What is the equation of the following line? Be sure to scroll down first to see all answer options. (8,2) (0, 0)​

The independent variable is the width of the dance floor (w), while the dependent variable is the area of the dance floor (A). Changes in w will affect the value of A.

The equation A = 25w describes the relationship between the area (A) of a rectangle dance floor and its width (w).

Thus, if the width of the dance floor is increased, the area of the dance floor will also increase.

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The intersection of this sphere with the -plane is (y+6)²+(z-4)²=21

The equation of a sphere centered at (h,k,l) and radius r is given by:

(x−h)²+(y−k)²+(z−l)²=r²

where x,y, and z represent the coordinates of the points on the surface of the surface.

so if the center is (-3,2,5) and radius r=4 then we can plug the values in the above formula:

consider the points  h=-3 k=2 l=5 and r=4.

(x−(-3))²+(y−2)²+(z−5)²=4²

(x+3)²+(y−2)²+(z−5)²=16.

If the sphere intersects the yz-plane then x=0

The resulting equation is an equation of a circle with a radius r=√21

and at the center with (6,-4) on the yz-plane

with yx-plane:

⇒(x−2)²+(y+6)²+(z−4)²=25

⇒ (0−2)²+(y+6)²+(z−4)²=25

⇒4+(y+6)²+(z−4)²=25

⇒(y+6)²+(z−4)²=25-4

⇒(y+6)²+(z−4)²=21

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for the functions f and g, fog is given by

fog (x) = 2 ( 2x ^2 +4x ) +3  = 4x^2 +8x+3

The equation of f(x) is  f ( x ) = 2 x+ 3 and g ( x ) = 2x^ 2+ 4x

then fog is given by

fog (x) = 2 ( 2x ^2 +4x ) +3

         = 4x^2 +8x+3

The graph of g(x) is shifted 3 units to the left. This is a horizontal translation.

For horizontal translation, we follow the following rule >>>

Let parent function be f(x), then

• f(x+a) is the parent translated "a" units left

• f(x-a) is the parent translated "a" units right for function

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The function y = e⁻ᵃ is a solution to the differential equation y' + y = 0 that satisfies the initial condition y(0) = 1.

Here we need to find a function that satisfies a differential equation and an initial condition.

The differential equation is given as

=> y' + y = 0.

To solve this differential equation, we need to find the general solution, which is a function that satisfies the equation for all values of t.

The characteristic equation for this equation is

=> m + 1 = 0,

which gives us m = -1 as the only solution.

This means that the general solution can be expressed as y = c1e⁻ᵃ, where c1 is an arbitrary constant.

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The length of side MN from triangle MNP is 30.78

Please see the attached picture below as reference of triangle MNP.

From the case, we know that:

∠M = 90°

∠P = 72°

∠N = 18°

PM = 10

To solve this problem we need to find the length of side NP first using cos formula to angle P.

Cos ∠P = PM

                 NP

Cos 72° = 10 / NP

0.309 = 10 / NP

NP = 32.36

Next, we will use the same approac to angle N:

Cos ∠N = MN

                 NP

Cos 18° = MN / 32.36

MN = 0.951 x 32.36

MN = 30.78

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Kayla -24

Leanne-18

Step-by-step explanation:

4+3=7

42÷7=6

6x4=24

3x6=18

Answer: Let's call the number of marbles that Kayla gets x. Then, Leanne gets 3x marbles. The total number of marbles that the girls receive is x + 3x = 4x, so 4x must equal 42 marbles:

4x = 42

Dividing both sides by 4:

x = 10.5

Since the number of marbles that each girl receives must be an integer, we round down to the nearest whole number. So, Kayla gets 10 marbles and Leanne gets 3 * 10 = 30 marbles.

Step-by-step explanation:

The numeric value of the exponential function at x = 7 is given as follows:

f(7) = -192.

The definition of an exponential function is given as follows:

y = ab^x

In which the parameters are defined as follows:

When x = 0, y = -1.5, hence the parameter a is given as follows:

y = -1.5.

When x = 2, y = -6, hence the parameter b is obtained as follows:

-1.5b² = -6

b² = 4.

b = 2.

Hence the function is defined as follows:

y = -1.5(2)^x.

Hence the numeric value at x = 7 is given as follows:

y = -1.5(2)^7

y = -192.

