The closest star to Earth is approximately 3.99 x 10¹3 kilometers away.
When written in standard notation, how many zeros does this number contain
before the decimal point?
A. 11
B. 12
C. 13
D. 15

Answer: 6

Step-by-step explanation: How do you find a range?

You can find the range from numbers by subtracting the highest number from the lowest.

Here we have 7, 1, 7, 2, 1, 3, 4, 3.

You can put these in order:

1, 1, 2, 3, 3, 4, 7, 7.

Our highest number is 7 and our lowest is 1.

7-1=6.

6 is your range.

Answer: x=11

Step-by-step explanation: 180-14 7= 33= angle EFB (angle in a straight line add up to 180)

Angle FBC= EFB= 33 (Alternate angles)

Angle DEB = EBC= 4x

4x- Angle FBC (33) =x

33= 3x

11=x

7. e = 2A - f

72. Area = 615.8 in.²

Circumference = 88.0 in.²

73. Area = 615.8 in.²

Circumference = 88.0 in.²

74. Missing length = √40 ≈ 6.3

75. Missing length = √45 ≈ 6.7

76. Scale factor = 18/6 = 3

77. Scale factor = 12/4 = 3

Area = πr²

Circumference = 2πr

7. A = (e + f)/2

2A = e + f

2A - f = e

e = 2A - f

72. r = 14 in.

Area = πr² = π(14²) = 615.8 in.²

Circumference = 2π(14) = 88.0 in.²

73. r = 30.2/2 = 15.1

Area = πr² = π(15.1²) = 615.8 in.²

Circumference = 2π(15.1) = 88.0 in.²

74. Missing length = √(6² + 2²) [Pythagorean Theorem]

Missing length = √40 ≈ 6.3

75. Missing length = √(6² + 3²) [Pythagorean Theorem]

Missing length = √45 ≈ 6.7

76. Scale factor = 18/6 = 3

77. Scale factor = 12/4 = 3

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The correct statements regarding the linear function in the graph are:

A linear function is modeled by:

y = mx + b

In which:

From the points, we have that:

Hence these points form a straight line with a slope of 1.5, that is:

y = 1.5x + b.

When x = 1, y = 3, hence we use it to find b as follows:

3 = 1.5 + b

b = 1.5.

Hence the relation is:

y = 1.5x + 1.5.

Since the y-intercept is different of 0, we have that:

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Answer:

Step-by-step explanation:

Point slope form y-y₁ = m(x-x₁)

y-14 = 12(x + 6)

y-14 = 12x + 72

y = 12x + 86

Side of the given square room  flooring is 12 foot  

What is a square and its area?

A Square is a closed, two dimensional shape which has four sides and all four sides are equal and at 90 degree angle to each other .

As  all four sides are equal, Let each of the side of a square is a

Area of the square is given by = a*a

Given that a designer paid $4 per square feet for a square flooring

Total amount spent by the designer = $600

Total area of flooring = total amount spent /rate of per unit area

                                  = $600/$4 square foot =150 sq foot

Let the side of the given square flooring be x

Then area of the floor = [tex]x^{2} =150\\[/tex]

Thus side of the room floor = [tex]x=\sqrt{150}[/tex] = 12.25 = 12 foot

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Answer:

Step-by-step explanation:

By solving this algebraic equation we get x=4 that

2x=11-3 2x=

x=8/

x=

so by putting 4 in above equation the answer will be true

But we have to find where the equation gets false so put any number except 4 in above equation i.e the simple case putt zero x=

11=2(0)+

11=

which is false also putt x=1 the equation will be also false.

o when we putt any number except 4 in that equation we it will be false.

Answer:

x = 4

Step-by-step explanation

11=2x+3

11-3=2x+3-3

Answer:

269 R 15

Step-by-step explanation:

R means remainder

So if u divide 4857 by 18 you will get 269 reminder 15.

Answer:

0.04

Step-by-step explanation:

I hope this is the answer you are looking for and I hope this helps!

The hotel should order 39000 bars of soap if the hotel goes through on an average of 750 soaps each week.

In everyday terms, an average is one number chosen to represent a list of numbers; it is often the sum of the numbers divided by the number of numbers in the list (the arithmetic mean).

Average is calculated by dividing the sum of the data by the frequency of the data.

Average=sum ÷ frequency

For example if the average of the data set {1,2,3,5,10}=(1+2+3+5+10)÷5=21÷5=4.2

Now for the given question average is given as 750 bars of soap.

We know that there are 52 weeks in a year.  ∴ frequency=52

Hence sum of all the averages will give the total number of soap ordered by the hotel in a year.

Sum=average × frequency

or, sum=750 × 52

or, sum=39000 bars of soap.

hence the hotel orders 39000 bars of soap in one year.

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1) The supply when the price is 40 dollars would be; S(40) = 66.677

2)  The instantaneous rate of change of the supply with respect to price when the price is 40 dollars is; 0.0794

We are given the function that represents the number of CD players a retail chain is willing to sell per week at a price of dollars as;

S(p) = 70p/(p + 2)

1) The supply when the price is 40 dollars would be;

S(40) = 70(40)/(40 + 2)

S(40) = 2800/42

S(40) = 66.677

2) The instantaneous rate of change would be gotten by finding the derivative of the supply function to get;

S'(p) = 140/(p + 2)²

Thus;

S'(40) = 140/(40 + 2)²

S'(40) = 0.0794

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Figures with at least 4 lines of symmetry are:

So, according to the given image, we can say that circle, square, rectangle, and oval can have at least 4 lines of symmetry.

Therefore, figures with at least 4 lines of symmetry are:

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Answer:

  (-7, 5)

Step-by-step explanation:

You want to know the image of the point (-4, -6) after reflection in the x-axis and translation 3 left and 1 down.

The composition ...

  [tex]T_{-3,-1}\circ r_{\text{x-axis}}[/tex]

is interpreted to mean reflection in the x-axis occurs first, then translation by (-3, -1).

That is, a composition of transformations is evaluated right to left.

Reflection in the x-axis moves a point from below the x-axis to the same distance above the x-axis. That is, the sign of the y-coordinate changes:

  (-4, -6) ⇒ (-4, 6) . . . reflection in the x-axis

The translation vector is added to the coordinates of the point:

  (-4, 6) +(-3, -1) = (-4-3, 6-1) = (-7, 5)

The image of the point is located at (-7, 5).

Answer:

-31

Step-by-step explanation:

2 negatives make a positive so you have -51-17+37 which equals -31

Using the concept of linear equation we can conclude that the number of marbles sold by Mark is 23 and the number of marbles sold by Don is 72.

An equation is said to be linear if the highest power of the variable is 1. It is also called as  one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variable is x and A is the coefficient of x, while B is a constant.

Let the number of marbles Mark sells be ‘x’

then, the number of marbles Don sells can be given by ‘3x+3’

Total number of marbles sold=95

We can for equation by adding the number of marbles Mark sells and the number of marbles Don sells  to the total number of marbles sold. The equation formed is

x+3x+3=95

4x+3=95

4x=95-3

4x=92

x=23

The number of marbles Mark sells =23

Number of marbles Don sells=3x+3

Substituting value of ‘x’

Number of marbles Don sells=(3×23)+3

Number of marbles Don sells=69+3

Number of marbles Don sells=72

Thus, the number of marbles sold by Mark is 23.

While, the number of marbles sold by Don is 72.

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1) The composite function is f ° g (x) = x / (2 + x). The domain of the composite function is all real numbers except - 2 and the range of the composite function is all real numbers except 1.

2) The composite function is g ° f (x) = 2 · x + 1. Both the domain and the range of the composite function is all real numbers.

Let a, b be functions, there is a composition when the independent variable of one of the functions is substituted by the other function. For instance,

a ° b (x) = a [b (x)]

The domain of a function is the set of x-values such that the function exists, whereas the range of it is the set of y-values.

If we know that f(x) = 1 / (2 · x + 1) and g(x) = 1 / x, then the composite functions and their domains are:

f ° g (x)

f ° g (x) = f [g (x)]

f ° g (x) = 1 / [2 · (1 / x) + 1]

f ° g (x) = 1 / [(2 + x) / x]

f ° g (x) = x / (2 + x)

The domain of the composite function is all real numbers except - 2 and the range of the composite function is all real numbers except 1.

g ° f (x)

g ° f (x) = g [f (x)]

g ° f (x) = 1 / [1 / (2 · x + 1)]

g ° f (x) = 2 · x + 1

Both the domain and the range of the composite function is all real numbers.

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Answer:

1, 2 and 3

Step-by-step explanation:

The numbers are 1, 2 and 3

When we add together : 1+ 2+ 3 = 6 and

When we multiply: 1 × 2 × 3 = 6

Answer:

Step-by-step explanation:

You want to solve the 6th-degree equation x^6 -9x^3 +10 = 0.

The equation is basically quadratic in x^3. Substituting z = x^3, we have ...

  z^2 -9z +10 = 0

  (z -10)(z +1) = 0 . . . . . factored form

  z = 10, z = -1 . . . . . . . values of z that make the factors zero

Now, we have two cubic equations to solve:

The real root is given by the cube root function. The imaginary roots are that value multiplied by 1∠±120° = (-1/2 ±(√3)/2i). Then the six roots are ...

__

Additional comment

The product ∛10√3 can be simplified to ...

  [tex]\sqrt[3]{10}\sqrt{3}=(10^{2/6})(3^{3/6})=(10^23^3)^{1/6}=\sqrt[6]{2700}\approx 3.7315903[/tex]

The expression for Five more than the quotient of a number and 3 is 7 is (n/3) +5 =7.

The unknown number y is 6.

Any combination of terms that have undergone operations like addition, subtraction, multiplication, division, etc. is called as an algebraic expression (or variable expression).

given that Five more than the quotient of a number and 3 is 7.

the unknown number is y.

variable = y

now find the value of y.

This statement should be transformed into an equation.

A number divided by three can be written as

y/3.

Adding 5 now results in equation is

(y/3) + 5.

This is supposed to equal 7, therefore the equation is

(y/3) +5 =7.

now solve the equation

deducting 5 from both sides, you can solve for y to get

y/3 = 2.

Multiply 3 to both sides so that y is 6.

n = 6.

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When something is bisected, the following is achieved:

When an object is bisected, it means that it is being cut in half.

Cutting something in half means that you will leave two equal pieces. Bisecting therefore leads to something being cut in half.

Bisecting is used in various mathematical formulas such as when bisecting angles.

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The equations of the parabolas are given as follows:

a) f(x) = -(x + 6)² - 2.

b) g(x) = (1/32)(x - 6)² + 2

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

In item a, the vertex is at (-6,-2), hence:

f(x) = a(x + 6)² - 2

When x = -8, f(x) = -6, hence we use it to find a as follows:

-6 = 4a - 2

4a = -4

a = -1.

Hence:

f(x) = -(x + 6)² - 2.

In item b, the vertex is at (6,2), hence:

g(x) = a(x - 6)² + 2

When x = -2, g(x) = 4, hence we use it to find a as follows:

4 = 64a + 2

64a = 2

a = 1/32.

Hence:

g(x) = (1/32)(x - 6)² + 2

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The greatest common side represents the congruent squares in a rectangular shaped grid.

What is greatest common side?

The greatest common side or the greatest common factor defines the two images which has exactly same shape as well as shape size. And it is also known as congruent which means same. It uses the integer factor algorithms for the calculation.

The congruent comes in different shapes like square, parallelogram, rhombus, rectangular etc. In all these types, some sides are exactly equal.

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For every 21 liters of petrol a car can run for 80 km- 58.2 liters of petrol would be required to ensure the car has enough petrol of a trip that is 224 km unitary method

It is provided that to run 80km car requires 21 liters of petrol

To know how much petrol is required for a trip of 224 km, we first would require to know how much petrol is required to run 1 km

This is called unitary method

Petrol required by car to run 1 km would be petrol required by car to cover 80kms of distance divided by 80 km of distance = 21 liters of petrol/ 80 km distance

                                                      = 21/80

                                                      =0.26 liters

So, petrol required by car for a trip of 224 km= 0.26 liters  ×224km

                                                                          = 0.26× 224

                                                                           =  58.24 liters

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The expression to know many magazines kadien have left will be 60 - 5x.

From the information, Kadien had 60 magazines and he sells x magazines per day for 5 days.

The expression to calculate the number that will be left will be:

= 60 -(5 × x)

= 60 - 5x

The expression is 60 - 5x.

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Answer: B) as the x-values go to negative infinity, the functions values go to positive infinity.

Step-by-step explanation:

The average cost price of 2000 printed tennis balls will be $1500.

The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.

Given that a local college's service organization purchased 2,000 tennis balls with the school's logo on them. Tennis balls cost $.50 each from Sports Depot, and a one-time stamp costing $500 was added on top of that.

Total cost = ( 2000 x 0.5 ) + 500

Total cost = 1000 + 500

Total cost = $1500

Therefore, the average cost price of 2000 printed tennis balls will be $1500.

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If the relation has its domain in the x-axis and its range in the y-axis, then the relation is not a function. But if its domain is in the y-axis and its range is in the x-axis, then the relation is a function.

Relations are characterized by three elements:

A relation is a function if and only if each element of the domain is related only to one element of the range. It must be mentioned that the answer may differ depending on what we assume as domain and range.

If the x-axis represents the domain and the y-axis represents the range, then relation is not a function, but if the x-axis is the range and the y-axis is the domain, the given relation is a function.

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The solutions to the questions are

The figure represents the given parameter.

On the figure, we have the following shapes:

The area is calculated as

Area = Area of rectangle 1 + Area of rectangle 2

So, we have

Area = 7 * 5 + 3 * 10

Evaluate

Area = 65

Hence, the area of the floor is 65 square feet

On the figure, we have the following shapes:

The perimeter is calculated as

Perimeter = Perimeter of rectangle 1 + Perimeter of rectangle 2

So, we have

Perimeter = 2 *(7 + 5) + 2 * (3 + 10)

Evaluate

Perimeter = 50

Hence, the perimeter of the floor is 50 feet

The total cost is calculated as

Total Cost = Cost of baseball * Area of baseball + Cost of tile * Area of tile

So, we have

Total Cost = 2 * 7 * 5 + 2.5 * 3 * 10

Evaluate

Total Cost = 145

Hence, the total cost to buy tile and baseboards for your bathroom is $145

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