A taxi company charges a $2.00 base fare plus an additional fare based on a per-mile rate and a per-minute rate. Ryan's first taxi ride was 3.0 miles, took 7 minutes, and cost $8.50. His second taxi ride was 7.0 miles, took 14 minutes, and cost $16.00. If his third taxi ride took 10 minutes and cost $13.50, approximately how many miles was the third taxi ride

It costs $4 for 2 visits, $8 for 4 visits, $10 for 5 visits, and $16 for 8 visits.

2 visits: c = 2v = 2(2) = $4,

4 visits: c = 2v = 2(4) = $8,

5 visits: c = 2v = 2(5) = $10,

8 visits: c = 2v = 2(8) = $16.

2 visits: c = $30, cost per visit = $15

4 visits: c = $60, cost per visit = $15

5 visits: c = $75, cost per visit = $15

8 visits: c = $120, cost per visit = $15

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The antithesis of an exponential function is a logarithmic function. A logarithmic function and an exponential function both use the same base.

Writing y = log2 x or f(x) = log2 x represents the logarithmic function for the equation x = 2y. Even today, the base is still 2. Y equals log base b of x, or more simply, "y equals log to the base b of x," is how y = logb x is typically read. Similarly to exponential functions, b > 0 and b 1.

Consequently, the table's data is represented by the logarithmic function f(x) = log3(x).

Table provided:

                    x           f(x)

                    25          2

                   125          3

                   625         4

We can write x in this case as powers of 5, so that

[tex]$25=5^2$$125=5^3$$625=5^4$$\Rightarrow f(x)=5^{f(x)}$[/tex]

After dividing the log in half, we now have

[tex]$\log x=\log 5^{f(x)}$$\Rightarrow \log x=f(x) \log 5 \ldots .\left[\log (a)^m=m \log (a)\right]$[/tex]

[tex]$\Rightarrow f(x)=\frac{\log x}{\log 5}$$\Rightarrow f(x)=\log _5 x \ldots \ldots\left[\log _a b=\frac{\log b}{\log a}\right]$[/tex]

A base-log function [tex]$f(x)=\log _5 x$[/tex], then, reflects the data in the table.

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Answer:

the answer is in the images

Using the equation we know that the required value of x is (B) 30 cm.

Basically, an equation is when you have two expressions with the same value on either side of an "equal to" sign.

For example, 3x + 5 = 15.

There are lots of different types of equations, like linear, quadratic, and cubic, among others.

So, looking at the diagram, the equation is true.

x/75 = 12/30

Solve as follows:

30x = 12 * 75

30x = 900

30x/30 = 900/30

x = 30

Therefore, using the equation we know that the required value of x is (B) 30 cm.

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Correct question:

What is the value of x?

(A) X= 4.8 cm

(B) X= 30 cm

(C) X= 93 cm

(D) X= 187.5 cm

It's the last one

Because its one fourth of the original ones minus the original giving you the answers -3, 4.5, -1.5, 1.5, 3, -1.5, 3 and 3 again.

Answer: The ratios do form a proportion. The cross products are equal (16 * 22 = 26 * 12)

Step-by-step explanation:

Answer:

Step-by-step explanation: 7 x + 9 = 23. 7x+9=23. Subtract 9 from both sides. Subtract 9 from both sides.

7x=23-9. 7x=23−9. Subtract 9 from 23 to get 14. Subtract 9 from 23 to get 14.

7x=14. 7x=14. Divide both sides by 7. Divide both sides by 7.

x=\frac{14}{7} x=714​ Divide 14 by 7 to get 2. Divide 14 by 7 to get 2.

As a result, according to Pythagoras' Theorem, the third side, or hypotenuse, has a value of 8 units, whereas the other two sides are 6 and 7.

The Pythagorean Theorem, often known as the Pythagorean Theorem, is the fundamental Euclidean geometry relationship between the three sides of a right triangle. The area of a square with the hypotenuse side equals the sum of the areas of squares with the other two sides, according to this rule. The Pythagorean Theorem says that the square that spans a right triangle's hypotenuse opposite the right angle equals the sum of the squares that span its sides. It is sometimes written as the generic algebraic notation a2 + b2 = c2.

given

x2 = a2 + b2

x2 = 6*6 + 28

x2 = 36 + 28

x2 = 64

x = 8

As a result, according to Pythagoras' Theorem, the third side, or hypotenuse, has a value of 8 units, whereas the other two sides are 6 and 7.

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The required two-column proof that the triangles are congruent is explained below.

A triangle is a three sided plane shape whose the sum of internal angles is 180^o. Thus two or more triangles are said to be congruent when their corresponding sides and measure of internal angles are equal.

When two triangles are congruent, it can be proven in all respect that they are thus equal (considering their corresponding length of sides and measure of internal angles).

The two column proof required in the question is given below:

        STATEMENT                                     JUSTIFICATION

1. <WXZ ≅ <YXZ                                  Property of an angle bisector.

2. <XZW  ≅ <XZY                                Definition of a perpendicular bisector.

3. WX ≅ YX                                          Congruent sides of a triangle.

4. WZ ≅ YZ                                           Definition of a midpoint.

Therefore,

ΔWXZ ≅  ΔYXZ                                    Angle-Angle-Side theorem

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Answer:

y = -4/1x + 28

Step-by-step explanation:

y=Mx +b

slope (m): -4/1

Y intercept (b): 28

No, Eric will not have enough banana bread to serve all 20 guests if he bakes only 3 loaves.

Eric is making banana bread to serve 20 guests, and he wants each guest to have 1/6 of a loaf. This means that each loaf will be divided into 6 equal portions, and each guest will receive one of these portions.

Eric plans to bake 3 loaves of banana bread. As 1 loaf can serve 6 guests with 3 loaves he can serve a total of

3×6 = 18 < 20

So only 18 guests can be served with 3 loaves of bread.

--The question is incomplete, complete question is given below--

"Eric is making banana bread to serve 20 guests. He want each guest to have 1/6 of a loaf. If he bake 3 loaves of banana bread will eric have enough banana bread to serve all 20 guests?"

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Therefore , the solution of polynomials problem is Grouping technique using the greatest common factor (GCF) and others given below.

A mathematical expression made up of coefficients and uncertainty that only makes use of additions, subtractions, multiplications, and positive integer powers of variables is known as a polynomial. The formula x2 4x + 7 denotes a single indeterminate x polynomial. An expression in mathematics known as a polynomial is made up of variables (also known as indeterminates) and coefficients that may be added, subtracted, multiplied, and raised to negative integer powers of non-variables. An algebraic statement with variables and coefficients is called a polynomial. An expression can only contain the operations addition, subtraction, multiplication, and non-negative integer exponents. Polynomials are the name for these expressions.

There are several methods for factoring polynomials, but the most common methods are:

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The nearest whole number to which the new height of the image is enlarged is 9cm.

What is meant by height?

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12) The new height is 9cm it was originally 4cm wide and 3cm tall, scale factor is 3.

14) The new width is 12cm it was originally 2cm tall  and 4cm wide, scale factor is 3.

In mathematics, a scale factor is the proportion between corresponding measurements of an object and a representation of that object. The copy will be bigger if the scale factor is a whole number. A fraction scale factor means that the copy will be smaller.

To increase an object by a scale factor, measure each side of the object and multiply the result by the scale factor. A 2x2 cm square is presented to you.

Increase the square by a scale factor of 2.

To do this, multiply each side by 2.

The result is a 4x4cm square.

12) scale factor = 12/4

scale factor = 3

14) scale factor = 6/2

scale factor = 3

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A reflective pronoun is a pronoun  formed with -self or -selves that refers to the subject. Hence, option B is correct.

When a pronoun is used to refer to the same noun as both the subject and the object of a verb, it is known as a reflexive pronoun. The pronouns that in English finish in "self" or "selves" are things like "himself," "myself," "ourselves," etc.

Words like myself, you, him, her, it, ourselves, ourselves, and yourselves are examples of reflexive pronouns. They make a reference to someone or something. When the subject and the object of a verb are the same, reflexive pronouns are frequently used. I cut myself yesterday night while preparing dinner.

Thus, option B is correct.

