Elena's distance and times for a training run are given by the equation y=8.5x, where x represents distance in miles and y represents time in minutes

The values of of the functions f(x)=3x+2 and g(x)=x²-x are: (14) 14, (15) 26, (16) -4, (17) 2, (18)12, (19) 42 (20)7, (21)2, (22)2, (23)5 (24) 3x+5 (25) 9b²-3b

We should know that in each of the functions, we have to substitute the given values

The given functions are

f(x)=3x+2

g(x)=x²-x

(14) f(x)=3x+2

Substitute for x

f(4)=3*4+2

f(x)=12+2=14

(15) f(8)=3x+2

f(8)=3*8+2

Substitute for x

f(x)=24+2 = 26

(16) f(-2)=3*-2+2

Substitute for x

f(-2)=-6+2

f(x)=-4

(17) g(2)=2²-2

Substitute for x

g(x)=4-2

g(x)=2

(18) g(-3)=3²-(-3)

Substitute for x

g(x)=9+3 = 12

(19)g(-6)=-6²-(-6)

g(x)=36+6 = 42

(20) f(2)+1

Substitute for x

=2*3+1

=6+1

=7

(21)  f(1)-1

3*1-1 = 2

(22) g(2) -2

2²-2

4-2=2

23 = g(-1)+4

-1²+4

1+5=5

(24) f(x+1)

Substitute for x

= 3(x+1)+2

=3x+3+2

=3x+5

(25) g(3b)

Substitute for x

=(3b)²-3b

9b²-3b

In conclusion, the values of the values of of the functions f(x)=3x+2 and g(x)=x²-x are: (14) 14, (15) 26, (16) -4, (17) 2, (18)12, (19) 42 (20)7, (21)2, (22)2, (23)5 (24) 3x+5 (25) 9b²-3b

Learn more about substitution of https://brainly.com/question/10423146

#SPJ1

For 10 days that bag will last when Mr. Eder's buys 6 pound bag of dog food, using kg to pound conversion and simple basic arithmetic operation.

How to convert kg to pound ?

We know that 1 Kg = 2.20 pound.

The dog is to eat 1/4 * 2.20 = 0.55 pound food

Weight of bag brought by him = 6 pound

The basic operations are :

Addition : (+) To get sum of two or more values

e.g. a = 3, b = 5

Addition = 3+5

              = 8

Subtraction : (-) The result of subtraction is the “difference”

e.g. Subtraction of a and b = a-b

                                             = 3-5

                                            = -2.

Multiplication : (*) The result of multiplication is the “product”

e.g. Multiplication of a and b = 3*4

                                                = 12

Division : (/) The result of division is the “quotient”

e.g. Division of 4 and 2 is = 4/2

                                           = 2.

so, the number of days bag can be used = 6/0.55

                                                                     = 10.90

So, the bag can be used for complete 10 days.

Learn more about arithmetic operation using link:

https://brainly.com/question/13181427

#SPJ1

If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle. Explanation is given.

Lines that cross the angle under investigation are known as angle bisectors. To "bisect" is to split into two sections of equal size. Therefore, the bisected halves divide the considered angle in half.

According to the angle bisector theorem;

An angle bisector divides the opposing side of a triangle into two portions that are proportionate to the other two sides, according to the angle bisector theorem.

a point is equally far from both sides of an angle if it is on the angle's bisector.

According to the inverse of the angle bisector theorem, a point is on the angle's bisector if it is both in the interior of the angle and equally far from its sides.

The explanation with diagram is given in the image.

Therefore, If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle.

Learn more about angle bisector here;

https://brainly.com/question/12896755

#SPJ1

The equation of the line is 3y = -4x + 18 and the Graph can draw as given in the picture.

The slope-intercept form a line is given by  

where m is the slope of a line and c is the y-intercept.

