The linear equation that passes through the two given points is:
y = -2x + 4
How to write the equation of the line?A general linear equation can be written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
Particularly, if a line passes through the points (x₁, y₁) and (x₂, y₂) then the slope will be:
a = (y₂ - y₁)/(x₂ - x₁)
Here we know that the line passes through (-1, 6) and (4, -4), then the slope is:
a = (-4 - 6)/(4 + 1) = -2
y = -2x + b
To find the value of b, we can replace the values of any of the points in the equation, if we use (-1, 6) we will get:
6 = -2*-1 + b
6 = 2 + b
6 - 2 = b = 4
The linear equation is y = -2x + 4
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Use these formulas to help you complete the problems below. State the formula you are using. Set up an equation or show work. Solve.
If a polygon can be divided into 5 triangles when the diagonals are drawn from one of its vertices, how many sides does the polygon have?
The number of sides the polygon have 9.
What is Vertices?A vertex is a point on a polygon where two rays or line segments meet, the sides, or the edges of the object come together. Vertex is the plural form of vertices.
Given:
We have a polygon can be divided into 5 triangles when the diagonals are drawn from one of its vertices.
As, we know the number of triangles in a polygon is = n−2
where n is the number of sides (or vertices)
So, the number of sides the polygon have
n= 5+ 2
n = 7 sides
Thus, the polygon is Heptagon.
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The price of Stock A at 9 A.M. was $13.52. Since then, the price has been increasing at the rate of $0.05 each hour. At noon the price of Stock B was $14.27. It begins to decrease at the rate of $0.14 each hour. If the two rates continue, in how many hours will the prices of the two stocks be the same?
The number of hours that the prices of the two stocks be the same will be 4 hours.
What is the solution to the equation?In other words, the collection of all feasible values for the parameters that satisfy the specified mathematical equation is the convenient storage of the bunch of equations.
Let 'x' be the number of hours and 'y' be the price of stocks. Then the equations are written as,
y = 13.52 + 0.05x ...1
y = 14.27 - 0.14x ...2
From equations 1 and 2, then we have
13.52 + 0.05x = 14.27 - 0.14x
0.14x + 0.05x = 14.27 - 13.52
0.19x = 0.75
x = 3.947 ≈ 4 hours
The number of hours that the prices of the two stocks be the same will be 4 hours.
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according to the table, what is the probability that a randomly chosen physical therapist does not use the gym membership given that they bring their lunch to work? give your answer as a fraction in simplest form.
The probability that a randomly chosen physical therapist does not use the gym membership given that they bring their lunch to work is 2/3, in simplest form.
The table shows the information about the gym membership and lunch habits of 100 physical therapists.
Given that a physical therapist brings their lunch to work, we can use the information in the table to calculate the probability that they do not use the gym membership. To do this, we'll use the formula:
P(not using gym membership | brings lunch) = P(not using gym membership and brings lunch) / P(brings lunch)
We can use the information in the table to find the values of P(not using gym membership and brings lunch) and P(brings lunch).
P(not using gym membership and brings lunch) = 40/100 = 2/5
P(brings lunch) = 60/100 = 3/5
So, the probability that a randomly chosen physical therapist does not use the gym membership given that they bring their lunch to work is:
P(not using gym membership | brings lunch) = P(not using gym membership and brings lunch) / P(brings lunch) = (2/5) / (3/5) = 2/3
Therefore, the probability that a randomly chosen physical therapist does not use the gym membership given that they bring their lunch to work is 2/3, in simplest form.
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k
m
(x-30)°
y
n
(x+50)
Find the values of x and y that make k || j and
m || n.
x=
y =
0
The value of variables x and y are,
⇒ x = 80°
⇒ y = 130°
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Since, A parallelogram is forming here,
Then, Opposite angels are going to be equal.
Thus, We get;
⇒ y = (x + 50)°
Now, As you know that sum of all angles of a quadrilateral equals 360°
Hence, We get;
2 {(x + 50) + (x - 30)} = 360°
(x + 50) + (x - 30) = 180°
2x + 20 = 180
2x = 160
x = 80°
So, We get;
⇒ y = (x+50)
= 80 +50
= 130°
And,
⇒ x = 80°
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Translate the following sentence into an equation: "The product of 3 and x increased by 7 equals 25 ."
the diagram below shows the graph of y=x^2+2x-3 for the domain -4 2. use the graph to determine the scale used on the x- axis, the value of y for which x= 1.5, the values of x for which y=0 and the range of values of y, giving your answer in the form a
Answer:
no sisiejdirjr diendieje jdisjeidi
Answer:
awnser is b
Step-by-step explanation:
eg 2023 ........................................
solve the following pair of simultaneous equation graphically
X+2y=3,2x-y=7
Answer:
(x, y) = (3.4, -0.2)
Step-by-step explanation:
You want a graphical solution for the system of equations ...
x +2y = 32x -y = 7GraphThe graph and solution are shown in the attachment. A graphing calculator is a nice bit of useful technology for this. The solution is ...
(x, y) = (3.4, -0.2)
The first line has x-intercept 3 and y-intercept 1.5.
The second line has y-intercept -7 and slope 2. It crosses the x-axis at x=3.5, so will cross the first line in the 4th quadrant.
A GP surgery is recording the waiting time of its patients and produces the
cumulative frequency graph shown below.
100
Cumulative frequency
80
60
40
20
0
5
10
15
Waiting time (mins)
20
25
a) How many patients waited for more
than 20 minutes?
b) Find the median waiting time.
17
patients
minutes
The number of patients that waited for more than 20 minutes is 74
The median waiting time is 17
How to determine the number of patientsFrom the question, we have the following parameters that can be used in our computation:
The graph
Where
x = Waiting time
y = Cumulative frequency
This means that
y = Number of patients that waited x or more time
From the graph, we have
(x, y = (20, 74)
So, the number of patients is 74
The median waiting timeFrom the question, we have the following parameters that can be used in our computation:
Maximum CF = 100
Divide by 2 to calculate the median
Median = 100/2
Evaluate
Median = 50
From the graph, we have
(x, y = (50, 17)
So, the median is 17
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Classify each ordered pair as a solution or not a solution of the inequality y
a inequality y <2/7 x − 5.
The ordered pairs (21, 0) and (6, -4) are the solutions to the given inequality.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
The given inequality is y<2/7x-5.
Here,
Put (x, y)=(21, 0) in the given inequality, we get
0<2/7(21)-5
0<1
So, it is solution
Put (x, y)=(6, -4) in the given inequality, we get
-4<2/7(6)-5
-4<12/7-5
-4<1.7-5
-4<-3.3
So, it is solution
Put (x, y)=(0, -5) in the given inequality, we get
-5<2/7(0)-5
-5<-5
Which is not true, it is not a solution
Put (x, y)=(7, -3) in the given inequality, we get
-3<2/7(7)-5
-3<-3
Which is not true, it is not a solution
Therefore, the ordered pairs (21, 0) and (6, -4) are the solutions to the given inequality.
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An equilateral triangle is similar to a scalene triangle.1) Always2) never3) sometimes
Option 3) Sometimes is the correct answer, Sometimes an equilateral triangle is similar to a scalene triangle.
If the respective sides are proportional and the corresponding angles are congruent, two triangles are comparable. An equilateral triangle has three congruent sides and three congruent angles, so any triangle that is similar to an equilateral triangle must also have three congruent angles. However, a scalene triangle has no congruent sides and no congruent angles, so it is possible for a scalene triangle to be similar to an equilateral triangle only if it has the same angle measurements as an equilateral triangle, but with different side lengths. Therefore, a scalene triangle can be similar to an equilateral triangle, but it is not always the case.
In general, if two triangles are similar, it means that they have the same shape but possibly different sizes. In the case of an equilateral triangle and a scalene triangle, if they are similar, then it means that the scalene triangle has the same angles as the equilateral triangle, but its sides are of different lengths. So it is possible for a scalene triangle to be similar to an equilateral triangle, but not in all cases.
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688588478685758486759+2345678909876545355=
Answer:
6.9x10^20
Step-by-step explanation:
688588478685758486759+2345678909876545355=
6.90934158E20
five times a number is 120
Answer: The Number is 24.
Step-by-step explanation:
1) Set unknown number to a variable (I'm going to do x).
2) Set up equation: 5x = 120.
3) Simplify by dividing both sides by 5: 5x/5 = 120/5 = 24.
Consider the function f(x) = (x - 3)^2
a. How could you restrict the domain of f(x) so that its inverse will be a function?
b. Graph f(x) with its restricted domain and then graph its inverse on the same set of axes.
c. Find the equation of the inverse of f(x) with its restricted domain.
Answer:
Step-by-step explanation:
a) As the function is a quadratic you could restrict the domain by taking only values either side of the line x = 3. This means the domain will be
a) 3<x<∞
Or
b) -∞<x<3
b) the graph is attached below.
c) The equation of the inverse of f(x) can be found by switching x and y:
X = (y-3)²
√x = y - 3
y = √x + 3
However this takes in positive and negative values of the square root function. So in order to restrict this, we can take the positive square root only.
Thus y = +√x + 3
simplify
1/2 - 1/4 + 1/8
Juan the trainer offers two solo workout plans: Plan A and Plan B. Each client does either one or the other (not both). Juan trained on Wednesday and Thursday last week. The table below shows the number of Plan A and Plan B clients Juan trained each day and the total time (in hours) he trained.
Wednesday Thursday
Number of
Plan A workouts
Number of
Plan B workouts
Total time
(in hours)
Let be the length (in hours) of each Plan A workout.
Let be the length (in hours) of each Plan B workout.
(a) Write a system of equations that could be used to find the length (in hours) of each type of workout.
(b) How long (in hours) was each type of workout?
A system of equations that could be used to find the length (in hours) of each type of workout
7a + 9b = 12
5a + 3b = 6
Solve this system of equations by multiplying both sides of one of the equation so that when the equations are added or subtracted there will only be one variable.
-I will multiply both sides of the 2nd equation by -3
-3*(5a + 3b) = 6*-3
-15a - 9b = -18
-Now I will get rid of the variable b by adding the two equations together.
7a + 9b = 12
+ -15a - 9b = -18
-8a = -6
a = -6/-8
a= 3/4 (45 minutes)
-Now plug 3/4 into one of the original equations as a to solve for b.
-I will use the 2nd original equation.
5a + 3b = 6
5(3/4) + 3b = 6
15/4 + 3b = 6
3b = 9/4
b = 9/12 = 3/4 (45 minutes)
Both workout plans last the same amount of time.
Plan A lasts 45 minutes.
Plan B lasts 45 minutes.
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What is the growth factor of 2% decreased
The growth factor of a 2% decrease is 0.98.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
The growth factor of 2% decreased.
This means,
100% - 2%
= 98%
= 98/100
= 0.98
Thus,
0.98 is the growth factor of a 2% decrease.
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The following formula gives the volume V of a cone, where r is the radius of the base and his
the height:
= 1/3r²h
V =
Answer:
Step-by-step explanation: The answer is that because if you think about it and do the problem you would be able to get that answer.
Which statement describes the relationship between −2 and −4? Responses −2 is located to the left of −4 on a horizontal number line because −2>−4. negative 2 is located to the left of negative 4 on a horizontal number line because negative 2 is greater than negative 4. −2 is located to the left of −4 on a horizontal number line because −2<−4. negative 2 is located to the left of negative 4 on a horizontal number line because −2<−4. −2 is located to the right of −4 on a horizontal number line because −2>−4. negative 2 is located to the right of negative 4 on a horizontal number line because negative 2 is greater than negative 4. −2 is located to the right of −4 on a horizontal number line because −2<−4. negative 2 is located to the right of negative 4 on a horizontal number line because −2<−4.
−2 is located to the right of −4 on a horizontal number line because −2>−4. Therefore, option C is the correct answer.
What is number line?A number line is a visual representation of numbers on a straight line. This line is used to compare numbers that are placed at equal intervals on an infinite line that extends on both sides, horizontally or vertically.
Given that, -2 and -4 is located on number line.
Negative integers on the number line located left to zero.
If the greater integer with negative sign and go farther on left of 0 on number line, the value of integers decreases.
Therefore, option C is the correct answer.
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help plsplspls
Find the value of the following expression and round to the nearest integer:
34
Σ 400(0.93)n-2
n=2
The value of the expression is 5193.
How to find the value of the expression?From the question, we have the following parameters that can be used in our computation:
From the notation, we have the following values:
The first term, a = 400
The common ratio, r = 0.93
The number of terms, n = 34 - 1 = 33
The sum of the geometric progression is represented as:
Sum = a(1-rⁿ)/(1-r)
Sum = 400(1-0.93³³)/(1-0.93)
Sum = 5193
Therefore, the value of the expression is 5193
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X=a+b+4 and a directly proportional to y squared , b is inversely proportional to y when y=2 x=18 when y=1 x=-3 find x when y=4
X = 11 when y = 4 when X=a+b+4 and a directly proportional to y squared , b is inversely proportional to y.
Given that a is directly proportional to y^2 and b is inversely proportional to y, we can write the following two relationships:
[tex]a = k * y^2[/tex]
[tex]b = m / y[/tex]
where k and m are constants. From the first equation, we can find the value of k when y = 2:
[tex]a = k * 2^2[/tex]
[tex]k = a / 4[/tex]
And from the second equation, we can find the value of m when y = 2:
[tex]b = m / 2[/tex]
[tex]m = 2b[/tex]
Substituting these values into the equation X = a + b + 4, we can find X when y = 2:
[tex]X = (k * 2^2) + (m / 2) + 4[/tex]
[tex]X = (a / 4) * 4 + 2b + 4[/tex]
[tex]X = a + 2b + 4[/tex]
[tex]X = 18[/tex]
We can now use the value of k and m to find X when y = 4:
[tex]X = (k * 4^2) + (m / 4) + 4[/tex]
[tex]X = (a / 4) * 16 + (2b) / 4 + 4[/tex]
[tex]X = 4a + 2b + 4[/tex]
Substituting the value of X = 18 when y = 2, we can solve for a and b:
18 = 4a + 2b + 4
14 = 4a + 2b
7 = 2a + b
Solving the system of equations for a and b, we find:
a = 5
b = 2
Finally, substituting these values into the equation X = a + b + 4, we can find X when y = 4:
X = (5) + (2) + 4
X = 11
Therefore, X = 11 when y = 4.
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What is the azimuth of an object that is ten degrees south of east?
Answer:
Step-by-step explanation:
135°
Quite commonly, azimuths or compass bearings are stated in a system in which either north or south can be the zero, and the angle may be measured clockwise or anticlockwise from the zero.
I hate math why is this necessary
Answer:
3
Step-by-step explanation:
Slope = rise/ run = change in y / change in x = 3 / 1 = 3
this is VERY necessary in all of the engineering and physics worlds of which you have yet to be acquainted...... these fields enable you to have a smart phone, a car, a bank account, a computer , rockets etc.
. BASKETBALL In 2005, the average ticket prices for Dallas Mavericks games and Boston Celtics games are shown in the table below. The change in price is from the 2004 season to the 2005 season. Team Average Ticket Price Change in Price Dallas $53.60 $0.53 Boston $55.93 –$1.08
a. Assume that tickets continue to change at the same rate each year after 2005. Let x be the number of years after 2005, and y be the price of an average ticket. Write a system of equations to represent the information in the table. b. In how many years will the average ticket price for Dallas approximately equal that of Boston?
Answer:
a. Let's call the average ticket price for Dallas in 2005 as "d" and the average ticket price for Boston in 2005 as "b". Then the system of equations can be written as:
y_d = d + 0.53x (where y_d represents the price of an average ticket for Dallas after x years)
y_b = b - 1.08x (where y_b represents the price of an average ticket for Boston after x years)
b. To find the number of years in which the average ticket price for Dallas will approximately equal that of Boston, we need to solve the equation y_d = y_b for x. Plugging in the equations for y_d and y_b, we get:
d + 0.53x = b - 1.08x
Rearranging and solving for x, we have:
1.61x = b - d
x = (b - d) / 1.61
Now we just need to plug in the values for d and b from the table:
d = 53.60
b = 55.93
x = (55.93 - 53.60) / 1.61 = 2.33 years
So it will take approximately 2.33 years for the average ticket price for Dallas to approximately equal that of Boston.
Step-by-step explanation:
Answer: a. Let x be the number of years after 2005, and y be the price of an average ticket. Then, we can write the following system of equations to represent the information in the table:
For Dallas:
y = 53.60 + 0.53x
For Boston:
y = 55.93 - 1.08x
This system of equations represents the average ticket price y for Dallas and Boston as a function of the number of years x after 2005, with the change in price from the 2004 season to the 2005 season given in the table.
b. To find the number of years when the average ticket price for Dallas will approximately equal that of Boston, we can set the two equations equal to each other and solve for x:
53.60 + 0.53x = 55.93 - 1.08x
2.33x = 2.33
x = 1
So, the average ticket price for Dallas and Boston will approximately equal each other after 1 year. Therefore, in 2006, the average ticket price for Dallas will approximately equal that of Boston.
Step-by-step explanation:
What is the volume of the solid figure?
Enter your answer in the box
Volume of the composite shape is = 114 ft³
What is volume of composite shape?Volume is a measure of three-dimensional space.
A composite shape can be defines as a shape created with two or more basic shapes. We often refer to composite shapes as compound and complex shapes as well.
Now, According to the question:
The shape above shows two cuboid joined together.
Volume of the base cuboid = lbh
= 6×3×1 = 18ft³
Volume of the second cuboid = lbh
= 4×3×8 = 96 ft³
Volume of the composite shape = 18ft³ + 96ft³
= 114 ft³
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Which word best describes the degree of overlap between the two data sets?
A.
high
B.
moderate
C.
low
D.
none
The word that best describes the degree of overlap between the two data sets is C. low
What is the meaning of data overlap ?In statistics, data overlap refers to the situation where two or more groups being compared have some individuals or data points that have similar or identical values. When this happens, it can make it more difficult to accurately distinguish between the groups and to draw meaningful conclusions from the data.
From the given data, we can see that one data set is positively skewed while the other is negative. This shows that the data overlap is quite low.
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Find the gradient of the line that passes through (3, 7) and (1, 10).
Answer:
-1.5
Step-by-step explanation:
The gradient of a line can be found using the formula:
gradient = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are the coordinates of two points on the line.
So for the line that passes through (3, 7) and (1, 10), the gradient can be found as:
gradient = (10 - 7) / (1 - 3)
gradient = 3 / -2
gradient = -1.5
So the gradient of the line that passes through (3, 7) and (1, 10) is -1.5.
A jar contains 18 strawberry, 24 cherry, and 19 lime-flavored candies. The rest of the candys are chocolate there are 82 candys in all. If n represents the number of chocolates in the jar, what equation could you use to find n?
The equation which is used to find the number of chocolates candy in the jar is given by 18 + 24 + 19 + n = 82 , the number of chocolate candy in the jar is equal to 21.
Number of strawberry candy in the jar = 18
Number of cherry candy in the jar = 24
Number of lime flavored candies = 19
Let 'n' be the number of chocolate candy in the jar
Total number of candy in the jar = 82
Equation used to represent the given condition is :
18 + 24 + 19 + n = 82
⇒ 61 + n = 82
⇒ n = 82 - 61
⇒ n = 21
Therefore, the equation required to represent the number of chocolate candy is 18 + 24 + 19 + n = 82 and the value of n is equal to 21.
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Pedro fills up his truck with gas he paid $2.75 a gallon which of these represents an amount and price of gas that Pedro purchased select all that apply
The options that represent an amount and price of gas that Pedro purchased are 19 gallons of gas for $52.25, 16 gallons of gas for $44. So options C and D are correct.
To calculate the amount of gas and the total price that Pedro purchased, we need to use the formula:
Price = Cost per gallon * Number of gallons
Dividing the total price by the cost per gallon will give us the number of gallons purchased. We can then compare this with the given options to see which one(s) match.
Using the given cost per gallon of $2.75, we can check each option:
a) 13.75 gallons of gas for $41.25
Price = $2.75/gallon * 13.75 gallons = $37.81
This option does not match the total price of $41.25, so it is not correct.
b) 22 gallons of gas for $71.5
Price = $2.75/gallon * 22 gallons = $60.50
This option does not match the total price of $71.5, so it is not correct.
c) 19 gallons of gas for $52.25
Price = $2.75/gallon * 19 gallons = $52.25
This option matches the total price of $52.25, so it is correct.
d) 16 gallons of gas for $44
Price = $2.75/gallon * 16 gallons = $44
This option matches the total price of $44, so it is correct.
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Complete question is:
Pedro fills up his truck with gas he paid $2.75 a gallon which of these represents an amount and price of gas that Pedro purchased select all that apply.
a) 13.75 gallons of gas for $41.25
b) 22 gallons of gas for $71.5
c) 19 gallons of gas for $52.25
d) 16 gallons of gas for $44
Write a general formula to describe the following variation: F is directly proportional to the square of d, and F = 40 when d = 5.
Answers:
40 = 5k
F = 8d
F = 1.6*d^2
F = kd
A general formula to describe is F = 1.6×d² will be correct answer.
What in math is a proportional?A relationship is considered proportional if the ratio remains constant. For instance, the average number of apples produced per tree is a measure of proportionality, and the number of trees in an orchard is inversely related to the number of apples produced in a harvest. When two quantities are proportionate with one another, then expand and contract at the same pace, keeping the relationship constant.
Finding the general formula we obtain:
F=kd²
40=k×5²
k=1.6
so, F =1.6×d².
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a statistics professor finds that when he schedules an office hour for student help, an average of students arrive. find the probability that in a randomly selected office hour, the number of student arrivals is
The probability of 3 students arriving at a randomly selected office hour is 0.27(27%). This can be calculated by using the Poisson distribution equation which is P(x)=e^(-λ)*(λ^x/x!).
In the above equation, λ is equal to the average number of arrivals which is 3.3. Plugging these values into the equation gives us P(3)= e^(-3.3)*(3.3^3/3!) = 0.27, this means that the probability of 3 students arriving in randomly selected office hours is 0.27.The Poisson distribution is used to calculate the probability of a certain number of events occurring in a fixed interval of time or space. It is commonly used in engineering, economics, and other fields.
This equation is especially useful in situations like this one where the arrival rate is known and the probability of a certain number of arrivals needs to be determined.
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A statistics professor finds that when she schedules an office hour for student help, an average of 3.3 students arrive. Find the probability that in a randomly selected office hour, the number of student arrivals is 3.
