a fifth-degree polynomial can have a maximum of how many relative extrema and points of inflection? explain. a fifth-degree polynomial can have at most critical numbers, and hence relative extrema. it can have at most points of inflection.

You can expect 95% of your customers to stay in your store between range of  39.7 minutes and 49.9 minutes.

To determine the range in which 95% of your customers would stay in your store, we will use the properties of a normally distributed data set with a mean of 44.8 minutes and a standard deviation of 2.6 minutes.
Identify the mean and standard deviation.
The mean is 44.8 minutes, and the standard deviation is 2.6 minutes.
Determine the z-score for a 95% confidence interval.
A 95% confidence interval corresponds to a z-score of 1.96. This means that 95% of the data lies within 1.96 standard deviations from the mean.
Calculate the range using the z-score, mean, and standard deviation.
To find the lower and upper limits of the range, we will multiply the standard deviation (2.6 minutes) by the z-score (1.96) and then subtract or add the result to the mean (44.8 minutes).
Lower limit: Mean - (Z-score × Standard deviation)
44.8 - (1.96 × 2.6) = 44.8 - 5.096 ≈ 39.7 minutes
Upper limit: Mean + (Z-score × Standard deviation)
44.8 + (1.96 × 2.6) = 44.8 + 5.096 ≈ 49.9 minutes
State the range in which 95% of customers would stay in the store.

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Using the given secant line, we know that the required angle ∠a is 15° respectively.

A secant in geometry is a line that crosses a curve at least two different points.

The Latin verb secare, which means to cut, is where the word secant originates.

A secant crosses a circle at precisely two points in a case of circle.

The Latin word secant, which means to cut, is used in mathematics to define a line that passes through the points P and Q of any arbitrary curve whose equation is y=f(x).

So, we know that:

c = 55° and b = 25°

And, the formula is:

∠a = c - b/2

Now, insert values as follows:

∠a = c - b/2

∠a = 55 - 25/2

∠a = 30/2

∠a = 15°

Therefore, using the given secant line, we know that the required angle ∠a is 15° respectively.

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1) You will Rewrite both side by combining like terms. Thus, option D is correct.

2) Yes, they have same solution x = 2.

Balancing an equation in math typically refers to solving an equation for a specific variable. The goal is to isolate the variable on one side of the equation and simplify the other side. The steps for balancing an equation in math can vary depending on the type of equation, but here are some general steps to follow:

1) Identify the variable you want to solve for.

You have given:

5x - 2 + x = x - 4

Also

5x - x = x - 4

Here, as you can see x - 4 is common in both equation, (option D) Rewrite one side (or both) by combining like terms i.e. x - 4:

5x - 2 + x = 5x - x = x - 4

4x - 2  = 4x  = x - 4

4x - 4x - 2  = x - 4

- 2 = x - 4

4 - 2 = x

x = 2

Thus, You will Rewrite both side by combining like terms. Thus, option D is correct.

2) Yes, they have same solution x = 2

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The length of the two equal sides of the isosceles trapezoid is 11.3 millimeters.

What is trapezoid?

A trapezoid, also known as a trapezium in some countries, is a two-dimensional geometric shape with four sides. It is a quadrilateral that has at least one pair of parallel sides, which are called bases.

Let's start by labeling the sides of the isosceles trapezoid as follows:

The shorter base: b1 = 6.3 mm

The longer base: b2 = 16.1 mm

The two equal sides: s

We know that the perimeter P of the trapezoid is given by:

P = b1 + b2 + 2s

Substituting the values we have, we get:

45 mm = 6.3 mm + 16.1 mm + 2s

Simplifying this equation, we get:

22.6 mm = 2s

Dividing both sides by 2, we get:

s = 11.3 mm

Therefore, the length of the two equal sides of the isosceles trapezoid is 11.3 millimeters.

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The vertices of the ellipse are (-4,2) and (4,2), since these points lie on the major axis of the ellipse which is horizontal.

Two of the focuses given in the issue, (−4,2) and (4,2), are both situated on a similar even line. This implies that the significant hub of the oval should be level. Two different focuses given in the issue, (2,2) and (- 9,2), are likewise situated on this level line. Thusly, the focal point of the oval is the midpoint between the focuses (- 4,2) and (4,2), which is (0,2).

The other two focuses given in the issue, (−5,5) and (−5,−1), are situated on an upward line that goes through the focal point of the oval. This implies that the minor pivot of the oval should be vertical.

The vertices of the oval are the places where the significant hub meets the circle. Since the significant hub goes through the focuses (−4,2) and (4,2), the vertices of the oval are (- 4,2) and (4,2).

In this way, the vertices of the oval are (- 4,2) and (4,2).

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Answer:

To solve this problem, we can use the Pythagorean theorem, which states that the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse.In this case, the height of the monitor is one leg of the right triangle, and the width of the monitor is the other leg. The distance between opposite corners is the hypotenuse.Let w be the width of the monitor in inches. Then we have:w^2 + 18^2 = 30^2Simplifying and solving for w, we get:w^2 + 324 = 900

w^2 = 576

w = 24Therefore, the width of Mia's new monitor is 24 inches.

Step-by-step explanation:

The clοsest οptiοn tο the actual area οf the οbject is D. 64 square inches.

Area is a measure οf the amοunt οf space inside a twο-dimensiοnal shape, such as a square, rectangle, triangle, circle, οr any οther shape that has a length and a width. It is usually measured in square units, such as square inches, square feet, οr square meters.

Tο find the area οf the οbject, we need tο break it dοwn intο smaller shapes and add up their areas.

First, we can see that the οbject can be divided intο a rectangle with dimensiοns 8 inches by 4 inches (UWVZ), a triangle with base 4 inches and height 6 inches (VXY), and a trapezοid with bases 6 inches and 8 inches, and height 4 inches (WXYU).

The area οf the rectangle is:

A_rectangle = length × width = 8 in × 4 in = 32 square inches

The area οf the triangle is:

A_triangle = 1÷2 × base × height = 1÷2 × 4 in × 6 in = 12 square inches

The area οf the trapezοid is:

A_trapezοid = 1÷2 × (base1 + base2) × height = 1÷2 × (6 in + 8 in) × 4 in = 28 square inches

Therefοre, the tοtal area οf the οbject is:

A_οbject = A_rectangle + A_triangle + A_trapezοid

= 32 square inches + 12 square inches + 28 square inches

= 72 square inches

Therefοre, the clοsest οptiοn tο the actual area οf the οbject is D. 64 square inches.

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The image of the point (0,1) after a rotation of 270 degrees counterclockwise about the origin is the point (1,0).

What is trigonometry?

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles.

A rotation of 270 degrees counterclockwise about the origin corresponds to a transformation in which every point in the plane is rotated 270 degrees counterclockwise about the origin.

To find the image of the point (0,1) under this transformation, we can use the following formula for a counterclockwise rotation of a point (x,y) about the origin by an angle of θ:

x' = x cos(θ) - y sin(θ)

y' = x sin(θ) + y cos(θ)

Plugging in the values x = 0, y = 1, and θ = 270 degrees, we get:

x' = 0 cos(270°) - 1 sin(270°) = 0 - (-1) = 1

y' = 0 sin(270°) + 1 cos(270°) = 0 + 0 = 0

Therefore, the image of the point (0,1) after a rotation of 270 degrees counterclockwise about the origin is the point (1,0).

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Answer:

Step-by-step explanation:inconclusive

The solutions to the quadratic function f(x) = 25x^2 - 81 are x = 9/5 and x = -9/5.

First, we need to rewrite the function in standard quadratic form:

f(x) = 25x^2 - 81

To solve this quadratic function using the square root method, we want to isolate the x^2 term and divide both sides by the coefficient of x^2, which is 25:

25x^2 - 81 = 0

25x^2 = 81

x^2 = 81/25

Taking the square root of both sides, we get:

x = ±(9/5)

Therefore, the solutions to the quadratic function f(x) = 25x^2 - 81 are x = 9/5 and x = -9/5.

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By answering the presented question, we may conclude that Therefore, Pythagorean the length of the third side of the triangle is [tex]2/\sqrt(5)[/tex]and the height is 4/5.

