A road-building company plans to construct a bridge across a pond to connect Main Street and Second Street, as shown in the diagram below. How long will this bridge need to be? Show your work.

Answer:

[tex] y = \dfrac{2}{3}x - 1 [/tex]

Step-by-step explanation:

[tex] 2x - 3y = 3 [/tex]

Subtract 2x from both sides.

[tex] -3y = -2x + 3 [/tex]

Divide both sides by -3.

[tex] y = \dfrac{-2}{-3}x + \dfrac{3}{-3} [/tex]

[tex] y = \dfrac{2}{3}x - 1 [/tex]

Answer:

number is 8

Step-by-step explanation:

let the number be n then trebling it ( multiplying it by 3 ) is 3n, then subtracting 6 from this is 3n - 6 , so

3n - 6 = 18 ( add 6 to both sides )

3n = 24 ( divide both sides by 3 )

n = 8

that is the number thought of is 8

The correct option for the given expression is [tex]4\sqrt[3]{3}\sqrt[4]{2}[/tex]

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given that, an expression, [tex]\sqrt[3]{24} \sqrt[4]{32}[/tex], we need to simplify it,

Factoring them,

24 = 2 x 2 x 2 x 3

32 = 2 x 2 x 2 x 2 x 2

Therefore,

[tex]\sqrt[3]{24} = 2\sqrt[3]{3}[/tex]

[tex]\sqrt[4]{32} = 2\sqrt[4]{2}[/tex]

[tex]\sqrt[3]{24} \sqrt[4]{32}[/tex] =  [tex]4\sqrt[3]{3}\sqrt[4]{2}[/tex]

Hence, the correct option for the given expression is [tex]4\sqrt[3]{3}\sqrt[4]{2}[/tex]

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Step-by-step explanation:

=6+(-4)(2-3)²

=6+(-4)(-1)²

=6-4×1

=2

The closest option to the cone area is 923.2 m². 

A cone is a shape formed from a series of line segments or lines that connect a common point, called a vertex or vertex, to all points on the base of a circle that do not contain vertices. The distance from the apex of the cone to the base is called the height of the cone.

To solve this problem, we need to find the surface of the cone. Formula for the surface area of cone:

A = [tex]\pi[/tex]r² + [tex]\pi[/tex]rℓ

where r is the radius of the base, ℓ is the height of the depression, and π is a constant of approximately 3.14159.

First, we find the radius of the base. Since the bottom line of the cone is listed as 18 feet and we know the radius is 14 feet, we can use the Pythagorean theorem to find the height of the cone.

h² = ℓ² - r²

h² = 19.3² - 14²

h ≈ 11.48 feet

Now we can compute the surface.

A = [tex]\pi[/tex](14)² + [tex]\pi[/tex](14)(19.3)

A ≈ 923.2 square feet

So the closest option to the cone area is 923.2 m². 

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Answer:

f(x)>[tex]\sqrt{1-x}[/tex]

Step-by-step explanation:

because it is above the x axis it is >

Because it is -x is moves to the right

because it is a dotted line and not solid it is >

Step-by-step explanation:

To find the inverse of the exponential function y = (3/2)^x, we need to interchange the roles of x and y, and then solve for y.

So, starting with y = (3/2)^x, we can write:

x = (3/2)^y

To solve for y, we can take the logarithm of both sides with base 3/2:

log(3/2) x = y

Therefore, the inverse of the exponential function y = (3/2)^x is:

y = log(3/2) x

or in exponential form:

y = (log base 3/2) x

This function is the logarithmic function with base 3/2.

3x^2 + 4x - 3 = ( 3x -2 ) (x + 2) + 1

Remainder Theorem is an approach of Euclidean division of polynomials. According to this theorem, if we divide a polynomial P(x) by a factor ( x – a); that isn't essentially an element of the polynomial; you will find a smaller polynomial along with a remainder.

Given:- p(x) = 3x^2 + 4x - 3 and g(x) = 3x - 2

p(x) ÷ g(x)

3x^2 + 4x - 3  ÷ ( 3x - 2)  

[tex]\frac{3x^2+4x-3}{3x-2} =(x+2 )+ \frac{1}{3x-2}[/tex]

Quotient =  x + 2

Remainder = 1

Hence, 3x^2 + 4x - 3 = ( 3x -2 ) (x + 2) + 1

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This is the same result as if we had just taken the product of 5 by itself, which is also equal to 0.

Product is an item or service that is created by a business or organization to meet the needs of their customers. It is anything that is offered to a market for sale or trade. Products can be tangible, such as physical goods or intangible, such as services, ideas, or experiences. Companies need to create products that offer value to their customers. This includes making sure that the product meets the customer's needs, is of good quality, and is priced appropriately.

An empty product is a mathematical term that is used to describe a product of two or more numbers, where the result is equal to the product of just one of the numbers. This is because when you multiply any number by zero, the result is zero. Therefore, if a product contains a zero, then the result will be the same as if you only multiplied one of the numbers in the product. For example, if we take the product of 5 and 0, then the result is 0. This is the same result as if we had just taken the product of 5 by itself, which is also equal to 0.

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The answer is m = 0.

The slope of the linear function is given as follows:

3/2.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The slope represents the rate of change of a linear function, meaning that it is calculated as the change in y divided by the change in x.

Considering points (-4,-4) and (-2, -1), we have that when x increases by 2, y increases by 3, hence the slope is given as follows:

m = 3/2.

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The unit rate for the problems are;

a. 50pages/hour

b. 4points / game

c. 8 car washed /hour

d. 8 ounces of peanut/ dollar

A unit rate means a rate for one of something. We write this as a ratio with a denominator of one. For example, if you ran 100 yards in 10 seconds, you ran on average 10 yards in 1 second.

a. The unit rate = number of pages/ time

= 100/2 = 50pages/hour

b. The unit rate = number of points /number of games

= 20/5 = 4 points per game

c. The unit rate = number of car washed/ time

= 40/5 = 8car washed per hour

d. unit rate = number of ounces of peanut/ number of dollars

= 20/2.5 = 8 ounces of peanut per dollar

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The value of x is -1 and 3 for which x makes the equation.

What is factorization?

Writing a number or other mathematical object as the result of numerous factors—typically smaller or simpler objects of the same kind—is known as factorization or factoring in mathematics.

Here, we have

Given: 1 + (x-1)² = 5

We have to solve it for x and find the value of x.

1 + (x-1)² = 5

We solve this equation by factorization and we get

1 + x² - 2x + 1 = 5

x² - 2x + 2 -5 = 0

x² - 2x - 3 = 0

x² + x - 3x - 3 = 0

x(x+1) -3(x+1) = 0

(x+1)(x-3) = 0

x= -1, 3

Hence, the value of x is -1 and 3 for which x makes the equation.

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The area of the triangle ABC is, 9 sq units.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points.

Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know, The area of a triangle is (1/2)×base×height.

Given, x equals 3 less than 6 which is,

x = (6 - 3).

x = 3.

Now, The base of the triangle is x units and the height is 2x units.

Therefore, The area of the triangle is,

= (1/2)×(3)×2(3).

= 9 sq units.

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Answer:

20 + 5 + 2 and two 1 cents will make 29 Euro cents.

20 + 5 + 2 and two 1 cents will make 29 Euro cents.

20 + 5 + 2 and two 1 cents will make 29 Euro cents.

20 + 5 + 2 and two 1 cents will make 29 Euro c

Step-by-step explanation:

Answer: A quarter and 4 pennies

Step-by-step explanation:

25+4=29

As a result, 7 is the number of w that solves the problem.

In mathematics, a denominator is the lowest integer in a proportion that indicates how many equal portions are split into a whole. It is a fraction's division. In this case, the fraction is 4, so there are four components overall.

To solve for w in the equation (W+3)/4 = (W-2)/2, we can start by cross-multiplying to eliminate the denominators:

2(W+3) = 4(W-2)

Expanding the brackets:

2W + 6 = 4W - 8

Simplifying:

2W = 14

W = 7

Therefore, the value of w that satisfies the equation is 7.

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Based on the information, it can be inferred that the probability that a person has four or more cell phones in their home is 0.0494

To find the probability that a person has four or more cell phones in their home, we must carry out the following mathematical procedure.

We must find the total number of people surveyed and the percentage that each group represents:

Now we must establish the probability. For this we must carry out the following mathematical procedure:

According to the above, the probability that someone answers that four or more cell phones are used in her house is 0.0494.

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Because the cost equation is c(x)=7000+4x, the marginal profit at a production level of 3000 is $9.4 per unit.

An equation in mathematics is a claim made regarding the equivalence of two expressions. It includes one or more variables (unknown values) and describes how those variables and/or constants relate to one another. For instance, the line on a coordinate plane denoted by the equation y = 3x + 5 has a y-coordinate that is equivalent to three times the x-coordinate plus five. Three and five are constants in this equation, while x and y are factors. Finding the value(s) of the dependent variables) that make the equation true is one way to answer an equation. In the example above, we can enter y = 11 into the equation .

given

We must first determine the revenue function, which is provided by, in order to determine the marginal profit at a production level of 3000:

14x - x/1000x = R(x) = xp(x) = 14x - x2/1000

where the demand function is given by p(x) = 14 - x/1000.

The benefit function is next, and it is provided by:

P(x) = R(x) - C(x) = (10x - x2/1000 - 7000) + (4x) = 14x - x2/1000

where the cost function, C(x), equals 7000 plus 4x.

We must take the derivative of the profit function with regard to x and evaluate it at x = 3000 in order to determine the marginal profit:

P'(3000) = 10 - 3/5 = 9.4

Because the cost equation is c(x)=7000+4x, the marginal profit at a production level of 3000 is $9.4 per unit.

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Any input number of t outside of the range [0, 3] would therefore be meaningless given the circumstances of the issue.

An equation in mathematics is a claim that two expressions are equivalent. Mathematical operations like addition, subtraction, multiplication, division, and exponentiation may be used. It typically includes one or more variables. A connection between two or more variables can be represented by an equation, and it can also be used to determine the value of an unknown variable. Finding the values of the factors that make the equation true is the first step in solving an equation.

given

The projectile is in the air for a maximum of three seconds, so the domain of h(t) is [0, 3], since the equation depicts the projectile's height in feet after t seconds.

Any input number of t outside of the range [0, 3] would therefore be meaningless given the circumstances of the issue.

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By answering the above question, we may infer that The inaccuracy, equation when rounded to the closest tenth of a percent, is around 6.6%. The measurement's percent error is 6.6% as a result.

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.

The following formula may be used to get the percent error:

percent error is calculated as follows: 100% divided by (actual value - measured value).

Whereas, "|" stands for absolute value.

In this instance, the measured measurement is 8.5 inches, whereas the real value is 9.1. Hence, by entering these values into the formula, we may obtain:

error = |(9.1 - 8.5) / 9.1| x 100% error = 6.59%

The inaccuracy, when rounded to the closest tenth of a percent, is around 6.6%. The measurement's percent error is 6.6% as a result.

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The number of students who scored more than 70 but less than 80 is zero.

A stem-and-leaf diagram is a quantitative analysis of a collection of data points that are separated into a "stem" (the first digit of the number) and a "leaf" (the remainder of the number) (the last digit of the number).

To find the number of students who scored more than 70 but less than 80, we need to look at the stem-and-leaf plot and count the number of leaves that fall within this range.

Stem 7 has a leaf of 6, which represents a score of 76. Therefore, at least one student scored between 70 and 76.

The stem 8 has leaves of 2, 5, and 8, which represent scores of 82, 85, and 88, respectively. Therefore, no students scored between 76 and 80.

Therefore, the number of students who scored more than 70 but less than 80 is zero.

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Answer:

30k^2+55k+25

Step-by-step explanation:

30k^2+30k+25k+25

=30k^2+55k+25

[tex]30k { }^{2} + 30k + 25k + 25[/tex]

[tex]30k ^{2} + 55k + 25[/tex]

The values of the piecewise function {h(x)} for different values of {x} is given above.

An algebraic expression is a made up of terms both constants and variables. For example, we can write -

2x + 3y + z

5x + y

x + 8y

Given is the relation as -

y = {- x² - 6x - 9          for   x < - 2}

y = {x/3 - 4              for x > - 2}

The given function is a piecewise function. We can write the values for different values of {x} as -

{x} = - 4

y{4} = - (-4)² - 6(-4) - 9 = - 1

{x} = - 3

y{-3} = - (-3)² - 6(-3) - 9 = - 0

{x} = - 1

y{-1} = -1/3 - 4= -4.3

{x} = 0

y{-1} = 0/3 - 4 = - 4

Therefore, the values of the piecewise function {h(x)} for different values of {x} is given above.

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Mark needs a score of 2 on the 5th test to pass the course

Let X be the score Mark needs to get on the fifth test to pass the course.

To find X, we can use the formula for the mean of five numbers:

(mean of 5 numbers) = (sum of the 5 numbers) / 5

We know that Mark needs a mean score of 10 to pass, so:

10 = (total score on all 5 tests) / 5

Multiplying both sides by 5, we get:

50 = total score on all 5 tests

We also know that Mark's mean score on the first four tests is 12, so:

(mean score on the first four tests) = (total score on the first four tests) / 4

12 = (total score on the first four tests) / 4

total score on the first four tests = 48

To pass the course with a mean score of 10, Mark needs a total score of 50, and he has already scored 48 on the first four tests. Therefore, he needs to score:

X = 50 - 48

X = 2

Mark needs a score of 2 on the fifth test to pass the course with a mean score of 10.

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a. The equation of the tangent plane is z = 1 + x.

b. The point (4/3, 8/3, 5) lies on both the plane T(0,1) and the line l.

c. The other points on the graph of f(x) whose tangent plane contains the line l are (-9/8, -1/2, -21/8) and (-25/32, -3/4, -47/32)

The function is defined as a mathematical expression that defines a relationship between one variable and another variable.

