The figure shows relationships of the dimensions of a square pool with an attached patio. Complete the equations and reasons to show that AC= BD

a WHOLE is always simplified to "1", and we can use any denominator for that, so 5/5 is 1, and 7/7 = 1, and [tex]\cfrac{4}{4}\implies \cfrac{113}{113}\implies \cfrac{1000000}{1000000}\implies \text{\LARGE 1}whole[/tex]

so hmmm for this case we'll be use thirds or namely the denominator of 3, so a whole bunch of basketballs was originally 3/3 of "b", "b" was the whole amount, so originally we had 3/3, but then during the day we sold 2/3 of them, so we were left with 3/3 - 2/3 = 1/3, and then 8 came back, because they were deflated or something, now the store has a total of 38 basketballs.

[tex]\stackrel{whole}{\cfrac{3}{3}b}~~ - ~~\stackrel{sold}{\cfrac{2}{3}b}\implies \cfrac{3b-2b}{3}\implies \cfrac{b}{3}\implies \stackrel{\textit{remaining in store}}{\cfrac{1}{3}b} \\\\\\ \stackrel{in~store}{\cfrac{1}{3}b}~~ + ~~\stackrel{coming~back}{8}~~ = ~~\stackrel{new~total}{38} \\\\\\ \cfrac{b}{3}+8=38\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}}{3\left( \cfrac{b}{3}+8 \right)=3(38)}\implies b+24=114\implies \stackrel{originally}{b=90}[/tex]

Marianne's age is 14 years old if her father's age is her age plus five to the power of four, less 365, minus 22, all divided by six.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

Marianne figured out that her father's age is her age plus five to the power of four, less 365, minus 22, all divided by six. If her father is 42.

Let x be the Marianne age

(x + 5⁴ - 365 - 22) (1/6) = 42

x + 238 = 252

x = 14 years

Thus, Marianne's age is 14 years old if her father's age is her age plus five to the power of four, less 365, minus 22, all divided by six.

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Answer: 32

Step-by-step explanation: 2(-3)2. -4

Rationalization is multiplying a surd by another similar surd to obtain a rational number. In mathematics, a surd is an expression involving a square, cube, or another kind of root symbol. The surd used for multiplication is called the rationalization factor (RF). Rationalize the denominator to make it easier to perform calculations with rational numbers. Rationalizing a denominator with a fraction removes all root terms, such as square roots and cube roots, from the denominator.

[tex]\frac{4}{\sqrt{\frac{4}{25}}}[/tex]

[tex]\begin{aligned}&\frac{4}{\frac{\sqrt{4}}{\sqrt{25}}}\\&\frac{\frac{4}{\sqrt{2^2}}}{\sqrt{5^2}}\end{aligned}[/tex]

[tex]\frac{4}{\frac{\sqrt{2^2}}{\sqrt{5^2}}}[/tex]

[tex]\frac{4}{\frac{2}{5}}[/tex]

[tex]\begin{aligned}&4 \div \frac{2}{5} \\&4\left(\frac{5}{2}\right) \\&\frac{4 \cdot 5}{2} \\&2 \cdot 5\end{aligned}[/tex]

[tex]10[/tex]

And if the question is like this,

[tex]$\frac{4 \cdot \sqrt{4}}{25}$$\frac{4 \cdot \sqrt{2^2}}{25}$$\frac{8}{25}$[/tex]

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Using the mathematical operation such as division, the swim team, which has 100 people on it, needs 7 minivans to take them on the other side of town.

If there are 100 people on the swim team that will be divided into minivans that can only occupied by 15 people, divide 100 by 15 to know how many vans they will need.

100 people ÷ 15 people/minivan

100 ÷ 15 = 6 r 10

This means that the swim team will need 6 minivans and still, 10 people don't belong to any minivan yet. So, 1 additional minivan will be needed for the remainder of 10 people.

Hence, the swim team will be needing 7 minivans to cater 100 people on their team.

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Answer:85.7 miles per hour

Step-by-step explanation:

The composite functions of the model taking the 20 % discount and then the 15 % discount is (D ◦ E)(x) = 0.68x.

In mathematics, function composition is an operation in which two functions, f and g, generate a new function, h, in such a way that h(x) = g(f(x)). This means that function g is being applied to the function x. So, in essence, a function is applied to the output of another function.

Define fog, the composition of f and g, as (fog)(x) = f(g(x)) for functions f and g. g should be applied to x. If fog(x) = x and gof (x) = x for all x values in the domain of f and g, then they are inverse functions.

In math, the domain (the x-values) of one function becomes the range (the y-value answers) of the next function. Composition notation is as follows: (f o g)(x) = f(g(x)) and exists read “f composed with g of x” or “f of g of x”.

Let D(x) = cost after applying the 15% discount,

E(x) = cost after applying the 20% employee discount, and x = cost of item(s).

Then D(x) = 0.80x and E(x) = 0.85x.

(D ◦ E)(x) = 0.68x.

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Answer:

Heya genial Gracia dispute

Part A:  Expression for the distance in meters between given two birds using subtraction = 2.5 - (-2.5)

Part B: The distance between two birds using additive inverse 2.5- (-2.5) =5 meters

An expression is an combination of numbers and mathematical operations such as addition, subtraction, division and multiplication with equating any two terms.

Additive inverse : Additive inverse of an number a is the number that  when adds to a gives zero .

Let b be additive inverse of a, then a + b =0

Then, b = -a

Given two birds A and B are at  points x= -2.5 and  y = 2.5 respectively

Therefore,  the expression for the distance in between given two birds

           = y - x  = 2.5- (-2.5)

We an clearly see that  -2.5 is additive inverse of 2.5

Distance between the two birds = 2.5 -(-2.5) =2.5 +2.5 = 5 meters

Therefore, the expression for distance between the two birds A and B is 2.5-(-2.5) and the distance is 5 meters.

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After factorization of the expression 9x²-25, the answer comes to:

So,

The given expression is: 9x²-25

Then,

Therefore, after factorization of the expression 9x²-25, the answer comes to:

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the answer is correct because you gave text evidence

The expansion of the expression log₈8 √3a⁵ is

1+ log 3/2log 8 +5 log a/ log 8.

Given that the expression is log₈8 √3a⁵.

We are required to expand the expression.

The change of base formula is used to write a logarithm operation again as a fraction of logarithms with a new base.

The expression is log₈8 √3a⁵.

log₈8 √3a⁵= (log 8 +log [tex]\sqrt{3}[/tex] +log [tex]a^{5}[/tex])/log 8

=1+ log 3/2log 8 +5 log a/ log 8      (We know that log [tex]m^{n}[/tex]=n log m)

Hence the expansion of the expression log₈8 √3a⁵ is

1+ log 3/2log 8 +5 log a/ log 8.

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The equation of the line in point-slope form is y-1 = 3 ( x + 1)

Equation of a line:

The equation of a line, in point-slope form, is designated  using:

y-y0= m( x - x0)

In which the point is given by(x0,y0)  and m is the slope.

Slope of the line below is 3 (given in the question).

This means that m = 3

(-1,1)

This means x= -1 and y =1

equation of the line

y - y0 = m( x- x0)

y-1 =m(x-(-1))

y-1=m(x + 1)

substituting the value of m is 3

y-1= 3 ( x + 1)

Therefore, The equation of the line in point-slope form is y-1= 3 (x + 1)

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Answer:

Mean - 67 inches

Median - 67 inches

Mode - 68 inches

Step-by-step explanation:

Definitions of the words:

Mean - The average number of the data set.

Median - The middle number in the data set when ordered from least to greatest.

Mode - The value that appears most frequently.

Mean:

We can add them up and divide by the number of values in the set, 7.

469 / 7 = 67

Median:

We can order them from least to greatest and see which one is the 4th one.

60, 62, 66, 67, 68, 68, 78.

67 is in the middle, so that is our median.

Mode:

Only 68 is repeated twice in the set, so 68 is the mode.

Hope this helped! Have a great day!

Step-by-step explanation:

to cross the y-axis x must be 0.

so,

y - 4×0 = 1

y = 1.

so, the point is

(0, 1)

Actual miles is [tex]\frac{2492}{13}[/tex]

According to the question,

Given that,

Map is 5.6 ft

scale of Map is 2.6 ft which is equal to 89 miles

Actual miles = [tex]\frac{5.6 * 89}{2.6}[/tex]

                    = [tex]\frac{498.4}{2.6}[/tex]

multiply both the numerator and denominator with the same integer

                    =  [tex]\frac{4984}{26}[/tex]

                    =  [tex]\frac{2492}{13}[/tex]

Actual miles is [tex]191\frac{9}{13}[/tex]  ≈ 1.916923 ×[tex]10^{2}[/tex]

Definition of miles per hour unit: ≡ 1 mi / 3600 s = 1609.344 m / 3600 s. In American public life, this is the most commonly used speed unit. Cars speeds are measured in mpg. Interpretation: The speed at which the body moves 1 mile (or 1609.344 metres) in 1 hour.

Definition of feet per second unit: ≡ 1 ft / 1 s = 30.48 cm / 1 s. Abbreviation is fps. In America, perhaps this is the second most commonly used speed unit in public life (after miles per hour). Definition: The speed at which the body moves 1 foot (or 30.48 centimetres) in 1 second.

Convert Miles to Feet

Multiply your speed in miles per hour by 5,280. This is the number of feet in a mile. The result is your speed in feet per hour. For example, 60 miles per hour times 5,280 feet per mile is 316,800 feet per hour.

Convert to Feet per Minute

Divide your speed in feet per hour by 60. This is the number of minutes in an hour. Therefore, the result is your speed in feet per minute. For example, 316,800 feet per hour divided by 60 minutes per hour is 5,280 feet per minute.

Convert to Feet per Second

Divide your speed in feet per minute by 60. This is the number of seconds in a minute. Therefore, the result is your speed in feet per second. For example, 5,280 feet per minute divided by 60 seconds in a minute equals 88 feet per second.

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After direct variation y =10 when x = 5.

So,

The initial statement is y = kx

Then to find y when x = 5.

When x = 5:

Therefore, after direct variation y =10 when x = 5.

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If Lindley requests an extension to file her individual tax return, the latest she could pay her tax due without penalty is April 15th.

A person or married couple must submit an official form known as an individual tax return to a federal, state, or local taxing authority in order to record any taxable income they received within a certain time period, typically the previous year.

This document is used to determine how much tax was paid in excess of what was required during that time period.

In this case, if Lindley requests an extension to file her individual tax return, the latest she could pay her tax due without penalty is April 15th.

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If Lindley requests an extension to file her individual tax return, the latest she could pay her tax due without penalty is:

April 15th.

October 15th.

August 15th.

November 15th.

None of the choices are correct.

If I were George Washington, I would have put two very different people to advise me because I would have a broader vision of government affairs.

George Washington (1732-1799) was an American politician and military man who stands out for being one of the most influential people in history and for having served as the first president of the United States between 1789 and 1797. He is considered the most important father of the Nation of the United States.

In 1789 he was unanimously elected by the other founding fathers as the first president of the United States. During his rule he tried to create a nation capable of maintaining peace with its neighboring countries, so he proclaimed neutrality to avoid any involvement in foreign conflicts.

For George Washington it was a challenge to occupy the position of the first president of the United States because he was going to lead a country that was just being formed. Due to the above, it was of vital importance to include all forms of thought and all visions in its government plan and way of governing.

Therefore, when assuming office as president of the United States, it would be of great importance to have advisers who would help him see from the point of view of other people so that his decisions would take into account the interests of all citizens to avoid uprisings and divisions.

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Answer:

the area is 935 square inches, and the perimeter is 39 inches

Step-by-step explanation:

Hey there!

In order to find the perimeter and area of the board, we must first list out the information we already know

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

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

There is a tiny pattern in here:

The original board has a length of 44 while the new one has the length of 11

This means that, the original board had dimensions 4 times the length of the new board

In order to find the area or perimeter, we need to know the width of the new board

To do this, we divide 1496 by 44

That gets us 34

This means that the width of the old board is 34

Now we divide 34 by 4 which gets us 8.5

This means, 8.5 is the width of the new board

Now that we know this, we can easily find the area and the perimeter of the new board

8.5 + 8.5 + 11 + 11 = 39

This means, the perimeter is 39

8.5 x 11 = 935

This means, the area is 935

This brings us to the conclusion that the area is 935 square inches, and the perimeter is 39 inches!

Answer:

$46

Step-by-step explanation:

So, the principal amount, P = $460

Yearly simple interest, R = 2.5% which equals 0.025

Time(T) which is 4 years.

The interest(I) for the amount, P at the rate of R yearly, after T years,

Elena's account will earn $46.

Answer:

you are very very very correct

Addition 3+ 12, an incomplete mathematical sentence. 1.3+ 12=13.3

Addition is a mathematical procedure that is used to add numbers. The sum of the given numbers is the result of adding the given numbers. For instance, if we add 2 and 3, (2 + 3), the result is 5. We used the addition function on two numbers, 2 and 3, to produce the sum, 5

Symbol for Addition

Different symbols are used in mathematics. One of the most used arithmetic symbols is the addition symbol. We read about adding two numbers, 2 and 3, in the definition of addition above. If we look at the addition pattern (2 + 3 = 5), the symbol (+) joins and completes the two integers.

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The equation of a line perpendicular to y = 4x - 3 that passes through the point (2,-2) is y = -1/3x - 3/2

The equation of the line is given as

y = 4x - 3

Rewrite the equation as

y = 4x - 3

A linear equation is represented as

y = mx + c

Where

Slope = m

So, we have

m = 4

The slopes of perpendicular lines are opposite reciprocals

This means that

m2 = -1/m1

So, we have

m = -1/4

Evaluate

m = -1/4

The equation of the perpendicular line is then calculated as

y = m(x - x1) + y1

Where

(x1, y1) = (2, -2)

This gives

y = -1/4(x - 2) - 2

Evaluate

y = -1/3x + 1/2 - 2

Evaluate the sum and the difference

y = -1/3x - 3/2

So, the equation of a line perpendicular to y = 4x - 3 that passes through the point (2,-2) is y = -1/3x - 3/2

Hence, the required equation of a line perpendicular to y = 4x - 3 that passes through the point (2,-2) is y = -1/3x - 3/2

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Step-by-step explanation:

1. -9x

2. 2(5x -3)

3.. -4x + 4y -9

4. 6x+18

5.-5x +42

6. (2x+5)

Answer:

Step-by-step explanation:

Answer:

This diagram is a straight edge and compass construction . A is the centerof one circle , and B is the centre of the other . A rhombus is a quadrilateral with 4 congruent sides

Step-by-step explanation:

Answer: 3

Step-by-step explanation:

First substitute values in :

8(3)(1/2)/ 2(1/2)(4)

Then simplify :

12/ 4

3

When the value of x will increase then decay factor will decrease the value of y.

Given that the decay factor describes how an advertisement loses its effectiveness over time.

Exponential decay will tell us the process of reducing an amount by a consistent percentage of rate over a particular period of time. Exponential decay is the reciprocal of exponential growth when a quantity decreases by the same factor in equal intervals of time, the constant coefficient of the exponential decay function is less than 1. This can be expressed as (1 - r) and is called the decay factor.

According to the definition of the decay factor, its say that when the value of x increases then the decay factor of the value of y will decrease.

Hence, the value of x will increase then decay factor will decrease the value of y.

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