A rectangle A with length 10 centimeters and width 5 centimeters is similar to another rectangle B whose length is 30 centimeters. Find the area of rectangle B.
A. 450 centimeters squared
B. 350 centimeters squared
C. 750 centimeters squared
D. 650 centimeters squared

All monuments cast a shadow when the sun is shining, as they block the sunlight and create a shadow on the ground or nearby surfaces. T

The size and shape of the shadow will depend on the position of the sun in the sky, the orientation of the monument, and its size and shape.

Some famous monuments that cast impressive shadows include the Pyramids of Giza, the Eiffel Tower, the Washington Monument, and the Stonehenge.

We can use proportions to solve the problem.

Let x be the length of Kyle's shadow.

We know that the length of the monument's shadow is 16 feet, and its height is  [tex]64 f[/tex] Feet. So the ratio of the length of the monument's shadow to its height is:

[tex]16/64 = 1/4[/tex]

This ratio is equal to the ratio of Kyle's shadow length to his height:

[tex]x/6.25 = 1/4[/tex]

To solve for x, we can cross-multiply:

[tex]x = 6.25/4 = 1.5625[/tex]

Therefore, the length of Kyle's shadow is approximately [tex]1.56[/tex] feet (or  [tex]18.72 inches)[/tex] .

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Answer:

285°

Step-by-step explanation:

x + x + 2x + 2x + 40 + 2x + 10 = (5 - 2)180

8x + 50 = 540

8x = 490

x = 61.25

2x + 40 = 2(61.25) + 40 = 285

Answer:

Step-by-step explanation:

Interior angles in a pentagon equal 540°.

Simplify

x°,x°,2x°, (2x+40) and (2x+10) = 8x+50

Calculate x

8x + 50 = 540

8x = 540 - 50 = 490

x = 490/8

x = 61.25°

Calculate largest angle

2x + 40, where x = 61.25°

=162.5°

The radius of the cylinder is r = 13 cm

The radius of a cylinder is the radius of the circular base of the cylinder.

Since the volume of a cylinder is 15, 919.8 cm³. If the height is 30 cm, we require it radius.

Using the formula for volume of a cylinder V = πr²h where

Making r subject of the formula, we have that

r = √V/πh

Since

Substituting the values of the variables into the equation for the radius, we have that

r = √V/πh

r = √(15,919.8 cm³/[3.142 × 30 cm])

r = √(15,919.8 cm³/94.26 cm)

r = √168.8924 cm²

r = 12.995 cm

r ≅ 13 cm

So, the radius r = 13 cm

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Therefore , the solution of the given problem of area comes out to be the area of the resulting picture is therefore 28 units.

By calculating how much space would be needed to fully cover its exterior, its overall size can be calculated. The neighboring area is considered when selecting a comparable item for a rectangular design. The surface area of something determines its overall dimensions. The number of sides between a cuboid four trapezoidal curves determines how much water it can hold.

Here,

The following algorithm determines the area of a parallelogram:

=> Base area * height

We can write: given that the trapezoid RKMT has an area of 343 units2,

=>  Base(RKMT) x Height(RKMT) = Area(RKMT) = 343

All of the parallelogram's linear measurements (lengths and widths) are multiplied by 2/7 when it is dilated by a scale factor of 2/7. As a result, the expanded parallelogram's base and height will be as follows:

=>  base(dilated) equals base x (2/7)(RKMT)

=>  Height(dilated) = Height * (2/7)(RKMT)

The dilated parallelogram's size will be as follows:

=> Area(dilated) = base(dilated) x height(dilated)

=>  (2/7) x base(RKMT) x (2/7) x height(RKMT)

=>  (4/49) x Area(RKMT)

=> (4/49) x 343

=> 28

The area of the resulting picture is therefore 28 units2.

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Answer:

Step-by-step explanation:

(a) The formula to calculate the amount of money in the account after t years with an initial deposit of P and an annual interest rate r compounded annually is:

A = P(1 + r)^t

In this case, P = $500, r = 0.015 (1.5% expressed as decimal), and the interest is compounded annually, so the equation is:

A = 500(1 + 0.015)^t

Simplifying this gives:

A = 500(1.015)^t

Therefore, the equation that represents the amount of money in the savings account as a function of time in years is A = 500(1.015)^t.

