Mr. Davies plans to place an aquarium on a shelf in his living room. The length of the shelf is inches, and the aquarium is inches long. Which estimation is best for centering the aquarium on the shelf?

The number of roots of a polynomial is always less than or equal to the degree of the polynomial because the degree of f(x) is the sum of the degrees of the factors

The number of roots of a polynomial is equal to the number of values of x that make the polynomial equal to zero.

The degree of a polynomial is the highest exponent of the variable in the polynomial. For example, the polynomial x² + 3x + 2 has a degree of 2, because the highest exponent of x is 2.

It can be shown mathematically that the number of roots of a polynomial is always less than or equal to the degree of the polynomial. This is known as the Fundamental Theorem of Algebra.

Since each of the factors has a degree of 1, the degree of f(x) is the sum of the degrees of the factors, which is equal to 3.

Therefore, the number of roots of a polynomial is always less than or equal to the degree of the polynomial.

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When a prism and pyramid have the same base and height, their volumes are inversely proportional: the volume of the pyramid is one-third that of the prism.

A pyramid is a three-dimensional object that has faces made of triangles and a base made of polygons. The base is the bottom, while the faces are the sides.

A prism is a three-dimensional object having two identically shaped and sized polygonal bases and rectangular sides. In the actual world, a cardboard box serves as an illustration of a prism.

When a pyramid and a prism have bases and heights that are equivalent, the pyramid can fit inside the prism.

In reality, when this is the case, the pyramid occupies precisely one-third of the prism's volume. When a prism and pyramid have the same base and height, their volumes are inversely proportional: the volume of the pyramid is one-third that of the prism.

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Answer:

Rhombus

Step-by-step explanation:

A rhombus is a type of quadrilateral in which all four sides are of equal length. Also, the diagonals are perpendicular to one another and bisect each other too.

Therefore, as a result square root property can be used to solve a quadratic equation.

Describe equation.

To create an equation, the equal sign is placed between two numerical or variable expressions, as in 4x+9=25.

The answer is a number that may be used in an equation to replace the variable.

According to the given question:

In order to isolate the variable being solved,

the square exponents are removed using the Square Root Property.

The positive and negative values of the number that, when multiplied by itself, equals x are provided by the formula x=±√c x = ± c.

Therefore , as a result square root property can be used to solve a quadratic equation.

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Each side of the fountain is 5 units .

Given :

All the sides of the hexagon are equal.

Vertices of the fountain are :

( 10.5 , 8 ), ( 14.5 , 5 ), ( 10.5, 2 ), ( 5.5, 2 ), ( 1.5, 5 ), and ( 5.5, 8 ).

we know that ,

Distance = √( x2 - x1 )^2 + ( y2 - y1 )^2

= √( 14.5 - 10.5 )^2 + ( 5 - 8 ) ^2

= √4^2 + 3^2

= √ 16 + 9

= √25

= 5 units

we know that all the sides of the hexagon are equal so the length of each side of hexagon or fountain is 5 units .

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The mileage for which company A charge less than company B , m < 65 ( an Inequality using the number of miles driven).

The subtraction property of inequality is applied when an inequality holds the addition operator previously, i.e

x + a < b => x + a - a < b - a

=> x< b - a.

The division property of inequality is mainly applied to the shift coefficient of the variable to another side of the inequality, i.e

2x< b => 2x/2<b/2

⇒ x< b/2.

We have, ryan is going to rent a truck for one day. There are two companies say company A and company B, in which ryan have to choose one for rent a truck for one day.

Let , Total cost charged by company A = $a

Total cost charged by company B = b

The number of miles driven = m miles

For Company A, initail fee = $40 and

Additional charge = .80 cents/mile driven

so, a = 40 + 0.8m --(1)

For Company B, initail fee = $53 and

Additional charge = .60 cents/mile driven

so, b = 53 + 0.6m --(2)

We want to know the mileage at which company A charges less than B i.e a < b

Now, using equation (1) and (2) ,

40 + 0.8m < 53 + 0.6m

Simplify the above Inequality,

=> 40 + 0.8 m - 40 < 53 - 40 + 0.6 m

=> 0.8 m < 13 + 0.6 m

=> 0.8 m - 0.6 m < 13 + 0.6 m - 0.6 m

=> 0.2 m < 13

=> m < 13/0.2

=> m < 130/2 = 65

Hence, required Inequality is m< 65.

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Complete question :

ryan is going to rent a truck for one day. There are two companies he can choose from, and they have the following prices.

Company A charges an initial fee of $40 and an additional .80 cents for every mile driven.

Company B charges an initial fee of $53 and an additional .60 cents for every mile driven.

For what mileages will Company A charge less than Company B? Write your answer as an inequality, using m for the number of miles driven

The equation of the line that is parallel to the line y = - 5x + 3 will be y = - 5x + c.

Let the equation of the line be ax + by + c = 0. Then the equation of the parallel line that is parallel to the line ax + by + c = 0 is given as ax + by + d = 0.

The equation of the line is given below.

y = - 5x + 3

Then the equation of the line that is parallel to the line y = - 5x + 3 will be written as,

y = - 5x + c

The equation of the line that is parallel to the line y = - 5x + 3 will be y = - 5x + c.

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Answer:

[tex] \sf \: 375g \: is \: 2.5\% \: of \: 15kg[/tex]

Step-by-step explanation:

Conversion of 15 kg into grams,

→ 1 kg = 1000 g

→ 15 kg = 15000 g

Let's find the percentage,

→ (375g ÷ 15kg) × 100

→ (375/15000) × 100

→ 0.025 × 100

→ 2.5%

Hence, the answer is 2.5%.

So the value of the line integral given point scale is [tex]\frac{15}{16}[/tex] -4cos6-6 .

To evaluate the line integral X signed by ideas oversee. Where C is the line segment from 2 to 36

First we find the vector determined by the two points

So ,

36 -2 = 34

Starting point is 2.

The segment can be para militarized as vitally equal to 2+3T+40 =3T 2+40 .

They belonging to close interval 0- one. Next we find the derivative of the Para militarism action y¹T= 34.

This implies the strength of y¹T = [tex]\sqrt{3^{2}+4^{2} }[/tex]

= 5

Finally we calculate the integral X signed by ideas oversee which is equal to treaty sign 2+ 40×DT Over 0- one.

Now report 2+ 40 equal to you. So implies 4DT is equal to DU and when T is equal to zero.

20=U

So next this integral becomes 15×2 to 6 Juju -2 x 4.

Comes out to be 15 x 16. 0-2. Sign your deal. Now applying integration by parts.

We have 15 x 16. 0-2 cause you plus integration of causal deal Limit 2- 6.

Now we have 15/16. On applying the limits -4 cos six plus sign 6- sign too.

So therefore final answer becomes [tex]\frac{15}{16}[/tex] -4cos6-6 .

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Answer:

10 + 2z

Step-by-step explanation:

2( 5+z)

10 + 2z

There were total 600 songs downloaded of standard quality

What is Linear Equation in Two Variable?

A linear equation in two variables is one that is stated in the form ax + by + c = 0, where a, b, and c are real integers and the coefficients of x and y, i.e. a and b, are not equal to zero.

Solution:

Let, number of songs of Standard Quality Downloaded be x

number of songs of High Quality Downloaded be y

According to the Question:

x + y = 960 ----------(i)

2.5x + 4.7y = 3192 ----------(ii)

Multiplying the equation 1 by 2.5

2.5x + 2.5y = 2400 ----------(iii)

Substracting Equation 3 from equation 2

2.2y = 792

y = 360

So, x = 600

There were total 600 songs downloaded of standard quality

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Answer:

The difference of two squares is a method of factorising used when an algebraic expression includes two squared terms, one subtracted from the other: a 2 – b 2 When we are subtracting a squared term from another squared term we can use the difference of two squares method. Square numbers are sometimes called perfect squares.

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Step-by-step explanation:

The equation 3x2 + Kx - 30 has equal roots when the discriminant (D) of the equation is equal to zero.

The discriminant of a quadratic equation is given by the formula D = b2 - 4ac, where a = 3, b = K, and c = -30.

Substituting these values into the formula, we get:

D = K2 - 4(3)(-30)

D = K2 + 360

Therefore, K2 = -360, and K = √(-360) = 6√(-5)

Therefore, the value of k for which the roots of the equation 3x2 + Kx - 30 are equal is 6√(-5).

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The coordinates of point A are (23/5, 44/5).

