Given the piecewise function below, evaluate the function as indicated

The length of the rectangle is 15.9 inches. The solution has been obtained by using the arithmetic operations.

What are arithmetic operations?

The four fundamental operations, often known as "arithmetic operations," can be used to explain any real number. Operations like quotient, product, sum, and difference come after operations like division, multiplication, addition, and subtraction in mathematics.

We are given that the perimeter of a rectangle is 42.4 inches and the length is three times its width.

Let the width be 'x'.

So, length will be 3x.

From this, we get

⇒ Perimeter = 2 (length + width)

⇒ 42.4 = 2 (3x + x)

⇒ 42.4 = 2 (4x)                             (Using addition operation)

⇒ 42.4 = 8x                                  (Using multiplication operation)                

⇒ x = 5.3                                      (Using division operation)

So,

⇒ Length = 3 * 5.3

⇒ Length = 15.9 inches

Hence, the length of the rectangle is 15.9 inches.

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The selling prices of the sculpture, painting, and photograph were 166.5 million, 107.0 million, and 57.6 million respectively.

Let's call the selling prices of the sculpture, painting, and photograph as S, P, and Ph respectively.

From the first sentence, we know that:

S + P + Ph = 308.0 million

From the second sentence, we know that:

P = Ph + 49.4 million

And from the third sentence, we know that:

P + Ph = S + 24.4 million

Now we can substitute the second equation into the third equation:

(Ph + 49.4 million) + Ph = S + 24.4 million

Simplifying:

2Ph + 49.4 million = S + 24.4 million

2Ph = S - 25 million

Substituting this into the first equation:

S + P + Ph = 308.0 million

S + (Ph + 49.4 million) + Ph = 308.0 million

2Ph + S = 258.6 million

Now we can substitute the equation we derived earlier:

S + 2Ph - 49.4 million = 258.6 million

S + 2Ph = 308.0 million

Substituting 2Ph = S - 25 million:

S + S - 25 million = 308.0 million

2S = 333.0 million

S = 166.5 million

Now we can use this value to find P and Ph:

P = Ph + 49.4 million

P + Ph = S + 24.4 million

Substituting S = 166.5 million in both equations:

P + Ph = 190.9 million

P = Ph + 49.4 million

Solving these two equations simultaneously:

Ph = 57.6 million

P = 107.0 million

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Using the conversion factor we know that we will spend 180.69€ on memorabilia items.

A conversion factor is a number that is used to multiply or divide one set of units into another.

If a conversion is required, it must be done using the correct conversion factor to get an identical value.

A fraction that is equal to "1" is a conversion factor.  

The numerator and denominator are the same amounts, but they are expressed in different units.  It is used to change a number's unit of measurement.  

By multiplying the initial number by the fraction that is equal to "1," you can change the units without changing the original number's value.

So, in the given situation:

$200 = euros?

We know that:
$1 = 0.90€

Then,

$200 = 180.69€

Therefore, using the conversion factor we know that we will spend 180.69€ on memorabilia items.

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Answer: $702.39

Step-by-step explanation: To find the total cost of the laptop with sales tax included, we need to add the sales tax to the listed price.

First, we need to calculate the amount of sales tax.

Sales tax = 9.75% of 639.99

Sales tax = 0.0975 x 639.99

Sales tax = 62.40

Now we can find the total cost of the laptop with sales tax included:

Total cost = listed price + sales tax

Total cost = 639.99 + 62.40

Total cost = 702.39

Therefore, the total cost of the laptop with sales tax included is $702.39.

The calculated area of each piece is 1/12 acre

If Barry buys a plot of land that measures 1/4 acre, then the total area of the land is 1/4 acre.

If he divides the land into 3 equal pieces, then each piece will have 1/3 of the total area.

So the area of each piece will be:

Area of each piece = (1/3) x (1/4) acre

Multiplying the fractions, we get:

Area of each piece = 1/12 acre

Therefore, each piece of land will have an area of 1/12 acre.

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Answer:

2

Step-by-step explanation:

The numerical coefficient is the number that is multiplied to a variable.

Example.

2x^2 + 7y^3

The numerical coefficients would be 2 and 7.

So for your problem it would be 2 since 2 is the number being multiplied to x and y.

If the room is 12'x20' with 8' ceilings and the tile costs $4.75 per square foot,  the total cost is $1140.

To calculate the cost of replacing the tile in the kitchen, we need to first calculate the total area of the floor.

Area of the floor = Length x Width = 12 ft x 20 ft = 240 sq ft

Since we know the cost per square foot of tile, we can now multiply the total area of the floor by the cost per square foot to find the total cost:

Total cost = Area of the floor x Cost per square foot

Total cost = 240 sq ft x $4.75/sq ft

Total cost = $1140

Therefore, it will cost $1140 to replace the tile in the kitchen, assuming there are no additional costs such as labor or materials for removing the old tile.

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The justification of the  angles with a combined degree measure of 90⁰ are complementary angles is proved by part 3. ∠1 is complementary to ∠2.

In the figure,

Measure of angle 1 = 40 degrees.

Measure of angle 2 = 50 degrees

Angle 2 is complementary to angle 3.

Proof of the result,

Measure of ∠1 = 40 degrees  ( given  )

Measure of ∠2 = 50 degrees ( given )

Measure of ∠1 + measure of ∠2 = 40° + 50°

⇒ Measure of ∠1 + measure of ∠2 = 90°

⇒ Angle 1 and angle 2 are complementary to each other.

Complementary angles are such pairs of angles whose sum is equal to 90°.

It is given that

Angle 2 is complementary to angle 3.

This implies ,

m ∠1 + m ∠2 = m ∠2 + m ∠3

⇒ m ∠1  = m ∠3

⇒ m ∠1  ≅ m ∠3

Therefore, the part 3 . ∠1 is complementary to ∠2 gives the justification for the proof of complementary angles.

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The value -5°C represents the temperature outside as measured by the digital thermometer in Olivia's car.

In this context, the value -5 represents the temperature outside in Celsius degrees.

The minus sign indicates that the temperature is below freezing point. The Celsius scale is a temperature scale that uses the freezing point of water (0°C) and the boiling point of water (100°C) at standard atmospheric pressure as its reference points.

Thus, a temperature of -5°C means that it is five degrees Celsius below the freezing point of water.

The negative sign indicates that the temperature is below zero degrees Celsius, which is the freezing point of water.

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Answer:

To find the surface area of a rectangular prism, we can use the formula:

Surface Area = 2lw + 2lh + 2wh

where l, w, and h are the length, width, and height of the rectangular prism, respectively.

Given that the rectangular prism is 12 units high, 5 units wide, and 10 units long, we can substitute these values into the formula:

Surface Area = 2(10)(5) + 2(10)(12) + 2(5)(12)

Surface Area = 100 + 240 + 120

Surface Area = 460 square units

Therefore, the surface area of the rectangular prism is 460 square units

The value of 'x' in the given figure is 14.73.

The given figure is a Right-angled triangle.

According to the Pythagorean Theorem, the square of the hypotenuse is equal to the sum of squares of the adjacent side and the opposite side.

In the given figure,

Hypotenuse is 19.

The adjacent side is 12.

The opposite side is x.

Now, we have to find the value of x.

According to the theorem,

19² = 12²+x²

361 = 144+x²

x² = 361 - 144

x² = 217

x = √217

x = 14.73

Therefore, the value of 'x' in the given figure is 14.73.

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There are four significant digits in the number 9.15 x 10⁴.

The digits that provide the number with useful information are known as the important digits.

As they add to the value of the number in this instance, the numbers 9, 1, and 5 are all important.

The exponent, 4, just instructs us on how many places to relocate the decimal point, therefore it has no bearing on the number of significant digits.

Therefore, the number 9.15 x 10⁴ has four significant digits.

