Study the road plan shown in the figure. A service station will be built on the highway, and a road will connect it with Cray. How long will the new road be? A.54.2 mi B. 312 mi C. 46.2 mi D.400 mi

The pattern of the sequence 1 1 2 3 5 8 13 is that each term is obtained by adding the previous term and the term before that.

The sequence 1 1 2 3 5 8 13 is also a famous example of the Fibonacci sequence. The Fibonacci sequence is a sequence of numbers in which each term is the sum of the two preceding terms. In this case, the first two terms of the sequence are 1 and 1, and the rest of the terms are obtained by adding the previous two terms.

It's also possible to express the pattern of the Fibonacci sequence by using the formula, F(n) = F(n-1) + F(n-2) where F(n) is the nth term of the sequence.

Learn more about Fibonacci Sequence here:

https://brainly.com/question/29764204

#SPJ4

Answer:

[tex]y= \frac{x}{2x−1}[/tex]

Step-by-step explanation:

To find the inverse function, swap x and y, and solve the resulting equation for x.

If the initial function is not one-to-one, then there will be more than one inverse.

So, swap the variables: y=x/2x−1 becomes x=y/2y−1.

Now, solve the equation x=y/2y−1 for y.

y=x/2x−1

The price of the adult ticket is $9

Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation.

Set up equations to represent the problem.

Let the A and S represent the prices of adult and student ticket respectively. So we can write:

4A + 10S = 106 --- (1)

4A + 9S = 99  --- (2)

Subtracting (2) from (1) will give:

S = 7

Put S = 7 into (1):

4A + 10S = 106

4A + 10(7) = 106

4A + 70 = 106

4A = 106 - 70

4A = 36

A = 36/4

A = 9

Thus, the price of the adult ticket is $9

Learn more about word problems on:

brainly.com/question/13818690

#SPJ1

Answer:

The total number count we are looking at from the numbers 30 to 65 is 36. So that is a total of 72 digits making up this numbers from 30 to 65. Also, we can see that the whole range of numbers 0 to 9 is being used for this range

Answer:

271.2

Step-by-step explanation:

Write it down and remove the decimals and do long multiplication. After that, count the decimal points and add them back ro the answer

Answer:

271.2

Step-by-step explanation:

move the decimal point 2 places to the right in the two numbers and multiple

[tex]2825 \times 960 = 2712000 [/tex]

and then move you decimal point 4 places to the left so your finally answer should be 271.2

The maximum number of drinks Liam can buy is 4 without over exceeding his price.

Unitary method:

The unit method is a method of obtaining a single-unit value from a multiple-unit value and obtaining a multiple-unit value from a single-unit value. This is the method used for most calculations in mathematics. This method is useful when solving problems involving proportions and proportions, algebra, geometry, and more.

The unit method allows us to find missing values. For example, if a pack of juice costs $5. Then you can easily see that the cost is 5 packages, or $25.

According to the Question:

If Liam has $30 to spend and he must buy at least 9 drinks and tacos altogether, it means that,

$3.50 for 5 tacos

⇒ 3.50 x 5 =  $17.50

Now,

9 - 5 tacos = 4 drinks

Cost of 4 drinks x $2 = $8

The total price :

$17.50 + $8 = $25.50 out of $30 price limit

Thus, the number of drinks that she could buy is 4.

Learn more about Maximum Number:

https://brainly.com/question/1563742

#SPJ4

Answer:

B.  x + 10 ≥ 70;  x ≥ $60

Step-by-step explanation:

Given:

The equation that models the given parameters is:

To solve for x, subtract 10 from both sides of the equation:

[tex]\implies x+10-10 \geq 70-10[/tex]

[tex]\implies x \geq 60[/tex]

Therefore, Kelvin needs to withdraw at least $60 from the bank.

Translation type of transformation can be defined as moving a figure to a new location with no change to the size or shape of the figure.

