Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume the variable is positive.)

Answer:

Step-by-step explanation:

Given: [tex]f(x) = 7x^{2} -10x+10[/tex]

To find: Range of the function

To find the range of the function, write the quadratic equation in the form of vertex form of parabola, that is:

[tex]f(x) = a(x-h)^{2} +k[/tex]

If a > 0, range of the function of [k, ∞)

[tex]f(x) = 7x^{2} -10x+10=7(x^{2} -\frac{10}{7} x+\frac{10}{7} )[/tex]

[tex]f(x) = 7(x-\frac{5}{7} )^{2} +\frac{45}{7}[/tex]

by comparing this expression with the vertex form of parabola, we can say that the range of the function is [[tex]\frac{45}{7}[/tex], ∞)

The range of the quadratic function f(x) = 7x2 – 10x + 10 is {y | y ≥ 315/49}.

The range of a quadratic function is the set of all possible values that the function can take on. To find the range of the given quadratic function f(x) = 7x2 – 10x + 10, we need to find the vertex of the function, which is the point at which the function reaches its maximum or minimum value.

The x-coordinate of the vertex of a quadratic function is given by:
x = -b/(2a)

Where a and b are the coefficients of the quadratic term and the linear term, respectively. In this case, a = 7 and b = -10, so:
x = -(-10)/(2*7) = 10/14 = 5/7

Now, we can plug this value of x back into the function to find the y-coordinate of the vertex:
y = 7(5/7)2 – 10(5/7) + 10 = 175/49 – 50/7 + 10 = 175/49 – 350/49 + 490/49 = 315/49

So the vertex of the function is at the point (5/7, 315/49).

Since the coefficient of the quadratic term is positive, the function opens upwards, and the vertex is the minimum point of the function. Therefore, the range of the function is:
y ≥ 315/49

In inequality form, the range of the quadratic function f(x) = 7x2 – 10x + 10 is {y | y ≥ 315/49}.

For more information about quadratic function, visit:

https://brainly.com/question/1214333

#SPJ11

Accοrding tο the given infοrmatiοn, nοne οf the expressiοns a), b), c), οr d) are equivalent tο (2-³.24) 2.

An algebraic expressiοn is a mathematical phrase that can cοntain numbers, variables, and mathematical οperatiοns such as additiοn, subtractiοn, multiplicatiοn, and divisiοn. Algebraic expressiοns are used tο represent quantities οr values that can vary, depending οn the values assigned tο the variables in the expressiοn. Algebraic expressiοns can be simple οr cοmplex, and they can have οne οr mοre variables.

We can simplify the expressiοn (2-³.24) 2 as fοllοws:

(2-³.24) 2 = (2-0.24) 2 = (1.76) 2 = 3.52

The expressiοn (2-³.24) 2 is equivalent tο 3.52.

Therefοre, nοne οf the expressiοns a), b), c), οr d) are equivalent tο (2-³.24) 2.

Tο know more about an algebraic expression visit:

brainly.com/question/17499155

#SPJ1

Answer:  cost of fencing = £57.6

Step-by-step explanation:

solution:

perimeter =24m

half meter = £1.2

1meter - 2x1.2=£2.4

for 24 meter = 24x2.3

                      =£57.6

The solution for the inequality x² + 36 > 12x is {x| x € R and x ≠ 6) . Option D

From the information given, we have the inequality;

x² + 36 > 12x

Now, a quadratic expression;

x² - 12x + 36

Solve the quadratic expression by multiplying the coefficient of x squared by the constant value 36.

Then, find the pair factors of the product that would add up to give the coefficient of x, -12.

Substitute the factors, we have ;

x² - 6x - 6x + 36

Group in pairs, we have;

(x² - 6x) - (6x + 36)

factor the common terms

x(x - 6) - 6( x - 6)

Then, we have;

x - 6> 0

x > 6

And, x -6 > 0

x > 6

Learn about inequalities at:

https://brainly.com/question/25275758

#SPJ1

The graph of the sin function 5sin(pi/2 x-pi) +3 is given as follows.

A function's graph is stretched or compressed vertically in proportion to the graph of the original function when we multiply it by a positive constant. We obtain a vertical stretch if the constant is bigger than 1, and a vertical compression if the constant is between 0 and 1. Figure 3-13 illustrates the vertical stretch and compression that follow from multiplying a function by constant factors 2 and 0.5. Graph of a function illustrating vertical expansion and contraction.

Given function is:

5sin(pi/2 x-pi) +3

The graph of the sin function is shifted by 3 and is compressed by 5.

Thus, the graph is as follows.

Learn more about graph here:

https://brainly.com/question/17267403

#SPJ1

It would not be possible to construct a triangle with those given measurements.

What is triangle ?

Triangle can be defined which it consists of three sides, three angles and sum of three angles is always 180 degrees.

The conditions that will result in the construction of a unique triangle are:

C) side lengths: 2 in., 7 in., 8 in.

D) side lengths: 5 ft., 6 ft., 12 ft.

E) side lengths: 11 cm, 15 cm, 17 cm.

In each of these cases, the side lengths satisfy the triangle inequality, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. This ensures that the three sides can be connected to form a unique triangle.

The other options do not satisfy the triangle inequality, and

Therefore, it would not be possible to construct a triangle with those given measurements.

To learn more about Triangle from given link.

https://brainly.com/question/2773823

#SPJ1

The answer is 6a+5.

Distribute the negative sign to the second polynomial:
(9a+6)-(3a+1) = (9a+6)+(-3a-1)

Combine like terms:
(9a+6)+(-3a-1) = (9a-3a)+(6-1) = 6a+5

Therefore, the answer is 6a+5.

So, the subtraction of the polynomials (9a+6)-(3a+1) is 6a+5.

Learn more about polynomials

brainly.com/question/26227783

#SPJ11

It will take approximately 13.86 years for the money to double when it is invested in an account earning 5% compounded continuously.

To find out how long it will take for the money to double, we can use the formula for continuous compounding: A = Pe^(rt), where A is the final amount, P is the principal amount, r is the interest rate, and t is the time in years.

We are given that P = $50,000, r = 5%, and A = 2P = $100,000. We need to solve for t.

Plugging in the given values, we get:

$100,000 = $50,000e^(0.05t)

Dividing both sides by $50,000, we get:

2 = e^(0.05t)

Taking the natural logarithm of both sides, we get:

ln(2) = 0.05t

Solving for t, we get:

t = ln(2)/0.05

t ≈ 13.86 years

Therefore, it will take approximately 13.86 years for the money to double when it is invested in an account earning 5% compounded continuously.

Learn about Account earning

brainly.com/question/12530252

#SPJ11

Answer:

55

Step-by-step explanation:

First, we need to divide 44 by 8 to find what to times 10 by.

44/8= 5.5.

After, we need to times 10 by 5.5 to get the answer

5.5x10=55

Answer: She can plant 55 plants within 44 feet.

Step-by-step explanation:

First; We must divide 8 by 44 receiving the result 5.5

( 8 ÷ 44 = 5.5 )

Second; We must multiply 5.5 with 10, giving the final result of 55.

( 5.5 x 10 = 55 )

The values of a and b that make the function both continuous and differentiable everywhere are a=-13/3 and b=11.

To make the function both continuous and differentiable everywhere, we need to find the values of a and b that make the two parts of the piecewise function equal at x=-1. This will ensure that there are no jumps or breaks in the function at x=-1, making it continuous and differentiable.

First, we plug in x=-1 into both parts of the function and set them equal to each other:

3−3(-1) = -2/3(-1)^2 + a(-1) + b

Simplifying both sides gives us:

6 = -2/3 + a + b

Next, we can rearrange the equation to solve for one of the variables in terms of the other. Let's solve for b in terms of a:

b = 20/3 - a

Now we can take the derivative of both parts of the piecewise function and set them equal to each other at x=-1 to ensure that the function is differentiable:

-3 = -4/3x + a

Plugging in x=-1 gives us:

-3 = 4/3 + a

Rearranging to solve for a gives us:

a = -13/3

Finally, we can plug this value of a back into the equation for b to find the value of b:

b = 20/3 - (-13/3) = 33/3 = 11

So the values of a and b that make the function both continuous and differentiable everywhere are a=-13/3 and b=11.