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A substitution reaction is a reaction in which one group of molecules gets replaced by another group of molecules in an aqueous medium.

The substitution reactions are classified into three groups,

In the nucleophilic reactions the atom is said to be rich in electron , whereas, in the electrophilic reaction, the atom is known to be  an electron-deficient species.

The primary difference between substitution and elimination reactions is that substitution reactions replace one group with another, whereas elimination reactions merely remove the group. The main distinction between the groups is the number of stages involved in the reaction.

Example , R-Br + OH− → R-OH + Br−

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In mathematics, a differential equation is an equation involving one or more functions and their derivatives. The derivative of a function defines the rate of change of the function at some point.

According to the given Question:

Differential equation:

In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives.  In applications, a function generally represents a physical quantity, a derivative its rate of change, and a differential equation defines the relationship between the two. Such relationships are common. Therefore, differential equations play an important role in many fields such as engineering, physics, economics and biology.

The study of differential equations consists primarily of studying their solutions (the set of functions that satisfy each equation) and the properties of those solutions. Only the simplest differential equations can be solved with explicit formulas. However, many properties of solutions to particular differential equations can be determined without exact computation. In many cases, when a closed formula for the solution is not available, the solution can be approximated numerically using a computer. Although the theory of dynamical systems focuses on qualitative analysis of systems described by differential equations, many numerical methods have been developed to determine solutions with some degree of accuracy.

A first-order linear differential equation is an equation that can be written in the form y0 + p(x)y = q(x). where p and q are continuous functions on the interval I. The second-order linear differential equation has a similar form.

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a. The simple interest for 4 years would be $960.

b. The amount at the end of the 4 years would be $2160.$

A man deposited $1200 in his bank account. A simple interest of 20% per annum was paid on his deposit.

a. For calculating simple interest for the 4 years

We have been given data as:

Principal (P) = $1200

Rate of Interest (R) = 20%

Time (T) = 4 years

⇒ Simple interest  = P × R × T

Substitute the value of P, R, and T in the above formula,

The simple interest for 4 years would be:

⇒ 1200 x 20% x 4 = 960

b. For calculating the amount at the end of the 4 years

The amount at the end of the 4 years would be:

1200 + 960 = 2160

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When an image is enlarged using a scale factor between 1 and 1, the image does not change in size.

A scale factor of 1 means that the image is not being enlarged or reduced in size; it is remaining the same size. Therefore, the image will appear the same as it did before the enlargement.

A scale factor of less than 1 means that the image is being reduced in size, and a scale factor greater than 1 means that the image is being enlarged in size. But when it comes to scale factor between 1 and 1, the image will not change in size, it will appear the same as it was before.

It's important to note that when you're enlarging an image using a scale factor that's less than 1, the image becomes smaller but when you're using a scale factor greater than 1 the image becomes larger.

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The 5 coordinate systems are Cartesian Coordinate System, Polar Coordinate System, Cylindrical Coordinate System, Spherical Coordinate System, Elliptic Coordinate System.

1. Cartesian Coordinate System: This system uses two perpendicular axes (X and Y) to determine the location of a point. The point's coordinates are the distances from the origin point (0, 0). The axes divide the plane into four quadrants and the coordinates can be positive or negative. The axes are also referred to as the x-axis and y-axis.

2. Polar Coordinate System: This system uses an angle and a distance from a fixed origin point to specify a point. The angle is measured in radians and the distance is measured from the origin. The coordinates of the point are usually written as (r, θ).

3. Cylindrical Coordinate System: This system combines the two-dimensional polar system and the one-dimensional Cartesian system. It uses three coordinates, (r, θ, z) to determine a point's location in three-dimensional space. The r coordinate is the distance from the origin, θ is the angle measured from the z-axis, and z is the height.

4. Spherical Coordinate System: This system uses three coordinates, (r, θ, φ), to determine a point's location in three-dimensional space. The r coordinate is the distance from the origin, θ is the angle measured from the z-axis, and φ is the angle measured from the x-axis.

5. Elliptic Coordinate System: This system uses two coordinates, (a, b), to specify a point on an ellipse. The a coordinate is the distance from one of the ellipse's foci, and the b coordinate is the distance from the other. This system is useful for describing orbits, such as those of planets.

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Answer:

Triangle: 15 cm

Rectangle: w = 2.5 cm

Step-by-step explanation:

Rectangle: A = w · l

2.5 · 6 = 15cm

Triangle: A = hᵇb/2 = 6 · 5/2 = 15 cm

I hope this helps!

Answer:

-11/12

Step-by-step explanation:

Complete transformations and then enter the final coordinates of the figure will be: A(2,2) B(1,-2) C (4,-4)

If a point (x, y) is translated by 4 units horizontally right and 1 unit upwards, coordinates of the image point will be,

(x, y) → (x + 4. y + 1)

Therefore, vertices of the image triangle ABC will be,

A(2, 2) → A'(2+4, 2+1)

         → A'(6, 3)

B(5, -1) → B'(5+4, -1+1)

         → B'(9, 0)

C(1, -2) → C'(1+4, -2+1)

Then reflected across y-axis.

Rule for the reflection across y-axis will be,

(x, y) → (-x, y)

A'(6, 3) → A"(-6, 3)

B'(9, 0) → B"(-9, 0)

C'(5, -1) → C"(-5, -1)           → C'(5, -1)

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The Function given as [tex]y=3^{x}[/tex] is an Exponential function and the base is 3 and the exponent in the function is x .

What are Exponential function ?

The exponential Functions are defined as a function written as [tex]f (x) = a^{x}[/tex], where the "variable x" is called exponent and the "number a" is a constant called the base of the function and base should be greater than 0.

the given function is [tex]y=3^{x}[/tex] ,

So , according to the definition of Exponential Function ,

we can see that the base of the function is 3 and is greater than 0 ,

the exponent is x .

Therefore , the function [tex]y=3^{x}[/tex] is an Exponential Function .

The given question is incomplete , the complete question is

Is [tex]y=3^{x}[/tex] an exponential function ?

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On solving the provided question we can say that based on the provided graph obtaining a doctorate after earning a master's degree.

Mathematicians use graphs to logically convey facts or values using visual representations or charts. A graph point will typically reflect a relationship between two or more things.

so here,

based on the provided graph  obtaining a doctorate after earning a master's degree.

High education is generally highly valued by employers. People with greater education tend to be seen as candidates with a larger variety of skill sets than other candidates with lower level of education, which would positively affect their income level (although this may not always be the case).

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The correct question is -

Based on the information provided in the graph, for which of the following situations could you expect to have the greatest increase in salary? a. Having a high school diploma and going to college for a year. b. Having an associate’s degree and getting a bachelor’s degree. c. Having a bachelors degree and getting a master’s degree. d. Having a master’s degree and getting a doctorate degree.

The value of x is given as follows:

x = 13.7.

The value of x is obtained using similar triangles, which share these two following features:

The proportional side lengths are given as follows:

Hence the proportional relationship of these lengths is given as follows:

x/16 = 6/7.

Meaning that the value of x is obtained as follows:

7x = 16 x 6

x = 16 x 6/7

x = 13.7.

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The product of two complex numbers, with a result of 821, is given as follows:

(26 + 12.04i)(26 - 12.04i) = 821.

Complex numbers are numbers that are composed by a real part and by an imaginary part, and have the notation given as follows:

z = a + bi.

In which:

The most important complex numbers relation is given as follows:

i² = -1.

Meaning that the easiest way to obtain the desired product is multiplying complex-conjugate numbers, as follows:

(a + bi)(a - bi).

Applying the subtraction of perfect squares, we have that:

(a + bi)(a - bi) = a² - (bi)²

(a + bi)(a - bi) = a² - b²i²

(a + bi)(a - bi) = a² + b² (as i² = -1).

Then, attributing a = 26, the value of b is obtained as follows:

a² + b² = 821

26² + b² = 821

[tex]b = \sqrt{821 - 26^2}[/tex]

b = 12.04.

Meaning that the product is given as follows:

(26 + 12.04i)(26 - 12.04i) = 821.

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Answer:c

Step-by-step explanation:

c

Answer:

46.28

Step-by-step explanation:

i did pemdas