Here we use the Slope intercept form to find the line of the equation by using the equation we will draw the graph of the line

Here we have

Slope of line = -4/3

The point of the line

As we know y = mx + c is the line Here m is the slope of the line

From the given data, m = -4/3

=> y = (-4/3)x + c

=> 3y = -4x + 3c

Given that the point on the line is (-6, 2)

=> 3(2) = -4(-6) + 3c

=> 6 = 24 + 3c

=>  3c = 18

=> c = 6

Therefore,

The equation of the line is 3y = -4x + 18 and the Graph can draw as given in the picture.

Learn more about the Slope intercept form at

https://brainly.com/question/29146348

#SPJ1

yes, z can lie between x and y but z can also lie on another side of x in Number lines.

With an example, define number line?

Number lines in mathematics are horizontal straight lines on which numbers are arranged in equal intervals.

                  A number line can be used to visualize all the numbers in a succession. The endpoints of this line go on forever.

What does the math number line mean?

A horizontal line with uniformly spaced numerical increments is called a number line. How the number on the line can be answered will depend on the numbers that are provided.

                               How a number is used—for example, to plot a point—depends on the question that goes with it.

Learn more about  number line

brainly.com/question/13425491

#SPJ4

The value of the variable x is -2

An algebraic expression can be defined as an expression made up of terms, variables, coefficient, factors and constants.

These expressions are also made up of arithmetic or mathematical operations, which includes;

From the information given, we have;

2 ^ (x + 3) * 3 ^ (x + 4) = 18

Now, let's find the factors of 18 in 2's and 3's, we have;

2 ^ (x + 3) * 3 ^ (x + 4) = 2^1 × 3^ 2

Collect the common factors, we get;

x+ 3 + x + 4 = 1 + 2

collect like terms

2x = 3 - 7

2x = -4

make 'x' the subject of formula

x = - 2

Hence, the value is -2

Learn more about algebraic expressions here:

https://brainly.com/question/4344214

#SPJ1

Santiago creates a playlist of Latin dance music. The playlist contains bachata, salsa, and mambo tracks, as shown in the table. Santiago puts the playlist on shuffle mode. What is the probability that the first track he hears is a salsa track?

Answer:8/20

Step-by-step explanation:i did the quiz and it is correct

Answer:

[tex]51.4^{\circ}[/tex]

Step-by-step explanation:

Since this is a right triangle, the cosine formula says

[tex]\cos(x) = \dfrac{5.3}{8.5}[/tex]

[tex]\longrightarrow cos(x) = 0.6235[/tex]

[tex]So\\\\x = \cos^{-1}(0.6235) = 51.4256^{\circ}[/tex]

Rounded to the nearest tenth this would be
[tex]51.4^{\circ}[/tex]

The perimeter of the object is the sum of the lengths of all the sides

which is 302 units.

Perimeter is the sum of the lengths of all the sides of a planar two-dimensional figure.

In the case of a circle, we call it perimeter circumference it is the distance around the circle.

Given, A figure has side lengths EF = 71, FD = 80, ED = 74, IG = 40, and

HG = 37.

Now the perimeter of this figure is the sum of the lengths of all the sides which is,

= (EF + FD + ED + IG + HG).

= (71 + 80 + 74 + 40 + 37).

= 302 units.

learn more about perimeter here :

https://brainly.com/question/6465134

#SPJ1

the value of y is 3 when the value of x is 8.

what is proportional relationship?

When two variables are correlated in a manner that their ratios are equal, this is known as a proportional relationship. In a proportional connection, one variable is always a constant value multiplied by the other, which is another way to think of them. The "constant of proportionality" is the term used to describe that constant.

Given x and y will have a proportional relationship if the ratio of x to y will be equal for all given values.

Given y is inversely proportional to x

When x=3, y=1/x = 8

So when x = 8 the value of y =3

Hence the value of y is 3 when the value of x is 8.

Learn more about proportional relationship , by the following link.

brainly.com/question/12242745

#SPJ1

0.117 Or 11.7% chance of n should the player choose in order to maximize the probability of winning a prize.

The probability of precisely x successes on n further trials in an experiment with two potential outcomes is referred to as the binomial probability (commonly called a binomial experiment).

When a procedure is performed a certain number of times (for example, in a group of patients), the result for each patient can either be a success or a failure, the binomial distribution model enables us to calculate the probability of witnessing a defined number of "successes."

The probability of winning a prize remains the same for. n = 10 or n=20 or n = 100; the probabilities are the same.

Given that,

p = 0.5, So, q = 1 - 0.5 = 0.5.

If 70% of 'n' games are won then 30% of n games must be lost.

Let n = 10.

Therefore, P ( x = 3) = [tex]^{10}C_3p^7q^3[/tex]

or, P ( x = 3) = [tex]^{10}C_3(0.5)^7(0.5)^3[/tex]

or, P (x = 3) = 120×0.0078×0.125.

or, P (x = 3) = 0.117 Or 11.7% chance.

Now, Changing the value won't have any effect as all the 'n's are multiple of 10 and we'll have same probability.

To know more about probability refer to:

https://brainly.com/question/15557838

#SPJ1

The total amount that Mikaela spent on the paddleboard will be  $449.80.

The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.

The percentage is also called the indicating hundredths.

As per the given,

Original price = $699

The selling price = $699 - 40% of $699

⇒ $699 - 0.40 x $699 = $419.4

The state tax (assuming it applied to the selling price) will be as,

7.25% of $419.4 = (7.25/100) x 419.4 = $30.4065

Final amount = $419.4 + $30.4065 = $449.80

Hence "Mikaela will have spent $449.80 in total on the paddleboard".

For more about the percentage,

brainly.com/question/13450942

#SPJ1

Solving this equation gives us a half-life of approximately 1.36 years. Rounded to two decimal places, the half-life of this substance is 1.36 years.

The half-life of a substance is the amount of time it takes for half of the atoms in a sample of the substance to decay.

To find the half-life, you can use the following formula:

half-life = (time) * ln(2) / ln(initial mass / final mass)

half-life = (1 year) * ln(2) / ln(32 mg / 25.5 mg)

Solving this equation gives us a half-life of approximately 1.36 years.

To learn more about half-life visit:

https://brainly.com/question/24710827

#SPJ4

Answer:

find my dad

Step-by-step explanation:

Answer:

y = 1/4x - 4

Step-by-step explanation:

4x + y = 3

y = -4x + 3

Perpendicular slope = 1/4

y = 1/4x + b

-3 = 1/4(4) + b

-3 = 1 + b

b = -4

y = 1/4x - 4

Answer:

f^-1(x) = 2(x-2)^2 + 1

f^-1(x) = (x+3)^3

Step-by-step explanation:

The inverse of a function is found by switching the roles of the dependent and independent variables. In other words, we can find the inverse of a function by interchanging the x and y values in the equation. So, the inverse of the function f(x) = 2(x-2)^2 + 1 can be written as f^-1(x) = 2(x-2)^2 + 1.

1. To find the inverse function explicitly, we can use the following steps:

2. Replace f(x) with y in the original function to obtain y = 2(x-2)^2 + 1.

3. Solve for x in terms of y to obtain x = +/- sqrt((y-1)/2) + 2.

The inverse function f^-1(x) can then be written as f^-1(x) = +/- sqrt((x-1)/2) + 2.

Note that this inverse function is not a one-to-one function, because for some values of x (namely, x < 1), the function has two possible values of y (i.e. it has two solutions). Therefore, the inverse function is not a function in the strict mathematical sense, but it is still a useful concept in certain contexts.

To find the inverse of a function, we switch the roles of the dependent and independent variables, so the inverse function can be written as x = ^3√y-3.

1. To find the inverse function explicitly, we can use the following steps:

2. Replace y with x in the original function to obtain x = ^3√y-3.

3. Solve for y in terms of x to obtain y = (x+3)^3.

The inverse function can then be written as f^-1(x) = (x+3)^3.

Note that this inverse function is a one-to-one function, meaning that for every value of x, there is only one corresponding value of y. Therefore, the inverse function is a function in the strict mathematical sense.

Answer:

(sqrt3)/2

Step-by-step explanation:

Sin(x)=opposite/hypotenuse

30, 60, 90 right triangle.

ratio of sides are 1, sqrt3, and 2.

Locate the 60 degree angle on the triangle

The opposite side is sqrt3

The hypotenuse is 2

so its (sqrt3)/2

Answer:

√3/2 or 0.866

Step-by-step explanation:

The length of the line segment with endpoints P(2, 1, -4) and Q(-1, 5, 3) is 8.60 units

To find the length of a line segment with endpoints P(x1, y1, z1) and Q(x2, y2, z2) in three-dimensional space, we can use the distance formula:

length = √((x2 - x1)² + (y2 - y1)² + (z2 - z1)²)

Substituting the coordinates of P and Q into the formula, we get:

length = √((-1 - 2))²  + (5 - 1))²  + (3 - (-4)))² )

          = √((-3))²  + (4))²  + (7))² )

         = √(9 + 16 + 49)

         = √(74)

        = 8.60 units

Therefore, the length of the line segment is 8.60 units

Learn more about the length of line segment on:

brainly.com/question/17704491

#SPJ1

Answer:

D

Step-by-step explanation:

multiply by 8 and add 5.

so,

we need to do this for every unit value and see, if the result is the same as the listed output value.

5 -> 5×8 + 5 = 45

6 -> 6×8 + 5 = 53

7 -> 7×8 + 5 = 61

8 - > 8×8 + 5 = 69

9 -> 9×8 + 5 = 77

10 -> 10×8 + 5 = 85

so, D is the correct answer.

The probability of men whose height falls between 70 and 73 inches is  0.273. Therefore, the percent of men whose height falls between 70 and 73 inches is 27.3%. Therefore, the solution is 27.3%.

The standard deviation is a quantity that reveals how much variance from the mean there is, including spread, dispersion, and spread. A "typical" variation from the mean is shown by the standard deviation. Because it uses the data set's original units of measurement, it is a well-liked measure of variability.

We are informed that the heights of men in the U.S are normally distributed with a mean of 70 inches and a standard deviation of 3 inches. We need to determine the percent of men whose height falls between 70 and 73 inches. We would first evaluate the probability that the height of a randomly selected individual would fall between 70 and 73 inches;

This can be done in stat-crunch;

Click Stat, highlight on Calculators then click Normal

In the pop-up window that appears click Between

Enter the given values of mean and standard deviation; 70 and 3 respectively

Enter the values 70 and 73 in the next set of boxes in that order

Finally, click on compute;

Stat-Crunch returns a probability of 0.273. Therefore, the percent of men whose height falls between 70 and 73 inches is 27.3%. Therefore, the solution is 27.3%.

To know more about Standard Deviation refer to:

brainly.com/question/23907081

#SPJ4

When she uses 5 bags of coffee every day at her café, half of a bag of coffee lasts for 10 days.

Multiplication is the inverse of division. If 3 groups of 4 add up to 12, 12 split into 3 equal groups adds up to 4 in each group in division. The basic purpose of splitting is to determine how many equal groups develop or how many people are in each group when distributing equally. Division is a basic operation that divides an integer. It's best to imagine of it as a group of things being distributed among a group of individuals, as in the preceding example.

Here,

number of bags needed in a day=5

number of days 1/2 bag last,

=5÷1/2

=10 days

Half of bag of coffee last for 10 days when she uses 5 bags of coffee every day in her café.

To know more about division,

https://brainly.com/question/28598725

#SPJ1

Answer:  BD = 5

Step-by-step explanation:

[tex]a^{2} +12^{2} =13^{2}[/tex]

[tex]a^{2} =13^{2}-12^{2}[/tex]

[tex]a = \sqrt{25}[/tex]

[tex]a = 5[/tex]

Therefore BD = 5

Answer:

A and D

Step-by-step explanation:

so sorry im in school

x+y=4

 -y.  -y

x=4-y

4-y-y=2

4-2y=2

-4      -4

-2y= -2

/-2.   /-2

y=1

x+1=4

  -1 -1

x=3

so A and D is correct

Answer:

Below

Step-by-step explanation:

m = slope = rise / run

m = 5 for this equation

rise /run = 5

15 / run = 5

run = 3

The graph of the function f(x) = x(x - 5)(x - 3) is given by the image shown at the end of the answer.