A line segment is a section of a straight line that is enclosed by two clearly defined endpoints and contains every point on line b within.

Given:

The ratio = 2:3

P is (1,4) and H is (19,28)

Calculate the mid-point coordinates as shown below,

E = (1 + 19 / 2), (28 + 4 / 2)

E = (10, 16)

Calculate the coordinates of point A,

A = (2 × 10 + 3 × 1 / 2+3) , (16 × 2+ 4 × 3 / 2+3)

A = (23/5, 44/5)

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On observing the provided question, we can say that - In Korea, 10th grade is = 16 or 17 year old ,  11th grade is = 17 or 18 and  12th grade is = 18 or 19.

Grading may be done using letters, numbers, percentages, points, or descriptions. The most prevalent grades are in the form of letters, and they usually correspond to a variety of percentages or points. Many people consider "A" and "B" grades to be "good." D and F grades are referred to as "poor grades." Commonly regarded as average is a "C."

We can say that

In Korea,

10th gradis = 16 or 17 year old ,

11th grade is = 17 or 18 and  12th grade is = 18 or 19.

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Find the slopes and their product should be - 1 for the diagonals to be perpendicular.

The points p and q have zero y-coordinate, so they are on the y-axis.

The points r and s have same y-coordinate b, so they are on the parallel line to the y-axis.

The points p and r are opposite to each-other, similarly points s and q are opposite points. So the diagonals are pr and qs. This is also known from the order of vertices in the name of the quadrilateral.

Slopes are:

The product of slopes:

The diagonals are perpendicular if:

Step-by-step explanation:

Find the arithmetic sequence for -16,-21,-26,-31

-21 - (-16) = -5

-26 - (-21) = -5

-31 - (-26) = -5

Answer:

Each following number is five less than the previous.

Answer:

To determine Beau's front-end ratio, you need to calculate the percentage of his monthly income that will be taken up by his mortgage, homeowner's insurance, property taxes, credit card payment, and car payment.

First, add up all of Beau's monthly expenses: $1,025 (mortgage) + $635 (homeowner's insurance) / 6 (months in a half year) + $4,785 (property taxes) / 12 (months in a year) + $2,000 (credit card payment) + $250 (car payment) = $3,715.83.

Next, divide this total by Beau's monthly income: $3,715.83 / ($89,750 / 12) = $3,715.83 / $7,479.17 = 0.49, or approximately 49%.

Since this ratio is expressed as a percentage, the final answer is 49%. Therefore, the correct answer is (d) 24%.

The statement as an inequality expression is 12.75 < 7x

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

12 and 3/4 less than the product of 7 and a number x

Express the numbers as fractions

So, we have the following representation

12 + 3/4 less than the product of 7 and a number x

Introduce the inequality symbols

So, we have

12 + 3/4 < the product of 7 and a number x

Next, we have

12 + 3/4 < 7x

Express as decimal

12.75 < 7x

hence, the expression is 12.75 < 7x

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The value of the function (f - g)(x) would be [tex](f-g)(x)=x^2-11x+4[/tex].

Option (A) is correct.

What are composite functions?

A composite function is generally a function that is written inside another function. The composition of a function is done by substituting one function into another function. For example, f [g (x)] is the composite function of f (x) and g (x). The composite function f [g (x)] is read as “f of g of x”.'

Given:

                [tex]f(x)=4x^2-5x\\\\g(x)=3x^2+6x-4[/tex]

Now by using the definition of composite functions we can write,

      [tex](f-g)(x)=f(x)-g(x)\\\\(f-g)(x)=4x^2-5x-(3x^2+6x-4)\\\\(f-g)(x)=4x^2-5x-3x^2-6x+4\\\\(f-g)(x)=x^2-11x+4[/tex]

Hence, the value of the function (f - g)(x) would be [tex](f-g)(x)=x^2-11x+4[/tex].

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∠ABP = ∠CBP (By angle bisector).∠PXB = ∠PYB (All right angles are congruent).BP = BP (Common side).ΔBXP = ΔBYP (By ASA rule).PX = PY (corresponding sides of congruent triangles are the same).

If two figures are exactly the same in sense of their length side all things then they will be congruent.

In other meaning, if you can copy a figure then that copy and the original figure will be congruent.

As per the given two bisectors' angle.