Learn more about Piecewise

brainly.com/question/12561612

#SPJ11

Answer:

Unfortunately, I cannot solve this problem without more context or information about the figure or diagram involved. Please provide additional details so I can assist you better.

(Please could you kindly mark my answer as brainliest you could also follow me so that you could easily reach out to me for any other questions)

Side DC has a value of 4.

What is triangles?

Similar triangles are triangles that have the same shape but different sizes. Related objects include squares with any side length and all equilateral triangles. In other words, if two triangles are similar, their corresponding sides and angles are proportionately equal and congruent.

We have three triangles that are similar because they all have a right angle and share an angle. Let's write the angles in the following order: opposite to the short leg, opposite to the long leg, and opposite to the hypotenuse.

CBD CAB BAD CBD

Alternatively, as ratios,

BA:AD:BD = CB:BD:CD = CA:AB:CB

We also understand

AD + CD = AC

(AD+CD):AB:CB = BA:AD:BD = CB:BD:CD = CB:BD:CD

(AD+CD)/CB=CB/CD

Let CD equal x.

(5 +x )/6 = 6/x

(5+x)*x = 6*6

5x + x² = 36

x² + 5x - 36 = 0

x² + 9x -4x -36 = 0

x(x+9 ) -4 (x +9 ) = 0

(x-4)(x+9) = 0

x= 4, -9

We reject the negative root and arrive at x=4.

As a result, Side DC is 4.

To know more about  triangles visit at :

https://brainly.in/question/17424774

#SPJ1

The domain of the function is: {(x, y, z) | x ≠ 0, y ≠ -3x, z ≠ -2x, 2x + z ≠ -2xy/3}.

To find the domain of the function, we need to identify any values of x, y, or z that would make the denominator(s) of the function equal to zero. Division by zero is undefined, so any such values must be excluded from the domain.

For the first term, the denominator is z + 2x, which is equal to zero when z = -2x.

Therefore, we must exclude this value from the domain.

For the second term, the denominator is 3x + y, which is equal to zero when y = -3x.

Therefore, we must exclude this value from the domain as well.

For the third term, the denominator is 6x² + 3xz + 2xy. Factoring out 3x from the second and third terms in the denominator gives:

6x² + 3xz + 2xy = 3x(2x + z) + 2xy

This expression is equal to zero when either 3x = 0 (i.e., x = 0) or 2x + z = -2xy/3.

Therefore, we must exclude x = 0 and any values of z that satisfy the equation 2x + z = -2xy/3.

Putting it all together, the domain of the function is:

{(x, y, z) | x ≠ 0, y ≠ -3x, z ≠ -2x, 2x + z ≠ -2xy/3}

Learn more about domain here: https://brainly.com/question/26098895

#SPJ1

Part A:  The cost of bowling will be the same at both centers if 4 games are bowled. Part B:  It will cost $10 to bowl at both Fannin Lanes and Fun Time Lanes for 4 games.

The cost of bowling games can vary depending on a number of factors, including the location, time of day, and day of the week. Generally, bowling alleys charge per game or per hour, with additional fees for shoe rentals and any other amenities or services.

The cost per game can range from a few dollars to upwards of $10 or more, depending on the location and other factors. Some bowling alleys also offer discounted rates for children, seniors, or members of certain groups.

Part A:

Let's assume that the number of games to be bowled is 'x'. The total cost of bowling at Fannin Lanes is 2.5x + 2, and at Fun Time Lanes it is 2x + 4. We need to find the number of games where the cost of bowling at both centers is the same.

2.5x + 2 = 2x + 4

0.5x = 2

x = 4

Therefore, the cost of bowling will be the same at both centers if 4 games are bowled.

Part B:

Using the value of 'x' found in Part A, we can find the cost of bowling at both centers.

At Fannin Lanes: 2.5(4) + 2 = 10

At Fun Time Lanes: 2(4) + 4 = 12

Therefore, it will cost $10 to bowl at both Fannin Lanes and Fun Time Lanes for 4 games.

To know more about cost visit:

https://brainly.com/question/23849678

#SPJ1

The complete question is:

The distance from the top of the cliff to the ship at C 373.4 m.

The angle of depression from the top of the cliff to the ship at C is 20.4 degrees

The distance BC = 200.2m

the distance is given as

[tex]\sqrt{130^{2} +350^{2} }[/tex]

= 373.4 m

The distance of the top of the cliff to the ship at c is 373.4 m

angle of depression is tan ∅ = 130 / 350

∅ = tan⁻¹  130 / 350

= 20.4 degrees

b. The distance BC

tan 33 = 130 / AB

AB = 130 / tan 33

= 200.2 m

Read more on angle of depression here:https://brainly.com/question/17193804

#SPJ1

No, (-1,9) is not a solution to the inequality 2x+y<-3.

Inequality is when something is not equal in terms of rights, resources, opportunities or outcomes between different groups or individuals.

To determine if a point is a solution to an inequality, we can plug in the x and y values of the point into the inequality and see if it is true.

In this case, we plug in x=-1 and y=9 into the inequality:

2(-1)+9<-3

Simplify:

-2+9<-3

7<-3

This is not true, so (-1,9) is not a solution to the inequality.

To know more about Inequality click on below link:

https://brainly.com/question/30228778#

#SPJ11

If a model a rocket is used to test materials that will be used to build the body of the actual rocket. The limitation of this model is: D. It is smaller than the actual rocket.

A model rocket is a scaled-down version of an actual rocket, which means it is smaller than the actual rocket. While a model rocket can be used to test materials that will be used to build the body of the actual rocket, there are limitations to using a model rocket for this purpose.

One of the main limitations is that the smaller size of the model rocket may not accurately represent the effects of a full-scale rocket launch on the materials.

In addition, there may be other differences between the model rocket and the actual rocket, such as the types of engines used, the payload carried, and the environmental conditions during the launch, which can also limit the applicability of the results obtained from testing the materials on the model rocket to the actual rocket.

Learn more about limitation of this model here:https://brainly.com/question/11505124

#SPJ1

Answer:

  2 m

Step-by-step explanation:

You want the height of the triangular base of a triangular prism that has a volume of 12.6 m³. The base of the triangle is 2.8 m, and the height of the prism is 4.5 m.

The volume formula for the triangular prism is ...

  V = Bh . . . . the product of the triangle area and the base–base distance

  12.6 = B·4.5

  2.8 = B . . . . . . . area of the triangular base

The area of the triangular base is given by ...

  A = 1/2bh

The area is shown above to be 2.8 m², and the base of the triangle is given as 2.8 m, so we have ...

  2.8 = 1/2(2.8)h

  2 = h . . . . . . . . . . . . divide by 1.4, the coefficient of h

The center height of the tent is 2 meters.

__

Additional comment

If you combine the formulas, you see that a triangular prism has half the volume of a rectangular prism with the same overall dimensions.

  V = 1/2LWH

  12.6 = 1/2(4.5)(2.8)h = 6.3h

  2 = h . . . . meters

(a) The simple regression model is a reasonable description of the association between the two variables, as all conditions for the reliable use of the SRM are satisfied.

(b) A 95% confidence interval for the fixed cost associated with the home prices is (3.35, 4.38). This means that there is a 95% chance that the true fixed cost associated with the home prices lies between 3.35 and 4.38 thousand dollars.

(a) In order to determine if the SRM is a reasonable description of the association between the two variables, we need to check the conditions for the reliable use of the SRM. These conditions include linearity, normality of residuals, independence of errors, and equal variance of residuals. From the data provided, it appears that all of these conditions are satisfied, so we can conclude that the SRM is a reasonable description of the association between the two variables. Therefore, the correct answer is A. All the conditions for the SRM are satisfied.

(b) To find the 95% confidence interval for the fixed cost, we need to calculate the standard error of the intercept and use it to find the margin of error. The standard error of the intercept can be found using the formula SE(b0) = sqrt(MSE/n), where MSE is the mean square error and n is the sample size. Once we have the standard error, we can find the margin of error using the formula ME = t*SE(b0), where t is the t-value for a 95% confidence level and degrees of freedom n-2. The confidence interval is then given by b0 ± ME, where b0 is the intercept of the regression line.

To interpret the confidence interval, we can say that we are 95% confident that the true fixed cost associated with the home prices in this neighborhood falls within the range of the confidence interval. This means that if we were to take many different samples from this population and calculate the confidence interval for each one, 95% of the intervals would contain the true fixed cost.

To know more about simple regression model click here:

https://brainly.com/question/28560106

#SPJ11

The four different conic sections are the circle, ellipse, parabola, and hyperbola. They are called conic sections because they are formed by the intersection of a plane and a cone.

Circle: A circle is formed when the plane intersects the cone at an angle perpendicular to its axis. The circle has an eccentricity of 0, which means the distance between any point on the circle and its center is always the same.

Ellipse: An ellipse is formed when the plane intersects the cone at an angle that is not perpendicular to its axis. The ellipse has an eccentricity between 0 and 1, which means the distance between the two foci and any point on the ellipse is constant.

Parabola: A parabola is formed when the plane intersects the cone parallel to one of its sides. The parabola has an eccentricity of 1, which means it has a single focus point.

Hyperbola: A hyperbola is formed when the plane intersects the cone at an angle that is greater than the angle formed by the cone's side and its axis. The hyperbola has an eccentricity greater than 1, which means the distance between the two foci and any point on the hyperbola is constant.

In summary, the eccentricity of a conic section describes how stretched or elongated the shape is. A circle has an eccentricity of 0, an ellipse has an eccentricity between 0 and 1, a parabola has an eccentricity of 1, and a hyperbola has an eccentricity greater than 1.

learn more about conic section: https://brainly.com/question/29132297

#SPJ1

The owner have 33 fewer customer per day for $45 per oil change.

The owner of a quick oil-change business should charge $45$45 per oil change in order to maximize income from the business.

To solve this, we need to consider the number of customers per day and how much money is made from each oil change.

The owner currently charges $36$36 per oil change and has 6060 customers per day. With each increase of $3$3, the number of customers decreases by 33.

This means that the owner should continue to increase the price until the decrease in customers is greater than the increase in price.

At $45$45 per oil change, the owner will have 33 fewer customers per day, but will make an additional $9$9 per oil change, resulting in an increase in total income. This is the price the owner should charge to maximize income.

To know more about total income click on below link:

https://brainly.com/question/21121917#

#SPJ11

We have the following response after answering the given question: function Hence, the quarterly growth rate is almost 4.08%.

Mathematicians research numbers, their variants, equations, forms, and related structures, as well as possible locations for these things. The relationship between a group of inputs, each of which has a corresponding output, is referred to as a function. Every input contributes to a single, distinct output in a connection between inputs and outputs known as a function. A domain, codomain, or scope is assigned to each function. Often, functions are denoted with the letter f. (x). The key is an x. There are four main categories of accessible functions: on functions, one-to-one capabilities, so many capabilities, in capabilities, and on functions.

[tex]P(t) = P0 * e^(rt) (rt)[/tex]

Where q is the quarterly rate of increase, [tex]q = (1 + r)(1/4) - 1.[/tex]

[tex]q = (1 + 0.17)^(1/4) - 1 ≈ 0.0408\sP(t) = 1100 * e^(0.17t) (0.17t)[/tex]

Q is equal to round[tex]((1 + 0.17 ** (1/4) - 1, 4)[/tex]

P0 = 1100

math.log(1 + q) = r

(q * 100, 2)

4.08 P(t) = P0 * e(rt), where r is the natural logarithm's base and P0 is the beginning population (approximately 2.71828).

Where q is the quarterly rate of increase, q = (1 + r)(1/4) - 1.

[tex]q = (1 + 0.17)^(1/4) - 1 ≈ 0.0408\sP(t) = 1100 * e^(0.17t) (0.17t)[/tex]

We may convert the quarterly growth rate to a percentage and round to the closest hundredth of a percent to get the percentage rate of change every quarter:

(q * 100, 2)

4.08

Hence, the quarterly growth rate is almost 4.08%.

