Find the equation (in terms of x ) of the line through thepoints (-2,9) and (1,0)y =
Answers
To answer this question we will use the following formula for the equation of a line that passes through two given points:
\(y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1).\)Therefore the equation that passes through the points (1,0) and (-2,9) is:
\(y-0=\frac{9-0}{-2-1}(x-1).\)Simplifying the above result we get:
\(\begin{gathered} y=\frac{9}{-3}(x-1), \\ y=-3(x-1), \\ y=-3x+3. \end{gathered}\)Answer:
\(y=-3x+3.\)Related Questions
Write each equation in slope-intercept form. Identify the slope and y-intercept. Then graph the line described by the question. (If possible please show work)
Answers
Answer:
Step-by-step explanation:
Equation of the line is,
y = -x + 2
By comparing this equation with,
y = mx + b
Here, m = slope of the line
b = y-intercept
Therefore, slope of the line given in the graph = (-1)
y-intercept = 2
Now we will find the table for the points lying on the line,
x -6 -4 0 4 6
y 8 6 2 -2 -4
Now plot these points on the graph and join them to get the line.
find the height of right triangular prism
Answers
The side x of the triangular base prism is 0.4 centimetres.
How to find the side of a triangle prism?The diagram above is a triangular prism. The triangular base of the prism is a right triangle. Therefore, the unknown side x can be found using Pythagoras's theorem,
c²= a² + b²
where
a and b are the other legsc is the hypotenuse sideTherefore,
x² = 0.5² - 0.3²
x² = 0.25 - 0.09
x = √0.16
x = 0.4 cm
Therefore,
x = 0.4 centimetres.
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Line segment RS is the directed line segment from R(-6,-5) to S(4,0). What are the coordinates of the point that partitions the segment in the ratio 2:3?
Answers
Answer:
\((x,y) = (-2,-3)\)
Step-by-step explanation:
Given
\(R = (-6,-5)\)
\(S = (4,0)\)
\(Ratio = 2:3\)
Required
Determine the coordinate of the line ratio
Line ratio is calculated using:
\((x,y) = (\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n})\)
In this case
\((x_1,y_1) = (-6,-5)\)
\((x_2,y_2) = (4,0)\)
\(m:n = 2:3\)
The formula becomes:
\((x,y) = (\frac{2 * 4 + 3 * -6}{2+3},\frac{2 * 0 + 3 * -5}{2+3})\)
\((x,y) = (\frac{8 - 18}{5},\frac{0 - 15}{5})\)
\((x,y) = (\frac{-10}{5},\frac{-15}{5})\)
\((x,y) = (-2,-3)\)
valuate the summation for the indicated value of the variable. 1(1!) + 2(2!) + 3(3!) + 4(4!) + m(m!); m = 3
Answers
The answer of the given question based on the expression is , the value of the summation when m = 3 is 137.
What is Expression?In mathematics, an expression is a combination of numbers, variables, and operators that represents a value or a set of values. It can be a simple combination of numbers and variables or a more complex combination involving mathematical operations like addition, subtraction, multiplication, division, exponents, and roots. Expressions can be used to represent a wide range of mathematical concepts, from simple arithmetic to complex functions and equations.
To evaluate the summation 1(1!) + 2(2!) + 3(3!) + 4(4!) + m(m!), where m = 3, we substitute m = 3 and simplify:
1(1!)+2(2!) +3(3!) +4(4!) +3(3!)
= 1(1) + 2(2) + 3(6) + 4(24) + 3(6) (since n! = n(n-1)! for all positive integers n)
= 1 + 4 + 18 + 96 + 18
= 137
Therefore, the value of the summation when m = 3 is 137.
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Taylor is factoring the following expression but notices she got the wrong answer when checking her work. Identify what she did wrong and show her the appropriate way to factor.
Answers
Answer:
15x = 3 (5x)
Step-by-step explanation:
12 + 3 = 15
15x = 3 (5x)
Taylor forgot to add 3 to her answer and got the result of 3 x 4 which is 12.
The correct way for her to factor is to use Pemdas.
-kiniwih426
\(\\ \sf{:}\dashrightarrow 12x+3=3(4x)\)
\(\\ \sf{:}\dashrightarrow 12x+3=12x\)
\(\\ \sf{:}\dashrightarrow 12x-12x=3\)
\(\\ \sf{:}\dashrightarrow 0=3\)
No solutions ✓
Games at the carnival cost $3 each. The prizes awarded to winner cost $145.65. How many games must be played to make at least $50?
Answers
Answer:About 17 games
Step-by-step explanation:
$50 divided by $3 is about 17 games
Roberto reads 1/4 of the number of pages in a book. Manny reads 1/4!of the number of pages in a different book. Roberto says Manny and he read the same number of pages because 1/4=1/4.
Answers
Answer:
It is most likely they did not read the same number of pages
Step-by-step explanation:
You would need to know the number of pages in each book but since it is unknown, Roberto does not know if he and Manny read the same amount.
A theater wants to build movable steps that they can use to go on and off the stage. They want the steps to have enough space inside so they can also be used to store props.
Answers
The required amount of the space available is 0.045 cubic meter.
We need to determine Space inside the steps.
What is volume?The Volume is defined as the mass of object per unit density.
The required space = 0.3*0.4*0.5 - 0.15*0.5*0.2
= 0.06 - 0.015
= 0.045 cubic meter
Hence, the required amount of the space available will be 0.045 cubic meter.
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what's question 9? NEED ANSWER
Answers
Answer
I disagree
she said that the square root of 100 and of 121 is 4 and 5
the square root of 100 is 10 and the square root of 121 is 11.
The figure shows a two-dimensional
representation of a bird made out of
origami paper. Find m/1 and m/2.
Explain your reasoning.
(3x + 5)°
(4x-30)
Answers
In the given origami of the two dimensional figure , the value of angle 2 is 70° and the value of angle 1 is 110 °
Parallel lines are straight lines that do not intersect at any point in geometry.
Parallel planes are three-dimensional pathways that never intersect. Parallel curves do not touch or intersect and have a fixed minimum distance.
From the figure we can see that m∠1 = 4x-30 as they are vertically opposite angles.
Again m∠1 = 3x+5 as they are corresponding angles from the pair of parallel lines.
now let us solve the linear equation to calculate the value of x.
3x+5 = 4x-30
or, -x = -35
or, x = 35
Now
m∠1 = 3x+5 = 110
Therefore m∠2 = 180 -110 = 70 ( straight angle formed whose sum is 180)
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Determine whether the following statement is true or false.
Every system of equations has at least one solution
Choose the correct answer below.
O A. False, because every system of equations has at least two solutions.
OB. True, because the graphs of any two equations intersect in at least one point.
O C. True, because every system of equations has the solution (0,0) and have point(s) at which their graphs intersect.
OD. False, because a system of equations whose graphs are parallel lines has no solution
Answers
Answer:
B
Step-by-step explanation:
what is the standard deviation for city A and city B
Answers
Answer:
$0.8426
Step-by-step explanation:
steps are in the picture above.
Note:if you need to ask any question please let me know.
A triangle has an area of 64 cm² and a base of 10 cm².
What is the height of the triangle?plsssssssssssss help
Will give 5/5 if 2 ppl answer I can give brainlest
Answers
Answer:
Your answer is 12.8
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For any positive integer n, the value of n! is the product of the first n positive integers. For example, 4! = 4 * 3 * 2 * 1 =24. What is the greatest common divisor of 5! and 7! ?
Answers
The GCD of 5! and 7! is 2^3 * 3^1 * 5^1 = 120.
the greatest common divisor of 5! and 7! is 120.
To find the greatest common divisor (GCD) of 5! and 7!, we need to factorize both numbers and identify the common factors.
First, let's calculate the values of 5! and 7!:
5! = 5 * 4 * 3 * 2 * 1 = 120
7! = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5,040
Now, let's factorize both numbers:
Factorizing 120:
120 = 2^3 * 3 * 5
Factorizing 5,040:
5,040 = 2^4 * 3^2 * 5 * 7
To find the GCD, we need to consider the common factors raised to the lowest power. In this case, the common factors are 2, 3, and 5. The lowest power for 2 is 3 (from 120), the lowest power for 3 is 1 (from 120), and the lowest power for 5 is 1 (from both numbers).
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This is due today please helpppp meeee I really need help
Carla and Diane Bought identical suit cases at a different stores. Carla’s suitcase originally cost $85 and was on sale for 20% off the original price which suitcase was a the better deal? What do we know ? List important facts ? What do we want to find out ?? Solve ??? Show ur work? Explain starts ur Asnwer and give details ? And justify your steps ? Someone please help!!!
Answers
Answer:
Carla's suitcase was a better purchase.
Step-by-step explanation:
The complete question is:
Carla and Daniel bought identical suitcases at different stores. Carla's suitcase originally cost $75 and was discounted 19% Daniel's suitcase original cost $85 and was on sale for 20% off the original price. Which suitcase was the cheaper?
Solution:
Cost Price of Carla's suitcase = $75
Discount% for Carla = 19%
The amount paid by Carla is,
So, the amount paid by Carla was, $60.75.
Cost Price of Jeana's suitcase = $85
Discount% for Jeana = 20%
The amount paid by Jeana is,
So, the amount paid by Jeana was, $68.
Carla's suitcase was a better purchase.
On average, Nathaniel drinks
4/5 of a 10-ounce glass of water in
2 2/5
hours. How many glasses of water does he drink in one hour? Enter your answer as a whole number, proper fraction, or mixed number in simplest form.
Answers
Nathaniel drinks 3 glasses of water in one hour.
To find out how many glasses of water Nathaniel drinks in one hour, we need to calculate his drinking rate per hour.
In 2 2/5 hours, Nathaniel drinks 4/5 of a 10-ounce glass of water.
Let's convert the mixed number of hours to an improper fraction:
\(2\frac{2}{5} = \frac{(5 \times2 + 2)}{5}\)
\(=\frac{12}{5}\)
Now, we can set up a proportion to find his drinking rate per hour.
We know that \(\frac{12}{5}\) hours corresponds to \(\frac{4}{5}\) of a glass of water.
Let's assign "x" as the number of glasses he drinks in one hour.
The proportion is then
\(\frac{(\frac{12}{5} hours) }{(x glasses) } =\frac{(\frac{4}{5} glass)}{(1 hour)}\)
Cross-multiplying gives us
\((\frac{12}{5} )\times1=\frac{4}{5}\times(x)\)
Simplifying, we get
\(\frac{12}{5} =\frac{4}{5}\times x\)
Dividing both sides by \(\frac{4}{5}\), we find x:
\(x=\frac{(\frac{12}{5} )}{\frac{4}{5} }\)
\(x=\frac{12}{4}\)
\(x = 3.\)
Therefore, Nathaniel drinks 3 glasses of water in one hour.
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A linear regression equation and multiple linear regression equations can be used to calculate y if one is given the x values. However, a logistic regression equation cannot be used to calculate y when one is given x value.
a. True
b. False
Answers
Answer:
FALSE
Step-by-step explanation:
First, define y and x.
In statistics, we have what we call variables. Variables are items or symbols that can take on various values. We have dependent variables - whose values are derived from other variables in an equation - and independent variables - whose values are given and are used to determine the values of dependent variables.
Usually, y represents the dependent variable while x represents the independent variable. So the simplest form of regression equation is
y = f (x)
Said as "y is a function of x"
A logistic regression equation can be used to calculate y when x values are given.
Here, the independent variable function (the X function) is a logistic function and it is used to find a binary dependent variable (a Y value, out of two possible values).
In logistic regression equations, the value of Y is not numerical like 1, 0.2, 3/4, and so on. It is categorical, e.g.
Black/White, Gain/Lose, Pass/Fail, Eat/Drink, etc.
AND 3 REVIEW | 9 of 9
The 26 students in Mr. Brown's fifth-grade class each bought a poster for $0.79. Excluding tax, how much did the posters cost in al
Please help
Answers
Answer:
$20.54
Step-by-step explanation:
26 x 0.79 = 20.54
. Bert has a well-shuffled standard deck of 52 cards, from which he draws one card; Ernie has a 12-sided die, which he rolls at the same time Bert draws a card. Compute the probability that:
a. Bert gets a Jack and Ernie rolls a five.
b. Bert gets a heart and Ernie rolls a number less than six.
c. Bert gets a face card (Jack, Queen or King) and Ernie rolls an even number.
d. Bert gets a red card and Ernie rolls a fifteen.
e. Bert gets a card that is not a Jack and Ernie rolls a number that is not twelve.
Answers
Therefore , the solution of the given problem of probability comes out to be a)1/78 ,b)65/624 ,c)1/4 ,d)0 and e)12/13.
What is probability, exactly?The basic goal of any considerations technique is to assess the probability that a statement is accurate or that a specific incident will occur. Chance can be represented by any number range between 0 and 1, where 0 normally indicates a percentage but 1 typically indicates the level of certainty. An illustration of probability displays how probable it is that a specific event will take place.
Here,
a.
P(Bert gets a Jack and Ernie rolls a five) = P(Bert gets a Jack) * P(Ernie rolls a five)
= (4/52) * (1/12)
= 1/78
b.
P(Bert gets a heart and Ernie rolls a number less than six) = P(Bert gets a heart) * P(Ernie rolls a number less than six)
= (13/52) * (5/12)
= 65/624
c.
P(Bert gets a face card and Ernie rolls an even number) = P(Bert gets a face card) * P(Ernie rolls an even number)
= (12/52) * (6/12)
= 1/4
d.
P(Bert gets a red card and Ernie rolls a fifteen) = 0
e.
Ernie rolls a number that is not twelve, and Bert draws a card that is not a Jack:
A regular 52-card deck contains 48 cards that are not Jacks,
so the likelihood that Bert will draw one of those cards is 48/52, or 12/13.
On a 12-sided dice with 11 possible outcomes,
Ernie rolls a non-12th-number (1, 2, 3, etc.).
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Nao and Arban drive to work.
Nao drives 95 miles in 2.5 hours.
Arban drives 128 km in 1 hour 15 min.
Work out the difference between their average speeds in km/h.
1 mile = 1.6 km
Thank You.
Answers
Answer:
41.6 km/h
Step-by-step explanation:
Nao drives 95mi/2.5hr or 38 miles per hour, or 60.8 km/h
1 hr 15 min is the same as 1.25 hours
Arban drives 128km/1.25hr or 102.4 km/h
The difference is 102.4-60.8 = 41.6
what is the answer with work too please help is due 11:59
Answers
Step-by-step explanation:
So when it says ration from men to women is 4/5, men is 4 and women is 5.
You know that there are 60 men and you need to find the number of women.
The equation you would use is:
4 X ?= 60
then do ? X 5= the answer
Hope this helps.
Please answer ASAP I have 15 min help
Answers
this means she added before multiplying or dividing
Answer:
32
Step-by-step explanation:
she was supposed to divide and multiply first and then add those answers
6+6+20=32
Find the volume of a pyramid with a square base, where the side length of the base is
10.6
in
10.6 in and the height of the pyramid is
12.3
in
12.3 in. Round your answer to the nearest tenth of a cubic inch.
Answers
Answer:
V = 460.68
Step-by-step explanation:
V=(lwh)/3
Volume = (1/3) * base area * height
In this case, the base of the pyramid is a square with a side length of 10.6 inches, so the base area can be calculated as:
Base area = side length * side length
Let's calculate the base area first:
Base area = 10.6 in * 10.6 in
Next, we'll substitute the values into the volume formula:
Volume = (1/3) * (10.6 in * 10.6 in) * 12.3 in
Calculating this expression will give us the volume of the pyramid. Rounding the answer to the nearest tenth of a cubic inch will provide the final result.
The radius of a circle is 16 meters. What is that circle’s area?
Answers
Answer:
256pi or 804.248 m sq
Step-by-step explanation:
the formula for the area of a circle is pi*r^2 and we know the radius. so the area is pi*16^2=256pi. if you want the decimal answer it's around 804.248
By using graphical method, find optimal solution of the problem max z = 3x + y s.t 2x - y ≤ 5 -x + 3y ≤ 6 x ≥ 0, y ≥ 0
Answers
By analyzing the graph and evaluating the objective function at each vertex of the feasible region, we can find the optimal solution, which is the vertex that maximizes the objective function z = 3x + y.
To find the optimal solution of the given problem using the graphical method, we need to plot the feasible region determined by the given constraints and then identify the point within that region that maximizes the objective function.
Let's start by graphing the constraints:
1. Plot the line 2x - y = 5. To do this, find two points on the line by setting x = 0 and solving for y, and setting y = 0 and solving for x. Connect the two points to draw the line.
2. Plot the line -x + 3y = 6 using a similar process.
3. The x-axis and y-axis represent the constraints x ≥ 0 and y ≥ 0, respectively.
Next, identify the feasible region, which is the region where all the constraints are satisfied. This region will be the intersection of the shaded regions determined by each constraint.
Finally, we need to identify the point within the feasible region that maximizes the objective function z = 3x + y. The optimal solution will be the vertex of the feasible region that gives the highest value for the objective function. This can be determined by evaluating the objective function at each vertex and comparing the values.
Note: Without a specific graph or additional information, it is not possible to provide the precise coordinates of the optimal solution in this case.
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−8x+4y=
\,\,-24
−24
-7x+4y=
−7x+4y=
\,\,-16
−16
Answers
The values of x and y that are solutions to the simultaneous equation are; x = 8 and y = 10
How to solve the simultaneous equation?We are given the simultaneous equation as;
-8x + 4y = -24
-7x + 4y = -16
There are three main methods used to solve simultaneous equations and they are substitution method, elimination method and graphical method. However, in this case, we will make use of the elimination method.
We will Subtract eq 1 from eq 2 to get;
-7x - (-8x) = -16 - (-24)
x = -16 + 24
x = 8
Put 8 for x in eq 1 to get;
-8(8) + 4y = -24
-64 + 4y = -24
4y = -24 + 64
4y = 40
y = 40/4
y = 10
Thus, we conclude that those are the values of x and y required.
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Complete question is;
Find the solution to the simultaneous equation;
-8x + 4y = -24
-7x + 4y = -16
If you walk 100 m forward And 35 m backwards towards your starting point would what is the distance and displacement explain your answer
Answers
Answer:
imater?
Step-by-step explanation:
4
0
A
Compare and using the number line.
름
10
A
Which point represents ?
B
B
-|~
2
C
D
1
D
Enter
Answers
The point D represents 1 on the number line.
What is number line ?A number line is a visual representation of numbers arranged in sequential order. It is usually depicted as a horizontal line, with tick marks or hash marks at regular intervals, representing the numbers. Number lines can be used to represent a wide variety of mathematical concepts, such as fractions, decimals, negative numbers, absolute value, and ratios. They are also used to compare numbers and to help visualize the concepts of addition, subtraction, multiplication, and division. Number lines can also be used to explore inequalities, algebraic equations, and graphing.
The point D represents 1 on the number line.
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Un cuerpo de 30 kg de masa se encuentra a una altura de 5 metros en relación al suelo, siendo g= 9,8 m/s2, calcula la energía potencial del cuerpo
Answers
Answer:
bro speak english
SPEAK ENGLISH
the construction of creating the perpendicular bisector of PQ is started below. How would the construction be different if you changed the compass setting in the next step of the perpendicular bisector construction?
Answers
Answer: It will not create a perpendicular bisector.
Explanation:
If the compass is the same setting as the first arc and drawn from point B, the points of intersection of the arcs will pass through the midpoint of AB (thus creating a perpendicular bisector).
If you change the setting of the compass and draw an arc from point B, the points of intersection of the arcs will still create a perpendicular line but will not pass through the midpoint of AB (creating a perpendicular line but not a perpendicular bisector).
A perpendicular bisector divides a line segment into two equal segments.
If the compass setting is changed, the line will not be bisected.
To bisect a line, the positioning of the compass must be done as follows:
Place the compass at the endpoint of the line segment, then draw an arcRepeat the above process for the other endpoint of the line segment.Trace the point of intersection of the two arcs, to the line that is being bisected.The above points are what is being done in the given construction.
Any step or setting other than that, would not create a perpendicular bisector.
Hence, if the compass setting is changed, the perpendicular bisector of the line would not be drawn.
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