Now, According to the question:

Type of Transformation:

There are four types of transformation in geometry, namely translation, reflection, rotation, and dilation. In translation, it slides the figure in any direction while in reflection, it flips the figure over a point or a line. Also, in rotation the figure turns, while in dilation the figure is either enlarged or reduced.

The type of transformation can be defined as moving a figure to a new location, without any change in the figure's size or shape being called translation. In translation, the figure merely slides or moves in the same direction and distance.

Therefore, the answer is Translation.

Learn more about Dilation at:

https://brainly.com/question/13176891

#SPJ4

The quadratic equation written in the vertex form is:

f(x) = 2*(x - 2)^2 - 8

We know that for any parabola whose vertex is (h, k) and the leading coefficient is a, can be written in the vertex-form as:

f(x) = a*(x - h)^2 + k

In this particular case, we know that the vertex of the parabola is the point (2, -8), replacing that in the quadratic equation above we will get:

f(x) = a*(x - 2)^2  - 8

Now we also know that our parabola passes through the point (0, 0), then if we replace these values in the equation we will get:

f(0) = 0 = a*(0 - 2)^2 - 8

        0 = a*4 - 8

        8 = a*4

        8/4 = a

          2 = a

Then the quadratic equation in the vertex form is:

f(x) = 2*(x - 2)^2 - 8

Learn more about quadratic equations at:

https://brainly.com/question/1214333

#SPJ1

When t = 3, the exponential function has a value of 59.375.

The exponential function is a mathematical function denoted by f(x)=\exp or e^{x}. Unless otherwise indicated, the word refers to a positive-valued function of a real variable, however it can be extended to complex numbers or applied to other mathematical objects such as matrices or Lie algebras. A mathematical function of the following type is an exponential function: f (x) = an x, where x is a variable and an is a constant known as the function's basis. The transcendental number e, which is about 2.71828, is the most often encountered exponential-function base.

Here,

Given the exponential function h (t) = 475(0.5)^t

When t = 3

h(3) = 475(0.5)^3

h(3) =59.375

h(3) = 59.375

The exponential function when the value of t is 3 is 59.375.

To know more about exponential function,

brainly.com/question/21726902

#SPJ1

The first step in solving an inequality is to isolate the variable on one side of the inequality sign. This is also known as "clearing the inequality" of the variable. This can be done by using inverse operations such as addition, subtraction, multiplication, and division.

For example, if the inequality is 3x + 2 > 7, the first step is to isolate the variable x by subtracting 2 from both sides:

3x + 2 > 7

3x > 5

Then, divide both sides by 3 to get x > 5/3

This is the first step in solving an inequality, as now the variable x is isolated on one side of the inequality sign, and it's clear what the inequality is asking for.

It's important to note that when solving inequalities, it's crucial to keep the direction of the inequality sign the same, meaning if you multiply or divide by a negative number, you need to switch the direction of the inequality sign as well.

Also, it's important to check if the inequality is not valid, if the operation you are doing creates a division by zero, it will be an invalid inequality.

To know more on inequality

https://brainly.com/question/12189350

#SPJ4

The number of people visited the zoo from the state is  200

Number deals with quantity of people that came to the zoo from the state over the period.  These people must be from the state.

The given parameters that will help us to solve the question are:

The ratio is approximately 7 to 3.

The number of people = 2000

The sum of the ratios is equal to 7+3 = 10

This is to say that 10% of the people visited the zoo

10/100*2000/1

Therefore about 200 people visited the zoo

Learn more about number of people on https://brainly.com/question/17429689

#SPJ1

Answer:

5.6 or 28/5

Step-by-step explanation:

We know that A = 8 and B = 4

The expression is A/5 + B

8/5 + 4

The answer in decimal is 5.6

The answer in fraction is 28/5

The student whose measurement had the greatest percentage error is Tenicia with a measurement of 23mm.