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The missing values of h(x) to show it is a linear function are:

X=1, h(x)=3

X=3, h(x)=17

X=5, h(X)=31

So, the correct answer is (c)

A linear function is a mathematical relationship between two variables that produces a straight line when plotted on a graph, with a constant rate of change between them.

A function is a mathematical rule that assigns each input value to a unique output value. It can be represented graphically, algebraically, or with a table of values.

According to the given information:

To prove that h(x) is a linear function, we need to show that the difference in h(x) values between any two points is proportional to the difference in their corresponding x values.

Using the given values in the table, we can calculate the differences in h(x) values and x values:

Δh(x) = h(x) - h(x-1)

Δx = x - (x-1) = 1

Δh(x=1) = h(x=1) - h(x=0) = ? - (-4) = ?

Δh(x=3) = h(x=3) - h(x=2) = ? - 10 = ?

Δh(x=5) = h(x=5) - h(x=4) = ? - 24 = ?

If h(x) is a linear function, then the ratio of Δh(x) to Δx should be the same for all pairs of consecutive x values. We can use the given values of Δh(x=2) and Δx=1 to calculate this ratio:

Δh(x=2)/Δx = (10 - (-4))/2 = 7

We can now use this ratio to find the missing values of h(x):

Δh(x=1)/Δx = ?/1 = 7

Δh(x=3)/Δx = ?/1 = 7

Δh(x=5)/Δx = ?/1 = 7

?/1 = 7  =>  ? = 7

Therefore, the missing values of h(x) are:

X=1, h(x)=3

X=3, h(x)=17

X=5, h(X)=31

So, the correct answer is (c)

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Applewood Farmstand sold 102 pieces of apples over the weekend.

Graph is a data structure which consists of nodes (vertices) that are connected with each other. Graphs are used to represent relationships between different objects, such as networks, social connections, and pathways. Graphs are useful for representing data as they can provide a visual representation that is easy to interpret, and can be used to analyse patterns in the data. Graphs can also be used to represent problems such as shortest path problems, and can be used to solve problems such as finding the most efficient route between two points.

The graph shows that apples accounted for 32% of the total fruit sales. To find the exact number of apples sold, we can calculate the following:

Apples = (320 pieces of fruit) x (0.32)

Apples = 102 pieces

Therefore, Applewood Farmstand sold 102 pieces of apples over the weekend.

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Answer:

When we have a set of points, we can find the distance between them using the formula:

[tex]d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex], where d is the distance, x1 and x2 are one point and y1 and y2 are another point.

OB:

Thus, for OB, we can allow O(6, 6) to be our x1 and x2 point and we can allow B(9, 6) to be our y1 and y2 point:

[tex]d=\sqrt{(6-9)^2+(6-6)^2} \\d=\sqrt{(-3)^2+(0)^2} \\d=\sqrt{(-9)} \\d=3[/tex]

Thus, the first part/step in the equation is your subtraction expression to find the length of OB.

AB:

For AB, we can allow A(9, 10) to be our x1 and x2 point and we can allow B (9, 6) to be our y1 and y2 point:

[tex]d=\sqrt{(9-9)^2+(10-6)^2}\\ d=\sqrt{(0)^2+(4)^2}\\ d=\sqrt{16}\\ d=4[/tex]

The first part/step is your subtraction expression for the length of AB.

Answer:

We know that the x-coordinate of point A is -11, and that the distance between point A and point B is 15 units. Let's call the y-coordinate of point A "y". Then we can use the distance formula to find the two possible values of y:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

where (x1,y1) = (-11,y) is the coordinates of point A, and (x2,y2) = (1,2) is the coordinates of point B. Substituting the values, we get:

15 = sqrt((-11 - 1)^2 + (y - 2)^2)

15 = sqrt(144 + (y - 2)^2)

15^2 = 144 + (y - 2)^2

225 = 144 + (y - 2)^2

81 = (y - 2)^2

y - 2 = ±9

y = 2 ± 9

So the possible coordinates of point A are (-11,11) and (-11,-7).

The work done on an object if a force of 4 x − x^2 is applied from x = 0 to 3 is 9J

Work Done serves as the quantity of energy which is been moved by the  force  so that a particular energy can move  howver the relation between Work and Energy can be seen as a direct one.

Give that force= 4 x − x^2  from x = 0 to 3

Work done by force , F= ∫(4 x − x^2 )dx                  (0-3)

F= (4x^2/2 - x^3/3)

=[2x^2 -x^3/3]

= [2*3^2 -3^3/3 - 2*0^2 -0^3/3]

18 -9= 9

9J

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Answer:

Step-by-step explanation:

Hopefully this is right.

Area = r²

Which is pi times the the radius squared

The radius is 2, so 2² is 4, So we multiply 3.14, which is pi, by 4.

Multiply 3.14 by 4, and the answer is 12.56, the question says round to the nearest tenth, so the final answer will be 12.6

My math teacher back in 7th grade gave us this sentence to help us memorize the equations.

Cherry Pie Delicious (C=d), Apple Pie Are Too (A=r²)

Do the same with the other two questions, and the answer for question two will be 3.14, rounded to the nearest tenth will be 3.1

Hope this helps!

For a circle with a radius of 2, the area can be calculated using the formula:

Area = π x r^2

where π is approximately 3.14 and r is the radius.

Plugging in the values, we get:

Area = 3.14 x 2^2

Area = 3.14 x 4

Area = 12.56

Rounding to the nearest tenth, we get:

Area ≈ 12.6

Therefore, the area of the circle with radius 2 is approximately 12.6.

For a circle with a radius of 1, the area can be calculated using the same formula:

Area = π x r^2

Plugging in the values, we get:

Area = 3.14 x 1^2

Area = 3.14

Rounding to the nearest tenth, we get:

Area ≈ 3.1

Therefore, the area of the circle with radius 1 is approximately 3.1.

The linear inequalities in the given graph  is y ≥ x/2 -1 and  y< -1/2x -3.

Linear inequalities are the expressions where any two values are compared by the inequality symbols such as, ‘<’, ‘>’, ‘≤’ or ‘≥’. These quantities may be numerical, algebraic, or a combination of the two.

Here, we have,

The symbols "" and ">" signify tight inequalities, while "" and "" signify slack inequalities. A linear inequality has the same appearance as a linear equation, but uses a different symbol to link the two expressions.

we have,

In the given graph, the area above solid line,

points, (-2 , -2) , (0 , -1)

slope = 1/2

so,  y ≥ x/2 -1

The area below dashed line ,

points, (-2 ,-2) , (0 ,-3)

slope= -1/2

so, y< -1/2x -3.

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A 2-pound package of hamburger costs $7.00, and you pay $10.50 for a 3-pound package of hamburger.

To find the cost per pound of hamburger, we need to divide the total cost by the weight in pounds.

For the 2-pound package

Cost per pound = Total cost / Weight in pounds

Cost per pound = $7.00 / 2 lbs

Cost per pound = $3.50 per pound

For the 3-pound package

Cost per pound = Total cost / Weight in pounds

Cost per pound = $10.50 / 3 lbs

Cost per pound = $3.50 per pound

Therefore, the cost per pound of hamburger is the same for both packages, at $3.50 per pound.

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Answer:  formula 9x - 5y = -160 is not a direct variation.

Step-by-step explanation: The provided expression, 9x - 5y = -160, does not exemplify direct variation.

Direct variation is a correlation existing between two variables, wherein one is a constant scalar multiple of the other. Stated differently, should one variable increase by a defined magnitude, the corresponding variable will also experience a commensurate increase of identical magnitude.

The formula provided indicates the absence of a constant proportionality between the temperature in degrees Celsius (x) and the temperature in degrees Fahrenheit (y). It is noteworthy that the correlation amidst the variables x and y is non-linear in nature, thereby precluding its representation in the form of a direct proportionality.

Answer: It is not a direct variation.

Step-by-step explanation:

         While a linear equation is a direct variation, the y-intercept of a direct variation relationship must be 0. Here, that is not the case. Let us manipulate this equation into a slope-intercept equation.

Given:

   9x - 5y = -160

Add 5y and 160 to both sides of the equation:

   5y = 9x + 160

Divide both sides of the equation by 5:

   y = [tex]\frac{9}{5}[/tex]x + 32

32 ≠ 0

Answer:

11 dimes and nickels.

Step-by-step explanation:

22 total coins divided by 2 equals 11 for each.

the number 2 represents the dimes and nickels, 22 for the total amount of coins, and 11 for the answer.

Answer:15 nickels  and  7 dimes.

Step-by-step explanation:

Answer:

-2a⁴ b⁶ c³

Step-by-step explanation:

2a² b c³ (-a² b⁵)

determine the signs for multiplication or division

-2a²bc³a²b⁵

multiply the monomials

-2a⁴b⁶c³

(then done)

Answer:

F

Step-by-step explanation:

First, find the answer to (180 /5 + 4 x 12 - 10) which is 74.

Next, start with solving the possible answers.

Lastly, once you have solves determine which answer is the same, which is F.

Answer:

Yes, it is a polynomial identity (work below).

Step-by-step explanation:

Let's start by expanding the left side of the equation.

[tex](2x^2+y^2)^2=\\4x^4+y^4+4x^2y^2[/tex]

Now, let's expand the second side.

[tex](2x^2-y^2)^2+(2xy\sqrt{2} )^2=\\4x^4+y^4-4x^2y^2+4x^2y^2(2)=\\4x^4+y^4-4x^2y^2+8x^2y^2[/tex]

There are no like terms on the left side, so let's combine the like terms on the right side.

[tex]4x^4+y^4-4x^2y^2+8x^2y^2=\\4x^4+y^4+4x^2y^2[/tex]

Now, let's check if the left and right sides are equal:

[tex]4x^4+y^4+4x^2y^2= 4x^2+y^4+4x^2y^2[/tex]

Both sides are the same. Thus, the equation is a polynomial identity.

B) The domain for #1 and #2 is  ≥ -7 and the domain for #3 is -∞ ≤  ≤ ∞.

1. [tex](f + g)(x) = f(x) + g(x)[/tex]

The domain of [tex](f + g)(x)[/tex] is the intersection of the domains of [tex]f(x)[/tex] and [tex]g(x)[/tex]. Since [tex]f(x) = x^4[/tex] is defined for all real numbers [tex]\mathbb {R}[/tex], and [tex]g(x) = (x + 7)^(1/2)[/tex] is defined only for [tex]x > = -7[/tex] (since we can't take the square root of a negative number), the domain of [tex](f + g)(x)[/tex] is [tex]x > = -7[/tex].

2. [tex](f - g)(x) = f(x) - g(x)[/tex]

The domain of [tex](f - g)(x)[/tex] is also the intersection of the domains of [tex]f(x)[/tex] and [tex]g(x)[/tex]. Since [tex]f(x) = x^4[/tex] is defined for all real numbers [tex]\mathbb {R}[/tex], and [tex]g(x) = (x + 7)^(1/2)[/tex] is defined only for[tex]x > = -7[/tex], the domain of [tex](f - g)(x)[/tex] is also [tex]x > = -7[/tex].

3. [tex](fg)(x) - > (f(g(x))[/tex]

The domain of [tex]f(g(x))[/tex] is the set of all values of  [tex]x[/tex] such that [tex]g(x)[/tex] is in the domain of [tex]f[/tex]. Since the domain of [tex]f[/tex] is all real numbers [tex]\mathbb {R}[/tex], and [tex]g(x) = (x + 7)^(1/2)[/tex]  is defined only for [tex]x > = -7[/tex], the domain of [tex]f(g(x))[/tex] is [tex]x > = -7[/tex].

Therefore, the correct answer is option:

B) The domain for 1) and 2) is [tex]> = -7[/tex] and the domain for 3) is -∞ ≤ [tex]x[/tex] ≤ ∞.

Answer:

$98 a month

Step-by-step explanation:

1,176 divided by 12