(b) To find the amount of time it takes for the account balance to reach $800, we can set the equation A = 500(1.015)^t equal to 800 and solve for t:

500(1.015)^t = 800

Dividing both sides by 500:

(1.015)^t = 1.6

Taking the natural logarithm of both sides:

ln(1.015)^t = ln(1.6)

Using the power rule of logarithms:

t ln(1.015) = ln(1.6)

Dividing both sides by ln(1.015):

t = ln(1.6) / ln(1.015)

Using a calculator:

t ≈ 24.7

Therefore, it takes approximately 24.7 years for the account balance to reach $800.

Answer: 3

Step-by-step explanation:

3rd, lands on a vowel.

Answer: The spinner lands on a vowel.

Step-by-step explanation:

Probability to land on purple section: 1/10

Probability to land on letter D: 1/10

Probability to land on vowel: 3/10 (A, E, I)

Probability to land on red section: 2/10

3/10 > 2/10 > 1/10

The absolute value of inequality representing the range of John's weight is | x - 156 | ≤ 8.

An absolute value inequality is an inequality that contains an absolute value expression. The absolute value of a number represents the distance between that number and zero on a number line.

An absolute value expression is a mathematical expression that contains an absolute value function, denoted by vertical bars around a number or expression. The absolute value of a number is its distance from zero on a number line, so an absolute value expression represents a positive number, regardless of whether the original number was positive or negative.

As per the given question,

If John weighed 156 pounds give or take 8 pounds ten years ago, then his weight could have been anywhere from 156 - 8 = 148 pounds to 156 + 8 = 164 pounds.

To write this as an absolute value inequality, we can let x represent John's weight, and use the absolute value to represent the distance from the mean weight of 156 pounds. The inequality would be:

| x - 156 | ≤ 8

This inequality says that the distance between John's weight (x) and the mean weight of 156 pounds must be less than or equal to 8 pounds. In other words, John's weight must be within 8 pounds of 156, which represents the range of possible weights he could have had ten years ago.

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we have

13x+6y=−30------------- > 6y=-30-13x--------------- > y=(-30-13x)/6

x−2y=−4-- > 2y=x+4-------- > y=(x+4)/2

Using a graphing tool---------- > see attached figure

the solution of the system is the point (-2.625,0688)

the best estimate pair for the solution to the system is (−2.5, 0.75)

We have shown that KLMN has four congruent sides and opposite sides are parallel and perpendicular, which makes KLMN a square.

What is a graph?

A diagram (such as a series of one or more points, lines, line segments, curves, or areas) that represents the variation of a variable in comparison with that of one or more other variables.

To determine if KLMN is a square, we need to check if all four sides are congruent and if opposite angles are congruent.

We can find the length of each side using the distance formula:

KL = sqrt((10 - 6)^2 + (-5 - 0)^2) = sqrt(16 + 25) = sqrt(41)

LM = sqrt((5 - 10)^2 + (-9 - (-5))^2) = sqrt(25 + 16) = sqrt(41)

MN = sqrt((1 - 5)^2 + (-4 - (-9))^2) = sqrt(16 + 25) = sqrt(41)

NK = sqrt((6 - 1)^2 + (0 - (-4))^2) = sqrt(25 + 16) = sqrt(41)

So all four sides have the same length of sqrt(41), which is a necessary condition for a square.

To check if opposite angles are congruent, we can find the slope of each pair of opposite sides:

slope KL = (-5 - 0)/(10 - 6) = -5/4

slope MN = (-4 - (-9))/(1 - 5) = 5/4

slope LM = (-9 - (-5))/(5 - 10) = -4/5

slope NK = (0 - (-4))/(6 - 1) = 4/5

We can see that the slopes of KL and MN are negative reciprocals, as are the slopes of LM and NK. This means that opposite sides are parallel and perpendicular, respectively, which is another necessary condition for a square.

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We have demonstrated that KLMN is a square since it has four congruent sides and opposite sides that are parallel and perpendicular.

What is graph?

A visual representation of the variation of one variable with relation to one or more other variables, such as a collection of dots, lines, line segments, curves, or regions.

To determine if KLMN is a square, we need to check if all four sides are congruent and if opposite angles are congruent.

We can find the length of each side using the distance formula:

KL = sqrt((10 - 6)² + (-5 - 0)²) = sqrt(16 + 25) = sqrt(41)

LM = sqrt((5 - 10)² + (-9 - (-5))²) = sqrt(25 + 16) = sqrt(41)

MN = sqrt((1 - 5)² + (-4 - (-9))²) = sqrt(16 + 25) = sqrt(41)

NK = sqrt((6 - 1)² + (0 - (-4))²) = sqrt(25 + 16) = sqrt(41)

So all four sides have the same length of sqrt(41), which is a necessary condition for a square.

To check if opposite angles are congruent, we can find the slope of each pair of opposite sides:

slope KL = (-5 - 0)/(10 - 6) = -5/4

slope MN = (-4 - (-9))/(1 - 5) = 5/4

slope LM = (-9 - (-5))/(5 - 10) = -4/5

slope NK = (0 - (-4))/(6 - 1) = 4/5

We can observe that the slopes of KL, MN, LM, and NK are all negative reciprocals. Another prerequisite for a square is that the opposing sides must be parallel and perpendicular, respectively.

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In linear equation, value of expression is -5 and 0.

What in mathematics is a linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.  

                                   Equations with power 1 variables are known as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.

  -6d + 4a + 5c/5

1)

d = 1 , a = 1 , c = 3

=  -6d + 4a + 5c/5

= -6 * 1 + 4 * -1 + 5 * -3/5

= -6 -4 - 15/5

= -25/5

= -5

2)

 d = -10, a = -5 , c = -8

=    -6d + 4a + 5c/5

= -6 * -10 + 4 * -5 + 5 * -8/5

= 60 -20 - 40/5

 = 60-60/5

  = 0

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The alternative hypothesis states the presence of an association between class level and IQ score. The statement "Not all the population 1Q means are the same" is incorrect as it does not indicate any association between the two variables. A more appropriate alternative hypothesis would be "At least one of the population IQ means will be different" which suggests that the population IQ means are not all the same and there is an association between class level and IQ score.
In more technical terms, the alternative hypothesis can be expressed as:
H1: μ1 ≠ μ2 ≠ μ3 ≠ μ4

where μ

is the population mean IQ score for Seniors. This statement suggests that at least one of the population means will be different.

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The variables that the organizer can consider removing from the regression model are the Number of male visitors and Number of performance.

Based on the regression table provided, we can answer this question. The following is the regression table:Regression output table for night street fair variableNameCoefficientStandard Errort-StatP-ValueConstantb0.340.1402.430.023Number of male visitorsb10.6130.51320.750.462Number of female visitorsb10.9070.57918.830.000Number of retail standsb0.1160.0452.570.016Number of food (and beverage) standsb0.3160.0575.500.000Number of performanceb0.1460.1071.360.184The null hypothesis is rejected if p-value < 0.1; that is, there is a significant difference between the independent and dependent variables. The p-value of the Number of male visitors, the Number of female visitors, the Number of retail stands, the Number of food (and beverage) stands, and the Number of performances variables are 0.462, 0.000, 0.016, 0.000, and 0.184, respectively. As a result, the variables that are significant at the 10% level are the Number of female visitors, the Number of retail stands, and the Number of food (and beverage) stands. Therefore, the organizer should consider removing the Number of male visitors and Number of performance variables from the regression model. The variables that the organizer can consider removing from the regression model are the Number of male visitors and Number of performance.

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ABCD is a parallelogram,

a) Expression of FD in terms of m and n is equals to vector FD = ( 1/2)(m + n).

b) The value of k is equals to the 2n/(n - 2m).

According to the Parallelogram law of vector addition, if two vectors vector a and vector b represent two sides of a parallelogram in magnitude and direction, then their sum vector a + vector b = the diagonal of the parallelogram through their common point in magnitude and direction. We have a parallelogram ABCD, where vector AB

= m and vector BC = n. Point F is the midpoint of the line BD. Using the Parallelogram law, vector AB + vector BC

= vector BD = m + n

a)As we know, mid point F divides the diagonal BD into two equal parts FD, and DB. So, the expression of vector FD is

vector FD = ( 1/2) vector BD

=> vector FD = ( 1/2)(m + n)

b)Now, ADE is a straight line with AD: DE = k : 1

and vector FE = 2n - (1/2)m

vector FA = vector FD = n/2 + m/2

vector AE + vector FA = vector FE

=> vector AE = 3n/2 - m

AD : DE = k : 1 so k = 2n/(n - 2m). Hence, required value is 2n/(n - 2m).

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Complete question:

ABCD is a parallelogram where AB = m and BĆ = n В. с F is the midpoint of the line BD. a) Express FD in terms of m and n. FD = m A D E is the point such that ADE is a straight line with AD: DE = k:1 and FÈ = = 2n m b) Find the value of k. Note: Please make sure your final answer says k... Mina Minute Harian hand Question Progress.

Answer:

Were sorry! Answer is not available right now check in later.

Step-by-step explanation:

a. The exact value of the sum of -12 + 4 – 4/3 +4/9 – 4/27 +4/81 - … = -12/(1+1/3)  is 12/7.

b.The exact value of the sum of∑ (1/3)ⁿ = 6*1/3⁶(1/3¹¹-1)/(1/3-1)  is 3/2.

A.-12 + 4 – 4/3 +4/9 – 4/27 +4/81 - …

This is an infinite geometric series with first term a = -12 and common ratio r = 4/(-3). The sum of an infinite geometric series is given by:

S = a / (1 - r)

Substituting the values of a and r, we get:

S = (-12) / [1 - (4/(-3))]

Simplify the denominator by multiplying both numerator and denominator by (-3):

S = (-12) / [-3 - 4]

S = (-12) / (-7)

S = 12/7

Therefore, the exact value of the sum is 12/7.

B. 6*1/3⁶(1/3¹¹-1)/(1/3-1)

This is a geometric series with first term a = 1 and common ratio r = 1/3. The sum of a geometric series with n terms is given by:

S = a (1 - rⁿ) / (1 - r)

As n approaches infinity, rⁿ approaches zero and the sum converges to:

S = a / (1 - r)

Substituting the values of a and r, we get:

S = 1 / (1 - 1/3)

S = 3/2

Therefore, an expression that gives the exact value of the sum is 3/2.

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Step-by-step explanation:

1)561

2)5

3)40

4)90

5)3

6)500

7)200

8)100

9)5

10)50

In Python, to calculate FV (Future Value), you can use the following formula: "FV = PV * (1 + r) ^ n" Here, PV = Present Value, r = interest rate, and n = number of periods. There are different ways to implement this formula in Python, but one possible way is using a function.

Here is an example: function fv(pv, r, n): return pv * (1 + r) ** n

The function takes three arguments: pv, r, and n. Then it returns the future value computed with the formula. In your Python code, you can call the function and pass the required values. For example fv_result = fv(1000, 0.05, 10)print(fv_result)The output will be the future value of $1000 after 10 years with a 5% annual interest rate.

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The equation representing the relationship between dy/dt and dx/dt that is rate at which the length of the woman's shadow is changing is equal to option C. dy/dt =4× (dx/dt).

Woman is walking towards the street lamp.

Rate at which the length of her shadow is changing as she walks.

Let us consider the height of the street lamp as h = 20 feet.

Height of the woman be w = 5 feet.

And the distance between the woman and the street lamp be x.

Length of the woman's shadow be y.

Triangles formed by the woman, the street lamp, and their shadows are similar.

Sides of similar triangles are in proportion,

This implies,

h / y = (h + w) / (x + y)

Solving for y we get,

⇒h(x + y) = y(h + w)

⇒hx + hy = hy + wy

⇒y = hx / w

Rate at which the length of the woman's shadow is changing by differentiating both sides of this equation with respect to time,

⇒ dy/dt = h(dx/dt) / w

Substitute in the values for dx/dt = 3 ft/s, h and w we get,

⇒dy/dt = (20)(3) / 5

⇒dy/dt = 60 /5

⇒dy/dt =12

⇒dy/dt = 4(3)

⇒dy/dt =4× (dx/dt)

Therefore, the rate at which the length of the woman's shadow is changing is given by option C. dy/dt =4× (dx/dt) .

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Answer:

jwjwi7svwisg, I have y2ywgeu

Answer: To solve the equation 16=3x-7/2, you can follow these steps:

Multiply both sides of the equation by 2 to get rid of the fraction:

16 * 2 = (3x - 7/2) * 2

32 = 6x - 7

Add 7 to both sides of the equation to isolate the term with x:

32 + 7 = 6x

39 = 6x

Divide both sides of the equation by 6 to solve for x:

39 / 6 = x

6.5 = x

Therefore, the solution to the equation 16=3x-7/2 is x = 6.5.

Step-by-step explanation:

Answer:

ㅤ

ㅤㅤ [tex]\large{\blue{\star} \: {\underline{\boxed{\pmb{\tt{x = \dfrac{13}{2}}}}}}}[/tex]

ㅤ

Step-by-step explanation:

ㅤ

[tex]\large{\pmb{\tt{16 = 3x - \dfrac{7}{2}}}}[/tex]

ㅤ

[tex]\large{\pmb{\tt{\leadsto{16 + \dfrac{7}{2} = 3x}}}}[/tex]

ㅤ

[tex]\large{\pmb{\tt{\leadsto{\dfrac{2 \times 16 + 7}{2} = 3x}}}}[/tex]

ㅤ

[tex]\large{\pmb{\tt{\leadsto{\dfrac{32 + 7}{2} = 3x}}}}[/tex]

ㅤ

[tex]\large{\pmb{\tt{\leadsto{\dfrac{39}{2} = 3x}}}}[/tex]

ㅤ

[tex]\large{\pmb{\tt{\leadsto{39 = 2 \times 3x}}}}[/tex]

ㅤ

[tex]\large{\pmb{\tt{\leadsto{39 = 6x}}}}[/tex]

ㅤ

[tex]\large{\pmb{\tt{\leadsto{\dfrac{\cancel{39}}{\cancel{6}} = x}}}}[/tex]

ㅤ

[tex]\large{\purple{\boxed{\pmb{\tt{\leadsto{\dfrac{13}{2} = x}}}}}}[/tex]

ㅤ

━━━━━━━━━━━

ㅤ

[tex]\large{\underline{\underline{\sf{Verification:-}}}}[/tex]

ㅤ

• Substituting the value of (x) in the given equation,

ㅤ

[tex]\large{\pmb{\tt{\leadsto{16 = 3 \times \dfrac{13}{2} - \dfrac{7}{2}}}}}[/tex]

ㅤ

[tex]\large{\pmb{\tt{\leadsto{16 = \dfrac{39}{2} - \dfrac{7}{2}}}}}[/tex]

ㅤ

[tex]\large{\pmb{\tt{\leadsto{16 = \dfrac{39 - 7}{2}}}}}[/tex]

ㅤ

[tex]\large{\pmb{\tt{\leadsto{16 = \dfrac{\cancel{32}}{\cancel{2}}}}}}[/tex]

ㅤ

[tex]\large{\pmb{\tt{\leadsto{16 = 16}}}}[/tex]

ㅤ

As LHS = RHS,

Hence Verified

Answer: 8

Step-by-step explanation:

The sum of the interior angles in a triangle in 180.

So we can add up all the values and set it equal to 180 to find x.

4x + (5x + 5) + 103 = 180

9x + 108 = 180

9x = 72

x = 8

Answer:

x=8

Step-by-step explanation:

4x+5x+5+103=180

9x+108=180

9x=180-108

9x=72

x=72÷9

x=8

The cost of playing Ratio Rage is provided by the equation "Cost(s) of 1 expression Game: 5.5-3 RATIO RAGE!", but we don't know the value of the game's ratio.

An expression in mathematics is a collection of representations, numbers, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a mix of the two can be used as an expression. Mathematical operators include addition, subtraction, fast spread, division, and exponentiation. Expressions are often used in arithmetic, mathematic, and form. They are used in the representation of mathematical formulas, the solution of equations, and the simplification of mathematical relationships.

The equation "Cost (s) of 1 Game: 12.70 - n +9" gives the cost of playing Decimal Decisions, but we don't know the number of n, thus we can't determine the overall cost for a group of n persons.

Similarly, the cost of playing Ratio Rage is provided by the equation "Cost(s) of 1 Game: 5.5-3 RATIO RAGE!", but we don't know the value of the game's ratio.

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Answer:

x = -13/7

y = 54/7

Step-by-step explanation:

Y = 5x + 17                          Y = -2x + 4

5x + 17 = -2x + 4

7x + 17 = 4

7x = -13

x = -13/7

Not put -13/7 in for x and solve for y

y = 5(-13/7) + 17

y = 54/7

So, the answer is x = -13/7 and y = 54/7

Answer:   x = -13 / 7, y = 54/7

Step-by-step explanation:

To eliminate a variable, we can substitute y for 5x + 17

We get 5x + 17 = -2x + 4

7x = -13

x = -13 / 7

Substituting x into the 2nd equation y = 5 * -13 / 7 + 17

y = 119/7 - 65/7

y = 54/7

Answer:

10 is the answer of q u estion

the perimeter of the 3-on-3 court is 86 meters.

Why it is?

The lengths of the 3-on-3 court (perimeter only) are:

Length: 28 meters

Width: 15 meters

To calculate the length and width of the 3-on-3 court, we can use the dimensions provided by FIBA, the international basketball federation. According to FIBA, the official size of a 3-on-3 court is 15 meters in width and 28 meters in length.

The perimeter of the 3-on-3 court is the sum of all four sides, which can be calculated as follows:

Perimeter = 2 × Length + 2 × Width

Substituting the values of length and width from FIBA's dimensions, we get:

Perimeter = 2 × 28 meters + 2 × 15 meters = 56 meters + 30 meters = 86 meters

Therefore, the perimeter of the 3-on-3 court is 86 meters. It's important to note that the dimensions of the court may vary depending on the location and the level of play, so it's always a good idea to check the official regulations before setting up a court.

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Answer:

x = 6

Step-by-step explanation:

given a line parallel to a side of a triangle and it intersects the other two sides, it divides those sides proportionally , that is

[tex]\frac{x}{x+3}[/tex] = [tex]\frac{8}{12}[/tex] = [tex]\frac{2}{3}[/tex] ( cross- multiply )

3x = 2(x + 3)

3x = 2x + 6 ( subtract 2x from both sides )

x = 6

The equation for the line of best fit for the table above is y = 0.96x + 3.8. This equation can be determined by using the least squares method, which is a mathematical procedure for finding the best fit line for a given set of data points.

The determination of something is the process of making a decision or arriving at a conclusion about it. Determining something can involve a variety of methods, such as research, observation, analysis, and experimentation. It can also involve the use of deductive reasoning, inductive reasoning, intuition, and intuition combined with logic.

This method involves finding the sum of the squares of the differences between the given y-values and the corresponding y-values of the line, and then minimizing this sum by varying the slope and y-intercept of the line. In this case, the best fit line is found to have a slope of 0.96 and a y-intercept of 3.8.

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The equation for the line of best fit for the table above is y = 0.4x + 3.8.

An equation is a mathematical statement that describes the relationship between two or more variables. Equations are written using an equal sign and can be used to solve for unknown values. For example, the equation 2x + 5 = 15 can be used to solve for x; in this case, x = 5.

This equation can be determined by using the two-point form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept. The slope of the line can be determined by calculating the rise over run between the two points, which in this case is (6-5)/(7-3)
= 0.4.
The y-intercept of the line can then be determined by plugging in one of the points into the equation and solving for b,
which in this case is (5-0.4*3)
= 3.8.
Therefore, the equation for the line of best fit is y
= 0.4x + 3.8.

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If Lainey bought a set of 20 markers for $6, then the cost of one marker is $0.30.

To determine the cost of 1 marker, we need to divide the total cost of the set of markers by the number of markers in the set.

Lainey bought a set of 20 markers for $6, so the cost of the set is $6. To find the cost of 1 marker, we divide the cost of the set by the number of markers in the set:

Cost of 1 marker = Total cost of set / Number of markers in set

Cost of 1 marker = $6 / 20

Cost of 1 marker = $0.30

Therefore, the cost of 1 marker is $0.30.

In summary, to determine the cost of 1 item in a set, we divide the total cost of the set by the number of items in the set. In this case, Lainey bought a set of 20 markers for $6, so the cost of 1 marker is $0.30.

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Complete question is:

Lainey bought a set of 20 markers for $6. What is the cost of 1 marker?  

A graph of Triangle ABC after a dilation with a scale factor of 1/2 and center of dilation at D (-5, 5) is shown in the image attached below.

In Geometry, dilation is a type of transformation which typically changes the size of a geometric object, but not its shape.

Next, we would have to dilate the coordinates of the preimage by using a scale factor of 1/2 centered at the point D (-5, 5) by using this mathematical expression:

(x, y)  →  (k(x - a) + a, k(y - b) + b)

For coordinate A, we have;

Coordinate A = (1, -1)  →  (1/2(1 - (-5)) + (-5), 1/2(-1 - 5) +5)

Coordinate A = (1, -1)  →  (1/2(6) - 5, 1/2(-6) + 5)

Coordinate A' = (-2, 2).

For coordinate B, we have;

Coordinate B = (1, -3)  →  (1/2(1 - (-5)) + (-5), 1/3(-3 - 5) +5)

Coordinate B = (1, -3)  →  (1/2(6) - 5, 1/2(-8) + 5)

Coordinate B' = (-2, 1).

For coordinate C, we have;

Coordinate C = (3, -3)  →  (1/2(3 - (-5)) + (-5), 1/3(-3 - 5) +5)

Coordinate C = (3, -3)  →  (1/2(8) - 5, 1/2(-8) + 5)

Coordinate C' = (-1, 1).

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Answer:

[tex]5x {}^{3} - x + 5x + 2[/tex]

Step-by-step explanation:

Greetings!!!

So to find the sum of (f+g)(x) just simply add these two functions

Add like terms together

If you have any questions tag it on comments

Hope it helps!!!