A line passes through the point (2, 3) and has a slope of -2. Which is the equation of the line in point-slope form?
Answers
The correct answer is option B: [tex]\( y = -2x + 7 \).[/tex] To write the equation of a line passing through the point (2, 3) with a slope of -2, we can use the point-slope form of a linear equation.
The point-slope form is given as:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
Where [tex]\( (x_1, y_1) \)[/tex] is a point on the line and [tex]\( m \)[/tex] is the slope.
Given that the point is [tex]\( (2, 3) \)[/tex] and the slope is [tex]\( -2 \)[/tex], we can substitute these values into the point-slope form:
[tex]\[ y - 3 = -2(x - 2) \][/tex]
Now, we can simplify and rewrite the equation in various forms to match the options provided:
Option A: [tex]\( 2x + y = 7 \)[/tex]
To match this option, let's rearrange the equation:
[tex]\[ y - 3 = -2(x - 2) \][/tex]
[tex]\[ y - 3 = -2x + 4 \][/tex]
[tex]\[ 2x + y = 7 \][/tex]
So, option A is equivalent to the given equation.
Option B: [tex]\( y = -2x + 7 \)[/tex]
Let's solve the equation for [tex]\( y \):[/tex]
[tex]\[ y - 3 = -2(x - 2) \][/tex]
[tex]\[ y - 3 = -2x + 4 \][/tex]
[tex]\[ y = -2x + 7 \][/tex]
This matches option B.
Option C: [tex]\( y - 3 = -2(x - 2) \)[/tex]
This is already in point-slope form and matches the given equation.
Option D: [tex]\( y = -\frac{1}{2} x + 5 \)[/tex]
Let's solve the equation for [tex]\( y \):[/tex]
[tex]\[ y - 3 = -2(x - 2) \][/tex]
[tex]\[ y - 3 = -2x + 4 \][/tex]
[tex]\[ y = -2x + 7 \][/tex]
This does not match option D.
Therefore, the correct answer is option B: [tex]\( y = -2x + 7 \).[/tex]
The complete question is:
A line passes through the point (2, 3) and has a slope of -2. Which is the equation of the line in point-slope form?
A) 2x + y = 7
B) y = -2x + 7
C) y - 3 = -2(x - 2)
D) y = - 1 2 x + 5.
Related Questions
I WILL MARK BRAINLIEST!!!!!!!!!!
What is the length of segment AB?
A. 10
B. 12
C. 13
D. 15
Answers
considering you have to go up by two each unit; having to go up 6 boxes, then times two for what its counting by, would give you 12 !
Which of theses are log functions?
Answers
y=log3(x)
The logarithmic functions are the inverse of the exponential functions and they have the following form:
y=logb(x)
Therefore, as you can see, the function that has the form of a logarithmic function, is the first option.
Can you help me list the following stocks and bonds in order from highest default risk to lowest default risk?
-A municipal bond in a city with a population of 150,000
-A common stock in a company under federal investigation
-A preferred stock in a 150-year old firm with good business practices
Answers
From highest to lowest default risk, the investments would likely be ranked as follows: common stock in a company under federal investigation, a municipal bond from a relatively small city, and preferred stock in a stable, long-established firm.
Explanation:The default risk of a financial investment is the likelihood that the issuer of the instrument will be unable to meet their obligations, thereby causing a default. From the highest to lowest default risk, the list would likely be:
Common stock in a company currently under federal investigation: This company has the highest default risk because the investigation could lead to penalties, disruptions in its business, or damage to its reputation.A municipal bond from a city with a population of 150,000: Though generally considered safe, these bonds can still go into default. The default risk here is lower than the stock under investigation because municipal bonds are backed by the taxes and revenue of the municipality, making them more stable than corporations which are dependent on their business performance.A preferred stock in a 150-year old firm with good business practices: This has the lowest default risk. Preferred stocks have a lower risk than common stocks because they receive dividends before common stock and have a higher claim on the assets in case of bankruptcy. The age of the firm and its good business practices also suggest stability and reduced risk. Learn more about Default Risk here:https://brainly.com/question/34906573
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There are five students of different ages. Their median age is 13 years A) what are two possibilities for the ages of the three oldest students? B) if each student is a different age, how many students must be younger than 13? C) in complete sentences, describe what a median is to another student in the class. Pretend that the student was absent the day you learned about medians.
Answers
B) 2 students must be younger than 13
C) Like I said, the median is the middle measurement. If you have a list of numbers, you have to order them and take the middle number.
:) Have a nice day and maybe consider grading this answer brainliest? <3
The answers are explained in the solution.
What is median?Median in statistics is the middle value of a list of data when arranged in order. It is a measure of central tendency that separates the data into two halves: the upper half and the lower half.
Given that there are five students of different ages. Their median age is 13 years,
A) What are two possibilities for the ages of the three oldest students?
Answer = The median is the middle measurement. Their ages could be 13, 14 and 15.
B) If each student is a different age, how many students must be younger than 13?
Answer = 2 students must be younger than 13.
C) Describe what a median is to another student in the class?
Answer = Since the median is the middle measurement.
If you have a list of numbers, you have to order them and take the middle number.
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Mr. Grayson owns a wood company that sells trees, wood materials, and specialty items created from wood. (Score for Question 1: ___ of 4 points)
1. One of Mr. Grayson’s customers, Zenani, is creating an art wall on which she will display some art in triangular frames. She wants three frames, each in the shape of a right triangle.
(a) For the first frame, Zenani already has two wooden pieces that are 13 in. and 16 in. long. Zenani says that since she wants the frame to be a right triangle, there’s only one possible measurement for the last piece of wood. Is Zenani right? If so, what is that last measurement? If not, explain why not and give all possible measurements for the last wood piece. Round to the nearest tenth.
(b) For the second frame, Zenani asks Mr. Grayson to double the measurements of the first triangular frame to make a new frame in the shape of a right triangle. Will Zenani’s strategy work for the second frame? Explain why or why not.
(c) For the third frame, Zenani asks Mr. Grayson to add the same measurement to each of the sides of the original triangle frame to make a new frame in the shape of a right triangle. Will Zenani’s strategy work for the third frame? Explain why or why not. Answer: (
Score for Question 2: ___ of 4 points) 2.
Mr. Grayson gets a request from a customer to buy a palm tree of a specific height. Mr. Grayson’s tree nursery is very large and is organized by a coordinate plane map system. He finds a palm tree that he thinks might meet the customer’s specifications. The tree is located at coordinates . He calls his assistant to come over to help him determine the height of the tree. He asks his assistant where she’s located. His assistant says she is located at . Each unit on the coordinate grid represents 1 ft. How far is Mr. Grayson’s assistant from the tree? Round to the nearest tenth. Show your work. Answer:
(Score for Question 3: ___ of 3 points) 3.
Mr. Grayson orders a box that has a volume of . The box is in the shape of a cube. What is the longest stick that can fit in the box? Round your answers to the nearest whole number. Answer:
Please answer All of the questions to get the points
Answers
A) No; 9.3 or 20.6.
B) Yes, because the triangles are similar.
C) No, because the triangles will not necessarily be similar.
There is not enough information to answer Questions 2 or 3.
Explanation for Question 1:
A) We are not told which side is the longest, so these two sides could be placed anywhere in the Pythagorean theorem. They could either be both legs, or one could be the hypotenuse:
Hypotenuse: 13² + b² = 16²
169 + b² = 256
169 + b² - 169 = 256 - 169
b² = 87
b = √87 = 9.3
Both legs: 13² + 16² = c²
169 + 256 = c²
425 = c²
√425 = c
20.6 = c
B) The two triangles will be similar, since each pair of corresponding sides will have the same ratio (2, since it is doubled). Similar triangles have the same angle measures, so this must also be a right triangle.
C) Simply adding a value to each side will not preserve similarity. For example, if we had a triangle with sides 3, 4, and 5, adding 2 to each side would give us 5, 6 and 11. These do not have the same ratios; 3/5 is not the same as 4/6 or 5/11.
An object moves on a conveyor belt at a speed of 60 inches per second. Explain how you could conver the speed to feet per minute
Answers
[tex]60 \frac{in}{sec}* \frac{1ft}{12in}*\frac{60sec}{1min} =300 \frac{ft}{min} [/tex]
We can conclude that after converting 60 inches per second to feet per minute, we get 300 feet per minute.
On a skiing trip there are five people but only three pairs of skis how many different groups of three could ski
Answers
This is a combination of 5 items taken 3 at a time:
[tex]_5C_3=\frac{5!}{3!(5-3)!}=\frac{5!}{3!2!}=\frac{120}{12}=10[/tex]
Question 5 Unsaved
What is the equation for the sum of four consecutive numbers totaling 86.
Question 5 options:
4n=86
n+4=86
n+n+1+n+2+n+3=86
n+n+2+n++4+n+6=86
Answers
"The correct equation representing the sum of four consecutive numbers totaling 86 is [tex]\( n + (n+1) + (n+2) + (n+3) = 86 \).[/tex]
To solve this problem, let's denote the first of the four consecutive numbers as n
The sum of these four consecutive numbers is given by the equation:
[tex]\[ n + (n+1) + (n+2) + (n+3) = 86 \][/tex]
Now, let's simplify this equation by combining like terms:
[tex]\[ 4n + 1 + 2 + 3 = 86 \][/tex]
[tex]\[ 4n + 6 = 86 \][/tex]
Subtract 6 from both sides to isolate the term with n
[tex]\[ 4n = 86 - 6 \][/tex]
[tex]\[ 4n = 80 \][/tex]
Now, divide both sides by 4 to solve for n
[tex]\[ n = \frac{80}{4} \][/tex]
[tex]\[ n = 20 \][/tex]
So, the first number in the sequence is 20.
The four consecutive numbers are 20, 21, 22, and 23, and their sum is indeed 86.
Just say answer, no need to explain. Thanks
Answers
f (x) = x ^ 3
We have the following information:
Horizontal translations
Suppose that h> 0
To graph y = f (x + h), move the graph of h units to the left.
f (x) = (x + 5) ^ 3
Vertical translations
Suppose that k> 0
To graph y = f (x) + k, move the graph of k units up.
f (x) = (x + 5) ^ 3 + 4
Answer:
f (x) = (x + 5) ^ 3 + 4
option B
1. Which graph models the equation y = 3.5x?
2. Determine the equation of the line given by the graph.
A)y = 3x + 2(Wrong, I'm retaking the test)
B)y = 3x − 2
C)y = 1/3x + 2
D)y = 1/3x − 2
3.Determine the equation of the line given by the graph.
A)y = 2/3x - 1
B)y = 3/2x - 1
C)y = -2/3x - 1(Wrong, retaking)
D)y = -3/2x - 1
4.Determine the equation of the line given by the graph.
A)y = 5/3x - 4
B)y = 3/5x - 4
C)y = -5/3x + 4
D)y = -3/5x + 4
Answers
2) the y-intercept is -2 and the slope is up 3 over 1, so the answer has to be B
3) the answer is A because the up 2 over 3
4) the y-intercept is a positive 4, and the slope is going down 3 and to the right 5, and the line is decreasing so you know it has to be negative. the answer is D
what is the simplest form of this expression -x(7x+2)+x^2
Answers
-x (7x + 2) + x ^ 2
Rewriting we have:
(-7x ^ 2 -2x) + x ^ 2
Adding similar terms we have:
-6x ^ 2 - 2x
Answer:
The simplified expression is given by:
-6x ^ 2 - 2x
Equation:
=-x (7x + 2) + x ^ 2
=(-7x ^ 2 -2x) + x ^ 2
Add similar terms,
-6x ^ 2 - 2x
The simplified expression is given by:
-6x ^ 2 - 2x
What is the median out of 55,85,95,100,105,122,158,162,165,174
Answers
Which table shows the function y = -2x + 4? A) x y 0 4 1 2 2 0 B) x y 1 25 2 26 3 27 C) x y 0 -4 1 -2 2 0 D) x y -1 6 -2 8 -3 12
Answers
From looking at the A graph, you must plug in the x variable into y = -2x + 4.
y = -2(0) + 4 = 4
y = -2(1) + 4 = 2
y = -2(2) + 4 = 0
A spinner that has 5 areas of equal size, blue, red, green, yellow, and purple, is spun 25 times. The results are shown in the table. Are all outcomes equally likely according to the results of the experiment?
Answers
Answer:
The answer is D.) No its seems more likely to spin a blue or red than a green or a yellow
Step-by-step explanation:
No, it seems more likely to spin a blue or red than a green or yellow. According to the probability model, red and blue are landed on more often.
No, all outcomes equally likely according to the results of the experiment seems more likely to spin a blue or red than a green or a yellow
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
Given , spinner that has 5 areas of equal size, blue, red, green, yellow, and purple, is spun 25 times.
The results are shown in the table.
Color Frequency
Red 18
Blue 11
Green 8
Yellow 4
Purple 19
Total spin recorded = 25
Probability that the next spin will land on red or green or purple will be P(A∪BC) = P(A) + P(B) + P(C)
P(A∪BC) = 0.3 + 0.134 + 0.32 =0.754
= 75%
No, all outcomes equally likely according to the results of the experiment seems more likely to spin a blue or red than a green or a yellow
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A coin is flipped five times. Find the number of possible sets of heads and tails that have 2 heads. a. 0 c. 5 b. 1 d. 10
Answers
D. The amount of possible sets is C(5,2), which is equal with 10.
What is the apparent solution to the system of equations? y= -2x +3, y=1/3x - 4. Graph the system of eqiations
Answers
how do I find the depth to this rectangular prism
Answers
The same applies for the height as well.
A pencil costs $0.30 and a pen costs $0.50. You buy 10 pencils and the total Is $7.50. How many pens did buy?
Answers
This is because if you buy 10 pencils, it will cost a total of three dollars. 0.30 times 10=3.00. You then subtract this amount by 7.50, getting 4.50. 4.50 is the total amount that was spent on pens, but since you are trying to figure out how many pens were bought, you divide 4.50 by the cost of one pen (0.50).
This gives you 9.
Hope this helps~
How do you divide fractions
Answers
Keep the first fraction.
Change the division sign to a multiplication sign.
Flip the last fraction (reciprocal).
Example:
3/4 ÷ 1/2
Keep the 3/4.
Change the ÷ sign to ×.
Flip the 1/2 to 2/1.
New equation:
3/4 × 2/1 = 6/4 ⇒ 3/2
The answer for 3/4 ÷ 1/2 is 3/2.
How I learned it is the same way as doing it normally
Mary Alice is trying to answer the question. How many siblings does each member of her 30 person Biology class have. What is the best way to determine this?
A) Take a sample of 10 members of the class and then find the mean of the responses.
B) Survey each member of her 30 person class to determine how many siblings each person has.
C) Take a survey from the entire school and then look at the responses from students in a Biology class.
D) Look at the school enrollment roster to see how many siblings each member of the class has at the school.
Answers
The other answers wouldn't help that much.
B) Survey each member of her 30 person class to determine how many siblings each person has.
Plzz help me im going to most more like this because im not understanding it
Answers
In order to solve, you can use substitution. This means that you use one equation and solve for one variable, then use that one equation and plug it into the other equation. Here's how we'd do it:
WORK:
x = 12 - y (since x is already solved for, we'll use that to plug into the other given equation.
2(12 - y) + 3y = 29 (using substitution)
24 - 2y + 3y = 29
24 + y = 29
y = 5
Plug the value of y back into the first equation
x = 12 - 5
x = 7
ANSWER:
A - x = 7, y = 5
It seems as though you're having some trouble with these questions, PLEASE MESSAGE ME!! I'd be more than happy to help you work through as many problems as you need until you get the hang of it (plus, it doesn't cost you any points!)
Hope this helps!! :)
If there's anything else that I can help you with, please let me know!
One of the tallest living trees today is the Mendocino Tree found at Montgomery Woods State Park, California. Its height is about 11,200 centimeters. What is this height in scientific notation?
A. 0.112*10'-4cm
B. 1.12*10'4cm
C. 11.2*10'4cm
D. 1.12*10'-4cm
plz help me i need help
i will make brainiest
Answers
1.12 × 104
(scientific notation)
= 1.12e4
(scientific e notation)
11.2 × 103
(engineering notation)
(thousand; prefix kilo- (k))
11200
(real number)
B. 1.12*10'4cm should be the correct answer.
The height of the tree which is 11,200 centimeters is written as 1.12*10'4cm in scientific notation. The conversion involves placing the decimal point after the first digit and then counting the number of places moved, which forms the power of 10.
Explanation:The question is asking you to express the height of a tree, which is 11,200 centimeters, in scientific notation. Scientific notation is a way of writing very large or very small numbers into a format that is easier to read and understand. It is formatted as a number between 1 and 10 multiplied by 10 raised to a certain power.