The Pythagorean theorem is a fundamental mathematical principle that describes the connection between the sides of a right triangle. It asserts that the sum of the squares of the other two sides' lengths equals the square of the hypotenuse's length (the side opposite the right angle). The mathematical theorem is as follows: c2 = a2 + b2 Where "c" denotes the hypotenuse length and "a" and "b" indicate the lengths of the other two sides, known as the legs.

Let's use the formula for the area of a triangle:

[tex]A = 1/2 * b * h2/5 = 1/2 * (6/5) * h\\h = 4/5\\a^2 = (6/5)^2 - (4/5)^2\\a^2 = 36/25 - 16/25\\a^2 = 20/25\\a^2 = 4/5\\[/tex]

[tex]a = \sqrt(4/5)\\a = 2/\sqrt(5)[/tex]

Therefore, the length of the third side of the triangle is [tex]2/\sqrt(5)[/tex]and the height is 4/5.

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Answer:

1/6

Step-by-step explanation:

because the dice is most likly a 6 sided dice but if you need to simplify then it would be 1/2

Therefore, there are 18 oranges in each box.

An equation is a mathematical statement that shows that two expressions are equal to each other. It typically consists of two sides separated by an equal sign (=), with mathematical expressions or variables on each side. Equations can be used to describe many different relationships and properties in mathematics, science, and engineering.

Here,

To represent the relationship described in the problem, we can use the following model or diagram:

4 boxes with b oranges per box, plus 1 free orange = 73 oranges in total

This can be written as the equation:

4b + 1 = 73

To solve for b, we need to isolate it on one side of the equation. We can start by subtracting 1 from both sides to get:

4b = 72

Then, we can divide both sides by 4 to get:

b = 18

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the missing dimension (diameter) of the cylinder is approximately 18.9 inches, rounded to the nearest tenth.

what is cylinder ?

A cylinder is a three-dimensional shape that consists of two parallel circular bases connected by a curved surface. It can be thought of as a tube or a can, and is a common shape found in many everyday objects such as soda cans, tubes, and pipes.

In the given question,

To find the missing dimension (diameter) of the cylinder, we can use the formula for the volume of a cylinder:

V = πr²h

where V is the volume of the cylinder, r is the radius of the cylinder, and h is the height of the cylinder.

Since the diameter (D) is twice the radius (r), we can also write:

V = π(D/2)²h

Simplifying this expression, we get:

V = πD²h/4

Multiplying both sides by 4/πh, we get:

D² = 4V/(πh)

Taking the square root of both sides, we get:

D = 2√(V/πh)

Substituting the given values, we get:

D = 2√(7433 in.³/π(14 in.))

D ≈ 18.9 in.

Therefore, the missing dimension (diameter) of the cylinder is approximately 18.9 inches, rounded to the nearest tenth.

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Michael was swimming abοut 0.08 meters per secοnd faster in the 50-meter freestyle than in the 100-meter freestyle.

Time is the duratiοn between twο events. Speed is the measure οf hοw fast sοmething mοves οver a given distance. Distance is the amοunt οf space between twο pοints οr οbjects.

Tο find οut hοw much faster Michael swam the 50-meter freestyle than the 100-meter freestyle, we need tο calculate the difference between their speeds.

Let's first find οut Michael's speed in meters per secοnd fοr each race.

Fοr the 50-meter freestyle:

speed = distance / time = 50 meters / 23.04 secοnds ≈ 2.17 meters/secοnd

Fοr the 100-meter freestyle:

speed = distance / time = 100 meters / 47.77 secοnds ≈ 2.09 meters/secοnd

Nοw, tο find the difference in speed, we can subtract the speed οf the 100-meter freestyle frοm the speed οf the 50-meter freestyle:

2.17 meters/secοnd - 2.09 meters/secοnd ≈ 0.08 meters/secοnd

Therefοre, Michael was swimming abοut 0.08 meters per secοnd faster in the 50-meter freestyle than in the 100-meter freestyle.

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The parabola's equation is therefore for A: y  = 7x2 - 5$1.

As a result, the parabola's equation for B  is y = -1/2(x - 1)² + 4.

A parabola with vertex (h,k) has the basic equation y = a(x-h)² + k². In this instance, h=0 and k=-5 are equal because the vertex is at $(0,-5)$. Moreover, the parabola has a point at (-1 . 2). When we substitute these numbers in the general parabola equation, we obtain:

2 = a(-1-0)² -5

7 = a

The parabola's equation is therefore y = 7x2 - 5$1.

A cone and a plane perpendicular to its side cross to create a symmetrical open plane curve known as a parabola1. It is a U-shaped curve whose vertex and axis of symmetry characterise it. The line dividing the parabola into its two mirror counterparts is known as the axis of symmetry. The parabola's vertex is where the axis of symmetry intersects it.

A parabola's vertex is represented by the equation y = a(x - h)²+ k, where (h,k) represents the vertex. We may utilise the vertex version of the equation and substitute the values of h, k, and the x and y coordinates of the point to determine the equation of a parabola that passes through a particular point and has a certain vertex.

B.  Here, the vertex is (1, 4), and the point (5,-4). In the vertex form equation, we may therefore substitute h=1, k=4, x=5, and y=-4 to obtain:

-4 = a(5 - 1)²2 + 4 \s-8 = 16a

a = -1/2

As a result, the parabola's equation is y = -1/2(x - 1)² + 4.

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On solving the provided question we can say that The amount of water lost is: [tex]V_lost = V1 - V2 = 346.36 cm^3 - 401.94 cm^3 = -55.58 cm^3[/tex]

A cylinder is a three-dimensional geometric shape made up of two parallel congruent circular bases and a curving surface connecting the two bases. The bases of a cylinder are always perpendicular to its axis, which is an imaginary straight line passing through the centre of both bases. The volume of a cylinder is equal to the product of its base area and height. A cylinder's volume is computed as V = r2h, where "V" represents the volume, "r" represents the radius of the base, and "h" represents the height of the cylinder.

[tex]V1 = \pi r^2h = \pi (3.5 cm)^2(9 cm) = 346.36 cm^3\\[/tex]

Next, let's calculate the volume of the ball:

The radius of the ball is 5/2 = 2.5 cm. The volume of the ball is:

[tex]V_ball = (4/3)\pi r^3 = (4/3)\pi (2.5 cm)^3 = 65.45 cm^3\\V_disp = V_ball = 65.45 cm^3\\h_new = 9 + (V_disp/\pi r^2) = 9 + (65.45 cm^3)/(\pi (3.5 cm)^2) = 10.77 cm\\V2 = \pi r^2h_new = \pi (3.5 cm)^2(10.77 cm) = 401.94 cm^3\\[/tex]

The amount of water lost is:

[tex]V_lost = V1 - V2 = 346.36 cm^3 - 401.94 cm^3 = -55.58 cm^3[/tex]

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The predicted number of green or yellow piece in 50 selection is 18

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

The number of candies

Where we have

Yellow or green = 6 + 3

Yellow or green = 9

Also, we have

Total = 25

So, we have

P(Yellow or green) = 9/25

In 50 selections, we have

Yellow or green = 9/25 * 50

Yellow or green = 18

Hence, the predicted times is 18

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The triangles KJL and GJL are not similar in figure 1 whereas in figure 2 the triangles RST and RPQ are similar by SSS similarity criteria.

The triangles are said to be similar if all the angles in one triangle are equal or congruent to the corresponding angles in another triangle and the sides are proportional. There are different criterias for similarity of triangles namely SSS, SAS, ASA/AAS and RHS. According to the criteria/rule

SSS(SIDE-SIDE-SIDE):two triangles are said to be similar if three sides of one triangle are proportional to the corresponding sides of another triangle.

SAS(SIDE-ANGLE-SIDE):The triangles are said to be similar if two sides are proportional and an included angle is congruent to the two sides and included angle of another triangle.

ASA(ANGLE-SIDE-ANGLE):The triangles are said to be similar if two angles are congruent and an included side is proportional  to the two angles and included side of another triangle.

RHS(RIGHT-HYPOTENUSE-SIDE):The triangles are said to be similar if one angle is right angle in both triangles, also the hypotenuse and any one side is proportional  to the hypotenuse and any one side of another triangle.

Q11)In ΔKJL and ΔGJH,

∠KJL = ∠GJH {vertically opposite angles}

But the sides aren't proportional to each other.

∴The given triangles are not similar.