To draw the sketch of the graph, we need to consider these three following features:

The function in this problem is defined as follows:

f(x) = x(x - 5)(x - 3).

From the factor theorem, the x-intercepts are taken from the linear factors, as follows:

The y-intercept is the value of y when the graph of the function crosses the y-axis, that is, the value of y when x = 0, hence:

f(0) = 0(0 - 5)(0  -3) = 0.

In the problem, we have a cube function, hence:

More can be learned about functions at https://brainly.com/question/24808124

#SPJ1

Answer:

1/64

Step-by-step explanation:

1/8 x 1/8 = 1/64

The correct option regarding the correlation coefficient of the data-set is given as follows:

C. As budgets increased, the gross revenue increased; r = 0.62.

The correlation coefficient is an index between -1 and 1 that measures the relationship between two variables, as follows:

The coefficient is obtained with a correlation coefficient calculator, inserting the points of the data-set into the calculator.

From the table given by the image, the points are given as follows:

(0.3, 2.05), (0.25, 0.39), (0.2, 1.35), (0.2, 1.24), (0.2, 0.63), (0.18, 0.79), (0.18, 0.53), (0.18, 0.35).

Inserting these points into a calculator, the value of the coefficient is given as follows:

r = 0.62.

Meaning that there is a positive relation amount the variables, and option C is correct.

Option D would be correct if 0.62 was the slope of the line of best fit, hence this is not the case.

More can be learned about correlation coefficients at brainly.com/question/16355498

#SPJ1

Answer:

answer is attached.

Step-by-step explanation:

The length of the other leg of the triangle is 11.7 inches

Now, According to the question:

We have the right triangle

The length of the right triangle is 24 inches

The length of the hypotenuse is 26.7 inches

To find the length of the other leg of the triangle

We know that the Pythagorean theorem.

The Pythagorean theorem states that the sum of the squares of the two legs is equal to the hypotenuse squared.

Let the length of the other leg of the triangle be 'x'

According to the information:

[tex]24^2 + x^2 = 26.7^2[/tex]

576 + [tex]x^{2}[/tex] = 712.89

[tex]x^{2}[/tex] = 712.89 - 576

[tex]x^{2}[/tex] = 136.89

x = [tex]\sqrt{136.89}[/tex]

x = 11.7

Hence, The length of the other leg of the triangle is 11.7 inches.

Learn more about Pythagorean Theorem at:

https://brainly.com/question/343682

#SPJ4

Observing the provided figure and using the transformation rule of geometry, The required transformation to map figure H onto figure I is reflection along y=x axis.

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

In a mirror line, reflection is a type of transformation that reverses the shape so that each point is at the same distance from the mirror line as its reflected point.

Figure H

Mapped onto figure I

The required transformation:

reflection along y=x.

To learn more about transformations visit:

https://brainly.com/question/11709244

#SPJ1

Answer:

The cake cost $6.00

Step-by-step explanation:

Let c = the cost of the cake

Let t =  the cost of the tea

c = 2t

c + 5t = 21  Substitute 2t for c

2t + 5t = 21  Combine like terms

7t = 21  Divide both sides by 7

[tex]\frac{7t}{7}[/tex] = [tex]\frac{21}{7}[/tex]

t = 3  

A cup of tea costs $3.00

c = 2t  Substitute 3 for t

c = 2(3)

c = 6

A cake costs $6.00

Answer:

Cake: £6

Step-by-step explanation:

1c = 2t             Eq. 1

1c + 5t = 21      Eq. 2

c = cost of a cake

t = cost of a cup of tea

Replacing Eq. 1 in Eq 2:

2t + 5t = 21

7t = 21

t = 21/7

t = 3

From Eq. 1:

c = 2t

c = 2*3

c = 6

Check:

From Eq. 2:

c + 5t = 21

6 + 5*3 = 21

6 + 15 = 21