Answer: Yes, it is linear expression
Step-by-step explanation:
The equation is y=mx + b
Here we have 7x, which we have the slope
We don't see the y-intercept, so it is 0
11-14 are confusing can anyone help and tell me how to get the written answer
Answer:
11) KF = DB
12) DC=YZ
13) <C = <W
14) <S and <K
Step-by-step explanation:
11) For this question, we want to try and use SSS to prove the triangles are congruent. SSS stands for side-side-side postulate, so all sides have to be equivalent. We already have ED = FB as given, and DF = DF due to reflexive property. From this information, we already have two sides. Additional information that would be needed to figure out the third side is KF = DB, as it's the only side we are missing.
12) For this question, we want to use SAS postulate, which stands for side-angle-side. We already have one side congruent, which is BC=YX. We have one angle congruent which is <C = <Y. With this information, we have one side and one angle. This means that we need to find another side that is congruent. The side that we need to find here is DC=YZ, as it will help us prove the triangles are congruent with SAS.
13) For this question, we want to use AAS, which stands for angle-angle-side. We already have one angle congruent, which is <CDE = WDE. We have one side congruent as well, which is DE = DE due to reflexive property. With this given information, we have one angle and one side. We only need one more angle before the other angle to figure this out. The angles that are needed are <C = <W.
14) For this question, we want to use ASA, which stands for angle-side-angle. The one angle we have already is <KTM = <UTS, which is because of vertical angles are congruent. The one side that we have is ST=TK. With this, we have one angle and one side. We just need one more angle to prove this, which would be <S and <K.
Remember, for triangle congruency postulates, they have to be in order. They cannot just be out of order. For example, in question 14, we have to find the measures in order. First we need an angle, side, and then another angle. The first angle is <S and <K, then the side we have is ST=TK, and then our last angle, <KTM = <UTS.
Waterworks is a company that manufactures and sells paddleboards. Its profit P, in hundreds of dollars earned, is a function of the number of paddleboards sold x, measured in thousands. Profit is modeled by the function [tex]p(x)=-3x^{3}+45x^{2} -132x[/tex]. What do the zeros of the function tell you about the number of paddleboards that Waterworks should produce?
In order to make a profit, Waterworks must produce more than ___ and fewer than ____ paddleboards.
Waterworks must produce more than 4 and fewer than 11 paddleboards.
What do you mean by polynomial?
A polynomial is defined as an expression consisting of variables, constants, and exponents combined by mathematical operations such as addition, subtraction, multiplication, and division (not division by a variable). Based on the number of terms in the expression, it is classified as monomial, binomial, and trinomial.
It is given that Waterworks is a company that manufactures and sells paddleboards. Its profit P, in hundreds of dollars earned, is a function of the number of paddleboards sold x, measured in thousands. Profit is modeled by the function
[tex]p(x) = -3x^{3}+45x^{2} -132x[/tex]
zeroes of the p(x) will show the quantity at which profit = 0 i.e. breakeven
Let p(x) = 0
[tex]-3x^{3} +45x^{2} -132x =0[/tex]
-3x ([tex]x^{2} -15x+44[/tex]) = 0
-3x ([tex]x^{2} -11x-4x+44[/tex] ) = 0
-3x (x(x-11) - 4(x-11)) = 0
-3x (x-11) (x-4) = 0
-3x = 0 or x-11 = 0 or x-4=0
x = 0,11,4
So,profit is obtained when 4<x<11.
Therefore, Waterworks must produce more than 4 and fewer than 11 paddleboards.
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The area of a triangle is 474. Two of the side lengths are 87 and 19 and the included angle is acute. Find the measure of the included angle, to the nearest tenth of a degree.
Answer:
Let $x$ be the measure of the included angle. We can use the formula for the area of a triangle to find an equation in terms of $x$.