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After three days Thurber will have studied the same total amount of time for both math and science and the time is 165 minutes for both.

Given data :

Today,  he studies 15 minutes math and 75 minutes science and from now on, 50 minutes math and 30 minutes science. So if he studies for 1 day total time for math and  science will be:

Math = 15 + 50 = 65

Science = 75 + 30 = 105

2nd day:  

Math = 65 + 50 = 115

Science = 105 + 30 = 135

3rd day:  

Math = 115 + 50 = 165

Science = 135 + 30 = 165

So, after three days Thurber will have studied the same total amount of time for both math and science and the time is 165 minutes for both.

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Answer:

Each child gets $36666.67, each grandchild gets $18333.33

Step-by-step explanation:

220000/6= 36666.67,

36666.67/2= 18333.33

Answer:

  {-√6, -1, 1, √6}

Step-by-step explanation:

You want the roots of the quartic 3x^4-21x^2+18.

We can find the roots by factoring to linear factors:

  = 3(x^4 -7x^2 +6)

  = 3(x^2 -6)(x^2 -1) . . . . . . . 6 = (-1)(-6) are factors with a sum of -7

  = 3(x -√6)(x +√6)(x -1)(x +1) . . . . . a^2 -b^2 = (a -b)(a +b)

The roots of the quartic are ±√6 and ±1.

The system of equations are 7x + 5y = 200 and 5x + y = 112. The cost of each t shirt is $20 while the cost of each pants is $12.

An equation is an expression showing the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on depending on the degree.

Let x represent the cost of each t shirt and y represent the cost of each pants.

The shopper purchased 7 t shirts and 5 pairs of pants for $200, hence:

7x + 5y = 200    (1)

Also, he purchased 5 t-shirts and one pair of pants for $112, hence:

5x + y = 112     (2)

Solving the two equations simultaneously gives:

x = 20, y = 12

The system of equations are 7x + 5y = 200 and 5x + y = 112

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To solve this we would divide the pirce of the soups by their container ounces

$2.38÷14=$.17 per ounce

$5.28÷30=$.176 per ounce

We do not use a thrid decmal place when talking about money so we would round $.176 (since the third decmial place is greater than or equal to 5) up to $.18

Therefore Two 14 ounce containers of soup is a better deal per ounce.

Based on the scatterplot, 50 beats per minute is the best prediction of the resting heart rate, in beats per minute, of a person who exercises an average of ​​​​​​​8 hours each week.

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The required point of intersection of the two lines is (-2, 7/3).

The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.

The equation "y = 2/3x + 3" represents a line in the coordinate plane. It has a slope of 2/3 and a y-intercept 3. The equation "x = -2" represents a vertical line. It has no slope and the x-coordinate of all its points is -2.

Since the two equations represent lines, we can find their point of intersection by setting the two equations equal to each other and solving for y.

So, we have:

2/3x + 3 = y

and

x = -2

Substituting x = -2 into the first equation, we get:

2/3(-2) + 3 = y

Solving for y:

y = -2/3 * -2 + 3 = 4/3 + 3 = 7/3

Thus, the point of intersection of the two lines is (-2, 7/3).

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Answer:

Step-by-step explanation:

Ln means log to the base e and 3x+1 is an exponent

So the answer is:

4 = e^(3x+1).

The triangle PQR is an equilateral triangle

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

PQ=QR.

m/P = (2x - 26) and m/R= (x+17)

When two sides of a triangle are congruent, then the triangle is an isosceles triangle

Using the above as a guide, we have the following:

2x - 26 = x + 17 --- base angles of an isosceles triangle

So, we have

x = 43

This gives

m/P = 2 * 43 - 26 = 60

m/R= 43 + 17 = 60

If two angles of a triangle measure 60 degrees, then the third angle is 60 degrees

This implies that the triangle is an equilateral triangle

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The measure of the angle Q is 46.4°

Recall that the sum of the angles of a triangle is equal to 180 degrees

We are told that

PQ = QR

Q = 100°

As PQ and QR are equal so,

By theorem angle opposite to equal sides are equal so,

We can say that angle P = angle R = X

Therefore by angle sum  property of the triangle,

angle P + angle Q + angle R = 180°

X +(2x - 26)+ (2x - 26) = 180°

This implies that 5x-52=180

Collecting like terms

5x=180+52

5X = 232°

X =46.4°

Therefore the measure of R = 40°

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Answer:6

Step-by-step explanation:

Let the number be x.

Now, 3x+6=24

3x=24-6

3x=18

x=18/3

x=6

Answer:

6

Step-by-step explanation:

We can work the problem backwards

Since something gives 24 that means it equals 24

= 24

Something increased by 6, so something added by 6

Something + 6 = 24

Making something = x

x + 6 = 24

If we subtract 6 from both sides

x = 18

Trice a number, so divide this number by 3

x = 6

Trice of 6 is 18... 18 increased by 6 gives 24

The two numbers which could be used for two in function are 5/2 and - 3.

The definition of a function is a "well-behaved" relation is one in which, given a starting point, we know the exact one ending spot to go to; given an x-value, we get only and precisely one corresponding y-value. Because functions pair information, they are all relations, but not all relations are functions. A subset of all of your relations are well-behaved family members, just as all mathematical relations are well-behaved functions.)

Given f(x)=x²+x

and f(2t)=30

When x = 2t, x²+x = 30

Substitute the value of x in function

(2t)²+2t = 30

4t² + 2t = 30

2(2t² + t) = 30

2t² + t = 15

2t² + 3t - 5t - 15 = 0

2t(t +3) - 5(t + 3)

(2t - 5)(t + 3)

t = 5/2

t = -3

Thus, The two numbers which could be used for two in function are 5/2 and - 3.

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Fill the 3-gallon jug all the way.

Pour those 3 gallons of water into the 5-gallon jug.

Fill the 3-gallon jug all the way again, and pour as much as it takes to fill the 5-gallon jug (which is 2 gallons).

Now you have 5 gallons in the 5-gallon jug and 1 gallon in the 3-gallon jug.

Empty the 5-gallon jug.

Pour the 1 gallon in the 3-gallon jug into the 5-gallon jug.

Now fill the 3-gallon jug all the way, and pour all 3 gallons into the 5-gallon jug, which, added to the 1 gallon already in there, and leaves you with exactly 4 gallons.

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Fill the 3-gallon jug all the way.

Pour those 3 gallons of water into the 5-gallon jug.

Fill the 3-gallon jug all the way again, and pour as much as it takes to fill the 5-gallon jug (which is 2 gallons).

Now you have 5 gallons in the 5-gallon jug and 1 gallon in the 3-gallon jug.

Empty the 5-gallon jug.

Pour the 1 gallon in the 3-gallon jug into the 5-gallon jug.

Now fill the 3-gallon jug all the way, and pour all 3 gallons into the 5-gallon jug, which, added to the 1-gallon already in there, leaves you with exactly 4 gallons.

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The two different expressions for the total cost will be written as:-

C = 2S x 1.065

C = 0.13S + 2S

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that Benita buys 2 shirts for the same price, s. The sales tax rate is 6.5%.

The two expressions for the total cost of the two shirts will be:-

C = 2S x ( 1 + 0.065)

C = 2S x ( 1.065)

The second way of writing the expression is:-

C = 2S x  0.065 + 2S

C = 0.13S + 2S

Hence, the expressions are C = 2S x 1.065 and C = 0.13S + 2S.

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Factoring, utilizing square roots, completing the square, and the quadratic formula are the four ways to solve a quadratic equations.

An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax² + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term. First, there must be a term other than zero in the coefficient of x² (a ≠ 0) for an equation to be a quadratic equation. The x² term is written first when constructing a quadratic equation in standard form, then the x term, and finally the constant term. The numerical values of a, b, and c are often expressed as integral values rather than fractions or decimals.

Factoring, utilizing square roots, completing the square, and the quadratic formula are the four ways to solve a quadratic problem.

To factor an equation with quadratic terms:

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From least to greatest; Elliot, Jeanette, Lucy.

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.

Elliot = 45/54 x 100%

Lucy = 88%

Jeanette = 38/44 x 100%

Elliot = 83%

Lucy = 88%

Jeanette = 86%

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Answer: Plugging in the values x=2, y=3, and z=4 into the expression x(2y+z)², we get:

2(2(3)+4)² = 2(10)² = 2 * 100 = 200

So the expression evaluates to 200.

Step-by-step explanation:

The number of children and adult that were there are 117 aand 178 respectively.

Two hundred ninety-five people go to the public swimming pool on a hot summer day. The daily prices are 1.75 for children and 2.00 for adults. The recipients admission total of 560.75 dollars.