Percentage error refers to the difference between the estimated value and the actual value which is then expressed as a percentage. In the question given, the students and their values are; Layne, 26 mm, Tenicia, 23 mm, and Juan 25 mm.

Juan was the only student who had no error in the value obtained because she got the exact figure of 25 mm. Tenicia recorded the greatest value because the difference between the actual and estimated value was apart with so much difference. Her error was an 8% error.

25 -23/25 × 100

= 8%

Learn more about percentage error here:

https://brainly.com/question/1600371

#SPJ1

A constant polynomial is a polynomial with a degree of 0, meaning it has no variable terms. The only possible constant polynomial is the term with a coefficient of 3, which is 3.

This can be seen by looking at the formula for a polynomial, which is:

P(x) = a0 + a1x + a2x2 + ... + anxn,

where a0 is the constant term, a1 is the linear term, a2 is the quadratic term, and so on. Since this polynomial has no variable terms (x = 0), the only possible constant polynomial is the term with a coefficient of 3.

To calculate the value of a constant polynomial, you simply substitute 0 for x in the equation above. For example, in the polynomial 3, the value would be 3 when x = 0.

P(0) = 3

Therefore, the answer is option b, 3.

Learn more about constant polynomial here:

https://brainly.com/question/12356729

#SPJ4

The slope of the equation of the line 3f - s = 24 is 3.

The equation of a line can be represented in slope intercept form as follows:

y = mx + b

where

Therefore, let's model the equation of the line y = mx + b to 3f - s = 24. Then, we can locate the slope in the equation.

Hence,

3f - s = 24.

add s to both sides of the equation

3f - s + s = 24 + s

3f = 24 + s

subtract 24 from both sides of the equation

3f = 24 + s

3f - 24 = 24 - 24 + s

s = 3f - 24

Therefore, the slope is 3.

learn more on slope intercept form here: brainly.com/question/29150985

#SPJ1

The triangles QRS and TUV are similar. They are similar as ΔTUV = 3ΔQRS.

What are triangles?

Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.

There are two similar looking triangles, ΔQRS and ΔTUV.

In ΔQRS, the measure of line segment QR = 9 units

In ΔQRS, the measure of line segment RS = 10 units

In ΔQRS, the measure of line segment QS = 11 units

In ΔTUV, the measure of line segment TU = 27 units

In ΔTUV, the measure of line segment UV = 30 units

In ΔTUV, the measure of line segment TV = 33 units

The pattern here can be seen that -

For the line segment TU -

3 (QR) = TU

3 (9) = 27

Similarly, for the line segment UV -

3 (RS) = UV

3 (10) = 30

Similarly, for the line segment TV -

3 (QS) = TV

3 (11) = 33

Therefore, the triangle TUV is three times scaled version of triangle QRS.

To learn more about triangles from the given link

https://brainly.com/question/25215131

#SPJ1

Answer:

Step-by-step explanation:

0.25

Step-by-step explanation:

Today, we are going to be talking about the three-way principle of mathematics. Basically, there are three ways to solve a problem in math: verbally, graphically, or by example. In this lesson, we will discuss each of these principles by solving sample problems using each type.

A polygon having seven sides and seven angles is called a heptagon. Seven straight sides and seven corners, or vertices, make up a heptagon. It's also referred to as a "septagon" at times.

A seven-sided polygon is called a heptagon. A closed figure with seven vertices, it is. Another name for a heptagon is a septagon.

There are various sorts of hexagons, depending on the angles and diagonals.

Regular and Irregular Heptagons

Concave and Convex Heptagon

The following are some heptagon's characteristics:

(1) The inner angles of a heptagon add up to 900 degrees.

(2) A heptagon's outside angles add up to 360 degrees.

(3) The internal angle of a normal heptagon measures approximately 128.57 degrees.

(4) The size of a typical heptagon's central angle is roughly 51.43 degrees.

(5) There are fourteen diagonals in a heptagon.