The area of a triangle is given by $\frac{1}{2}bh$, where $b$ is the length of the base and $h$ is the length of the altitude from the base to the opposite vertex. In this case, the base is 87 and the altitude is the length of the line segment from the vertex opposite the included angle to the base, which we can find using the Law of Sines:
$$\frac{h}{\sin x} = \frac{19}{\sin(180^\circ-x)}$$
$$h = \frac{19\sin x}{\sin(180^\circ-x)}$$
Substituting this expression for $h$ into the formula for the area of the triangle, we get
$$\frac{1}{2}bh = \frac{1}{2} \cdot 87 \cdot \frac{19\sin x}{\sin(180^\circ-x)} = 474$$
Solving this equation for $x$ is somewhat difficult, but we can use a calculator or computer to approximate the value of $x$. Using a calculator, we find that $x \approx 31.4^\circ$. Rounding to the nearest tenth of a degree, the measure of the included angle is $\boxed{31.4^\circ}$.
Step-by-step explanation:
If an antelope eats 7kg of vegetation in 2 days how many killograms of vegetation does it eat per day
Antelope eats 3.5kg of vegetation per day .
What are fractions?
A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.
Given :
antelope eats 7kg of vegetation in 2 days
Thus , vegetation eated per day = 7 / 2 = 3.5 kg
Hence , antelope eats 3.5kg of vegetation per day .
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What is the vertex of this question
The vertex of the parabola y = x² - 16x + 24 will be at (8, -40). Then the correct option is D.
What is the equation of the parabola?Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.
Then the equation of the parabola will be given as,
y = a(x - h)² + k
The equation is given below.
y = x² - 16x + 24
Convert the equation into vertex form, then we have
y = x² - 16x + 24
y = x² - 2·8·x + 8² - 8² + 24
y = (x - 8)² - 64 + 24
y = (x - 8)² - 40
The vertex of the parabola y = x² - 16x + 24 will be at (8, -40). Then the correct option is D.
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Currently my bank balance is R2 000. What will the new balance be if I withdraw R600 from the account in each of the next 3 months?
Answer:
R200
Step-by-step explanation:
R200
Ninth grade math and I need help.
Answer:
Step-by-step explanation: By using the verticle line test, because the line has passed more than one point, it is NOT A FUNCTION.
If 9, 12, 15 is a Pythagorean Triple, which of the following could also be a Pythagorean Triple?
a) 5,7,9
b) 17, 20, 23
c) 36, 48, 60
d) 19, 22, 25
Answer:
c) 36, 48, 60
Step-by-step explanation:
A Pythagorean Triple is a set of positive integers (a, b, c) that follows the rule:
[tex]\boxed{a^2+b^2=c^2}[/tex]
where a < c and b < c.
It always consists of:
all even numbers, ortwo odd numbers and an even number.When a and b are both even, c is even.
When one of a and b is odd and the other is even, c is odd.
(5, 7, 9) cannot be a Pythagorean Triple since it consists of all odd numbers.
(17, 20, 23) is not a Pythagorean Triple since:
[tex]\implies 17^2+20^2=23^2[/tex]
[tex]\implies 289+400=529[/tex]
[tex]\implies 689 \neq 529[/tex]
(36, 48, 60) is a Pythagorean Triple since:
[tex]\implies 36^2+48^2=60^2[/tex]
[tex]\implies 1296+2304=3600[/tex]
[tex]\implies 3600=3600[/tex]
(19, 22, 25) is not a Pythagorean Triple since:
[tex]\implies 19^2+22^2=25^2[/tex]
[tex]\implies 361+484=625[/tex]
[tex]\implies 845\neq 625[/tex]
10mm
5mm
13mm
Trapezium
The area of the trapezium will be = 90[tex]mm^{2}[/tex]
According to the figure of the trapezium =
Let us consider the length of base a = 5mm
length of base b = 13mm
height h of the trapezium = 10mm
According to the formula of the area of trapezium
= (1/2) x h x (a + b)
= (1/2) x 10 x (13 + 5)
= 5 x 18
= 90[tex]mm^{2}[/tex]
Therefore, the area of the trapezium will be = 90[tex]mm^{2}[/tex]
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The complete question here could be- Find the area of the trapezium given base a= 5mm, base b= 13mm and height h= 10mm
Reduce 45/99 to the standard form
Answer:
= 4.54545 × 10^-1
Step-by-step explanation:
[tex] \frac{45}{99} = \frac{5}{11} [/tex]
= 0.45454545
= 4.54545 × 10^-1
I hope this helped
what is the equation in slope intersept form of the line that passes through the point (2,-2) and is perpendicular to the line represented by y=2/5x +2
The line that goes through the point (2,-2) and is perpendicular to the line shown by y=2/5x +2 will have the slope intercept equation 5x+3y=6.
