A poster at the train station shows the number of miles to different stations and the time it takes for the train to travel there.

Distance to Stations

Time in Minutes
(x) Distance in Miles
(y)
24 18
44 33
76 57
96 72

What is the constant of proportionality for this relationship?

Answer: The zeros of the function f(x) = x^2 + 5x + 5 are given by the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

In this case, a = 1, b = 5, and c = 5. Plugging these values into the formula, we get:

x = (-5 ± √(5^2 - 4(1)(5)))/2(1)

x = (-5 ± √(25 - 20))/2

x = (-5 ± √(5))/2

x = (-5 ± √5)/2

The zeros of the function are:

x = (-5 + √5)/2 and x = (-5 - √5)/2

in simplest radical form

x = (-5 + √5)/2 and x = (-5 - √5)/2

Step-by-step explanation:

The expressions are equivalent to -5/8 - ( -1/8 - 1/2) include:

A. -5/8 + (1/8 + 1/2)

B. -5/8 + 5/8

D. -5/8 - (-1/8 + (-1/2))

From the information, Mike watches a caterpillar climbing on a tree trunk and then writes the expression -5/8 - (-1/8 - 1/2) to show the change, in feet, of the caterpillar’s height on the tree trunk.

The change, in feet, of the caterpillar’s height on the tree trunk will be:

= -5/8 - ( -1/8 - 1/2) include:

= - 5/8 + 5/8

= 0

Learn more about fractions on:

brainly.com/question/78672

#SPJ1

At 7.4 ( round to nearsest tenth) meters mark will Ario be present when Miguel starts the race. So, option (c) is right choice here.

We have, Miguel and his brother Ario are both deciding to a race.

Total length of pool = 25 meters

But they are standing 3 meters from one side of a 25-meter pool when both are decide to race.

So, the length of racing area = 25 - 3 = 22 meters.

Also, Miguel said that he will start when the ratio of Ario’s completed meters to Ario’s remaining meters is 1 : 4. Let us assume, the Ario’s completed meters be "x meters" . Then, Ario’s remaining meters = 22 - x

so, x : 22- x = 1 : 4

=> x/(22 - x) = 1/4

=> 4x = 22 - x

=> 5x = 22

=> x = 22/5 = 4.4

Ario position when Miguel starts the race with respect to pool's length = 4.4 meter + 3 meters

= 7.4 meter

Hence, required length is 7.4 meters.

To learn more about ratio , refer :

https://brainly.com/question/573032

#SPJ4

Complete question:

We have to rearrange the question as

Miguel and his brother Ario are both standing 3 meters from one side of a 25-meter pool when they decide to race. Miguel offers Ario a head start. Miguel says he will start when the ratio of Ario’s completed meters to Ario’s remaining meters is 1:4. At what meter mark will Ario be when Miguel starts the race? Round to the nearest tenth.

a) 4 meters

b) 6 meters

c) 7.4 meters

d) 7 meters

The nearest ten of 741 is 740.

The number system or the numeral system is the system of naming or representing numbers. We know that a number is a mathematical value that helps to count or measure objects and it helps in performing various mathematical calculations.

In mathematics, there are various number systems such as the decimal number system, binary number system, octal number system, and hexadecimal number system.

Round the number to the nearest ten. 741 is between 740 and 750.

Looking at the 1 in the one's place. It's less than 5, so round down to 740.

Thus, the nearest ten of 741 is 740.

To know more about number system visit: brainly.com/question/17429689

#SPJ4

Divide the first term of the dividend by the first term of the divisor to divide polynomials using long division.

Divide the dividend's first term by the divisor's first term to get the quotient's first term. Multiply the divisor by the quotient's first term and subtract the product from the dividend to get the remainder. This residual is now handled as a fresh dividend, but the divisor stays unchanged.

Polynomial division steps:

Step 1: Take the dividend's first term (x^2) and divide it by the divisor's first term to get the quotient's first term.

Step 2: In this situation, multiply the divisor(x - 2) by the answer(x), then insert the product beneath the dividend(x^2 + 2x + 3).

Step 3: Subtract to create a new polynomial.

For more questions on Polynomials

https://brainly.com/question/28119824

#SPJ4

The range of the function f(x) = |x-1| is all non-negative real numbers from 0 to infinity.

The range of a function is all the possible values that can be outputted from the function. The range of the function f(x) = |x-1| is determined by looking at the expression and analyzing its behavior for different values of x.

