Which graph represents a function? ​

There are √34 miles between the house and the library

The given parameters are

Distance between house and market, x = 3 miles

Distance between market and library, y = 5 miles

The number of miles between the house and the library is calculated as

Distance = √x² + y²

Substitute the known values in the above equation

So, we have

Distance = √3² + 5²

Evaluate the exponents in the above equation

So, we have

Distance = √9 + 25

Evaluate the sum in the above equation

So, we have

Distance = √34

Hence, there are √34 miles between the house and the library

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The equation to find the volume in terms of P, n, R , and T is:

[tex]V=\frac{n R T}{P}[/tex]

The ideal gas law is the general gas equation. It is a good approximation to find behavior of gases under different conditions. This law says that the product of pressure in the atmosphere and volume is equal to product of moles and temperature. We generally use an equation to define these relations.

Equation of ideal gas law

P V=n R T

where,

P = pressure measured in atmosphere

V = volume measured in liters

n = number of moles present in gas

T = temperature

R = gas constant

Ideal gas equation shows several direct and indirect variations between the different elements ,  such as in the equation pressure (P) shows direct variation with n and T , and inverse variation with volume (V).

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Explanation:

E = event space = {1}

The event space is the set of things we want to happen. There's only one outcome and it's the "1" (since it's smaller than 2)

S = sample space = {1,2,3,4,5,6}

There are 6 items in the sample space.

Divide the two counts to get the fraction 1/6 which is the probability of rolling a result less than 2. In other words, the probability of landing on "1" is 1/6 since there's one face with that label out of 6 faces total.

Side note: 1/6 = 0.1667 = 16.67% approximately

In mathematics, an inverse function is one that "reverses" another function. The inverse of the function y = 5 - 2x²  is f ⁻¹(x) = √2(−x+5)/2, −√2(−x+5)/2

The inverse function of a function f in mathematics exists a function that reverses the operation of f. If the inverse of f exists, it is shown by the f⁻¹. The inverse of f exists if and only if f exists bijective.

An inverse in mathematics is a function that "undoes" another function. In other words, if f(x) produces y, then y entered into the inverse of f produces x. An invertible function is one that has an inverse, and the inverse is represented by the symbol f ⁻¹.

Interchange the variables.

x = 5 − 2y²x = 5 - 2y²

Solving for y

y = √2(−x+5)²y = 2(-x+5)²

y = −√2(−x+5)²y = -2(-x+5)²

Replace y with f ⁻¹(x)

f ⁻¹(x)=√2(−x+5)²,−√2(−x+5)² f ⁻¹(x)=2(-x+5)²,-2(-x+5)²

The inverse of the function y = 5 - 2x²  is f ⁻¹(x) = √2(−x+5)/2, −√2(−x+5)/2.

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Answer:
x= 7+y/2

The slope is 2

Step-by-step explanation:

An expression that models the cost of each marker, when the cost of x + 2 markers is x³ + 5 x² + 2 x - 8, is x² + 3 x - 4

Given,

Total number of markers = x + 2

The total cost of markers = x³ + 5 x² + 2 x - 8

An expression to model the cost of each marker can be found by dividing the total cost of markers by the total number of markers.

This implies, the expression can be given as :

(x³ + 5 x² + 2 x - 8) / (x + 2)

               x² + 3 x - 4

          _______________

x + 2 |   x³ + 5 x² + 2 x - 8

            x³ + 2 x²

           ________________

                    3 x² + 2 x

                    3 x² + 6 x

           ________________

                             - 4 x - 8

                             - 4 x - 8

          _________________

                                       0

The quotient of this division is the expression that the cost of each marker.

Therefore, An expression that models the cost of each marker when the cost of x + 2 markers is taken into account. x³ + 5 x² + 2 x - 8, is x² + 3 x - 4

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Answer:

1/3, 2/7, and 3/10

Step-by-step explanation:

2/8 = 0.25

3/8= 0.375

1/3=0.333333

2/7=0.28571

3/10=0.3

Answer:

1.55 is the correct answer

Answer:

If you like to round 1.553 to the nearest hundredth, leaving only two numbers after the decimal point, then ask your teacher for help instead of letting yourself down. The result you'll get is 1.55

Step-by-step explanation:

Number Rounded to Nearest 100th

1.553 1.55

1.554 1.55

1.555 1.56

1.556 1.56

1.557 1.56

1.558 1.56

1.559 1.56

1.56          1.56

1.561 1.56

1.562 1.56

A triangle with an area of 108 square feet has a base length and height equal to 24 feet and 9 feet, respectively.