Q12)Consider the triangles ΔRST and ΔRPQ ,

∠SRT = ∠PRQ {Common angle}

As we know that, =  { and }

By basic proportionality theorem, we can say that ST is parallel to PQ.

∴∠RST = ∠RPQ {corresponding angles} and

∠RTS = ∠RQP {corresponding angles}

All angles of ΔRST are congruent to corresponding angles of ΔRPQ.

The sides are proportional to each other:

RS= 35 units; RP= 35+14=49 units

ST=25 units; PQ=35 units

RT=30 units ; RQ=30+12=42 units

All three sides are proportional.

∴ ΔRST and ΔRPQ are similar by SSS.

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the probability of drawing a red, then a blue, and then a white marble is [tex]=\frac{7}{225}[/tex]

To find probability, we take the number of ways the specific event can occur and divide it by the number of ways any event can occur.

The probability of drawing a red marble is: (of red marbles) / (total # of marbles) = 3/(3 + 7 + 5) = 3÷15 = 1÷5.

The probability of drawing a blue marble is: ( of blue marbles) / (total # of marbles) = 5/(3 + 7 + 5) = 5÷15 = 1÷3.

The probability of drawing a white marble is: ( of white marbles) / (total # of marbles) = 7/(3 + 7 + 5) = 7÷15.

Now, we want these events to all to occur for us. So, we must multiply them by each other: (1/5) * (1/3) * (7/15)  [tex]=\frac{7}{225}[/tex]

Thus, the probability is [tex]=\frac{7}{225}[/tex]

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The value of angle C is 68°.

In geometry, complementary angles are two angles that add up to 90 degrees (a right angle). In other words, when two angles are placed adjacent to each other, and they form a right angle, they are considered complementary angles.

For example, if angle A is 40 degrees, then angle B, which is adjacent to angle A and together they form a right angle, is considered to be a complementary angle. Angle B would be 90 - 40 = 50 degrees.

Complementary angles can be found in many geometric shapes and objects, such as squares, rectangles, and triangles. In a right triangle, the two acute angles (the angles that are not the right angle) are always complementary.

Vertical angles are always congruent, which means that angle B is also 22°.

Since angle B and angle C are complementary, their sum is equal to 90°.

Thus, we can write the equation:

angle B + angle C = 90°

Substituting the known value of angle B, we get:

22° + angle C = 90°

Simplifying the equation, we get:

angle C = 90° - 22°

angle C = 68°

Therefore, the value of angle C is 68°.

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Atoms of oxygen most different from atoms of nitrogen as they have different masses.

A subatomic particle known as an atom is made up of a nucleus composed of protons and neutrons, which is encircled by a swarm of electrons. The atom is the fundamental unit of the chemical elements, and the chemical elements are differentiated from one another by the count of protons present in their atoms. For instance, sodium is any atom that comprises 11 protons, and copper is any atom that includes 29 protons. The isotope of the element is characterized by the number of neutrons. Solid blue crystals can also be a form in which oxygen exists, with molecules that are diatomic.

Interestingly, Priestley was not immediately aware that he had discovered oxygen, and instead believed he had obtained a certain component of air. In a hermetic device, he observed the breakdown of mercury oxide and used a lens to direct sunlight onto the oxide.

In terms of the interaction between nitrogen and oxygen, these substances react in the presence of an electric current. Nitrogen is a stable molecule and does not readily react with other substances.

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Let us call the number of children "c" and the number of adults "a." Based on the facts provided, we can then construct two equations: c + a = 259 (equation 1) (equation 1).  

1.5c + 4a = 676 (2nd equation)

In equation 1, we may solve for one variable in terms of the other:

c = 259 - a

So, in equation 2, substitute this expression for "c":

1.5(259 - a) + 4a = 676

Distribute the 1.5:1:1:1:1:1:1:1:

388.5 - 1.5a + 4a = 676

Merge similar terms:

2.5a = 287.5

Multiply by 2.5:

a = 115

This translates to 115 adults being accepted. We can plug this number back into equation 1 to find "c":

c + 115 = 259

c = 144

As a result, 144 youngsters were hospitalised.

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What is an angle?

It is the opening that forms the intersection of two lines.

The sum of two angles:

What is a rectangle?

A rectangle is a polygon with four sides, with the characteristic that its opposite sides are equal.

