A garden table and a bench cost $621 combined. The garden table costs $79 less than the bench. What is the cost of the bench?

The value of the expression as given in the task content is; 28.

It follows from the task content that the value of the expression is to be determined given the parameters for m and n.

Since the given expression is; | m² - 7 | + n²

Therefore, when m = -2 and n = 5, we have that;

| (-2)² - 7 | + 5²

= | 4 - 7 | + 25

= | -3 | + 25

= 3 + 25

= 28.

Ultimately, the value of the expression according to the given parameters is; 28.

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a. The integral to determine the area enclosed by the inner loop is:

A = ∫0^2π2+4sin(θ)dθ

This integral can be solved using the substitution u = 4sin(θ). This will give us the following integral:

A = ∫0^2π2 + udu

Next, we apply the power rule to the integral and solve for A.

A = 2θ + (u^2)/2 | 0^2π

A = 2θ + (4sin(θ)^2)/2 | 0^2π

A = 2π + 4[1 - cos(2θ)]/2 | 0^2π

A = 2π + 2 - cos(2π)

A = 4π - 1

b. To find the area between the loops, we can use the following integral:

A = ∫2^4π2+4sin(θ)dθ

Using the same substitution, we have:

A = ∫2^4π2 + udu

A = 2θ + (u^2)/2 | 2^4π

A = 2θ + (4sin(θ)^2)/2 | 2^4π

A = 2π + 4[1 - cos(2θ)]/2 | 2^4π

A = 2π + 2 - cos(4π)

A = 4π + 1

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The slope of points with same y coordinate but a different x coordinate is 0

this is because change in y is zero

The slope, m of the linear function is calculated using the formula

= change in y / change in x

This is represented mathematically as

m = (y₀ - y₁) / (x₀ - x₁)

In this case change in y is zero since it is same point

y₀ = y₁

And when a number in the numerator is zero the division will result to a quotient of zero and hence the line is a horizontal line

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The true statement is "No, you cannot prove that the two right triangles are congruent with the information given."

From the question, we have the following parameters that can be used in our computation:

As a general rule, congruent triangles would have same dimensions and angles

In the scenario, we understand that Sidewalk B and Sidewalk A form a right angle.

This and the other information does not provide information to determine the congruency because the lengths of the sides of either triangle or the angles are missing.

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Answer: 3 , 1 1/2

Step-by-step explanation:

Solve for

x

by simplifying both sides of the equation, then isolating the variable.

Exact Form:

x

=

3

,

3

2

Decimal Form:

x

=

3

,

1.5

Mixed Number Form:

x

=

3

,

1

1

2

The steps for dividing the 3 digit numbers by 3 digit numbers is solved with the help of multiplication and subtraction.

The process of division is defined as  the process of breaking a number up into equal parts, and finding out how many equal parts can be made.

Here we need to find the way to divide 3 digit numbers by 3 digit numbers.

The steps to solve the given division is written as,

The first steps is to take the first digit of the dividend from the left and then we have to  check if this digit is greater than or equal to the divisor.

Now then we have to divide it by the divisor and write the answer on top as the quotient.

Then we have to do the subtract operation the result from the digit and write the difference below.

Then the final steps is to bring down the next digit of the dividend and this process is repeated until we get the remainder as zero.

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150

The median is where the line inside the box sits.  That's the halfway point between all of the data.  (Halfway in terms of "if you line everything up and it's the data point in the middle.")

Since division by zero is not defined, 1/0 is not infinity, and 0/0 is not indeterminate.

We must keep in mind that, except in the case of limitations, the value of 1 divided by 0 is infinite. The phrase "infinity" denotes the size of the number. When it comes to limits, we merely presume that limit x's value tends toward something rather than being equal to anything. We thus treat it as infinite.

Since it is not a real number, infinity is only used to symbolise extraordinarily big real numbers. The result of 1 divided by infinity is 0. The quotient of nonzero real numbers that divide infinity is infinity, and the rule of thumb is that any real number divided by infinity is zero.

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Answer:

18.19

Step-by-step explanation:

15% of 20 = 3

20 - 3 = 17

7% of 17 = 1.19

17 + 1.19 = 18.19

Answer:

0.456 kg

Step-by-step explanation:

The process of inverse the function is  f⁻¹(x) = x/2.

In math the term function is known as a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.

Here we have to explain the process of solve inverse functions with examples.

While we take the function for examples as

f(x) = 2x.

Now, we have to do the following steps to identify the inverse of the function,

Here the first steps is to replace f(x) by y in the equation describing the function, then we get

=>  y = 2x

Now, we have to interchange x and y in a simple terms now we have to replace replace every x by a y and vice versa, then we get,

=> x = 2y

Then the next step is to Solve for y, here we get

=> y = x/2

Finally replace y by f⁻¹(x)

Therefore, the inverse of the function is

=> f⁻¹(x) = x/2.

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The two triangles in this problem are similar, and the reason for their similarity is given as follows: AA.

Similar triangles are triangle that share these following two features:

The two right triangles in this problem are similar, as they have two common angle measures, given as follows:

As the angles have two common angle measures, the reason is given as follows:

AA.

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The quotient of the expression -6x²y + 12x² + 15zy - 15 divided by -3 is 2x²y - 4x² - 5zy + 5

From the complete question, we have the following parameters that can be used in our computation:

quotient of  -62"y' + 12x2? 15zy - 15 divided by -3

Express properly

So, we have

-6x²y + 12x² + 15zy - 15 divided by -3

To solve this question, we simply divide each term of the expression by -3

So, we have the following representation

(-6x²y + 12x² + 15zy - 15)/-3

Evaluate the quotient

2x²y - 4x² - 5zy + 5

Hence, the solution is 2x²y - 4x² - 5zy + 5

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The jam recipe that has more strawberry flavor is Recipe A.

In order to determine which recipe has more strawberry flavor, determine how many cups of strawberry is needed for one cup of sugar. In order to do this, divide the cups of strawberry by the cups of sugar.

Cups of strawberry needed for one cup of sugar = cups of strawberry / cups of sugar

Cups of strawberry needed for one cup of sugar in recipe A = 3 ÷ 1/2

3 x 2 = 6  

Cups of strawberry needed for one cup of sugar in recipe B = 5 ÷ 1 = 5

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Yes, it is possible to draw a triangle.

This will be done by the property: the sum of two sides of a triangle should be more than the third side.

(5cm + 9cm) =10 cm

14 cm = 10 cm

LHS>RHS

A triangle is possible.

A triangle is a polygon with three edges and 3 vertices. The terminology for categorizing triangles is more than two thousand years vintage, having been defined on the first actual page of Euclid's elements.

In Euclidean geometry, any three factors, while non-collinear, decide a completely unique triangle and simultaneously, a unique plane (i.e. a -dimensional Euclidean space). In different words, there's best one plane that consists of that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is the best one plane and all triangles are contained in it; however, in higher-dimensional Euclidean spaces, this is not real. this text is ready triangles in Euclidean geometry, and in particular, the Euclidean plane, except wherein otherwise stated.

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The length of the shadow of Hayden is approximately 32 inches.

Charlie and Hayden are standing outside.  Charlie is 64 inches tall and casts a shadow of 30 inches.

Hayden is 68 inches tall. The length of the shadow of Hayden can be calculated as follows:

Using proportion,

64 / 30 = 68 / x

where

x = length of the shadow of Hayden

Therefore,

64 / 30 = 68 / x

cross multiply

64x = 68 × 30

64x = 2040

divide both sides by 64

x = 2040 / 64

x = 31.875

Hence,

Length of the shadow of Hayden = 32 inches

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Answer:

5/10

Step-by-step explanation:

hi I atleast have. to have 20 characters so yeah

Answer: 5 tenths

Step by steps:

Step-by-step explanation:

58 = 2(l+b)

58 = 2(x+x)+5

58 = 2x + 5

2x = 58-5

2x = 53

x = 53/2

x = 26.5

So, length = 26.5 + 5 = 31.5

Hence, the length and breadth are 31.5 and 26.5 respectively.

The interior angle measurement of a regular polygon with 42 sides is 150 degrees.

The interior angle measure of a regular polygon is determined by the formula (n-2)*180/n, where n is the number of sides of the polygon. In the case of a regular polygon with 42 sides, this formula can be expressed as (42-2)*180/42, which simplifies to 150 degrees. Therefore, the interior angle measure of a regular polygon with 42 sides is 150 degrees. This means that each interior angle of the polygon is 150 degrees. The exterior angle measure of a regular polygon with 42 sides would be 10 degrees, which can be calculated by subtracting the interior angle measure from 180 degrees. Knowing the angle measure of both the interior and exterior angles of a regular polygon with 42 sides is useful for a variety of applications, such as modeling or designing.

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Answer:270

Step-by-step explanation:

We have to find (f/g)(5). Therefore, (f/g)(5) is 270.

The Area of the rectangle is (40x²+ 49x + 15)cm²

The area of a rectangle in geometry is the region covered by the rectangle in a two-dimensional plane.  The area of the rectangle is the region occupied by a rectangle within its four sides or boundaries.

A rectangle is a sort of quadrilateral, a two-dimensional object with four sides and four vertices. The rectangle's four angles are all right angles or equal to 90 degrees. The rectangle's opposite sides are equal and parallel to one other.

Given that,

Length of rectangle=(8x+5)cm

Breadth of rectangle=(5x+3)cm

Area of rectangle=Length×Breadth

Area of rectangle=(8x+5)(5x+3) = (40x²+ 49x + 15)cm²

Therefore, the Area of the rectangle is (40x²+ 49x + 15)cm²

Correct question: A rectangle is (8x+5)cm long and (5x+3)cm broad.

Find its area or perimeter.

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the triangles can be proved similar by AA congruence.

What is congruent of the triangle?

The shapes maintain their equality regardless of how they are turned, flipped, or rotated before being cut out and stacked. We'll see that they'll be placed entirely on top of one another and will superimpose one another. Due to their identical radius and ability to be positioned directly on top of one another, the following circles are considered to be congruent.

Any two figures can be perfectly positioned over one another to demonstrate their congruence. The relationship between two figures that are said to be congruent is described using the word "congruence."

As both the triangles are right angle so the left side triangle the angles are 90, 54 and 38.

Similarly for the right-sided triangle again the angles are 90, 54 and 38.

Hence the triangles can be proved similar by AA congruence.

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Answer:

AA

Step-by-step explanation:

yes

Answer:

√21 is irrational

Step-by-step explanation:

√21 = 4.58257569495584 which is a non-terminating decimal.

Therefore √21 is irrational.

Answer: No, it cannot be a rational number.

Step-by-step explanation:

A rational number is defined to be a whole number (ex. 1, 2, 3) or can be decimals that continuously repeat the digits after the point. In the case of a square root, they can be rational--but this only applies to perfect squares: √100, √64, √16, etc, which would give an outcome of a whole number. Therefore, √21 is not a rational number, as the decimal value is 4.57257, and is not continuous (ex. 3.666666).

[tex]g(x) = 4x^2 + 3x[/tex]

So, [tex]g(x+a) = 4(x+a)^2 + 3(x+a)[/tex], since we're just substituting (x+a) for x.

If we clean that up a bit,

    [tex]\begin{aligned}g(x+a) &= 4(x+a)^2 + 3(x+a)\\[0.5em] &= 4(x^2+2xa+a^2) + 3x+3a\\[0.5em] &= 4x^2+8xa+4a^2 + 3x+3a\end{aligned}[/tex]

Now putting this all together:

    [tex]\begin{aligned}g(x+a)-g(x) &= ( 4x^2+8xa+4a^2 + 3x+3a) - (4x^2+3x)\\[0.5em] &= 4x^2+8xa+4a^2 + 3x+3a - 4x^2-3x\\[0.5em]&= 8xa+4a^2 +3a\end{aligned}[/tex]

Remember that [tex](x+a)^2 = (x+a)(x+a) = x^2+2xa+a^2[/tex]

The highest common factor of 48 and 504​ is 24.

An equation is an expression showing the relationship between numbers and variables.

The highest common factor or HCF of a group of numbers is the greatest number which divides the given numbers without remainder.

48 = 2 * 24

504 = 2 * 21 * 24

The HCF of 48 and 504 is 24

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Answer:

SQ = 24

PT = 12

<QPR = 23°

Step-by-step explanation:

SQ= 12+12=24

PT=12

<PRS is alternate to <QPR

<QPR=23°

N(b) =75 because p(b) =n(b) /n(s)

0.75=n(b)/100

n(b)=0.75*100=75

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