The number of children and adult can be calculated as follows;

Using equations,

let

x = number of children

y = number of adult

Therefore,

x + y = 295

1.75x + 2y = 560.75

multiply equation(i) by 2

2x + 2y = 590

1.75x + 2y = 560.75

subtract the equation

0.25 x = 29.25

x = 29.25 / 0.25

x = 117

Hence,

y = 295 - 117

y = 178

Therefore,

number of children = 117

number of adult = 178

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The volume of the rectangular prism given the length, width and height is 6 14/27 cubic feet.

The correct answer choice is option B

Volume of a rectangular prism= length × width × height

Length= 1 5/6 ft

Width = 1 1/3 ft

Height = 2 2/3 ft

Volume of a rectangular prism= length × width × height

= 1 5/6 × 1 1/3 × 2 2/3

= 11/6 × 4/3 × 8/3

= (11 × 4 × 8) / (6 × 3 × 3)

= 352 / 54

= 6 28/54

= 6 14/27 cubic feet

In conclusion, the volume of the rectangular prism is 6 14/27 cubic feet

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The statement about Raj's data sets which true is The average boy plays 8.5 hours more per week than the average girl.

Technically, a dataset is a collection of related items that can be accessed individually or in certain management combinations as a single unit. Datasets can be organized into several types of data structures. Examples of dataset in the business world can be seen from names, salaries, employee contact information, to sales figures, and so on.

In conclusion, a dataset is a collection of data that is ordered and obtained from a collection of information. The collection of information itself is obtained from observation, measurement, study, or analysis to become data. Data can be facts, numbers, names, or even descriptions. Therefore, datasets are closely related to data mining activities which help data scientists analyze data into coherent information.

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The family would more likely choose the stock option, if the period of investment is 20 years,after calculating the simple & compound interest.

$999.60 is 1.02 times $980, and $1,019.59 is 1.02 times $999.60.

They may choose bonds or savings account depending on the assumptions they make about the time frame of the investment.

The value of the bonds b=1,000+20x and value of the stocks is s=980⋅(1.02)x , where x is the number of years since the investment were made.

For 10 years, the value of the bond will be

b=1,000+200=1,200 dollars.

The value of the stock will be s=980⋅(1.02)10≈1,195 dollars.

They should choose the bond option if the period of investment is 10 years.

For 20 years, the value of the bond will be

b=1000+400=1,400 dollars.

The value of the stock will be 980⋅(1.02)20=1,456980⋅(1.02)20=1,456 dollars.

So they choose the stock option, if the period of investment is 20 years.

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The complete question is attached below.

If the of respondents are identified as 1 for "yes" and 2 for "no" and 3 for "maybe" and 4 for "anything else" then , the data are considered at the nominal level of measurement .

The Level Of Measurement of a data set refers to the type of values that a variable can take and the properties that these values have.

In the survey , the respondents are identified as 1 for "yes," 2 for "no," 3 for "maybe," and 4 for "anything else."

These values are categorical, meaning they are names or labels for different categories. The data collected at this level is referred to as nominal level of measurement. This level of measurement is used when the variables are categorical and the order of the categories does not matter.

Therefore , the data collected in this survey is nominal and is used to describe categories or names, rather than numerical values.

The given question is incomplete , the complete question is

In a survey, the of respondents are identified as 1 for "yes" and 2 for "no" and 3 for "maybe" and 4 for "anything else" . the average (mean) is calculated for 665 respondents and the result is 1.5 ,

the data are at what level of measurement ?

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Answer:

brooooooooooo I got x=0

Given equation is a first-order nonlinear ordinary differential equation (ODE): y' - (x + y - 1)^2 = 0

What is differential equation ?

A differential equation is an equation that contains at least one derivative of an unknown function, either a normal differential equation or a partial differential equation.

This equation can be solved using various methods, such as numerical methods or analytical methods like the implicit function theorem or the method of characteristics. However, finding an exact solution can be challenging and may not always be possible.

If you would like to find an approximate solution to this ODE, you could use numerical methods such as Euler's method, Runge-Kutta method, or the finite difference method. These methods can provide a numerical approximation to the solution for a given range of x and a specified initial condition.

The given equation is a first-order nonlinear ordinary differential equation (ODE):

y' - (x + y - 1)^2 = 0

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