Given that the cross-section of the lean-to shelter is in the shape of a triangle, its area is the area of a triangle.

A = 1/2bh

where b is the length of the base

h is the height

If the base of the triangle is 6​ feet more than twice its height, then we have b = 6 + 2h.

A = 1/2bh

A = 1/2(6 + 2h)(h)

A = h^2 + 3h

If the area of the triangle is 108 square feet, then

A = h^2 + 3h

108 = h^2 + 3h

h^2 + 3h - 108 = 0

Getting the roots of the polynomial.

h^2 + 3h - 108 = 0

(h - 9)(h + 12) = 0

h = 9     ;     h = -12

Since h must be a positive number, h = 9 feet.

Substitute the value of h in the equation for b.

b = 6 + 2h

b = 6 + 2(9)

b = 6 + 18

b = 24 feet

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Based on the given values in the table that shows different speed-distance-time relationships, the value of A is 140 meters and the value of B is 3 hours.

To find the distance, the formula is:
= Speed x time

The distance of A is:

= 35 x 4

= 140 meters

To find the time taken, the formula is:
= Distance / speed

The time in B is:

= 81 / 27

= 3 hours

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Answer:

[-2,infinitysymbol)

Step-by-step explanation:

If you have a graph to look at, the domain is like you are walking up and down the x-axis (which is actually not up/down but left/right) and you're stating where this graph exists.

If you walked all the way over to -10 and looked up or down, the graph just doesn't exist over there.

The graph exists from -2, including -2, so use the SQUARE bracket [.

On the right side there's an arrow on the graph so it keeps going forever. Thats infinitysymbol.

Always wrap a parenthesis ), around the infinity symbol.

Interval notation uses the [SQUARE] brackets or (parenthesis) and even though it looks like a point, its not. It means

[FromHere, ToHere) and answers the question, where is the graph?

It should be noted that when Albert uses a grid to multiply 27 by 13, the product that will be gotten will be 351.

What isn't a product?

It should be noted that in mathematics, a product or an expression that specifies factors to be multiplied is the outcome of multiplication.

The multiplicand, multiplier, and product are the components of a multiplication sentence. The first number is the multiplicand, the second number is the multiplier, and the result is the product.

It should be noted that based on the information, we want to multiply 27 and 13. This will be illustrated thus:

= 27 × 13

= 351

Therefore, when when Albert uses a grid to multiply 27 by 13, the product that will be gotten will be 351.

Note that the information is incomplete and was solved based on the available information given.

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Based on the total cost of making hamburgers, and the cost per hamburger the equation to find the number of hamburgers made is 13,025 = 2.05x + 2,000

The cost of a single hamburger is $2.05 and this is in addition to a fixed cost of $2,000 for fixed costs.

This means that the number of hamburgers x, can be found by the formula:
Total cost of hamburgers = Cost per hamburger x Number of hamburgers + Fixed costs

Using x and the given figures gives:
13,025 = 2.05x + 2,000

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Answer:

f(x) = x + 6

Step-by-step explanation:

if the y-intercept is decreased by 3 units in the slope formula where b is the y-intercept, then the answer is x + 6

The scatter plot is shown in attached images and the line of best fit for the data set is y=24.6607x+24.7637.

The given data set is (3,100),(5,150),(7,195),(9,244),(11,296),(13,346),(15,396).

Plot the points on a coordinate plane.

Calculate the mean of the x -values and the y -values.

[tex]\begin{aligned}\bar{X}&=\frac{3+5+7+9+11+13+15}{7}\\ &=\frac{63}{7} \text{ or } 9\\ \bar{Y}&=\frac{100+150+195+244+296+346+396}{7}\\ &=\frac{1727}{7}\text{ or }246.71\end[/tex]

Now, we will calculate the [tex]\sum_{i=1}^{n}(x_{i}-\bar{X})(y_{i}-\bar{Y})[/tex] and [tex]\sum_{i=1}^{n}(x_{i}-\bar{X})^{2}[/tex], we get

[tex]\sum_{i=1}^{n}(x_{i}-\bar{X})^{2}=112[/tex]

and [tex]\sum_{i=1}^{n}(x_{i}-\bar{X})(y_{i}-\bar{Y})=2762[/tex]

Calculate the slope.

[tex]\begin{aligned}m&=\frac{\sum_{i=1}^{n}(x_{i}-\bar{X})(y_{i}-\bar{Y})}{\sum_{i=1}^{n}(x_{i}-\bar{X})}\\ &=\frac{2762}{112}\\ &=24.6607\end[/tex]

Calculate the y -intercept.

Use the formula to compute the y -intercept.

[tex]\begin{aligned}b&=\bar{Y}-m\bar{X}\\ &=246.71-(24.6607\times 9)\\ &=246.71-221.9463\\ &=24.7637\end[/tex]

Use the slope and y -intercept to form to find the equation of the line of best fit.

The slope of the line is 24.6607 and the y -intercept is 24.7637 .

Therefore, the equation is y=24.6607x+24.7637.

Draw the line on the scatter plot.

Hence, the scatter plot is shown in attached image and the line of best fit for given data set (3,100),(5,150),(7,195),(9,244),(11,296),(13,346),(15,396) is y=24.6607x+24.7637.

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The statement is true that the lines are neither perpendicular nor parallel.

The slope is the ratio of the vertical changes to the horizontal changes between two points of the line.

Slope tells how vertical a line is thus more the slope is, the more the line is vertical. When slope is zero, the line is horizontal.

The Slope of parallel lines are same, similarly Slopes of perpendicular lines are negative reciprocal of each other.

Parallel lines have the same slope beacuse the slope is like a measure of steepness and since parallel lines are of the same steepness, thus, are of the same slope.

If there are two lines perpendicular to each other, then their slopes are negative reciprocal of each other meaning if one line's slope is 'a', then its perpendicular line's slope would be -1/a

We have been given that the slope of line a is 5 and the slope of line b is 1/5.

The statement is true that the lines are neither perpendicular nor parallel.

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Answer:

x = 6

Step-by-step explanation:

multiply by 6 the whole equation to eliminate fractions and convert the coefficients and independent numbers to integers:

[tex]4x-1=3x+5[/tex]

[tex]4x-3x=5+1[/tex]

[tex]x=6[/tex]

Hope this helps

Answer:

[tex]x = 6[/tex]

Step-by-step explanation:

In the equation:

[tex] \frac{2}{3} x - \frac{1}{6} = \frac{1}{2} x + \frac{5}{6} [/tex]

Multiply both sides of the equation by the common denominator which is 6

[tex] \frac{2 \times 6}{3} x - \frac{1 \times 6}{6 } = \frac{1 \times 6}{2} x + \frac{5 \times 6}{6} [/tex]

[tex] ⟹ \frac{12}{3} x - \frac{6}{6} = \frac{6}{2} x + \frac{30}{6} [/tex]

Reduce the fraction

[tex]4x - 1 = 3x + 5[/tex]

Now, collect like terms to find the value of x

[tex]4x - 3x = 5 + 1[/tex]

Therefore:

[tex]x = 6[/tex]

Answer:

It would take 5 mechanics to repair 22 cars in 5 hours

Step-by-step explanation:

2 garage mechanics take 3 hours to repair 6 cars.

to repair 1 car, 1 garage mechanics take = (2×3)/6 = 1 hour

So In 1 hour, 1 car can be repaired by 1 mechanic

22 cars can be repaired in 1 hour by = 22/1 = 22 mechanics

22 cars can be repaired in 5 hours by = 22/5 = 4.4 = 5 mechanics

(4.4 mechanics are not possible. There should be 5 mechanics)

There is no solution for the equation 2 + √x + 5 = 4 for x ∈ R.

An extraneous solution is one that results from the process of addressing the problem but is not a legitimate solution to the problem, such as the answer to an equation.

A formula known as an equation uses the equals sign (=) to express how two expressions are equal.

Consider the equation,

2 + √x + 5 = 4

√x + 7 = 4

Subtracting 7 from each side of the equation.

√x + 7 - 7 = 4 - 7

√x = - 3

Since √f(x) cannot be negative for x ∈ R.