(a) The partial derivatives of f(x) at this point:

∂f/∂x = 2x + y²

∂f/∂y = x² + 2xy

Evaluating these at (0,1), we get:

∂f/∂x(0,1) = 1

∂f/∂y(0,1) = 0

So the equation of the tangent plane is:

z = f(0,1) + ∂f/∂x(0,1)(x-0) + ∂f/∂y(0,1)(y-1)

z = 1 + x

(b)

The plane T(0,1) contains the line l:

2x = y = (z+3)/2

Substituting y = 2x and z = 2y-3, we get:

z = 2(2x) - 3 = 4x - 3

So any point on the line l can be written as (x, 2x, 4x-3).

Substituting these values into the equation of the plane, we get:

4x-3 = 1 + x

3x = 4

So x = 4/3, y = 8/3, and z = 5.

Therefore, the point (4/3, 8/3, 5) lies on both the plane T(0,1) and the line l.

(c) To find all other points on the graph of f whose tangent plane contains the line l, we need to find the intersection of the graph of f with the plane T(0,1) + λ(2,0,1), where λ is a scalar. This gives us the system of equations:

x² + y²xy = 1 + x + 2λ

2x + y² = 0

y - 1 = λ

Solving for x and y in terms of λ, we get:

y = λ + 1

x = -(y²)/2 = -(λ+1)²/2

Substituting these values into the first equation, we get:

(λ+1)² + (λ+1)²(-(λ+1)²/2) = 1 - (λ+1)²/2 + 2λ

Simplifying and solving for λ, we get:

λ = -1/2, -1/4

Therefore, the other points on the graph of f(x) whose tangent plane contains the line l are:

(-9/8, -1/2, -21/8) and (-25/32, -3/4, -47/32)

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Answer:

She read 4/5 of a book per month

Step-by-step explanation:

4/5= 4/5per month

Step-by-step explanation:

To find out how many books Tanisha read each month, we can use the formula:

books read per month = total number of books ÷ total number of months

Using the information given in the problem, we know that Tanisha read 4 books in 5 months. So we can plug those values into the formula:

books read per month = 4 ÷ 5

Simplifying the fraction by dividing the numerator and denominator by their greatest common factor, which is 1, we get:

books read per month = 4/5

Therefore, Tanisha read 4/5 of a book per month, or equivalently, 0.8 books per month.

please give me a brainliest.

Answer:

Step-by-step explanation:

here are step-by-step explanations for each part of the problem:

A. To find the mean, you add up all of the prices and divide by the number of prices. So:

Mean = (350 + 400 + 500 + 650 + 725 + 850 + 1700) / 7

Mean = 517.86

Rounded to the nearest dollar, the mean is $518.

B. To find the median, you need to put the prices in order from smallest to largest and then find the middle value. In this case, there are seven prices, so the middle value is between the 3rd and 4th prices:

350, 400, 500, 650, 725, 850, 1700

The median is the average of the 3rd and 4th prices, so:

Median = (500 + 650) / 2

Median = 575

The median price is $575.

C. Quartiles divide the data set into four equal parts, so you need to find the values that separate the lowest 25%, the next 25%, the next 25%, and the highest 25% of prices.

To find the quartiles, you can use the following steps:

Put the prices in order from smallest to largest:

350, 400, 500, 650, 725, 850, 1700

Find the median (Q2) as calculated in part B:

Median = $575

Divide the data set into two halves, below and above the median. If the median is included in both halves, exclude it from both.

Lower half: 350, 400, 500, 575

Upper half: 650, 725, 850, 1700

Find the median (Q1) of the lower half:

Q1 = (400 + 500) / 2

Q1 = 450

Find the median (Q3) of the upper half:

Q3 = (725 + 850) / 2

Q3 = 787.5

The four quartiles are Q1=$450, Q2=$575 (median), and Q3=$788.

D. The range is the difference between the highest and lowest values in the data set. So:

Range = highest value - lowest value

Range = $1700 - $350

Range = $1350

The interquartile range (IQR) is the difference between the third quartile (Q3) and the first quartile (Q1). So:

IQR = Q3 - Q1

IQR = $788 - $450

IQR = $338

F. To find the upper boundary for outliers, you add 1.5 times the IQR to Q3. So:

Upper boundary = Q3 + 1.5(IQR)

Upper boundary = $788 + 1.5($338)

Upper boundary = $1282

There are no values above the upper boundary, so there are no upper outliers.

Answer:

Step-by-step explanation:

We can simplify the expression using the rules of exponents:

(-27)^(-2/3) = 1/(-27)^(2/3)

Now, we can use the fact that (-a)^(2/3) = (a^(2/3)) to simplify the expression further:

1/(-27)^(2/3) = 1/(3^3)^(2/3) = 1/3^(3*2/3) = 1/3^2 = 1/9

Therefore, x = 1/9.