A rectangular hotel room is 5 meters by 7 meters. The owner of the hotel wants to recarpet
the room with carpet that costs $47.00 per square meter. How much will it cost to recarpet
the room?

The result of simplifying each number 100⁴.⁵  using the exponent rules is

10⁽⁴⁰⁾

To solve this exercise we have to resolve algebraic operations following the exponent rules.

100⁴.⁵

Base= 100 =  10²

The base number 100 is the same that: 10², then we get:

(10²)⁴.⁵

Using the power of a power rule that indicates that: the exponent result will be the multiplication of these exponents, we have:

10⁽²*⁴*⁵⁾

10⁽⁸*⁵⁾

10⁽⁴⁰⁾

In mathematics an exponent is the number of time that a number, called (base) is multiplied by itself. It is also called, power or index.

Example: 3² = 3*3 = 9

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The standard notation for the given terms is (1). 234.6; (2). 499.69; (3). 86; (4). 1.2; (5). 50.

Conversion of the different notation into standard notations is given below:

1. 2.3 x 102 = 234.6

2. 4.67 x 107 = 499.69

3. 9.1 x 10-5 = 86

4. 1.2 x 10⁰ = 1.2

5. 5x10 = 50

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Model for the Combined variation  is  [tex]F = \frac{km}{d^{2} }[/tex]

Equation to find the mass of the rocket in terms of F and d is :

[tex]m=\frac{F d^{2} }{k}[/tex]

A force is the quantity that change the motion of the object. Force is that influence which can cause any object having some mass, to change it's position or to accelerate from it's original position.

Force (F) and mass (m) of any object are  directly proportional to each other. More the mass of the object , more the force will require to accelerate it.

Mathematically, we can write the equation of force as :

F = m . a

where , m = mass of the object

             a = constant value

In the statement given,

As, force of gravity varies directly with its mass

Therefore, F= k m , where k is a constant

Also force is inversely varies with square of distance d

Thus, F = k / d²

Combining both equations :

[tex]F = \frac{km}{d^{2} }[/tex]  

and the equation of mass in terms of F and d can be written as :

[tex]m=\frac{F d^{2} }{k}[/tex]

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Since slopes m₁ and m₂ are equal to 5, it shows that these two lines are parallel.

Parallel lines can be defined as two (2) lines that are always the same (equal) distance apart and never meet.

In Geometry, two (2) lines are considered to be parallel if their slopes are the same (equal) and they've different y-intercepts. This ultimately implies that, two (2) lines are parallel under the following conditions:

m₁ = m₂

Note: m is the slope.

Mathematically, the standard form of the equation of a straight line is given by;

y = mx + b

Given the following equations:

y = 5x + 1

2y - 10x + 3 = 0  ⇒ y = 5x - 3/2

m₁ = m₂ = 5.

In this context, we can reasonably infer and logically deduce that these two lines are parallel.

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Complete Question:

The equation line L₁ is y = 5x + 1

The equation line L₂ is 2y - 10x + 3 = 0

Show that these two lines are parallel.

The resulting expression if the value of t is 23 is g(23) = -4g - 207

A function is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given the function below;

g(t)=−9t−4g

We are to determine the value of g(23). Substitute t = 23;

g(t)=−9t−4g

g(23) = -9(23) - 4g

g(23) = -207 - 4g

g(23) = -4g - 207

Hence the resulting expression if the value of t is 23 is g(23) = -4g - 207

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Answer:

y = -3x + 5

Step-by-step explanation:

slope-intercept form means it should look like

y = mx + b

9x + 3y – 15 = 0

3y = -9x + 15

y = -3x + 5

Answer:

108b^2

Step-by-step explanation:

(-6)(-18)=108

(b)(b)=b^2

108b^2

The amount invested in the bond with 5% simple interest is $16,666.67

The amount invested in the bond with 6.5% simple interest is $33,333.33  

What is simple interest?

The interest earned under a simple interest arrangement is determined as the amount invested multiplied by the interest rate and the time the investment lasts

I=PRT

let us assume that x was invested in the bond with 5%

interest on x=5%*x=0.05x

amount invested in other bond=50000-x

interest earned on 6.5%=(50000-x)*6.5%

interest earned on 6.5%=3250-0.065x

total interest=0.05x+3250-0.065x

total interest=3250-0.015x

total interest=3000

3000=3250-0.015x

0.015x=3250-3000

0.015x=250

x=250/0.015

x=$16,666.67

amount invested at 6.5%=$50,000-$16,666.67

amount invested at 6.5%=$33,333.33

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Given u = (-1,3), v=(2,4) , and w= ( 2,-5), then, by applying scalar multiplication on vector, 2u = (–2, 6)

In the two-dimensional coordinate system, vectors can be split into x-component and y-component.

We can write, for example, a vector q = (1,–5), which means:

x-component = 1

y-component = –5

Operations on vectors:

In the given problem:

u = (-1,3), v = ( 2,4) , and w = (2,-5)

Then,

2u =  2 (-1,3)

      = (2 . (-1), 2. 3) = (–2, 6)

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The value of x is 6 if E is the midpoint of the segment.

Given,

E is the midpoint, so DE = EF

DE = 3x

EF = 18

Since DE = EF,

3x = 18

x  =18/3

x = 6

If x = 6 , then

DE = 3x

DE = 3(6)

DE = 18

therefore, DE = EF since E is the mid point.

EF = 18

hence we get the value of x as 6.

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The given expression is a fraction raised to a power and will be solved by multiplication of exponents for both numerator and denominator.

When in an expression, the base is a fraction raised to a number (exponent), the exponent is applied to both numerator and denominator.

In this case, the base is x^-2/3/y^-1/3 and the exponent is 15.

Since (x^a)^b=x^ab

Multiplication of exponent applied to both numerator and denominator,

(x^⁻²/₃/y^⁻¹/₃)^¹⁵=x^⁻²/₃*15/y^⁻¹/₃*15

Simplifying,

x^⁻²/₃*15/y^⁻¹/₃*15=x^-10/y^-5

Since both numerator and denominator have negative exponents, it is not yet in the simplest form.

According to negative exponents rule, x^-a=1/x^a

To remove the negative exponent, the fraction should be reversed.

x^-10/y^-5=y^5/x^10

The simplest form of the expression (x^⁻²/₃/y^⁻¹/₃)^¹⁵ is y^5/x^10

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Answer:

[tex]6\frac{3}{5}[/tex]

Step-by-step explanation:

[tex]8 \div 5 = 1\frac{3}{5} \\\\1\frac{3}{5} + 7 = 8\frac{3}{5}\\\\8\frac{3}{5} - 2 = 6\frac{3}{5}[/tex]

The expression that means the same as the given expression is w ÷ 5

From the question, we are to determine which of the given expressions means the same as w/5

To do this, we will simplify each of the given expressions if possible

This expression cannot be simplified further

This expression cannot be simplified further

This expression can be written as w/5

This expression can be written as 5w

This expression cannot be simplified further

This expression can be written as 5/w

Hence, the expression is w ÷ 5

Here is the complete question:

Which Of the expressions below means same as w/5

w + 5

w - 5

w ÷ 5

5 × w

5 - w

5 ÷ w

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Tim needs 40ft fencing.

For fencing the square garden we need to ascertain perimeter of the square.

Perimeter of plot = 2*(a+b)

Where a = length of the plot

b=width of plot

length =12ft

width=8ft

Perimeter of plot = 2*(a+b) = 2*(12+8)ft=40ft

He needs 40ft fencing.

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Answer:

inverse I believe because it is the same statement but opposite

The least integer greater than each number for log₅1/47 = -3

All whole numbers and negative numbers are considered integers. This means that if we combine negative numbers with whole numbers, a collection of integers results.

Let y = log₅1/47

We know, logₐ x = y, only if a^y= x

Therefore, 5^y = 1/47

So, we must find an integer y such that 5 > 1/47

5^y > 1/47

5^{-3} > 1/47

(As, 5² = 25; 5³ = 125) (Since, 5² < 47, the answer will be 5³ as 5³ > 47)In this case, y = -3 will be the least integer to satisfy this inequality.

Therefore, the ultimate answer to the equation is log₅1/47 = -3

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Answer:

Point Y

Step-by-step explanation:

This dilation is an expansion, so in order for it to expand, the center of dilation need to be in the middle or near the middle of the pre-image.

What is a pre-image?

Noun. preimage (plural preimages) (mathematics) For a given function, the set of all elements of the domain that are mapped into a given subset of the codomain; (formally) given a function ƒ : X → Y and a subset B ⊆ Y, the set ƒ−1(B) = {x ∈ X : ƒ(x) ∈ B}.

What is an Image?

The new position of a point, a line, a line segment, or a figure after a transformation is called its image.

Center of Dilation:

The center of a dilation is a fixed point in the plane about which all points are expanded or contracted. The center is the only invariant (not changing) point under a dilation (k ≠1), and may be located inside, outside, or on a figure.

I hope this helps! :)

The time taken to reach $14200 in the bank with 4.25% interest compounded is 50 years

The time taken to reach 14200 with interest compounded semi-annually can be calculated by

[tex]A = P (1 +\frac{R}{100n})^{nT}[/tex]

where A is the total amount at the end of the period

          P is the principal amount

          R is the rate of interest

          n is the no. of interest compounded per year

          T is the time period

We know that A = 14200

                       P = 9000

                       R = 4.25%

                       n = 2

By substituting these values, we get

                    14200 = 9000 [1 + (4.25 /200[tex]]^{2T}[/tex]

                    14200/9000 =  [tex](1+0.02125)^{2T}[/tex]

                              1.5778 =  [tex](1+0.02125)^{2T}[/tex]

                          1.5778 =  [tex](1+0.02125)^{2T}[/tex]

                           1.5778  =[tex](1 +0.02125)^{2T}[/tex]

Taking logs on both sides,

                    log (1.5778) = log [tex](1+0.02125)^{2T}[/tex]

                    log (1.5778) = 2T log(1 +0.02125)

                              0.198 = 2T log(1.02125)

                             0.198 = 2T (0.00913)

                             0.918 = 0.01826 T

                                    T = 0.918 / 0.01826

                                    T = 50.27 yrs

                                    T ≅ 50 years

Therefore, the time taken to reach $14200 in the bank with 4.25% interest compounded is 50 years

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Answer:

[tex] a_{1} = 5[/tex]

Step-by-step explanation:

check the attached image for explanation

Answer:

-4

Step-by-step explanation:

If you graph the two coordinates the line is going down, so the answer is going to be negative. The slope is -4/1 but simplified is -4. Hope this helps. Have a great night.

Answer:

(-1,4)

(0,0)

(1,-4)

(1,-8)

Step-by-step explanation:

Substitute the value of x in the equation and find the corresponding y value.

 y = -4x

When x = -1     ; y = -4*(-1) = 4.

When x = 0    ; y = 0

When x = 1     ; y = -4*1 = -4

When x = 2    ; y = -4*2 = -8

10 (ln (e)) = 10, by the definition of logarithm.

Now,

By property of logarithm, ln (e) = 1

Thus, in the expression 10 (ln (e)) = 10 (1) = 10.

Hence, 10 (ln (e)) = 10, by the definition of logarithm.

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Answer:   Slope = 2.250/2.000 = 1.125

 x-intercept = 40/9 = 4.44444

 y-intercept = 40/-8 = 5/-1 = -5.00000

Step-by-step explanation:

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is -5.000 and for x=2.000, the value of y is -2.750. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -2.750 - (-5.000) = 2.250 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

ttttttgyygyyAnswer:

Step-by-step explanation:

gtgtggtgyyyhhyhyy

The logarithmic properties used are Quotient property, Product property, Power property and Product and Power Property.

In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as  .

   [tex]log_ax=N[/tex]

where, a is the base of function or equation

           x define expression

Mathematically, if  [tex]a^N=x[/tex]  is an exponential function then, this can be converted to logarithmic function as  [tex]log_ax=N[/tex].

There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.

Some important formulas of logarithms are :

The given expression is,

log 18

now, log 18 can be written in following four ways :

1. Using Quotient Property of logarithms

  [tex]log 18 = log \frac{36}{2} = log 36 - log 2[/tex]

2. Using Product Property of logarithms

   [tex]log 18 = log (9.2) = log 9+ log2[/tex]

3. Using Power Property of logarithms

   [tex]log 18 = log (324)^\frac{1}{2} = \frac{1}{2} log (324 )[/tex]

4. Using Product and Power Property of logarithms

   [tex]log 18 =l og 2.3^2 = log 2 +2log3[/tex]

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Step-by-step explanation:

5 digit number

5abcd

a = 2 or a = 3. but a = 3 means the upper limit of 53,000. and the sum of digits is 8 and not 21.

so, a = 2.

d = 3n

c = b

5 + a + b + c + d = 21

5 + a + 2b + 3n = 21

a + 2b + 3n = 16

2 + 2b + 3n = 16

2b + 3n = 14

so, n must be an even number to allow an even result (14). therefore, n = 0 or n = 2 (any larger even number n like 4 would not create a single digit result)

if n = 0, then 2b = 14, b = 7

if n = 2, then 2b + 6 = 14, 2b = 8, b = 4

so, we have the options

52770

52446

I suspect that 0 as 0×3 is not considered a multiple of 3 by your teacher, so only n = 2 (or d = 6) is a desired solution.

therefore, I would use

52446

as answer.

Answer:

Step-by-step explanation:

A: Function 2 only; at the point where x = 0, the value of the function is 5, which is greater than 3.
B: Function 3; the coefficient of x is the greatest out of all of them.
C: Function 4; the y-intercept of -1 only deviates from 0 by 1.

The simplification of the expression  (-27)²/₃   is 9.

We are given, (-27)²/₃ and we are required to simplify

What (-27)²/₃ means is that (-27) is to the power of 2 and 1/3

Let's start by finding out  [tex](-27)^{2}[/tex] .The result is, 729

Then, [tex]729^{1/3}[/tex]

= 9

The final result is 9

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Answer:

1742 is divided by 2.16 than answer is 418.75

Answer:

12

Step-by-step explanation:

since both are square it is 12

The gradient of the line joining R(-50, 460) and S(115, 55) is -2.45

The points on the line are given as

R = (-50, 460)

S = (115, 55)

The gradient of the line joining R(-50, 460) and S(115, 55) is calculated using

Gradient = (y2 - y1)/(x2 - x1)

This gives

Gradient = (460 - 55)/(-50 - 115)

Evaluate

Gradient = -2.45

Hence, the gradient of the line joining R(-50, 460) and S(115, 55) is -2.45

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