When x is less than 1, the expression becomes negative and the absolute value makes the result positive. Therefore, for x less than 1, the result will be a positive number greater than 0. When x is equal to 1, the result is 0. When x is greater than 1, the expression is already positive, so the absolute value does not change the result.

This means that for x greater than 1, the result will also be a positive number greater than 0. Therefore, the range of the function f(x) = |x-1| is all non-negative real numbers from 0 to infinity.

For more questions like Range click the link below:

https://brainly.com/question/24217266

#SPJ4

The difference in growth between June and July will be 0.58 inches.

The value of (3a^5b^-2)^0 × 3a^4 × (2a^4)^2 is 12a^12

It should be noted that the word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.

The difference in growth between June and July will be:

= 1.28 - 0.7

= 0.58 inches.

The value of (3a^5b^-2)^0 × 3a^4 × (2a^4)^2 is:

= 1 × 3a^4 × (2a^4)^2

= 3a^4 × 4a^8

= 12a^12

Learn more about word problem on

brainly.com/question/21405634

#SPJ1

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{80 + 56 \rightarrow \boxed{\textsf{8{(10 + 7)}}}\rightarrow 136}\\\\\large\text{Now let us break down the distributive property to if it is really}\\\large\text{equivalent to the original equation. }\\\\\mathsf{8(10 + 7)}\\\mathsf{= 8(10) + 8(7)}\\\mathsf{= 80 + 56}\\\mathsf{= 136}[/tex]

[tex]\huge\text{Therefore your answer should be: }\\\\\huge\boxed{\mathsf{8(10 + 7)}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

The sum of 2 and b is greater than or equals to -27 is expressed as 2 + b ≥ -27. Therefore, b ≥ -29

Inequalities are mathematical expressions involving the symbols >, <, ≥ and ≤.

Therefore, let's convert the words expression to a mathematical expression(inequality).

The sum of 2 and b is greater than or equals to -27 can be expressed as follows:

2 + b ≥ -27

Let's solve for b

2 + b ≥ -27

subtract 2 from both sides of the inequality

2 - 2 + b ≥ -27 - 2

b ≥ - 29

learn more on inequality here: https://brainly.com/question/30231190

#SPJ1

The corresponding sides and the corresponding angles along with the figure are given below.

A trapezium is a quadrilateral with four sides where two sides are parallel to each other.

We have,

From the given information we get the figure given below.

Trapezium ABCD.

Trapezium PQRS.

Now,

The corresponding sides are:

AB = RS

BC= SP

AD = RQ

CD = QP

The corresponding angles are:

∠B = ∠S = 90

∠C = ∠P = 90

∠A = ∠R

∠D = ∠Q

Thus,

The corresponding sides and angles are given above.

Learn more about trapezium here:

https://brainly.com/question/22607187

#SPJ1

Answer: The area of a rectangle is given by the formula: A = L x W

Where A is the area, L is the length and W is the width.

Given that the area of the rectangle is 32a^3b^4 square units, and the length is shown in the image, we can use the formula to find the width:

32a^3b^4 = L x W

To find the width, we need to divide both sides of the equation by L.

32a^3b^4 = L x W

W = 32a^3b^4 / L

As the length of the rectangle is given as 8a^2b^2, we can substitute it in the above equation to find the width of the rectangle

W = 32a^3b^4 / 8a^2b^2

W = 4ab^2

So the width of the rectangle is 4ab^2 square units.

We used the formula of the area of the rectangle and the given information of the area and length to find the width of the rectangle by isolating the width on one side of the equation.

Step-by-step explanation:

The area of shaded region when the rectangle sits inside a circle is 422.39 cm².

The area of a shape simply had to do with the total space that is taken by a particular shape. It shows the extent of the region on a curved surface and plane.

Since the rectangle sits inside the circle. Thus, the area of the shaded region will be the area of the circle minus the area of the rectangle.  That is:

area of shaded region = area of circle - area of rectangle

area of shaded region = πr² - LW

area of shaded region = (π × 12²) - (3 × 10)

area of shaded region = 144π - 30

area of shaded region = 422.39 cm²

Learn more about area of circle on:

brainly.com/question/15673093

#SPJ1

The equation in the form [tex]x^{2}[/tex] + bx = c is [tex]x^{2}[/tex] - 2x = 15.

By adding to both sides the term needed to complete the square is 1.

Factors of the perfect square trinomial are 5 and - 3.

As per the given data the given equation is:

[tex]x^{2}[/tex] - 2x - 15 = 0

1. Rewrite the equation in the form [tex]x^{2}[/tex] + bx = c

Since a = 1 keep the “x-terms” (both the squared and linear terms) on the left side but move the constant to the right side.

Add 15 on both sides of the equation.

[tex]x^{2}[/tex] - 2x - 15 + 15 = 0 + 15

[tex]x^{2}[/tex] - 2x = 15

2. Add to both sides the term needed to complete the square.

Divide by 2, followed by squaring (raising to the 2 nd power).

[tex]& x^2-2 x=15 \\[/tex]

[tex]& \left(\frac{-2}{2}\right)^2=1[/tex]

The output here, which is +1, will be added to both sides of the quadratic equation.

[tex]x^{2}[/tex] - 2x + 1 = 15 + 1

[tex]x^{2}[/tex] - 2x + 1 = 16

[tex](x-1)^2=16[/tex] (Perfect square trinomial express into square of a binomial)

3. Factor the perfect square trinomial.

[tex]\sqrt{(x-1)^2} & =\pm \sqrt{16} \\[/tex]

x - 1 = ± 4

x - 1 + 1 = ± 4 + 1

x = ± 4 + 1

x = 4 + 1           x = -4 + 1

x = 5                x = - 3

For more questions on quadratic Equations

https://brainly.com/question/15645424

#SPJ4

The value of {x} is equivalent to 7.

Given is a triangle ΔXYW.

The median of a triangle is a bisector of the angle. Median is found to be joining the vertex of the triangle with the opposite side of the triangle. So, we can write -

m∠1 = m∠2

(2x + 9) = (4x - 5)

2x + 9 = 4x - 5

14 = 2x

x = 7

Therefore, the value of {x} is equivalent to 7.

To solve more questions on triangles, visit the link below -

brainly.com/question/12413243

#SPJ1

The roots of the polynomial f(x) = x³ - x² - x - 15 are  3, -1 + 2i and -1 - 2i

A root of a polynomial is a value of x that makes the polynomial equal to zero. A polynomial is a mathematical expression that is made up of terms, each of which includes a variable (x) raised to a power, such as x^2, x^3, x^4, etc. The powers of x are called the degrees of the polynomial.

For example, the polynomial equation x^2 + 2x - 3 = 0 has two roots, x = -1 and x = 3.

The number of roots of a polynomial equation is determined by its degree. A polynomial equation of degree n has at most n roots. A polynomial equation of degree n can have n distinct roots, n-1 distinct roots, or even no roots at all.

f(x) = x³ - x² - x - 15

0 = x³ - x² - x - 15

The roots are 3, -1 + 2i and -1 - 2i

Learn more on roots of polynomial here;

https://brainly.com/question/2833285

#SPJ1

Domain = R or (-∞, ∞)

Range = R, because ∀ x ∈ R(Domain) y is also real.

How do you find the domain and range of f(x) =3x + 5

Clearly no real value of f(x) can make f(x) an imaginary value or value like ∞.

Domain = R or (-∞, ∞)

Range = R, because ∀ x ∈ R(Domain) y is also real.

As we observe, lines go off infinitely in both directions.

Therefore, the domain and range of this function are both set of reals or (-∞, ∞).

Example:

Suppose f(x) = 1/x

When x = 0, f(x) = 1/0 = infinity

Thus, the domain of f(x) cannot be R. Therefore, to define the domain the values of x which make f(x) = infinity are excluded from the set of reals.

Therefore the domain is R - {0}.

To know more about domain visit brainly.com/question/28135761

#SPJ4

Answer: x16/6

Step-by-step explanation:

Answer: 13.3 :D

Step-by-step explanation:

The density of the land will be 0.5 Deer/foot

Density is the amount of things (people, animals, plants, or items) in a given area. To compute density, divide the number of items by the area measured. A country's population density is the number of inhabitants divided by its area in square kilometers or miles.

The amount of a quantity (typically mass) per unit of area is known as surface density. Density=Quantity/Area.

The quantity of data that can be stored on a given unit of physical space on storage medium is measured as areal density.

Total number of deer = 12

Area occupied = 6 Sq. foot

So, the value of density = (6/12) 0.5 Deer/Foot

For more questions on Density

https://brainly.com/question/26364788

#SPJ4

The area of the triangle is calculated to be 15 cm^2.

To calculate the area of the triangle, we use the formula

Area= 1/2 * (base) * (height)

Here, we can consider a as the height of the triangle and b as the base of the triangle.

Given we have,

a = 6 cm and b = 5 cm

Substituting the values of height and base in the given formula, it becomes,

Area= 1/2 *a *b

=1/2 * 5 cm * 6 cm

=15 cm^2

This formula can be applied to any triangle, regardless of its size, as long as the base and height are known. It is important to note that the unit of measurement for the base and height must be the same for the formula to be correct.