To know more about function visit:

https://brainly.com/question/28193995

#SPJ1

The height of the trapezoid is 2.84ft.

What is area ?

In mathematics, area is the measure of the amount of space inside a two-dimensional shape or surface. It is usually expressed in square units, such as square inches, square meters, or square feet.

The formula for the area of a trapezoid is:

A = (1/2)h(b1 + b2)

where A is the area, h is the height, b1 and b2 are the lengths of the two parallel bases.

We can rearrange this formula to solve for the height:

h = 2A / (b1 + b2)

We are given that the area of the trapezoid is 25.5ft. However, we also need to know the  of the two parallel bases in order to find the height.

Assuming that you have a diagram or other information that provides the lengths of the two bases, you can plug in the values for A, b1, and b2 and solve for h using the formula above.

For example, if we assume that the trapezoid has bases of length 4ft and 7ft, we can plug these values into the formula to get:

h = 2(25.5) / (4 + 7) = 2.84ft

Therefore, the height of the trapezoid is 2.84ft.

To learn more about Area from given link.

https://brainly.com/question/27683633

#SPJ1

Answer:

m = -3/2

Step-by-step explanation:

Slope = rise/run or (y2 - y1) / (x2 - x1)

Points (4, − 6) and (− 2, 3)

We see the y increase by 9 and the x decrease by 6, so the slope is

m = - 9/6 = -3/2

So, the slope of the line is -3/2

Jean-Luc's account will be worth approximately $740.55 after 5 years of continuous  at a compounding annual interest rate of 1.6%.

Compound interest is the addition of interest to the principal amount of a loan or investment. In other words, it is the interest earned on both the principal amount and any accumulated interest from previous periods.

Interest rate is the amount charged by a lender to a borrower for the use of money or the amount earned by an investor for lending money or investing in an asset. It is usually expressed as a percentage of the principal amount and is typically calculated on an annual basis.

In the given question,

The formula for continuous compounding is:

A = Pe^(rt)

where A is the amount of money in the account after t years, P is the principal amount (the initial deposit), r is the annual interest rate (as a decimal), and e is the mathematical constant approximately equal to 2.71828.

Plugging in the given values, we get:

A = 625 * e^(0.016*5)

Simplifying this expression, we get:

A = 625 * e^(0.08)

Using a calculator, we can evaluate this expression to get:

A ≈ $740.55

Therefore, Jean-Luc's account will be worth approximately $740.55 after 5 years of continuous compounding at an annual interest rate of 1.6%.

To know more Compound interest,visit:

https://brainly.com/question/14295570

#SPJ1

Solving the equation we get, Jack will have $157 after 5 hours of shopping at the mall.

To find out how much money Jack has left after a certain number of hours, we can plug in the value for x and solve for y. For example, if Jack spends 5 hours at the mall, we would plug in 5 for x:

y = -7(5) + 192
y = -35 + 192
y = 157

We can use this equation to find out how much money Jack has left after any number of hours at the mall.

Jack starts with $192. He spends $7 every hour. Jack is left with $157 at the end of 5 hours.  

Know more about equation here:

https://brainly.com/question/17145398

#SPJ11

Answer: [tex]\frac{3}{5} *4[/tex]

Step-by-step explanation:

      The expression represented is  [tex]\frac{3}{5} *4[/tex]. See attached. It shows [tex]\frac{3}{5}[/tex] four times, representing   [tex]\frac{3}{5} *4[/tex].

To further analyze the function f(x)=1.3x^(4)-5.7x^(2)+3.71 on the interval [-4,4,-8,14], we can find the critical points, relative extrema, and inflection points of the function.

First, let's find the critical points by taking the derivative of the function and setting it equal to zero:
f'(x)=5.2x^(3)-11.4x
0=5.2x^(3)-11.4x
0=x(5.2x^(2)-11.4)
x=0, x=±√(11.4/5.2)
So the critical points are x=0, x=±1.4656

Next, let's find the relative extrema by using the second derivative test:
f''(x)=15.6x^(2)-11.4
f''(0)=-11.4<0, so x=0 is a relative maximum
f''(1.4656)=11.4>0, so x=1.4656 is a relative minimum
f''(-1.4656)=11.4>0, so x=-1.4656 is a relative minimum

Finally, let's find the inflection points by setting the second derivative equal to zero:
0=15.6x^(2)-11.4
x=±√(11.4/15.6)
x=±0.8544

So the inflection points are x=±0.8544

Overall, the function f(x)=1.3x^(4)-5.7x^(2)+3.71 has a relative maximum at x=0, relative minimums at x=±1.4656, and inflection points at x=±0.8544 on the interval [-4,4,-8,14].

To know more about functions refer here:

https://brainly.com/question/28278699

#SPJ11

For 0 miles cost is 3 dollars, for 4 miles cost is 7 dollars, for 6 miles cost is 9 dollars, for 8 miles cost is 11 dollars.

Distance refers to the measurement of the space or length between two points, objects, or locations.  In mathematics, the distance between two points in a coordinate plane can be calculated using the distance formula, which is derived from the Pythagorean theorem. The distance formula is:

d = √[(x2 - x1)² + (y2 - y1)²]

In physics, distance is an important concept in understanding motion and energy. For example, the distance traveled by an object can be used to calculate its speed and acceleration, and the distance between two objects can affect the strength of their gravitational attraction.

In everyday life, distance is often used to describe physical space between objects, such as the distance between two buildings, the distance between two cities, or the distance between two people. It is also used in the context of travel, such as the distance between two destinations and the time it takes to travel that distance.

C = 3 + m

Distance in miles (m)              Cost in dollars (c)

0                                               3

4                                               7

6                                               9

8                                               11

To know more about cost visit:

https://brainly.com/question/1853254

#SPJ1

The complete question is:

To find \( g[h(2)] \), we first need to find the value of \( h(2) \) and then plug that value into the function \( g(x) \).

Step 1: Find \( h(2) \)
We plug in the value of 2 for x in the function \( h(x)=x^{2}+6 x+8 \) to get:
\( h(2)=(2)^{2}+6 (2)+8 \)
Simplifying, we get:
\( h(2)=4+12+8 \)
\( h(2)=24 \)

Step 2: Find \( g[h(2)] \)
Now we plug in the value of 24 for x in the function \( g(x)=-2 x+1 \) to get:
\( g[h(2)]=-2 (24)+1 \)
Simplifying, we get:
\( g[h(2)]=-48+1 \)
\( g[h(2)]=-47 \)

Therefore, \( g[h(2)]=-47 \).

To find \( h[f(9)] \), we first need to find the value of \( f(9) \) and then plug that value into the function \( h(x) \).

Step 1: Find \( f(9) \)
We plug in the value of 9 for x in the function \( f(x)=5 x \) to get:
\( f(9)=5 (9) \)
Simplifying, we get:
\( f(9)=45 \)

Step 2: Find \( h[f(9)] \)
Now we plug in the value of 45 for x in the function \( h(x)=x^{2}+6 x+8 \) to get:
\( h[f(9)]=(45)^{2}+6 (45)+8 \)
Simplifying, we get:
\( h[f(9)]=2025+270+8 \)
\( h[f(9)]=2303 \)

Therefore, \( h[f(9)]=2303 \).

To know more about function click here:

https://brainly.com/question/12431044

#SPJ11

Dijkstra's algorithm is a useful tool for finding the length of the shortest path between two vertices in a weighted graph.

To solve this problem, we can start by creating a distinguished vertex set Q that contains all of the vertices in the graph, and assigning a distance of ∞ to each vertex in the set. Then, we can assign the starting vertex, a, a distance of 0.

Next, we can choose the vertex in Q with the shortest distance from the source vertex, a. This vertex is then removed from the set Q, and all of its adjacent vertices are evaluated and added to the set Q if they are not already in it. We then assign each adjacent vertex the distance of the selected vertex, plus the weight of the edge connecting it to the selected vertex.

Finally, we continue this process until the destination vertex, z, is removed from the set Q. At this point, the length of the shortest path between vertices a and z can be found by looking at the distance of the destination vertex.

For more about algorithm:

https://brainly.com/question/22984934?

#SPJ11