What is equation of line?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.
Here,
Slope of the line given=2/5
Slope of the line perpendicular=-5/2
coordinates=(2,-2)
y=mx+b
-2=-5/2*2+b
b=3
y=-5/2x+3
3y=-5x+6
5x+3y=6
The equation in slope intercept form of the line that passes through the point (2,-2) and is perpendicular to the line represented by y=2/5x +2 will be 5x+3y=6.
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For linear function f.f(2)= 0 and f(4)=-6.
Write function f in slope-intercept
How do you find the slope of the line when you have 2 points?
Hence, when [tex]m=-3,b=6[/tex], so the equation of slope is [tex]y=-3x+6[/tex].
What is the slope of line?
The slope of a line gives the measure of its steepness and direction. The slope of a straight line between two points says [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] can be easily determined by finding the difference between the coordinates of the points.
The slope is usually represented by the letter [tex]m[/tex].
Here given that,
The linear function [tex]f(2)= 0[/tex] and [tex]f(4)=-6[/tex].
Let the linear function is
[tex]y=mx+b[/tex]
[tex]x=2,y=0[/tex]
Then
[tex]0=m(2)+b\\\\2m+b=0[/tex] .......[tex](1)[/tex]
And for
[tex]f(4)=-6\\x=4,y=-6[/tex]
[tex]-6=m(4)+b\\\\4m+b=-6[/tex] ......[tex](2)[/tex]
Solving equation [tex](1)[/tex] and [tex](2)[/tex], we get
In equation [tex](1)[/tex]
[tex]b=-2m[/tex] ........[tex](*)[/tex]
Substitute [tex]b=-2m[/tex] in equation [tex](2)[/tex]
[tex]4m-2m=-6\\\\2m=-6\\\\m==\frac{6}{2}\\\\m=-3[/tex]
Put [tex]m=-3[/tex] in [tex](*)[/tex] equation
[tex]b=2m\\\\b=-2(-3)\\\\b=6[/tex]
Hence, when [tex]m=-3,b=6[/tex], so the equation of slope is [tex]y=-3x+6[/tex].
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It costs £80.50 to buy 7 skirts. How much does it
cost to buy 10 skirts? Give your answer in pounds
(£).
Answer:
£115
Step-by-step explanation:
--7x-7y= 28
2x - 7y = 1
please solve this systems of eqautions
After solving the equation the linear equation is x = 27/5 , y = 7/5.
What do you mean by linear equation?
Equations with the highest degree of 1 are called linear equations. This means that the exponent of the variable in the linear equation is greater than 1. The graph of a linear equation is always a straight line.
A linear equation is an algebraic equation in which each term has exponent 1, and the graph of this equation is always a straight line. For this reason, it is called a "linear equation".
Given system of equation:
7x - 7y = 28 ..........(1)
2x - 7y = 1 .............(2)
Solve this system of linear equation. Find the value of 7y from equation (1) and substitute in equation(2)
7x - 7y = 28
7x - 28 =7y .............(3)
Substitute this value in equation (2)
2x - (7x - 28) = 1
2x - 7x + 28 = 1
-5x + 28 = 1
5x = 28 - 1
5x = 27
x = 27/5
Substitute this value in equation (3)
7y = 7(27/5) - 28
7y = 189/5 - 28
7y = 49/5
y = 7/5
Therefore, x = 27/5 , y = 7/5
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Pls plss help me on this !!
Answer:
C) is 20
Step-by-step explanation:
3 inches x 5= 15
so we do the same with 4 minutes
4 minutes x 5= 20
What are the domain and range of this graph? f(x)=x^5+x^2
Therefore ,the domain and range of this graph f(x)=x^5+x^2
Domain : (-∞,∞), {x|x ∈ R} Range:(-∞,∞), {y|y ∈} R
what is domain?A function's domain is the set of possible values that can be entered. This set reflects the values of x in a function like f. (x). Its range refers to the set of possible values that a function can accept. These are the values that are returned by the function when we enter an x value.
Here,
The domain is all values of x that make the expression defined.
Interval Notation:
(−∞,0)∪(0,∞)
=>(-∞,∞)
The Range is all values of y that make the expression defined.
Interval Notation:
(−∞,0)∪(0,∞)
=>(-∞,∞)
Therefore ,the domain and range of this graph f(x)=x^5+x^2 Domain : (-∞,∞), {x|x ∈ R} Range:(-∞,∞), {y|y ∈} R
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Select the correct answer.
Which expression is equivalent to this polynomial expression?
(82²y9z³y+9y) - (6x³y - zy² + 4y)
OA. 8-3x²y - zy² + 13y
OB.
82² 15z²y + zy² + 5y
O C. -7z²y - zy² + 13y
OD.
-72²y + zy² + 5y
Answer:
B. Just Minus expression with same one
Write the expression that completes the equation to represent the
result of transforming y = |x| with the steps listed below.
1: Shift the function 5 units to the left.
2: Shift the function 4 units down.
y = | x + 5 | - 4
You subtract 4 outside the abs val to move the graph down.
You add 5 inside the abs val to move the graph left. (Inside translations are the opposite of what you'd expect.)
if a blood stain has a length of 3.0cm and a width of 1.5cm what is the angle of impact
If a blood stain has a length of 3.0cm and a width of 1.5cm, the angle of impact is 30 degrees
The length of the blood stain = 3 cm
The width of the blood stain = 1.5 cm
The equation for measuring the angle of impact is
sin (angle of impact) = The width of the blood stain / The length of the blood stain
Angle of impact = sin^-1 (The width of the blood stain / The length of the blood stain)
Substitute the values in the equation
Angle of impact = sin^-1(1.5 / 3)
= sin^-1(0.5)
= 30 degrees
Therefore, the angle of impact is 30 degrees
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A group of 10 students took tests in math, English, and chemistry.
The scatter plots compare the students’ scores on the tests
Complete the sentences to describe the data.
The math and English scores show
a positive correlation
a negative correlation
no correlation
The math and chemistry scores show
a positive correlation
a negative correlation
no correlation
The correlation of the scatterplots are defined as;
The math and English scores show; A positive correlation.
The math and chemistry scores show; A negative correlation
What is the correlation of the scatterplot?In correlation in statistics, it could either be positive correlation, negative correlation or no correlation at all.
A positive correlation is defined as a relationship between two variables that tend to move in the same direction. Thus, a positive correlation exists in the event that one variable tends to decrease while the other variable decreases, or one variable tends to increase while the other variable increases.
A negative correlation is defined as a relationship between two variables whereby one variable increases while the other decreases, and vice versa.
No correlation means there is no relationship between the two variables.
Now, for scatterplot of the math and English scores shown, we see that majority of the english scores increase as the maths scores increase and as sch it is a positive correlation.
Meanwhile, for the math and chemistry scores shown, majority of the maths score decreases with an increase in the chemistry score and as such this is a negative correlation.
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the salaries of pharmacy techs are normally distributed with a mean of $32,000 and a standard deviation of $3,000. if 25 pharmacy techs are selected at random, what is the probability their average salary is less than $33,200? the answer should be typed as a decimal with 4 decimal places.
The probability their average salary is less than $33,200 is = 0.6554
Given that,
Mean = $32,000
Standard deviation = $3,000
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Standard deviation (SD) is a widely used measurement of variability used in statistics. It shows how much variation there is from the average (mean). A low SD indicates that the data points tend to be close to the mean, whereas a high SD indicates that the data are spread out over a large range of values.
The Z score is used to calculate how many standard deviations above or below the mean the raw score is. It comes from,
z = (x- μ) / σ (Equation-1)
Where,
x=raw score,
μ=mean,
σ=standard deviation
μ=32,000,
σ=3,000
Average salary is less than $33,200
x < 33,200
We can substitute values in Equation-1,
z = (33,200-32,000)/3000
z = 1200/3000
z = 0.4
Using the normal distribution table as a guide,
P(x < 33,200) = P(z < 0.4)
P(x < 33,200) = 1-P(z>0.4)
P(x < 33,200) = 0.6554
Therefore,
The probability their average salary is less than $33,200 is = 0.6554
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For the three-part question that follows, provide your answer to each question in the given workspace. Identify each part with a coordinating response. Be sure to clearly label each part of your response as Part A, Part B, and Part C.
A bag contains three blue marbles, five red marbles, and four green marbles.
Part A: What is the probability of selecting three marbles where one is blue and two are green?
Part B: What is the probability of selecting one blue marble and then selecting three red marbles?
Part C: In your own words, write a short paragraph that explains your work for Parts A and B.
a) The probability of selecting three marbles where one is blue and two are green is of: 0.0818 = 8.18%.
b) The probability of selecting one blue marble and then selecting three red marbles is of: 0.0152 = 1.52%.
c) The probabilities were obtained dividing the number of desired outcomes by the number of total outcomes, and all the possible combinations were considered.
How to obtain the probabilities?The probabilities are obtained as the division of the number of desired outcomes by the number of total outcomes.
The outcomes with one blue and two green are given as follows:
Blue (3/12 probability) then two green, with 4/11 and 3/10 probabilities.Green then blue then green.Green, green then blue.Hence a multiplication for 3 is used for the probability, as follows:
p = 3 x 3/12 x 4/11 x 3/10 = 0.0818 = 8.18%.
For blue then three red, the outcomes are given as follows:
Blue (3/12 probability).Red: 5/11.Red: 4/10.Red: 3/9.Thus the probability is of:
p = 3/12 x 5/11 x 4/10 x 3/9 = 0.0152 = 1.52%.
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The length (L) of a rectangle of fixed area varies inversely as the width (W). If the
length of the rectangle is 6 feet when the width is 12 feet, find the length of the
rectangle when the width is 4 feet.
Answer:
Length of the rectangle is 18 ft when its width is 4ft
Step-by-step explanation:
Let us assume that the length is represented by l.
Let us assume that the width is represented by w.
As given
The length of the rectangle varies inversely with its width.
Thus
L x 1/w
l=k/w
Where k is the constant of proportionality .
As given
If the
length of the rectangle is 6 feet when the width is 12 feet,
l=6, w=12
putting the values in l = k/w
6 = k/12
k = 12 x 6
k=72
As given
width is 4ft
k= 72, w = 4
Putting the values in, L = k/w
L= 72/4
L=18 ft
Therefore the length of the rectangle is 18 ft when its width is 4ft
Hope this helps You
Roanne earned $5 for 1/2 of an hour of babyitting. How much would Roanne make in 1 hour
Using simple mathematical operations, we can conclude that Roanne will earn $10 in 1 hour.
What are mathematical operations?A mathematical "operation" is the process of calculating a value utilizing operands and a math operator.
There are predefined rules associated with the math operator's symbol that must be applied to the supplied operands or numbers.
The order of operations refers to the rules that govern how to solve an expression with several operations.
Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction are all referred to as PEMDAS (from left to right).
So, we know that:
Roanne earns $5 for 1/2 hour.
Roanne will earn in 1/2 * 2 = 1 hour:
5 * 2 = $10
Therefore, using simple mathematical operations, we can conclude that Roanne will earn $10 in 1 hour.
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If f(x) and its inverse function, f–1(x), are both plotted on the same coordinate plane, what is their point of intersection?
On a coordinate plane, a curve opens down and to the right in quadrants 3 and 4 and then changes direction and curves up and to the left in quadrants 1 and 4. The curve crosses the y-axis at (0, negative 2), changes direction at (1, negative 1, and crosses the x-axis at (2, 0).
The point of intersection of f(x) and [tex]f^{-1}[/tex](x) is (3, 3)
What is a function?"It defines a relation between input and output values."
"In function, for each input there is exactly one output."
What is inverse function?"The inverse function of x = f(m) is m =[tex]f^{-1}[/tex] , where x, m are real values"
For given question,
A function f(x) and its inverse function [tex]f^{-1}(x)[/tex], are both plotted on the same coordinate plane.
We know that the inverse function [tex]f^{-1}(x)[/tex] is the mirror image of the function f(x.)
This means, both the functions must be symmetric about the line y = x.
The curve of inverse function [tex]f^{-1} (x)[/tex] would cross the Y-axis at (0, 2), changes direction at (-1, -1) and crosses the X-axis at (-2, 0)
And both the functions intersect each other only on y = x
The point which satisfy the line y = x is (3, 3)
Therefore, the point of intersection of f(x) and[tex]f^{-1} (x)[/tex] is (3, 3)
The complete question is : If f(x) and its inverse function, f–1(x), are both plotted on the same coordinate plane, what is their point of intersection?
On a coordinate plane, a curve opens down and to the right in quadrants 3 and 4 and then changes direction and curves up and to the left in quadrants 1 and 4. The curve crosses the y-axis at (0, negative 2), changes direction at (1, negative 1, and crosses the x-axis at (2, 0).
A.(0, –2)
B.(1, –1)
C.(2, 0)
D.(3, 3)
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Simplify 2/3(6x-1/9)-x+3/6
Answer:
Step-by-step explanation:
3x+23/54
An step by step explanation of all of them would be great .
Btw I did 1 to 5 and they all worked
Solution of x is 1± 5√2 for the given quadratic equation.
What is quadratic equation?
Quadratics are often outlined as a polynomial equation of a second degree, which means that it contains a minimum of 1 term that's square. it's conjointly known as quadratic equations.
Main body;
11)
x² = 2x +48
The given is an quadratic equation:
solution of this can be found out using quadratic formula:
x =(-b ±[tex]\sqrt{b^{2} -4ac}[/tex])/2a
for this ,
x² -2x -48 = 0
a = 1
b= -2
c = -48
x =( 2±√ (4- 4*1*-48))/2
x = (2±√200)/2
x = 1± 5√2
Hence solution of x is 1± 5√2.
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(b) if the coupons are different, how many ways are there to distribute the coupons so that at least one woman receives a coupon?
By probability ,181753 are ways are there to distribute the coupons so that at least one woman receives a coupon.
What does the math term "probability" mean?
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out.
Statistics describes the examination of events subject to probability.
Number of ways such that the coupons are distributed such that at least one woman receives a coupon is computed as:
= Total number of ways to select 10 people from the 20 people - Total number of ways to select 10 men from the 15 men
= ( 20 10 ) - ( 15 10 ) = 184756 - 3003
= 181753
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The complete question is -
10 coupons are given to 20 shoppers in a store. Each shopper can receive at most one coupon. 5 of the shoppers are women and 15 of the shoppers are men.
(a) If the coupons are identical, how many ways are there to distribute the coupons so that at least one woman receives a coupon?
By probability ,181753 are ways are there to distribute the coupons so that at least one woman receives a coupon.
What does the math term "probability" mean?
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out.
Statistics describes the examination of events subject to probability.
Number of ways such that the coupons are distributed such that at least one woman receives a coupon is computed as:
= Total number of ways to select 10 people from the 20 people - Total number of ways to select 10 men from the 15 men
= ( 20 10 ) - ( 15 10 ) = 184756 - 3003
= 181753
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solve for x. Express your answer as a proper or improper fraction in simplest terms,
-1/2= 4/9x+5/6
x=
Answer: x=-3
Step-by-step explanation:
A taxi ride costs $4, plus an additional $3 per mile. Graph the line relating taxi ride costs to distance (in miles).
The required equation of line in slope intercept form is
y = 3x + 4
What is equation of line in slope intercept form?
The most general form of equation of line in slope intercept form is given by y = mx + c
Where m is the slope of the line and c is the y intercept of the line.
Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.
If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by
m = [tex]tan\theta[/tex]
The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.
The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.
Let the taxi is driven x miles and the total cost is $y
A taxi ride costs $4, plus an additional $3 per mile
Total cost = 4 + 3x
By the problem,
y = 4 + 3x
This is the required equation of line which represents the above situation.
The graph has been attached here.
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