A $2.00 base fare charge, and per-mile, and per-minute rates related as follows; 3•x + 7•y = 6.5 and 7•x + 14•y = 14, give the distance traveled in the third ride as 4.5 miles
How can the length of the third ride be calculated?The base fare = $2.00
Let x represent the per-mile rate, and let y represent the per-minute rate, we have;
The cost of Ryan's first taxi ride = $8.50
Distance traveled in the first ride = 3.0 miles
Time taken during the first ride = 7 minutes
Therefore;
2 + 3•x + 7•y = 8.5
Which gives;
3•x + 7•y = 8.5 - 2 = 6.5
3•x + 7•y = 6.5...(1)Distance traveled in the second ride = 7.0 miles
Duration of the second ride = 14 minutes
The second ride cost = $16.00
Therefore;
2 + 7•x + 14•y = 16
Which gives;
7•x + 14•y = 16 - 2 = 14
7•x + 14•y = 14...(2)Solving the above simultaneous equations by multiplying equation (1) by 2 then subtracting the result from equation (2) gives;
(7•x + 14•y) - 2 × (3•x + 7•y) = 14 - 2×6.5 = 1
x = 1
The per-mile rate, x = $13•x + 7•y = 6.5
7•y = 6.5 - 3•x
7•y = 6.5 - 3×1 = 3.5
y = 3.5/7 = 1/2 = 0.5
The per-minute rate, y = $0.5Duration of the third taxi ride = 10 minutes
Cost of the third ride = $13.50
Therefore;
2 + 1×a + 10×y = $13.50
Where a is the distance traveled during the third ride, we have;
2 + 1×a + 10×0.5 = $13.50
2 + a + 5 = 13.5
a = 13.5 - 2 - 7 = 4.5
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What logarithmic function represents the data in the table?
X f(x)
25 2
125 3
625 4
The antithesis of an exponential function is a logarithmic function. A logarithmic function and an exponential function both use the same base.
What is logarithm function?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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Help please! Triangle Proofs are so hard!
The required two-column proof that the triangles are congruent is explained below.
Properties of a congruent triangles.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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What are the 5 coordinate systems?
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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5
What is the slope of the line that contains the points -3,-
2
O
O
11
11
12
11
11
12
and (3, -8)?
Answer:
-11/12
Step-by-step explanation:
NEED HELP ASAP - Algebra 2 - 50 Points
Create two complex numbers a+bi, where b≠0, such that the product of your numbers is 821
The product of two complex numbers, with a result of 821, is given as follows:
(26 + 12.04i)(26 - 12.04i) = 821.
What are complex numbers?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:
a is the real part.b is the imaginary part.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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r to the nearest whole number.
12) Huong enlarged the size of a painting to a
width of 12 cm. What is the new height if
it was originally 4 cm wide and 3 cm tall?
14) Bill enlarged the size of a photo to a
height of 6 cm. What is the new width if
it was originally 2 cm tall and 4 cm wide?
The nearest whole number to which the new height of the image is enlarged is 9cm.
What is meant by height?
Height is a mathematical term that refers to the vertical distance between an object's top and base.On sometimes, it has the designation "altitude." The measurement of an item along the y-axis in coordinate geometry is referred to as height in geometry.Below are a few mathematical illustrations of height.Height is a measurement of vertical distance, or how high something or someone is (how tall they are) (how "high" a point is).For instance, "That building is 50 meters high," or "An airplane flies around 10,000 meters high."the height of something above the ground or another level of your choice. At a height of 15,000 meters, we flew.To learn more about height refer to
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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.
What is scale factor?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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Fill in the table to find how much it costs for 2, 4, 5, and 8 visits. Use the calculator to help you
solve.
8
Number of visits (v) Cost to get hair done (c) Cost per visit ()
2
4
5
8
$
$
$
It costs $4 for 2 visits, $8 for 4 visits, $10 for 5 visits, and $16 for 8 visits.
Fill in the table to find how much it costs for 2, 4, 5, and 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.
Therefore, it costs $4 for 2 visits, $8 for 4 visits, $10 for 5 visits, and $16 for 8 visits.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
As seen in the table above, the cost to get your hair done for 2, 4, 5, and 8 visits is $30, $60, $75, and $120 respectively.This means that no matter how many visits you make, the cost per visit stays the same at $15.This is a great deal for customers as they can enjoy the same services for a fixed price.This theory is called the "linear cost model." It is based on the idea that the cost of a product or service is proportional to the number of units that are purchased.In this case, the cost per visit is constant, and the total cost increases in a linear fashion as the number of visits increases.This model is useful for determining the cost of a service or product for a variety of customers, as the cost per unit is known.To learn more about linear cost model refer to:
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A reflective pronoun is a pronoun
formed with -self or -selves that is used for emphasis.
formed with -self or -selves that refers to the subject.
that is not formed with -self or -selves.
that is not plural or possessive.
A reflective pronoun is a pronoun formed with -self or -selves that refers to the subject. Hence, option B is correct.
What is reflective pronoun?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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Please me help on this!!!
Answer:
y = -4/1x + 28
Step-by-step explanation:
y=Mx +b
slope (m): -4/1
Y intercept (b): 28
A man deposited ghc 1200 in his bank account. A simple interest of 20% per annum was paid on his deposit.
Calculate the
a.simple interest for the 4 years
b.amount at the end of the 4 types
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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please help me! this is my last question
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.
What are substitution reactions How are they classified give one example of each?
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,
nucleophilic substitution electrophilic substitution homolytic substitution.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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What happens to an image when it is enlarged using scale factor between 1 and 1?
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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What is the y-intercept (b) of these two points.
(-2, 5) and (2, 1)
Answer:
the answer is in the images
A plumber $25 per hour of work plus a one-time $90 service call fee. which function represents y, the total cost of hiring the plumber for x hours?
What are the 5 methods of factoring polynomials?
Therefore , the solution of polynomials problem is Grouping technique using the greatest common factor (GCF) and others given below.
What are polynomials?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:
Grouping: This method involves grouping the first two and last two terms of a polynomial and factoring out the greatest common factor (GCF) from each group.Factoring by GroupingFactoring by grouping is a method of factoring polynomials that is similar to factoring by grouping. The idea behind factoring by grouping is to group together the first two and last two terms of a polynomial and then factor out the greatest common factor (GCF) from each group.Factoring by Inspection: This method involves looking at a polynomial and seeing if it can be factored into two binomials of the form (x + a) or (x - a).Factoring by using the synthetic Division: This method involves dividing a polynomial by a linear factor using synthetic division, which can reveal a linear factor in the polynomial.Factoring by using the quadratic formula: This method involves factoring a polynomial of degree 2 by using the quadratic formula.Factoring by using the difference of squares: This method involves factoring a polynomial that is a difference of squares.Factoring by using the sum and difference of cubes: This method involves factoring a polynomial that is a sum or difference of cubes.To know more about polynomials visit:
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Eric i making banana bread to erve 20 guet. He want each guet to have 1/6 of a loaf. If he bake 3 love of banan bread will eric have
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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Let C2(R) be the linear pace of all function from R to R that have two continuou
derivative and let Sf be the et of olution u(x) ∈ C2(R) of the differential
equation
u′′ u = f (x)
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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solve the problems below
8.8x2.1
2.5+7.8
2(7.2)+3.1
Answer:
46.28
Step-by-step explanation:
i did pemdas
PLEASE HELP!!
Complete the transformations
and then enter the final
coordinates of the figure.
A" ([?], [?])
B" ([?], [?])
C" ([?], [?]
Complete transformations and then enter the final coordinates of the figure will be: A(2,2) B(1,-2) C (4,-4)
How to find A, B, C?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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What is the value of x? responses x = 4. 8 cm x, = 4. 8 cm x = 30 cm x, = 30 cm x = 93 cm x, = 93 cm x = 187. 5 cm x , = 187. 5 cm.
Using the equation we know that the required value of x is (B) 30 cm.
What are equations?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
Tell whether the ratios form a proportion.
16/12 & 26/ 22
The ratios _____ (do or do not) form a proportion. The cross products are _____ (state the cross product or state "not equal")
Response:
Answer: The ratios do form a proportion. The cross products are equal (16 * 22 = 26 * 12)
Step-by-step explanation:
Based on the information provided in the graph, for which of the following situations could you expect to have the greatest increase in salary?
On solving the provided question we can say that based on the provided graph obtaining a doctorate after earning a master's degree.
What is graphs?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.
What is the value of x?
The value of x is given as follows:
x = 13.7.
How to obtain the value of x?The value of x is obtained using similar triangles, which share these two following features:
Congruent angle measures.Proportional side lengths.The proportional side lengths are given as follows:
x and 16.6 and 7.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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Find the hypotenuse use simplest radical form if necessary
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.
what is Pythagoras' Theorem ?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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Is Y 3 exponential function?
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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Can yall help me with this math question fast
Answer:c
Step-by-step explanation:
c
HELPPPPPPP Answer 5 questions and get lots of Points
How do you solve 7x 9 23?
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.
10 POINTS UP FOR GRABS!!! SHOW YOUR WORKING!!! :)
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!