Hence, there is no solution for x ∈ R of the equation.

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Answer:

12 hours

Step-by-step explanation:

First, figure out her hourly rate

Next, divide 252 by the hourly rate to figure out how many hours he will have to work

Multiply the hourly rate by number of hours worked to check your answer

At a rate of $21 per hour, he has to work for 12 hours to make $252.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, Ravi made $378 for 18 hours of work.

So, Ravi's unit rate or earnings per hour is $(378/18).

= $21.

Now, In one hour he makes $21.

Therefore, To make $252 he has to work (252/21) hours.

= 12 hours.

So, Ravi has to work for 12 hours to make $252.

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A) 0.10 is not part of this interval and as such we can say that it is not a plausible estimate for the proportion of the population that is

left-handed.

B) 0.10 is part of this interval and as such we can say that it is a plausible estimate for the proportion of the population that is

left-handed.

C) 0.10 is not part of this interval and as such we can say that it is not a plausible estimate for the proportion of the population that is

left-handed.

We are given that;

Population that is left-handed = 0.10

Margin of error =0.02.

A) Confidence interval = 0.07 ± 0.02

CL = (0.05, 0.09)

0.10 is not part of this interval and as such we can say that it is not a plausible estimate for the proportion of the population that is

left-handed.

b) Confidence interval = 0.087 ± 0.02

CL = (0.067, 0.107)

0.10 is part of this interval and as such we can say that it is a plausible estimate for the proportion of the population that is

left-handed.

c) Confidence interval = 0.128 ± 0.02

CL = (0.108, 0.148)

0.1 is not part of this interval and as such we can say that it is not a plausible estimate for the proportion of the population that is

left-handed.

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Answer:

32.4! or 9 with the square root of 13!

Step-by-step explanation:

You have to add the outside numbers and keep 13 the same. Then proceed answer that getting 32.4.

Hopefully this answered your question have a nice day! :D

Answer:

16

Step-by-step explanation:

The GCF of two non-zero integers, x(16) and y(48), is the greatest positive integer m(16) that divides both x(16) and y(48) without any remainder.

Answer:16

Step-by-step explanation: i did this question on a test before

The logarithmic form of the equation is [tex]log_{3}243=5[/tex] .

We have given an equation 243 = 3⁵ .

Taking log on both sides , we get

   [tex]log(243) =log3^5[/tex]                    ..(1)

Applying the property of logarithm which is given by [tex]loga^b=bloga[/tex] in equation (1) ,we get

        [tex]log(243) =5log3[/tex]

On rearranging the above equation , we get

         [tex]\frac{log243}{log3} =5[/tex]                          ..(2)

Applying the property of logarithm which is given by [tex]log_xy=\frac{log_ay}{log_ax}[/tex]\

  [tex]\frac{log243}{log3}[/tex]   can be written as  [tex]log_{3}243[/tex] using property

Putting in equation (2) , we get

     [tex]log_{3}243=5[/tex]

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Answer:

y = 1.2x

Step-by-step explanation:

The equation that represents the proportional relationship between cans of dog food, x, and total cost, y is

y = 1.2x

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x = 4 is an equation.

We have,

Pilar:

Cost of 2 cans of dog food = $2,40

We can write this as an equation:

2 = 2.40 ____(1)

Leo:

Cost of 3 cans of dog food = $3.60

We can write this as an equation:

3 = 3.60 ____(2)

From (1) and (2) we get,

The cost of dog food y is proportional to 1.2 of the cans of dog food x.

y = 1.2x

Thus,

The equation that represents the proportional relationship between cans of dog food, x, and total cost, y is

y = 1.2x

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Answer:

It is not a function because the number 4 (input) is being used more then once

The Algebraic expression for the final cost of the item using the variable c is 0.7455c

The cost of the item is c

Algebraic expression after discounting the cost by 30%

c - 30%of c

c- 0.3c

0.7c

Now, Algebraic expression after the application of 6.5% of sales tax

0.7c + 6.5%of 0.7c

0.7c +0.065(.7c)

0.7c +0.0455c

0.74.55c

Hence, 0.7455c is the algebraic expression for the final cost of the item using the variable c.

The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values.

We learned how to express an unknown number using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables.

Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added before a variable and then multiplied by it.

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