What is the measure of the angle formed by the diagonals of the rectangle ABCD?

The area of a rectangle can be determined by knowing its diagonals and the angle they form between them.

A = D² Sen(γ)/2

Being;

Being;

A = (7)(6)

A =  42cm²

Apply the Pythagorean theorem to determine D.

D² = AB² + AD²

replace;

D² = (7)² + (6)²

D² = 49  + 36

D² = 82

Substitute in A;

 42=82 Sen(γ)/2

Solve for γ;

 84=82 Sen(γ)


γ = Sen⁻¹(84/82)

γ =

The probability of getting a tail on the first flip, a head on the second flip, and another tail on the third flip is 1/8, or approximately 0.125.

What is probability?

Assuming that the coins are fair, meaning they have an equal probability of landing heads or tails, the probability of getting a specific sequence of outcomes is found by multiplying the probabilities of each individual outcome.

In this case, the probability of getting a tail on the first flip is 1/2, the probability of getting a head on the second flip is also 1/2, and the probability of getting a tail on the third flip is 1/2. Multiplying these probabilities together, we get:

(1/2) x (1/2) x (1/2) = 1/8

Therefore, the probability of getting a tail on the first flip, a head on the second flip, and another tail on the third flip is 1/8, or approximately 0.125.

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The professor should select a sample size of at least 247 students to ensure that the 97% confidence interval for the mean amount of time IRSC students spend studying each week has a width of no more than 1.7 hours.

To calculate the sample size needed for a confidence interval with a maximum width of 1.7 hours, we need to use the formula:

n = ((z * σ) / E)^2

where:

n is the sample size we need to find

z is the z-score corresponding to the desired confidence level (97% in this case)

σ is the population standard deviation (14.9 hours in this case)

E is the maximum margin of error we want in our confidence interval (1.7 hours in this case)

The z-score corresponding to a 97% confidence level is 1.8808 (which can be found using a z-table or calculator).

Substituting these values into the formula, we get:

n = ((1.8808 * 14.9) / 1.7)^2

n = 246.644

Rounding up to the nearest whole number, we get:

n = 247

Therefore, the professor should select a sample size of at least 247 students to ensure that the 97% confidence interval for the mean amount of time IRSC students spend studying each week has a width of no more than 1.7 hours.

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The distributive property allows us to distribute 4 to each term inside the parentheses, add the terms first, then distribute the result to x. It also allows us to distribute 6 to each term inside the parentheses, such as 6(x+y+z) = 6x + 6y + 6z.

The distributive property is a mathematical property that applies to operations, such as addition and multiplication, that involve two or more terms. The distributive property states that the result of multiplying a term by a sum or difference of terms is the same as multiplying each term inside the parentheses by the term outside the parentheses and then adding or subtracting the results.

1. Using the distributive property, we can distribute the 4 to each term inside the parentheses:

4(x+2) = 4x + 42 = 4x + 8

Therefore, the equivalent expression is 4x + 8.

2. Using the distributive property, we can add the terms inside the parentheses first, then distribute the result to x:

(6+8)•x = 14•x

Therefore, the equivalent expression is 14x.

3. Using the distributive property, we can distribute the 4 to each term inside the parentheses:

4(2x+3) = 42x + 43 = 8x + 12

Therefore, the equivalent expression is 8x + 12.

4. Using the distributive property, we can distribute the 6 to each term inside the parentheses:

6(x+y+z) = 6x + 6y + 6z

Therefore, the equivalent expression is 6x + 6y + 6z.

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Christina will need 220 feet of fence to enclose her yard.

The perimeter of a form is the space surrounding its edge. Find the perimeter of various forms by summing the lengths of their sides.

To solve this, we need to calculate the perimeter of the rectangular yard:

Perimeter = 2 × (Length + Width)

Plugging in the given dimensions:

Perimeter = 2 × (60 ft + 50 ft)

Perimeter = 2 × (110 ft)

Perimeter = 220 ft

Christina will need 220 feet of fence to enclose her yard.

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Christina wants to fence in her rectangular yard. The length of her yard is 60 feet, and the width is 50 feet. How many feet of fence will she need to enclose the entire yard?

Answer:

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Step-by-step explanation: