A triangle has a base of 7.2 centimeters and height of 10.24 centimeters. A large triangle has a base of question mark centimeters and a height of 25.6 centimeters.
The diagram represents the process of creating a scale drawing from an original using a scale factor of 0.4. The base of the original drawing must be:
17.6 cm
18 cm
33.5 cm
45 cm

The net change between the given values of the variable is;  - 3x² - 6xh - 3h² + 23

We are given the function;

f(x) = 5 - 3x²

x = 3

x = 3 + h

The net change is just looking for the difference between f(3) and f(3 + h). Thus, we will evaluate the function at x = 3 and x = 3 + h and then calculate f(3 + h) - f(3).

f(3 + h) = 5 - 3(x + h)²

= 5 - 3x² - 6xh - 3h²

f(3) = 5 - 3(3)²

f(3) = 5 - 27

f(3) = -18

Net Change = f(3 + h) - f(3)

=  5 - 3x² - 6xh - 3h² + 18

= - 3x² - 6xh - 3h² + 23

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Answer:The answer is 10/6 or 1 4/6 or 1 2/3.

Step-by-step explanation: you can do either one and it will be equal the same.

Answer:

1

Step-by-step explanation:

Summary. Currency value is determined by aggregate supply and demand. Supply and demand are influenced by a number of factors, including interest rates, inflation, capital flow, and money supply. The most common method to value currency is through exchange rates.

Based on the calculations, the features which are features of the circle include the following:

A circle can be defined as a closed, two-dimensional curved geometric shape with no edges or corners. Also, a circle refers to the set of all points in a plane that are located at a fixed distance (radius) from a fixed point (central axis).

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

(x - h)² + (y - k)² = r²

Where:

Given the following equation:

x² + 4x + y² - 2y - 4 = 0

x² + 4x + y² - 2y = 4

Next, we would evaluate the equation by using completing the square method:

x² + 4x + 4 + y² - 2y + 1 = 4 + 5

(x² + 2x + 2x + 4) + (y² - y - y + 1) = 9

(x + 2)² + (y - 1)² = 3²

By comparing the above equation with the standard form of the equation of a circle, we have:

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The Cost value of the car after 9 months is $55797.

According to the statement

We have to find that the value of the car after 9 months.

So, For this purpose, we know that the

The cost function can be used to find the average cost, which is the average amount of money it costs to produce a unit.

From the given information:

If you buy a car for $65,076 and it depreciates linearly at a rate of 19% per year, what will be its value after 9 months

Then

The depreciates linearly at a rate of 19% per year

It means the 19% of the value of the car is a :

Value of the rate of the depreciates = 19/100*65,076

Value of the rate of the depreciates = 0.19*65,076

Value of the rate of the depreciates = 12364.44

Value of the rate of the depreciates = 12365

It is he value decreased in a 12 months

Then

The value decreased in one month = 12365 /12

The value decreased in one month = 1030.41

The value decreased in one month = 1031.

Then

The value decreased in 9 months = 1031*9

The value decreased in 9 months = 9279

Then

The remaining value of the car = 65,076 - 9279

The remaining value of the car = 55797

So, The Cost value of the car after 9 months is $55797.

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Answer:

2.5

Step-by-step explanation:

The difference between the Y axis is 2, and the difference between the X axis is 5 so you divide 5 by 2 to get 2.5

Answer: 84 mph   60 mph

Step-by-step explanation:

Let her average speed to home was x mph

Hence, the average speed to her parents was (x+24) mph

Thus:

Jessie spent for the trip to her parents' house: 385/x hours

Jessie spent for the trip to home: 385/(x+24) hours

[tex]\displaystyle\\\frac{385}{x} +\frac{385}{x+24} =11\\\\385(x+24)+385(x)=11(x)(x+24)\\\\385x+9240+385x=11x^2+264x\\\\770x+9240=11x^2+264x\\\\770x+9240-770x=11x^2+264x-770x\\\\9240=11x^2-506x\\\\9240-9240=11x^2-506x-9240\\\\0=11x^2-506x-9240\\\\Divide\ both\ parts\ of\ the \ equation\ by\ 11:\\\\0=x^2-46x-840[/tex]

[tex]\displaystyle.\\Thus,\\\\x^2-46x-840=0\\\\D=(-46)^2-4*1*(-840)\\\\D=2116+3360\\\\D=5476\\\\\sqrt{D} =\sqrt{5476} \\\\\sqrt{D}=74 \\\\x=\frac{466б74}{2*1} \\\\x=\frac{46-74}{2} \\\\=\frac{-28}{2} \\\\x=-14\notin(x > 0)\\\\x=\frac{46+74}{2}\\\\x=\frac{120}{2} \\\\x=60\ miles\ per\ hour[/tex]

[tex]60+24=84\ miles\ her\ hour[/tex]

Answer: (2x+5)(2x-5)

Step-by-step explanation:

4x² - 25=

2²x² - 5²=

(2x)² - 5²=

(2x)(2x) - 5(5)=

(2x)(2x) - 5(2x) + 5(2x) - 5(5)=

2x(2x-5) + 5(2x-5)=(2x+5)(2x-5)

Answer:

        1

 - 1 -------

        5

Step-by-step explanation:

   3           3

1 ------ × - -------

   5           4

   8           3

 ------ × - -------

   5           4

   8(4)     3(5)

 ------ × - -------

   5(4)     4(5)

   32       15

 ------ × - -------

   20        20

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

32 × (-15) = -480

20 × 20 = 400

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

   480 ÷ 80

- -------

  400 ÷ 80

   6                  1

- ------- or  - 1 -------

   5                  5

I hope this helps!

we get that 6.255 × 10¹⁰  larger than 1.5 × 10⁸ by 417 times.

We are given two expressions:

6.255 × 10¹⁰ and 1.5 × 10⁸

We need to tell that how much times is 6.255 × 10¹⁰  larger than 1.5 × 10⁸.

We will do this with the help of division.

So, we get that:

= 6.255 × 10¹⁰  ÷ 1.5 × 10⁸

= 6.255 × 10¹⁰⁻⁸  ÷ 1.5

= 6.255 × 10²  ÷ 1.5

= 625.5 ÷ 1.5

= 417

Therefore, we get that 6.255 × 10¹⁰  larger than 1.5 × 10⁸ by 417 times.

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Answer:

d = 6

Step-by-step explanation:

-2 +3i+ 12i = 9i-(2-di)

-2 + 15i = 9i - 2 + di

-2 + 15i = -2 + 9i + di

6i = di

6 = d

Check the picture below.

notice, sides are equal, opposite sides are perpendicular to their counterparts.

The cost for a day at the amusement park as a function of the number of ride tickets purchased is y = 12 + 2.75x

Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient

The given parameters are:

Admission rate to the amusement park = $12

Cost of each ticket = $2.75

Let the number of tickets be x, and the total cost be y

So, the function can be represented as

y = Admission rate to the amusement park + Cost of each ticket * x

This gives

y = 12 + 2.75 * x

Evaluate the product

y = 12 + 2.75x

Hence, the cost for a day at the amusement park as a function of the number of ride tickets purchased is y = 12 + 2.75x

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According to the given data, It is Transformation of rotation by 180°.

Transformations are changes that appear in the shapes present on a coordinate plane by rotation, reflection or translation. A function, f, that maps to itself is called the transformation, that is if f = X → X'. This transformation can be any one of the translation, rotation, reflection, and dilation or the combination of operations like translation, rotation, reflection, and dilation. The translation is moving a function in a specific direction, rotation is spinning the function about a point, reflection is the mirror image of the function, and dilation is the scaling of a function.

The transformation that rotates each point in the shape at a certain number of degrees around that point is called transformation of rotation. The shape rotates counter-clockwise when the degrees value is positive and it rotates clockwise when the degrees value is negative. The general rules for transformation of rotation about the origin are given below,

To rotate 90º: (x,y) → (-y, x)

To rotate 180º (x,y) → (-x,-y)

To rotate 270º (x,y) → (y, -x)

given data: preimage → image

                   R( -4, 3 ) changes to R'( 4,-3 )

                   S( -1, 3 ) changes to S'( 1, -3 )

                   T( -4, 1 ) changes to T'( 4,-1 )

As we can notice similar trend in the data given in the question like 180° rotation, Thus we can conclude that the coordinate rule and transformation is Transformation of rotation.

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

Heyo! Your explanation is below, if necessary.

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

If it's 51 miles per hour, simply multiply the distance by the number of hours.

51 x 6 = 306

51 x 55/60 = 46.75

Now, add the products.

306 + 46.75 = 352.75

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

Have a great day/night!

~pinetreee :)

Answer:

Areas under the curve

Step-by-step explanation:

The area under a curve on an interval [a, b] is the integral of the function computed in this interval :  [tex]A=\int _a^b|f\left(x\right)|dx[/tex]

(1) For [tex]f\left(x\right)=3\sqrt{x}[/tex] with [tex]a=1,\:b=4[/tex]

area [tex]=\int _1^4\left3\sqrt{x}\;dx[/tex] = [tex]3\cdot \int _1^4\sqrt{x}dx[/tex] =

[tex]\int \sqrt{x}[/tex] = [tex]\frac{2}{3}x^{\frac{3}{2}}[/tex]

[tex]3\cdot\frac{2}{3}x^{\frac{3}{2}}[/tex] = [tex]2x^{\frac{3}{2}}[/tex]

At [tex]x = 4,[/tex] we get [tex]2\cdot4^{\frac{3}{2}}[/tex] = [tex]2\cdot8 = 16[/tex]

At [tex]x = 1,[/tex] we get [tex]2\cdot1^{\frac{3}{2}}[/tex] = [tex]2.1 = 2[/tex]

So area under the curve for [tex]f(x) = \:3\sqrt{x}[/tex] in the interval [tex][1, 4] = 14[/tex]

(2) [tex]f\left(x\right)=x-\frac{2}{3}\\[/tex]

[tex]\int \:x-\frac{2}{3}dx[/tex] = [tex]\int \:xdx-\int \frac{2}{3}dx[/tex]  [tex]=\frac{x^2}{2}-\frac{2}{3}x[/tex]

[tex]\left[\frac{x^2}{2}\right]^{27}_1 = \frac{27^2}{2} - \frac{1}{2} = \frac{729}{2}-\frac{1}{2} = \frac{728}{2} = 364[/tex]

[tex]\left[\frac{2}{3}x\right]^{27}_1 = \frac{2}{3}\cdot \:27 - \frac{2}{3}\cdot \:1 = 18-\frac{2}{3} = \frac{52}{3}[/tex]

[tex]\int _1^{27}\left|x-\frac{2}{3}\right|dx = 364-\frac{52}{3} = \frac{1040}{3}[/tex]  (Answer)

Considering the variance of Z and the relation between Y and Z, the variance of Y is given by:

Var(Y) = 36.

The variance of a variable, or a data-set, is given by the sum of the differences squared between each observation and the mean, divided by the cardinality of the data-set, which is the number of values in the data-set.

Hence:

These two bullet points above can be resumed by the equation given as follows:

Var(aX + B) = a²Var(X).

Hence:

Var(3Z + 2) = 9Var(Z).

Hence the variance of Y is given as follows:

Var(Y) = Var(3Z + 2) = 9Var(Z) = 9 x 4 = 36.

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The missing number is 36 so that the equivalent ratios become 3:1, so that the option D is correct.

_______________________________

It is given that Elsa used the multiplication table below to write ratios that are equivalent to 12-4 and one number is missing from the given ratios, we need to find that missing number.

Now, first of all let us understand what are equivalent ratios;

When we compare two ratios, they are said to be equivalent. To determine whether two or more ratios are equivalent, they can be compared to one another. For instance, the ratios 1:2 and 2:4 are equivalent.

Furthermore, in the given question we are given one ratio that is;

=> 12:4 which can also be written as,

=> 3:1

Now, let us assume that the other ratio is x:y than;

=> x:y

So, let us compare both the ratios as they are equivalent ratios;

=> x:y = 3:1

To calculate the other ratio, we need to divide it by 12 so that we get the equivalent ratio;

=> x/12 = 12/4

=> x/12 = 3

=> x = 12 × 3

=> x = 36

So,

=> 36/12 = 12/4

=> 3/1 = 3/1

Therefore, the missing number is 36 so that the equivalent ratios become 3:1, so that the option D is correct.

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The number of white tiles is 20 and the number of shaded tiles is 24

The ratio of white tiles to shaded tiles is given as 5:6

Total number of tiles = 44 tiles

Let x be the number of shaded tiles then the number of white tiles will be 44-x

Formualting the equation using the above variables we get:

Number of white tiles/Number of shaded tiles = Ratio of white tile/Ratio of shaded tile

= 44-x/x = 5/6

= 264-6x = 5x

= 264 = 11x

x = 24

Hence, the number of white tiles is 20 and the number of shaded tiles is 24

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The standard form of the given linear equation y = (-2/3)x + 5 is 2x + 3y = 15.

The standard form of a linear expression is expressed as;

Ax + By = C

Where A and B are the coefficient of x and y respectively and C is the constant term.

Given the equation in the question;

y = (-2/3)x + 5

Multiply both sides by 3

y = (-2/3)x + 5

3(y) = 3((-2/3)x + 5 )

Apply distributive property

3(y) = 3((-2/3)x + 5 )

3y = 3(-2/3)x + 3( 5 )

3y = -6/3x + 15

3y = -2x + 15

Now, move all terms containing variables to the left side of the equation

3y = -2x + 15
Add 2x to both sides

3y + 2x = -2x + 2x + 15

3y + 2x = 15

Reorder 3y and x

2x + 3y = 15

Therefore, the standard form of the given linear equation y = (-2/3)x + 5 is 2x + 3y = 15.

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According to the given statement the  fraction of pizza did Billy eat for a snack = 1/12

A fraction is a subset of a bigger whole. In arithmetic, the number is expressed as a quotient, which represents the numerator divided by that of the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in both the numerator and the denominator.

A fraction, often known as a fractional number, is used to represent a portion of a whole. Fractions are made up of two numbers: a numerator (the number above the line) as well as a denominator (which is below the line). The denominator is the number of equal pieces that anything is divided into.

Billy had = 2/3 of pizza

later he ate = 1/4

the pizza did Billy eat for a snack =

Now ,

total size of pizza be  = 1

Billy had = 2/3 of pizza

later he ate = 1/4

the pizza did Billy eat for a snack = total size of pizza -(2/3 of pizza + later he ate)

                                                        = 1 - (2/3 + 1/4)

                                                        = 1 - (11/12)

                                                        = 1/12

the pizza did Billy eat for a snack = 1/12

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Step-by-step explanation:

The answer to the problem is as follows:

For a box with x chocolates, the cost of packaging is C(x) = x^2 and the

weight is W(x) = x + 2.

Thus the cost per unit weight is C(x) / W(x) = x^2 / (x + 2).

I hope my answer has come to your help. God bless and have a nice day ahead!

The standard deviation of the sample number is 1.67.

According to the question we have been given a sample of 5 United states tourist.

We need to find the standard deviation of the sample. The formula for the standard deviation is given as :

                      [tex]\sigma[/tex] = √∑( xₙ - u)²/N

   where    σ = standard deviation

                 xₙ = each value of the sample

                 N = number of sample

                  u = mean

First the mean = (7+8+4+9+7)/5

                       =   7

∑( xₙ - u)² = (7 - 7)² + (8-7)² + (4-7)² + (9-7)²+ (7-7)²

                =  0² + 1² + (-3)² + 2² + 0²

                 = 1 + 9 + 4

                 = 14

Substituting the value sin the given formula we get

                σ = √(14/5)

                    = √2.8

                   = 1.67

Hence the standard deviation of the sample number is 1.67

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Step-by-step explanation:

log64 + log32 - log128

= log 2⁶ + log 2⁵ - log 2⁷

= 6log2 + 5log2 - 7log2

(sorry I can't continue from here... someone else can help...maybe?...sorrrrryyy)

The required rate of return for Mercury Inc., assuming that investors expect a 5% rate of inflation in the future is 18%.

Real risk free rate = 3%

Inflation Premium = 5%

Nominal risk free rate Rf = Real risk free rate + Inflation Premium = 3% + 5% = 8%

Market risk premium (Rm –Rf) = 5%

Beta = 2

As per CAPM, required rate of return:

= Rf + beta * (Rm – Rf)

= 8% + 2 * 5%

= 8% + 10%

= 18%

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Answer:

1. 12.54

2. 6.016

3. 0.162

4. 20.05

Step-by-step explanation:

Answer:

1. 12.54

2. 6.016

3. 0.162

4. 20.05

Explanation:

(I'm sorry if this sounds bad. I wrote it at two in the morning. you can go ahead and skip this if you want.)

It is common to discuss numbers when writing academic or professional documents.

It may be appropriate to spell out a number with a decimal if you're sharing statistics or explaining a mathematical concept.

Learning how to properly write decimals can help you create documents that meet expectations.

The proper way to convert worded forms into decimals:

Let's do an example.

Twenty-three and six-tenths,

We are given four numbers.

It is easy to see that Twenty-three equals 23.

But what about the decimal?

Decimals in worded form are always after "and," and they always have "th(s)" at the end, rather than what would appear there in regular numbered word form.

So, given "six-tenths," it is pretty simple.

Six-tenths=0.6

The reason for this is that the word "tenths," won't make it 0.16, because, in decimals, we always skip what would be oneths. The reason for this is; is that this only makes sense if there were "oneths," and dividing a "whole" into "oneths" resulted in the "whole"... So that spot was already taken.

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