Read more about Area of Triangles:

https://brainly.com/question/29156501

#SPJ4

Distance is calculated using the formula distance=√(y2²-y1²)+(x2²-x1²).

A pair of numbers called coordinates are used to locate a point or a shape in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane. The term "ordinate" refers to a point's separation from the x-axis when scaled with the y-axis. Cord's are the collective noun for the abscissa and ordinate. The study of algebraic equations on graphs is known as coordinate geometry. The plotting of points, lines, and curves on an x and y axis is an illustration of coordinate geometry.

Here,

The formula of distance according to class 9th is distance=√(y2²-y1²)+(x2²-x1²).

To know more about coordinates,

https://brainly.com/question/27749090

#SPJ4

The value of 1% of 200% is 1/50 or 0.02

A percentage is a way to express a number as a fraction of 100. It is often denoted using the symbol %. It can also be used to express a change in a value, such as a increase or decrease in percentage.

1% of 200% can be written as:

1% of 200% = (1/100) × (200/100)

1% of 200% = ( 1 × 200)/ (100 × 100)

1% of 200% = 200/10000

1% of 200% = 1/50 = 0.02

Learn more about percentage on:

brainly.com/question/843074

#SPJ1

Answer::8/24 are RedPick and return 2So it will be 7/25Again pick and return 2Then it is 6/26Now multiply the results8/24 …

Step-by-step explanation:

There are 5 elements in 32 proper subsets.

What are subsets?

If every element of set A is also an element of set B, then set B is a superset of set A, and set A is a subset of set B. A and B could be equal; if they are not, then A is a legitimate subset of B. Include refers to the property that one set is a subset of another.

Here, we have

Given:  32 proper subsets.

We have to find how many elements are in 32 proper subsets.

Subsets of a set having n elements = 2^n

2ⁿ = 32

n = 5

Hence, there are 5 elements in 32 proper subsets.

To learn more about the subsets from the given link

https://brainly.com/question/28469146

#SPJ1

Translating words into algebraic expressions means taking words and replacing them with mathematical symbols to create an equation. For example, the expression "five more than a number" can be written as "x + 5" where "x" represents the number.

Translating words into algebraic expressions is a useful skill when solving math problems. It involves taking words and replacing them with mathematical symbols to create an equation. For example, the expression "five more than a number" can be written as "x + 5" where "x" represents the number. By translating words into an algebraic expression, it becomes easier to solve problems using the correct equations. It is important to remember to use the correct symbols and to be mindful of the order of operations when translating words into algebraic expressions. When done correctly, translating words into algebraic expressions can help to make complex math equations easier to understand and solve.

Learn more about expression here

https://brainly.com/question/14083225

#SPJ4

log 7 can be approximated by using the common logarithm values of nearby integers.

log 7 = log 4 + log 2 + log (7/4)

log 2 = 0.3010

log (7/4) = 0.1403

log 7 = 0.6021 + 0.3010 + 0.1403 = 1.0434

To calculate the logarithm of 7 without a calculator, we can use the common logarithm values of nearby integers. First we determine the logarithm of 4, which is 0.6021. Then, the logarithm of 2 is 0.3010. Finally, the logarithm of the fraction 7/4 is 0.1403. We then add all of these together to get the logarithm of 7 which is 1.0434. Therefore, the logarithm of 7 is approximately 1.0434 when calculated without a calculator.

log 7 can be approximated by using the common logarithm values of nearby integers.

learn more about logarithm here

https://brainly.com/question/30085872

#SPJ4

The difference between exponential function and logarithmic function is their graph shows mirror image of each other.

A function of the form is a logarithmic function. It can be read as "y equals the log, base b, of x" or "y equals the log of x, base b." X > 0 and b > 0 and b 1 in both forms. y is not constrained in any way.

When the input variable x appears as an exponent in the formula f(x) = axe, an exponential function is indicated. The exponential curve is influenced by both the exponential function and the value of x. An essential mathematical function of the form is the exponential function. f(x) = a^x.

Examples of exponential functions include 2x, 10x, and ex; they have the form axe, where an is a constant. The cube root function, for example, "undoes" the cube function: 323=2. The logarithmic functions are the inverses of the exponential functions, that is, functions that "undo" the exponential functions.

To know more about logarithmic function visit:

brainly.com/question/3181916

#SPJ4

Answer:Y=15 X=9

Step-by-step explanation: