = 6 + 4 ( x - 2) for 2 < x ≤ 5

f ( x ) = 20 for x > 5

Therefore, we get that, the function will become:

f ( x ) = 3 x ; 0 ≤ x ≤ 2

f ( x ) = 6 + 4 ( x - 2) for 2 < x ≤ 5

f ( x ) = 20 for x > 5

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The coordinates of the point that is 3 / 10 of the way from point A to point B is C(x, y) = (0.9, - 3).

In this problem we find a line segment whose endpoints are known: A(x, y) = (- 3, - 6), B(x, y) = (10, 4), and of which we need to find a point C such that it is 3 / 10 of the way from point A to point B, whose exact location can be found by means of the line segment formula:

C(x, y) = A(x, y) + (3 / 10) · [B(x, y) - A(x, y)]

C(x, y) = (- 3, - 6) + (3 / 10) · [(10, 4) - (- 3, - 6)]

C(x, y) = (- 3, - 6) + (3 / 10) · (13, 10)

C(x, y) = (- 3, - 6) + (3.9, 3)

C(x, y) = (0.9, - 3)

The coordinates of the point that is 3 / 10 of the way from point A to point B is C(x, y) = (0.9, - 3).

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Answer:

tyyyy is my final answer

The type of solution to the given simultaneous equations is no solution

When it comes to linear simultaneous equations as given in the question, there are different types such as; one solution, no solution or infinitely many solution.

We are given the simultaneous equations;

y = 5x + 4   ---(1)

y = 5x - 2   ----(2)

Using elimination method, subtract eq 1 from eq 2 to get;

0 = -2 - 4

0 = -6

0 cannot be equal to -6 and as such there is no value of x that makes the simultaneous equations true. Thus, the type of solution to the given simultaneous equations is no solution

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Answer:

12

Step-by-step explanation:

[tex] \frac{3}{8} = \frac{?}{32} [/tex]

8*4=32

3*4=12

Step-by-step explanation:

please find attached file for the problem. hope it will help you , let me know if you have any further query

The angle between a diagonal of a cube and an adjacent edge is 54.75°;

Assuming the length of a side of the cube as 1 unit, the three sides are given by the vectors;

a = (1, 0, 0)

b = (0, 1, 0)

c = (0, 0, 1)

The diagonal is given by the vector, v = (1, 1, 1)

The angle between the diagonal and one edge of the cube is given by

cos θ = v. a / |v|.|a|

v. a = (1, 1, 1).(1, 0, 0)

= 1(1) + 1(0) + 1(0

= 1 + 0 + 0

v. a = 1

Magnitude of vector V = √[(1)² + (1)² + (1)²]

|v| = √3

Similarly, |a| = √1;

So, |v|.|a| = √3.√1 = √3

Now, cos θ = 1/√3

So, θ = cos¹(1/√3)

θ = 54.75°

Therefore, the required angle is 54.75°.

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Answer:

1. m ∠ 1 = 86°

  m ∠ 2 = 4°

- Problem in the picture

2. m ∠ 1 = 6°

   m ∠ 2 = 84°

Step-by-step explanation:

I'm confused, so I'll just solve both problems (assuming that they are the same type of angle)

1.

m Z1 = (x+84)° and m2 = 2xº.

m ∠ 1 = (x + 84)°

m ∠ 2 = 2x°

Complementary angles are equal to 90°

(x + 84) + 2x = 90

x + 84 + 2x = 90

3x + 84 = 90

      -84    -84

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

3x = 6

÷3  ÷3

-----------

x = 2°

m ∠ 1 = (x + 84)°

m ∠ 1 = (2 + 84)°

m ∠ 1 = 86°

m ∠ 2 = 2x°

m ∠ 2 = 2(2)°

m ∠ 2 = 4°

2. (Problem in the picture)

m ∠ 1 = (x - 6)°

m ∠ 2 = 7x°

Complementary angles are equal to 90°

(x - 6) + 7x = 90

x - 6 + 7x = 90

8x - 6 = 90

     +6    +6

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

8x = 96

÷8    ÷8

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

x = 12

m ∠ 1 = (x - 6)°

m ∠ 1 = (12 - 6)°

m ∠ 1 = 6°

m ∠ 2 = 7x°

m ∠ 2 = 7(12)°

m ∠ 2 = 84°

I hope this helps!

Answer:

[tex] \large{ \boxed{ \tt{answer : \boxed{ \tt{ k = 73 \degree}}}}}[/tex]

Please see the attached picture for full solution!

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Answer:

a) true

b) false

c) false

Step-by-step explanation:

Here are these 4 sets in order of including more numbers to including fewer numbers.

R = all real numbers

Z = all integers

W = all whole numbers

N = all natural numbers

a) true

b) false

c) false

If the coordinate points is reduced using the scale factor of 1/4, hence the resulting coordinate point will be;

F'(-2/4, 8/4) = (-1/2, 2)

G'(4/4, 8/4) = (1, 2)

I'(-6/4, -4/4) = (-1.5, -1) and;

H(8/4, -4/4) = (2, -1)

A scale factor is is a number used to enlarge a shape and each side is multiplied by the same number.

The given trapezoid has the coordinate points F(-2, 8), G(4, 8), I(-6, -4) and H(8, -4).

If the coordinate points is reduced using the scale factor of 1/4, hence the resulting coordinate point will be;

F'(-2/4, 8/4) = (-1/2, 2)

G'(4/4, 8/4) = (1, 2)

I'(-6/4, -4/4) = (-1.5, -1) and;

H(8/4, -4/4) = (2, -1)

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The system of inequalities are:

h + c ≤ 100

3h + 3.5c ≥ 80

Here are inequality signs and what they mean:

Here are the system of inequalities :

number of hamburgers sold + number of cheeseburger sold  ≤  total number of buns

(cost of one hamburger x number of hamburger sold) + (number of cheeseburger sold x number of cheeseburger sold) ≥ $80

h + c ≤ 100

3h + 3.5c ≥ 80

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Answer:

-4[tex]\leq[/tex]a<7

Step-by-step explanation:

-20[tex]\leq[/tex]5a -10<25  add 10

+10       +10  +10

-20 [tex]\leq[/tex]5a<35  Divide all the way through by 5

-4[tex]\leq[/tex]a<7

129 is the value of expression .

What is PEMDAS?

We use , P/E/M/D/A/S (Parenthesis, Exponents, Multiply, Divide, Add, and Subtract)

8^2 + 9(12/3*2) - 7

= 64 + 9(8) -7

= 64 + 72 - 7

= 129

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Answer:

a  c  e

Step-by-step explanation:

The number of co-workers that like gumdrops and chocolate is 7 (option b).

The mathematical operations that would be used to determine the answer are addition and subtraction.

Addition is determining the total value or summing two or more numbers. The sign used to represent addition is +. Subtraction is the process of determining the difference between two or more numbers. The sign used to denote subtraction is -.

The first step is to add the total number of people who like a particular type of candy : 10 + 8 + 2 + 3 + 5 = 28

The second step is to subtract that number gotten in the previous step from the total number of co-workers.

Co-workers that like both chocolate and gum drops = 35 - 28 = 7

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The equation for L, in terms of t, representing the amount Sophie owes her friend after t weeks is; L = 2t + 10

The general formula for equation of a line in Slope Intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

Now, from the given question, the table of values is;

Number of weeks         Amount of money owed

      0                                   10

      1                                     8

      2                                    6

      3                                    4

Now, since Sophie agreed to pay back her friend $2 per week and originally borrowed $10, it means that;

Slope = 2

y-intercept = 10

Thus, the equation for L, in terms of t, representing the amount Sophie owes her friend after t weeks is;

L = 2t + 10

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The position of the bicyclist at t=8 minutes is 3.2 km

Speed is the rate of change of position of an object in any direction.

position the way in which something or someone is placed or arranged.

when time t = 6 position d = 5

when time t = 5 position d = 2

when time t = 8 position d = x

therefore we can say

8 / x = 5 / 2

x = 8 * 2 /5

  = 3.2 km.

Hence the position of the bicyclist at t=8 minutes is 3.2 km.

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complete question:

The position "d" of a bicyclist (measured in kilometers) is a linear function of time "t" (measured in minutes). At time t=6 minutes, the position is d=5 km. If the bicyclists travels at 2 km for every 5 minutes, find the position of the bicyclist at t=8 minutes.

Answer:

Range is 12 and mean is -6

Step-by-step explanation:

To find the mean, add together all the numbers and divide by 7.