What is the slope of a line that goes through the points (1,-5) and (-3, 2)?
O
O
O
7
4
3
3
Answers
Answer:
[tex]\sf -\dfrac{7}{4}[/tex]
Step-by-step explanation:
Finding the slope of a line:(1, -5) ⇒ x₁ = 1 ; y₁ = -5
(-3, 2) ⇒ x₂ = -3 ; y₂ = 2
[tex]\sf \boxed{\bf Slope = \dfrac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]\sf =\dfrac{2-[-5]}{-3-1}\\\\= \dfrac{2+5}{-4}\\\\=\dfrac{7}{-4}\\\\= -\dfrac{7}{4}[/tex]
Related Questions
Help me with this pleaseeee
Answers
Answer:
2, 3
Step-by-step explanation:
[tex]g(x)=\frac{1}{2}(4x+6) \\ \\ =2x+3[/tex]
Find the value of r so the line that passes through the pair of points has the given slope. (6, 8), (r, −2), m=1
Answers
Answer:
r=-4
Step-by-step explanation:
use the slope formula
m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Then plug in x and y values and set that equal to m=1
1=[tex]\frac{-2-8}{r-6}[/tex]
multiply r-6 over
r-6=-10
r=-4
Please help me on this question!
Answers
To solve for x
You substitute -4 into y from one of the equations and you get x=-2
6x+5(-4)=-32
6x-20=-32
6x=-12
X=-2
In a math class with 23 students, a test was given the same day that an assignment
was due. There were 14 students who passed the test and 15 students who completed
the assignment. There were 12 students who passed the test and also completed the
assignment. What is the probability that a student chosen randomly from the class
did not complete the homework?
Answers
Answer: 8/23
Step-by-step explanation:
Make a two-way table
Did Assignment Didn't do Assignment
Passed 12 2
Did not pass 3 6
Total 15 8 = 23
2+6=8
8/23
At the beginning of the year, Salma had $35 in savings and saved an additional $8 each week thereafter. Henry started the year with $95 and saved $5 every week. Let SS represent the amount of money Salma has saved tt weeks after the beginning of the year and let HH represent the amount of money Henry has saved tt weeks after the beginning of the year. Write an equation for each situation, in terms of t,t, and determine the number of weeks after the beginning of the year until Salma and Henry have the same amount of money saved.
Answers
The number of weeks when Salma and Henry would have the same amount of money is 20 weeks.
How many weeks would they have the same amount?The form of the equations that represent the total amount of money saved is :
Total amount in the account = initial amount in the account + (amount added each week x number of weeks)
SS = $35 + ($8 x tt)
SS = $35 + $8tt
HH = $95 + ($5 x tt)
HH = $95 + $5tt
When they have the same amount in their account, the two equations woud be equal.
HH = SS
$95 + $5tt = $35 + $8tt
$95 - $35 = $8tt - $5tt
$60 = $3tt
tt = $60 / 3
tt = 20 weeks
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Hi could you help me on this question I don’t really know how to answer this..? I will mark brainliest!
Answers
The postulate that can be used to prove that the triangles are congruent is: AAS.
What is the AAS Congruence Postulate?The AAS congruence postulate states that if two angles and one non-included side of one triangle are congruent to corresponding two angles and one non-included side of another triangle, it can be proven that both triangles are congruent triangles.
From the image, we know that triangles RST and UVT have:
Two pairs of congruent angles, which are angle RST ≅ angle UVT and angle RTS ≅ UTV (vertical angles)
One pair of non-included congruent sides, which are RT ≅ UT.
Thus, we can conclude that they are congruent triangles based on the AAS congruence postulate.
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What is the shape of the base of the figure?
16 km
8 km
Answers
Answer: rectangle
Step-by-step explanation: brainliest please? i could really use it
Answer:
most likely 16 if its a long object or 8 if its a short one
Step-by-step explanation:
if u provided a graph it could help alot
What is the volume (in cubic units) of a sphere with a radius of 9 units and height of 7 units? assume that it = 3.14 and round your answer to the nearest tenth when necessary.
Answers
After solving with help of the formula to find the volume of the sphere we find that the volume of the sphere is 3053.63
The radius of the sphere = 9 units
Height of sphere =7 units
the value of π is given in the question =3.14
The volume of the sphere = 4/3 × π × r^3
= (4/3) × 3.14×9^3
= (4/3) × 3.14 × 27
= 4 × 3.14 × 9
= 36 × 3.14
= 3053.63
The volume of the sphere is 3053.63
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Segment addition and midpoints
In the figure below, B is between A and C, and C Is between B and D. If AC=8, BC=5, and BD=9, find AD.
Answers
The line segment AD is 12 units.
How to find the segment AD using midpoint?The midpoint is the middle point of a line segment.
It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints.
The midpoint is halfway between the two end points:
Therefore, B is between A and C.
C is between B and D.
Hence,
AC = 8
BC = 5
BD = 9
AD = ?
Therefore,
AD = AB + BC + CD
AB = AC - BC
AB = 8 - 5
AB = 3 units
CD = BD - BC
CD = 9 - 5
CD = 4 units
Therefore,
AD = 3 + 5 + 4
AD = 12 units
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what is the difference 2/5(d-10)-2/3(d+6)
Answers
The difference between 2/5(d-10)-2/3(d+6) is -56.
Firstly simplifying the terms to find the difference. Simplifying the first part -
Rewriting the expression
Expression 1 = 2/5(d - 10)
Multiplying the terms with the bracket
Expression 1 = 2d/5 - ((2×10)/5)
Multiplying the terms on Right Hand Side
Expression 1 = 2d/5 - 2×2
Performing multiplication
Expression 1 = 2d/5 - 4
Simplifying the second part -
Rewriting the expression
Expression 2 = 2/5(d + 6)
Multiplying the terms with the bracket
Expression 2 = 2d/5 + ((2×6)/5)
Multiplying the terms on Right Hand Side
Expression 2 = 2d/5 - 12×5
Performing multiplication
Expression 2 = 2d/5 - 60
Subtracting expression 2 from expression 1
Difference = 2d/5 - 60 - (2d/5 - 4)
2d/5 will be subtracted to give 0
Difference = - 60 + 4
Performing subtraction
Difference = - 56
Therefore, the difference between mentioned expressions is -56.
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Two cars leave from a place at the same time they travel in opposite directions one at 62 KM per hour the other at 48 KM per hour how long will it take before they are 550 KM apart
Answers
If two cars leaves from a place at the same time they travel in opposite directions and the speed of the first and second cars are 62 km per hour and 48 km per hours respectively , 5 hours will take before they are 550 km apart
The speed of the first car=62 km per hour
The speed of the second car=48 km per hour
Two cars leave from a place at the same time they travel in opposite directions
The relative speed of the car = Speed of the first car - (- Speed of the second car )
=62-(-48)
=110 km per hour
Time take = Distance between the two cars / Relative speed of the two care
=550/110
=5 hours
Hence, if two cars leaves from a place at the same time they travel in opposite directions one at 62 km per hour the other at 48 km per hour, 5 hours will take before they are 550 km apart
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Draw the net force arrow on the picture to the left.
Answers
Answer:
Step-by-step explanation:
A ball thrown straight upward from a height of 6 ft with an initial velocity of 55 ft per sec has height h(t) feet after t seconds,
where h(t)=-16t+55t+6. What is the ball's average velocity (that is, its average rate of change in height) during the
first second?
The average velocity during the first second is
(Type an integer or a simplified fraction.)
feet per second
Answers
Answer:
16t+55t+6t=77. 55-6=49
the volume of a cube is 64cm³. what is the total surface area.
Answers
Answer:[tex]96cm^2\\[/tex]
Step-by-step explanation:
64= [tex]x^3\\[/tex]
[tex]\sqrt[3]{64} =4[/tex]
So a side is 4, and surface area of one side is 4x4 = [tex]16cm^2[/tex]
cude has 6 faces, 16*6 = [tex]96cm^2\\[/tex]
Answer:
96 cm²
Step-by-step explanation:
If the side of a cube is a, then volume = a³
There are six surfaces for a cube and each surface has an area of a²
So total surface area = 6a²
Since we are given volume = 64 cm³, each side must be ∛64 = 4 cm
So total surface area = 6 x 4² = 6 x 16 = 96 cm²
3) Write the equation of the line (in slope-intercept) that passes through (3,10)
a) and is parallel to y = x - 1
b) and is perpendicular to y = x - 1
Answers
The Equation of line -
When line is parallel to line y = x - 1 is y = x + 7When line is perpendicular to line y = x - 1 is y = x + 7What is the slope intercept form of a line?
The slope intercept form of a line is given by -
y = mx + c
m is the slope of line
c is the y - intercept
Given is a line that passes through the point (3, 10) and in case [1] is parallel to line y = x - 1 and in case [2] is perpendicular to y = x - 1.
Case 1 - Line is parallel to the line y = x - 1
Assume that the equation of line is -
y = mx + c
Since, the line is parallel, both lines will have same slope and is given by -
m = 1
Since, the line passes through the point (3, 10) we can write -
10 = 1 x 3 + c
c = 7
We can write the equation of line parallel to line y = x - 1 as -
y = x + 7
Case 2- Line is perpendicular to the line y = x - 1 -
Assume that the equation of line is -
y = mx + c
Since, the line is perpendicular, the product of slopes of both lines will be equal to 1. The slope (m) of the line will be -
m x 1 = -1
m = -1
Since, the line passes through the point (3, 10) we can write -
10 = -3 + c
c = 13
We can write the equation of line perpendicular to line y = x - 1 as -
y = - x + 13
Therefore, the equation of line -
When line is parallel to line y = x - 1 is y = x + 7When line is perpendicular to line y = x - 1 is y = x + 7To solve more questions on Straight lines, visit the link below-
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HELPP ONBB- I just realized this is due today!!
Answers
The rate of change (m) = 9
The starting number (b) = 100
The equation is: y = 9x + 100
(0, 100) is the ordered pair for the starting number.
See the image for the graph of y = 9x + 100.
How to Create and Graph the Equation of a Line?To create the equation of a line, we need to determine the following:
Y-intercept/starting value = b
Slope of the line/rate of change = m
The ordered pair of the y-intercept or starting value is represented as (0, b), where b is the value of y on the y-axis where the line intercepts the y-axis and x = 0 at this point.
These values can be substituted into y = mx + b, which represents the equation of the line in slope-intercept form.
From the information given, we have:
Y-intercept/starting value (b) = 100
Slope of the line/rate of change (m) = 9
To write the equation of the line, substitute m = 9 and b = 100 into y = mx + b:
y = 9x + 100
The ordered pair for the starting number would be: (0, 100).
The image below shows the graph of y = 9x + 100.
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The head gardener at a botanical garden wants to plant rosebushes in parallel rows on either side of an existing footpath. How can the gardener ensure that that the rows are parallel
Answers
If the rows are perpendicular to the footpath, then the gardener ensure that that the rows are parallel.
Parallel:
Any two lines are said to be parallel if the Corresponding angles so formed are equal.
Given,
The head gardener at a botanical garden wants to plant rosebushes in parallel rows on either side of an existing footpath.
Here we need to find how can the gardener ensure that that the rows are parallel.
To know the answer, we have to consider the following,
Let us consider,
If the gardener digs every row at a 90° angle to the footpath, then each row will be exactly perpendicular to the foot path of the garden.
Which means,
If the rows are perpendicular to the footpath, then the rows are parallel.
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Solve for x: 4x + 1/2 (2x+4) > 12
a. x > 14/5
b. x < 14/5
c. x > 2
d. x < 2
Answers
Answer:
c. x > 2.
Step-by-step explanation:
4x + 1/2 (2x+4) > 12
4x + x + 2 > 12
5x > 10
x > 2.
[tex]1/1+\sqrt2+1/\sqrt2+\sqrt3+1/\sqrt3+\sqrt4[/tex]
Answers
+
9
√
2
+
8
√
3
6
And in decimal form it would be 7.43
suppose y varies directly with x, and y=6 when x=-3. find x when y=10
Answers
The value of the x, when y = 10 by the direct proportional is found as x = -5.
What is defined as the directly proportional?A direct proportion is an arithmetical comparison of two numbers whose ratio is equal to a fixed value. According to the proportion definition, two ratios are in proportion when they are equivalent. The proportions are represented by the symbol " ∝".As per the given question;
y is in the direct variation with x.
This can be written as; y ∝ x.
Or, y = kx
Where, k is proportionality constant.
put the values; y = 6 when x = -3
6 = -3 k
k = -2
Now, the value of x when y = 10.
y = kx ; put the value of y and k
10 = (-2)x
x = -5
Thus, the value of x in direct variation with y = 10 is found as x = -5.
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which is not a reason for the small size of cells? a. as the linear dimensions of a cell increase, the volume increases twice as fast as the surface area.
Answers
(C) "Eukaryotic cells must be smaller than prokaryotic cells due to the increased number of organelles" is not the reason for the small size of the cells.
What are cells?It is possible for cancer cells to separate from the primary tumor and move through the blood or lymphatic system to distant parts of the body, where they exit the blood vessels to create new tumors. Metastasis is the term for this. Cells that divide uncontrollably and invade neighboring tissues are what cause cancer. The type of cell that develops into cancer in adults is typically an epithelial cell. Body cavities and the exterior of the body are lined with epithelial cells. Environmental exposure to these cells over time can result in cancer.The reasons for the small size of cells are as follows:
Wastes and nutrients must pass through the plasma membrane to enter and exit the cell.There are limitations to how much cytoplasm the nucleus can regulate.The cytoplasm must allow materials to move through it quickly and effectively.The volume grows twice as quickly as the surface area as a cell's linear dimensions increase.Option (C) is not mentioned the reasons for the small size of the cell, so (C) is the answer.
Therefore, (C) "Eukaryotic cells must be smaller than prokaryotic cells due to the increased number of organelles" is not the reason for the small size of the cells.
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The complete question is given below:
Which is NOT a reason for the small size of cells?
A) nutrients and wastes must enter and leave the cell through the plasma membrane
B) the nucleus can only control a certain amount of cytoplasm
C) the increased number of organelles requires that eukaryotic cells be smaller than prokaryotes cells
D)materials must be able to move quickly and efficiently through the cytoplasm
E) as the linear dimensions of a cell increase, the volume increases twice as fast as the surface area
Mark is 6 years younger than 2 times his brother. If their combined age is 24, how old is mark?
Answers
Answer:
14
Step-by-step explanation:
You want to know how old Mark is if he is 6 years younger than twice his brother's age, and their combined age is 24.
RelationsLet m and b represent Mark's age and his brother's age, respectively.
The given relations are ...
m = 2b -6m + b = 24SolutionSolving the second equation for b, we have ...
b = 24 -m
Using that in the first equation gives ...
m = 2(24 -m) -6
m = 48 -2m -6
3m = 42 . . . . . . . . . add 2m, combine like terms
m = 14
Mark is 14 years old.
__
Check
Mark's brother is 24 -14 = 10. Twice that less 6 is 2×10 -6 = 14, which is Mark's age, as it should be.
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Lucy earns $15.75 per hour. Last week she worked 25 hours. What is her gross pay?
Lance has a yearly salary of $52,300 and pays 21% in taxes. Answer the following
a. How much does he pay in taxes?
b. What is his net pay?
c. If he receives two paychecks a month, how much will each paycheck be?
Answers
If Lucy earns $15.75 per hour. Last week she worked 25 hours her gross pay is $393.75 . If Lance has a yearly salary of $52,300 and pays 21% in taxes her taxed amount is $10,983, net pay is $41,317 and paycheck is $2,179.
Gross pay1. Gross pay
Using this formula to determine the gross pay
Gross pay = Amount earn per hour × Number of hours worked
Let plug in the formula
Gross pay = $15.75 per hour × 25 hours
Gross pay = $393.75
2a. Taxed amount
Amount in Tax = Salary × Tax percentage
Amount in taxes = $52,300 × 21%
Amount in taxes = $10,983
2b. Net pay
Net pay = Gross - Deduction
Net pay = $52,300 - $10,983
Net pay = $41,317
2c. Paycheck
Paycheck = $52,300 / 24 months
Paycheck = $2,179 per paycheck
Therefore we can conclude that the her gross pay is $393.75
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ASAP PLEASE IF YOU CAN
Given the linear equation below, create a table of values to obtain ordered pairs. Plot these ordered pairs to create a linear graph. Based on the graph you created, find three more solutions to the equation.
y equals 3 over 4 x minus 6
Answers
The three more solutions to the given linear equation are (2,-9/2), (6,-3/2), and (5,-9/4).
Given equation:-
y = (3/4)x - 6
We have to create a table of values to obtain ordered pairs.
Also, we have to plot these ordered pairs to create a linear graph and based on the graph we have created, we have to find three more solutions to the equation.
Let x = 0
y = 0 - 6 = -6
Ordered pair = (0,-6)
Let y = 0
0 = (3/4)x - 6
6 = (3/4)x
x = 8
Ordered pair = (8,0)
Let x = 4
y = 3 - 6 = -3
Ordered pair = (4,-3)
The graph of these three ordered pairs is attached below.
Based on the graph the other 3 ordered pairs that we can find are (2,-9/2), (6,-3/2), and (5,-9/4).
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Timmy is working with 2 sets of numbers.
Set A has all the odd number from 1-10.
Set B has all the even numbers from 2-20.
What is the ratio that represents the prime
numbers in Set A to the prime numbers in Set B?
(HINT: Think about what prime numbers are.)
Answers
Answer:
there's no ratio, or maybe u can help me out
Plot the image of point D under the dilation about the origin (0 , 0) with a scale factor of 3
Answers
The dilated picture of the point D dilation that is necessary is -6.
Given that,
To determine thee dilated image of point D (-2, 0), on the graph.
The graph is a demonstration of curves that gives the relationship between the x and y-axis.
The scale factor is defined as the ratio of modified change in length to the original length.
Here,Formerly point D is located at (-2, 0).
Now multiplying with the scale factor 3 the point goes
(-2 * 3, 0*3) => (-6, 0).
Thus, The required dilated image of the dilation of point D is -6.
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please help fast and provide explanation so I know how to find the answer
Answers
Option A 2X+y=1, the perpendicular graph, is correct.
What is x axis and y axis?Two parallel lines, known as axes (pronounced AX- eez), that are perpendicular to each other make up a coordinate grid. Typically, the term "x-axis" refers to the horizontal axis. The y-axis is the common name for the vertical axis. The origin is the location where the x- and y-axes intersect.A two-dimensional number line, such as two perpendicular number lines oraxes, can be thought of as a coordinate system. This coordinate system is typical: The x-axis and y-axis are the names of the horizontal and vertical axes, respectively.The vertical y-axis is aligned with the horizontal x-axis. "X is a cross hence the -axis is across" is one approach to remember which axis is which.To learn more about x axis and y axis refer to:
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7
The curve with equation y=pr²-4px-5p, where p is a constant does not intersect the line with
equation y=2x-12.
(a) Show that 9p²-8p+1 <0
(b) Find the set of possible values for p.
Answers
The set of possible values for "p" is ((4-√7)/9, (4+√7)/9).
The equation of the line is :y = 2x - 12The equation of the curve is :y = px² - 4px - 5pUsing the above two equations, we get the relationship that is given below :px² - 4px - 5p = 2x - 12px² - (4p+2)x - 5p+12 = 0(a) We are given that the curve and the line don't intersect, so the equation should not have a root.For the quadratic to not have a real solution, the discriminant is negative.b² - 4ac < 0[-(4p+2)]² - 4(p)(-5p+12) < 0(4p+2)² + 4(p)(5p-12) < 016p² + 4 + 16p + 20p² - 48p < 036p² - 32p + 4 < 09p² - 8p + 1 < 0(b) 9p² - 8p + 1 < 09p² - 8p + 1 = 0p = (4±√7)/9For the inequality to satisfy:p∈((4-√7)/9, (4+√7)/9)To learn more about equations, visit :
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Solve for the value of X
Thank you so much to anyone who solves this!!
Answers
Answer:
x=37
Step-by-step explanation:
3x + 3 + 2x - 8 = 180
solve for x and x = 37
hope this helped
have a good day sir ^^
Answer:
x=37
Step-by-step explanation:
180=5x+3-8
180=5x-5
+5 +5
185=5x
/5 /5
37=x
x=37
Given f(x)=√(3x-12)+2 what is the range in set notation? {y|y ∈ R, y ≥ }
Answers
The function f(x)=[tex]\sqrt{3x-12} +2[/tex]. The Domain of the function is 4, we can also write {y|y∈R,y≥4}
Given that,
The function f(x)=[tex]\sqrt{3x-12} +2[/tex]
We have to find the range of the function.
Range is nothing but y but in the equation we have x so we find domain.
The domain is the set of inputs that a function will accept is known as the domain of the function in mathematics. It is occasionally indicated by dom(f), where f is function.
More specifically, f:X--->Y the domain of f is X given a function. It should be noted that in contemporary mathematical terminology, a function's domain is a component of its definition rather than a quality.
Take the function
f(x)=[tex]\sqrt{3x-12} +2[/tex]
Now,
3x-12≥0
3x≥12
x≥12/3
x≥4
Therefore, The Domain of the function is 4, we can also write {y|y∈R,y≥4}
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Answer:
2
Step-by-step explanation:
2