∠ABP = ∠CBP (By angle bisector)

∠PXB = ∠PYB (All right angles are congruent).

BP = BP (Common side)

ΔBXP = ΔBYP (By ASA rule)

PX = PY (corresponding sides of congruent triangles are the same)

Hence "∠ABP Equals ∠CBP (By angle bisector). ∠PXB = ∠PYB (All right angles are congruent). BP = BP (Common side) (Common side). ΔBXP = ΔBYP (By ASA rule). PX = PY (matching sides of congruent triangles are the same) (corresponding sides of congruent triangles are the same).".

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I don't see the picture. Can you send it in the message.

Answer: they would cost  £5.25

Step-by-step explanation:  £2.25 divided by 3 = 0.75 0.75x7=  £5.25

Figure PQRS may be mapped onto image P'Q'R'S using only one transformation, which is a reflection.

There are four different ways to change a point, line, or geometric figure, and each one has an impact on the object's shape and/or placement. Pre-Image is the shape of the item before transformation, and image is the position and final shape of the object after transformation.

As a result, the coordinates for the figure PQRS are P(2,2) Q(5,2) R(5,6) and S(2,6), whereas those for the picture P'Q'R'S' are P(-6,2) Q(3,2) R(3,6) and S' (-6,6).

Reflection is a sort of transformation that flips a shape along a mirror line, also known as a line of reflection, such that each point is at the same distance from the mirror line as its mirrored point.

The y-axis reflects the PQRS figure, which is then translated left to 1 unit.

As a result, one transformation can reflect picture P'Q'R'S onto figure PQRS.

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The recursive rule can be used to find the nth term of the sequence aₙ = aₙ₋₁ + 2 which is an arithmetic progression.

What is arithmetic progression ?

Arithmetic Progression (AP) is a sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value. It is also called Arithmetic Sequence

From the given sequence we see that:

Common difference is 2

Find the first term:

a₁ + (n-1)d  = aₙ

a₁ + 3*2 = a₄

a₁ + 6 = 2

a₁ = -4

The recursive formula for this sequence is:

a₁ = -4

aₙ = aₙ₋₁ + 2

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Answer:

5 per day

Step-by-step explanation:

The slope of a line that is parallel to x + y = -4 is: -1.

If we have two lines that are parallel to each other, their slopes will be the same.

For example, if the slope of one line is 4, the slope of the line that is parallel to the line will also have a slope of 4.

To find the slope of the equation, x + y = -4, rewrite it in slope-intercept form, y = mx + b:

x + y = -4

y = -x - 4 [subtraction property of quality]

The slope is therefore -1. Therefore, the slope of the line that is parallel to the line whose equation is x + y = -4 is: -1.

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Answer:

  undefined

Step-by-step explanation:

You want the slope of the line through points (-1, 1) and (-1, 4).

The two points lie on the vertical line x = -1. A vertical line has undefined slope.

The slope of the line is undefined.

__

Additional comment

The slope is the ratio of rise to run. For a vertical line, the "run" is zero for any chosen "rise." Division by zero gives an undefined result.

Answer: If Debra, the mirror, and the bottom of the tree are points on the ground all on one line, then the two right triangles are these: LEFT: y and 33 as the legs and unknown hypotenuse. RIGHT: 6 and 9.7 as legs and unknown hypotenuse. The two angles at the mirror are of same measure; that is, the 33 and the hypotenuse of a LEFT triangle makes same angle measure as the 9.7 and the hypotenuse of the RIGHT triangle.

Note, these are two SIMILAR triangles.

y/33 = 6/9.7

In addition,  Y = 20.4

highlight%28y=20.4%29

Step-by-step explanation:

The transitive property of congruence is used to justify the statement.

According to the transitive property, if A and B are congruent and if B is congruent with C, then A must also be congruent with C. In other words, two things are congruent to each other if a third object is congruent to them.

Since AB and EF are both congruent to DE in the sentence "If AB DE, EF DE therefore AB EF," AB must likewise be congruent to EF in accordance with the transitive property.

The additional attributes you mentioned don't apply in this situation. According to the symmetric property, if A and B are congruent, then so is B. According to the reflexive quality, each item corresponds to itself. And congruence does not have the property of multiplication.

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Complete question:

if AB ≅ DE, EF ≅ DE then show that AB ≅ EF ?