(6) Convex heptagons are another name for regular heptagons.

(7) A heptagon has a total of five triangles.

To learn more about heptagon link is here

brainly.com/question/12630702

#SPJ4

The answer is the point (5, -27) and no other solution.

The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.

Given here: The equation y=-6x+23

Checking for  (5, -27) we get -27=-6×5+23

                                                      =-27

Hence, The answer is the point (5, -27)

Learn more about solution of linear equations here:

https://brainly.com/question/545403

#SPJ1

One solution exists for the given equation.A linear equation with one variable has only ever one solution.

A linear equation with one variable has only ever one solution. The unique solution of a linear equation is the location at which LHS and RHS are identical when substituted.

The solution must be an ordered pair when there are two linear equations operating simultaneously (x, y). In this case, the ordered pair will fulfill the set of equations.

Given:

2x + 5y = 4

-4x - 13y = 9

Now,

a 1 = 2,  b1 = 5 , = -4

a2 = -4 , b2 = -13, = 9

Now,  = 2 / -4

= 5 / -13

As, a1/ a2 = 2/-4

b1 / b2 = 5 /-13

Thus, the relationship mentioned above reflects intersecting lines.

So, there is only one solution to the given problem.

To learn more about unique solution refer to:

https://brainly.com/question/16157288

#SPJ1

Answer:

1,400

Step-by-step explanation:

y=mx+b

plug in 460 for b

y=mx+460

plug 20 for m

y=20x+460

and when graphed on a graph you would see the answer

The Order of the ordered pair is defined as the specific way in which the ordered pair is written having a composition of the x coordinate and the y coordinate .

What is Ordered Pair ?

The Ordered Pair is defined as the pair of numbers in a specific order.

For Example :  (x,y) , here for the given ordered pair , the element x is called as the abscissa and the element y is called as the ordinate .

The Order of the Ordered Pair (x,y) is the first element always represents the abscissa that means the x coordinate and the second element should always represent ordinate that means the y coordinate .

For Example : for the ordered pair (2,4) , the x coordinate of the point is 2 and the y coordinate of the point is 4 .

Learn more about Ordered Pair here

https://brainly.com/question/14350735

#SPJ4

Yes, the square of any number like X² is always positive.

Example:

If we calculate the square of a negative number, let's say -x, where x > 0, then (-x) (-x) = x².

Here, x² > 0.

Hence, the square of any number like X² is always positive.

To know more about the positive numbers, here

https://brainly.com/question/29711621

#SPJ4

Answer:

x = 92

y = 92

Step-by-step explanation:

164 + 102 + 90 + x + x = 540

2x + 356 = 540

2x = 184

x = 92

Answer:

x = 0.25y + 7/12

Step-by-step explanation:

12x - 3y = 7

12x = 3y + 7

x = 0.25y + 7/12

Answer: You can make more bracelets than necklaces. ✅

Step-by-step explanation:

You have 2.88 meters of copper wire and 5.85 meters of aluminum wire.

With 2.88 meters of copper wire, you can make 12 bracelets because each bracelet needs 0.24 meters of copper wire.

With 5.85 meters of aluminum wire, you can make 9 necklaces because each necklace needs 0.65 meters of aluminum wire.

So you can make 12 bracelets and 9 necklaces.

Therefore you can make more bracelets than necklaces.

The value of x for the given expression is,

⇒ x = 5/44

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The algebraic expression is,

'' 4 times x plus one third equals one third times x plus 4''.

Now, The mathematical expression is,

⇒ 4x + 1/3 = 1/3 (x + 4)

Solve for x as;

⇒ 4x + 1/3 = 1/3x + 3/4

⇒ 4x - 1/3x = 3/4 - 1/3

⇒ 11/3x = 5/12

⇒ x = 5 × 3 / 12×11

⇒ x = 15/ 132

⇒ x = 5/44

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ1