A collector of hand-woven rugs has an oval rug that is 42 years old and a circular rug that is 14 years old. How many years ago was the oval rug five times as old as the circular rug was then?

i need an equation plsss help.

The expression of 3D-3C is 6x²-12x+6 in the standard form when the D=1-x² and C = -1-3x²+4x.

Given that,

The equations,

D=1-x² and C = -1-3x²+4x

We have to find the expression 3D-3C in standard form.

Mathematical statements are called expressions if they have at least two terms that are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

We get,

3D-3C

3(1-x²)-3(-1-3x²+4x)

3-3x²+3+9x²-12x

6+6x²-12x

6x²-12x+6

Therefore, The expression of 3D-3C is 6x²-12x+6 in the standard form when the D=1-x² and C = -1-3x²+4x.

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Answer:

2

Step-by-step explanation:

Question:

1 + 1 = ?

1 + 1 = 2

The error made in the calculation was improper use of quotient rule of logarithm

The problem will be solved by using the rules of logarithm as done below

logₐ 2x + 2 ( logₐ x - logₐ y )

expanding the parenthesis

logₐ 2x + 2logₐ x - 2logₐ y

applying exponential rule of logarithm

logₐ 2x + logₐ x² - logₐ y²

applying product rule of logarithm

logₐ (2x * x²) - logₐ y²

logₐ (2x³)  - logₐ y²

applying quotient rule of logarithm

logₐ (2x³/ y²)

The error was that the quotient rule of logarithm was not properly applied

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Answer:

Step-by-step explanation:

General equation of circle:

Comparing with the general equation we see that the circle x² + y² = 36 has:

The circle radius of 6 units, so y = - 6 has only one common point.

Since there is only one common point of the circle and line, the line is tangent to the circle.

Answer:

0.65

Step-by-step explanation:

1.65 is 0.65 greater than 1

The standard deviation for the dataset (4, 4, 4, 4, 4) is zero (0)

To find a data set with 5 values for which the standard deviation is zero,

⇒ (4, 4, 4, 4, 4)

For the above dataset;

Mean μ = 4

Number of samples n = 5

Standard deviation σ = [tex]\sqrt{\frac{sumof(xi - x)^2}{n} }[/tex]

                                   = [tex]\sqrt{\frac{(4-4)^2+(4-4)^2+(4-4)^2+(4-4)^2+(4-4)^2}{5} }[/tex]

                                   = 0

Therefore, for the dataset (4, 4, 4, 4, 4) the standard deviation is zero(0).

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The area of the rectangle with one dimension sizes three more than twice the other dimension is A= x(2x+3)

We assume that there is rectangle ABCD with lines AB and CD are parallel with each other. Meanwhile lines BC and DA are parallel with each other. We could ssume that lines BC and DA are the shortest lines.

Please take a look at the picture below.

Based on the formula of rectangle, the area of rectangle could be calculated using the multiple between the longest line and the shortest line.

It could be written based on the rectangle we have into such formula:

A = AB × BC

A = CD × DA

A = AB × DA

A = CD × BC

If we input the rules from the question, then we could find the relationship between the shortest and the longest lines. Hence:

AB = CD = 2(BC) + 3

AB = CD = 2(DA) +3

if we assume that the shortest line is x, then we will get the formula:

BC = DA = x ...(1)

AB = CD = 2x+3 ...(2)

If we input equation (1) and (2) into the rectangle area formula, we will get the result:

A = AB × BC

A = (2x+3)

A = x(2x+3)

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One-half of the number is 18.

Given that

One-third of a number is 12.

Let "x" be the number

Given that,

One-third of a number is 12

Which means,

[tex]\frac{1}{3} *x = 12[/tex]

x = 3*12

x = 36

Thus the number is 36

Work out one-half of the number

one half of the number = [tex]\frac{x}{2}[/tex]

one half of the number = [tex]\frac{36}{2}[/tex]

one half of the number = 18

Hence the answer is, one-half of the number is 18.

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The true proportion of the similar triangles is [tex]\frac{AC}{AE} = \frac{BC}{BD}[/tex]

Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.

In other words, similar triangles are the triangles that have corresponding sides in proportion to each other and corresponding angles equal to each other.

Therefore,

ΔACE is similar to ΔBCD

Hence,

[tex]\frac{AC}{BC}=\frac{AE}{BD}=\frac{CE}{CD}[/tex]

Therefore, the proportion that is true for the ΔACE and ΔBCD is [tex]\frac{AC}{AE} = \frac{BC}{BD}[/tex]

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Answer:

y=-1/5x

Step by Step

y=mx+b

First find the slope

equation: y2-y1 divided by x2-x1

1-(-1)/-5-5

2/-10

simplified to -1/5

Now that we have the slope we need the y-int

using point slope form: y-y1=m(x-x1)

Let us use the point (5,-1)

y-(-1)=-1/5(x-5)

y+1=-1/5x+1

Subtract 1 to both sides

y=-1/5x

Answer:

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

Slope-intercept form is:

Given line in standard form:

Convert this to slope-intercept form:

Answer:

[tex]\boxed{y=\dfrac{3}{4}x-\dfrac{3}{4}}[/tex]

[tex]\implies \textsf{Slope}=\dfrac{3}{4}[/tex]

[tex]\implies \textsf{$y$-intercept}=-\dfrac{3}{4}[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]

Given equation:

[tex]-3x+4y+3=0[/tex]

To write the given equation in slope-intercept form, rearrange the equation to isolate y.

Add 3x to both sides of the equation:

[tex]\implies -3x+4y+3+3x=0+3x[/tex]

[tex]\implies 4y+3=3x[/tex]

Subtract 3 from both sides of the equation:

[tex]\implies 4y+3-3=3x-3[/tex]

[tex]\implies 4y=3x-3[/tex]

Divide both sides of the equation by 4:

[tex]\implies \dfrac{4y}{4}=\dfrac{3x-3}{4}[/tex]

[tex]\implies y=\dfrac{3}{4}x-\dfrac{3}{4}[/tex]

Compare the rearranged equation with the slope-intercept formula:

[tex]\implies \textsf{Slope}=\dfrac{3}{4}[/tex]

[tex]\implies \textsf{$y$-intercept}=-\dfrac{3}{4}[/tex]

The solution for f ( x ) = 72 is x = -3 ; which is not a viable solution in this scenario.

It follows from the task content that the solution for the function instance, f(x) = 72 is to be determined according to the given function.

Since the given function is; f ( x ) = − 4 x + 60;

The solution for f (x) = 72 can be determined as follows;

72 = - 4 x + 60

- 4x = 72 - 60

- 4x = 12

x = 12/-4

x = - 3

On this note, since x = -3 which is negative; it follows that it is not a a viable solution in this regard.

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The probability that at least one number is odd and the sum of the two numbers is even is 1/4

The probability that exactly one number is 6 and the product of the two numbers is at most 15 is 1/9

The easiest way to figure out probability problems with small data sets is to write out your entire sample space and then divide by the total:

Sample size = 6 * 6 = 36

S = {[1,1],[1,2],[1,3],[1,4],[1,5],[1,6],[2,1],[2,2],[2,3],[2,4],[2,5],[2,6],[3,1],[3,2],[3,3],[3,4],[3,5],[3,6],[4,1],[4,2],[4,3],[4,4],[4,5],[4,6],[5,1],[5,2],[5,3],[5,4],[5,5],[5,6],[6,1],[6,2],[6,3],[6,4],[6,5],[6,6]}

The only way to make a number combination that's even while 1 die is odd is to have 2 odd numbers.

{[1,1],[1,3],[1,5],[3,1],[3,3],[3,5],[5,1],[5,3],[5,5]}

This gives us 9 results.

The probability of this happening is 9/36 = 1/4 = 0.25

Now if we have to get a 6 with the product being at most 15 we know that the biggest number that 6 can be multiplied by is 2 which gives us 12.

We are left with 4 options:

{[1,6],[2,6],[6,1],[6,2]}

The probability of this happening is 4/36 = 1/9 = 0.1111...

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The latest time Dan should leave his house to get to work on time will be 10: 05 am.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Dan goes from Birmingham to Coventry by Bu. Be goes for 5 moments to stroll from greetings houe to the bu top in Birmingham. He goes for 20 moments to stroll from the Bu top in Coventry to work. Dan has to get to work by 10.30 am.

The total time is given as,

⇒ 5 + 20

⇒ 25 minutes

The latest time Dan should leave his house to get to work on time will be given as,

  10: 30 am

- 00: 25      

  10: 05 am

The latest time Dan should leave his house to get to work on time will be 10: 05 am.

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The non negative integers can be written of the form is 3281.

Given:

a7 * 3^7 a2 * 3^6 where ai {1, 0, -1}.

ai = 7,6,5,4,3,2,1,0

Total = 8

= [tex]3^{8}[/tex] = 6561

= 6561 - 1 /2

= 6560/2

= 3280 is negative integers

Non negative or positive integers = 6561 - 3280 = 3281

Therefore the non negative integers can be written of the form is 3281.

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Answer:665

Step-by-step explanation: Just add the CP and Profit

Answer:

$8.30 per keychain

Step-by-step explanation:

15.5 is the price of one hat so we multiply by 3

15.5x3=46.5

Now we subtract this from 96.30

96.3-46.5=49.8

Now divide by 6 to get each key chain price

49.8/6= 8.3

$8.30 for each keychain

Claire’s answer is u reasonable because of the work I did above

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The proof of Δ SUE is not an isosceles triangle. is shown below.

If there are two points A(a, b) and B( c, d) then the distance between these two points are

AB= √( c-a )² + ( d-b )²

Given:

S(-2, -4), U(2, -1) and E(8, -9)

Using Distance formula

SU= √( 2 -(-2))² + ( -1-(-4))²

SU = √4²+ 3²

SU = √16+9

SU =5

and, UE = √( 8 -(2))² + ( -9-(-1))²

UE = √6²+ 8²

UE = √36+64

UE =10

and, ES= ( 8 +2 ))² + ( -9+4)²

ES = √10²+ 5²

ES = √100+25

ES = 5√5

As, none of the two sides are equal.

So, Δ SUE is not an isosceles triangle.

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On solving the given equation for g you will get [tex]g=\frac{4\pi^2l}{T^2}[/tex]. Any equation can be solved by using properties of equality of eqatuion.

Which properties are use to solve the equation?

The following 4 properties are use to solve any equation:

(1) Addition: Add same number on both side of the equation.

(2) Subtraction: Subtract same number from both side of the equation.

(3) Multiplication: Multiply with the same number on both the sides of the equation.

(4) Division: Divide with the same number on both sides of the equation.

Now, consider the given equtaion.

[tex]l=\frac{gT^2}{4\pi^2}[/tex]

Multiply both sides with [tex]4\pi^2[/tex].

[tex]l(4\pi^2)=\frac{gT^2}{4\pi^2}4\pi^2\\l(4\pi^2)=gT^2[/tex]

Divide both sides with [tex]T^2[/tex]

[tex]\frac{4\pi^2l}{T^2}=\frac{gT^2}{T^2}\\\frac{4\pi^2l}{T^2}=g\\g=\frac{4\pi^2l}{T^2}[/tex]

Hence, on solving the given equation for g you will get [tex]g=\frac{4\pi^2l}{T^2}[/tex].

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The simplification of the given expression will be 54.

A numerical expression is algebraic information stated in the form of numbers and variables that are unknown. Information can is used to generate numerical expressions.

Given that the expression is 2 x 4 + 6 + 5  thex 8

To solve the given expression we have to first solve the multiplication operation.

2 x 4 + 6 + 5 x 8

8 + 6 + 40

Now add the terms;

8 + 6 + 40

= 54

Hence, the simplification of the given expression will be 54.

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quick clarification on "point E to line FH", well, point E is just a point, line FH goes to infinity both ways, so in essence how many distances are there? well, infinite many.

now, if the question is "distance closest from E to FH?", then there's only one choice, the closest distance to FH will be the perpendicular distance from E and that'd be the distance from E to G

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ E(\stackrel{x_1}{-4}~,~\stackrel{y_1}{-3})\qquad G(\stackrel{x_2}{1}~,~\stackrel{y_2}{2})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ EG=\sqrt{(~~1 - (-4)~~)^2 + (~~2 - (-3)~~)^2} \implies EG=\sqrt{(1 +4)^2 + (2 +3)^2} \\\\\\ EG=\sqrt{( 5 )^2 + ( 5 )^2} \implies EG=\sqrt{ 25 + 25 } \implies EG=\sqrt{ 50 }\implies EG\approx 7.07[/tex]

The function is odd because f(-x) = -f(x)

What is a Function?

A function is an expression, rule, or law in mathematics that describes a connection between one variable (the independent variable) and another variable (the dependent variable).

Solution:

For a function to be even it must satisfy the condition that,

f(-x) = f(x)

else,

if f(-x) = -f(x), then the function is odd

we are given with the function f(x) = [tex]4x^{3}[/tex]

replacing x by (-x)

f(-x) = 4(-x)^3

f(-x) = -4x^3

this implies that, f(-x) = -f(x)

Therefore, the function is an odd function

So, option D is correct

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Answer:

2555 days

Step-by-step explanation:

1 year is 365 days, and 365 x 7 = 2555.

Answer:

16 days

Step-by-step explanation:

(28×8)/14= 16

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The tip is 18%

From the question, we have

food and beverages cost = $25.30

meals tax = 8%

Tax = (8/100)* 25.3 =  $2.02

Bill = $25.30 + $2.02

= $27.32

After adding a tip, the total lunch cost was $32.24.

Tip = $32.24. -  $27.32  = $4.92

% of Tip  = (4.92 /  27.32) * 100 =  18 %

Multiplication:

Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.

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Answer:

The correct answer is B

Step-by-step explanation:

I went a weird way to get this.  I wrot the line in the slope intercept form and  then converted it to the standare form.

For the slope intercept form I need a slope and a y interctp.  I used the two points given to find the slope.  The slope is the change in y over the change in x.  From the points the y values are 3 and -1.  The x values are 1.2 and -4

[tex]\frac{3 - -1}{\frac{1}{2}- - 4 }[/tex] = [tex]\frac{3+1}{\frac{1}{4}+4 }[/tex] = [tex]\frac{4}{\frac{9}{2} }[/tex]

4 ÷[tex]\frac{9}{2}[/tex] = [tex]\frac{4}{1}[/tex] x [tex]\frac{2}{9}[/tex] = [tex]\frac{8}{9}[/tex]

[tex]\frac{8}{9}[/tex] is the slope

Now to find the y intercept

I will use

slope [tex]\frac{8}{9}[/tex] (m)

y = -1            from the point (-4,-1) given

x = -4            from the point (-4,-1) given

y=mx + b

-1 = [tex]\frac{8}{9}[/tex](-4) + b

-1 = [tex]\frac{-32}{9}[/tex]x + b       Add [tex]\frac{32}{9}[/tex] to both sides

[tex]\frac{23}{9}[/tex] = b

y = [tex]\frac{8}{9}[/tex]x + [tex]\frac{23}{9}[/tex]  Multiply all the way thorugh by 9

9y = 8x + 23  Subtract 9y from both sides

0 = 8x -9y + 23  Subtract 23 from both sides

-23 = 8x -9y

or

8x -9y = -23