To convert 11,200 into scientific notation, we first place the decimal point after the first digit, which results in 1.12. Secondly, we count the number of places moved. In this case, we moved the decimal point 4 places to the left. Therefore, 11,200 cm is equal to 1.12 × 10^4 cm. So, the correct answer is B. 1.12*10'4cm.
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Write an equation in standard form for the line whose slope is undefined and and passes through (-6,4).
Answers
A vertical line has an equation of the form x = k. In this case, since the line passes thru (-6,4), the eq'n of the line is x = -6.
The equation represents a vertical line passing through the point (-6, 4) is x= -6.
When the slope is undefined, it means that the line is vertical.
In this case, the line passes through the point (-6, 4).
A vertical line has the equation of the form x = k, where k is a constant. Since the line passes through (-6, 4), the equation of the line in standard form is:
x = -6
This equation represents a vertical line passing through the point (-6, 4).
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A businessman has 10 employees; his salary is equal to 6 times the average of employees' salary. If the 11 of them received a total of 64000 in a one year, what was the businessman's salary that year?
Answers
[tex]6x+10x=64000[/tex]
Solving for [tex]x[/tex]:
[tex]16x=64000[/tex]
[tex]x= \frac{64000}{16} [/tex]
[tex]x=4000[/tex]
The average salary of an employee is 4000, so the salary of the businessman will be [tex]6*4000=24000[/tex].
We can conclude that the business man's salary that year was 24000.
IF 3 QUARTS IS DIVIDE BY 16 PEOPLE HOW MANY OUNCES
Answers
Choose the justification for each step in the solution for equation 6X -9 equals 45
Answers
A scatterplot has a negative, linear correlation. Which statement is true about the relationship between the x- and y-values?
A) As the x-values increase, the y-values tend to increase.
B)As the x-values increase, the y-values tend to decrease.
C)As the x-values decrease, the y-values tend to decrease.
D)As the x-values decrease, the y-values tend to vary randomly.
Answers
Answer:
B
Step-by-step explanation:
as the x values increase, the y values tend to decrease
For the Scatter plot negative the x-values increase, the y-values tend to decrease.
What is Scatterplot?A linear function is a function that, when plotted, creates a straight line. Typically, it is a polynomial function with a maximum degree of 1 or 0. Nevertheless, calculus and linear algebra are also used to represent linear functions. The function notation is the only distinction. It is also important to understand an ordered pair expressed in function notation. When an is an independent variable on which the function depends, the expression f(a) is referred to as a function.
Given
A scatterplot has a negative, linear correlation.
Which is negative correlation means that with the increase/decrease in one variable the other variable also decrease/increase,
in which their is inverse proportion between two variables.
so values of x increase and values of y tend to decrease.
Hence option B is best suitable answer.
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Kimela’s little sister likes to swing the playground. Yesterday, Kimela pulled the swing back and let it go. The swing traveled a distance of 9 feet before heading back the other way. Each swing afterward was only 70% as long as the previous one. Find the total distance the swing traveled.
Answers
To find the total distance traveled by the swing, we use the sum of an infinite geometric series formula with the first swing distance being 9 feet and a common ratio of 0.7. The sum equals 30 feet, indicating the total distance the swing traveled.
The question involves finding the total distance traveled by a swing that starts with an initial swing length and then decreases by a certain percentage with each subsequent swing. It can be classified as a series problem in mathematics, specifically dealing with a geometric series.
First swing distance is 9 feet. Each subsequent swing is only 70% of the previous, which means the ratio is 0.7. We want to find the sum of this geometric series. The total distance traveled by the swing is the sum of the distances traveled in each direction, so the swing's distances form an infinite series. To find the total distance traveled, we use the formula for the sum of an infinite geometric series:
S = [tex]\frac{a}{1-r}[/tex]
where S is the sum of the series, a is the first term, and r is the common ratio (in this case, 0.7). Plugging in the values, we get:
S = [tex]\frac{9 feet }{(1 - 0.7)}[/tex] = 9 feet ÷ 0.3 = 30 feet
Hence, the total distance traveled by the swing is 30 feet.
The height of a ball in feet is modeled by
[tex]y = - 16x {}^{2} + 72x[/tex]
where X is the time in seconds after the ball is hit. How long is the ball in the air?
(May I also get steps on how to solve these kind of questions please?)
Answers
The value of time of the ball in the air is,
⇒ 4.5 seconds
What is Quadratic equation?An algebraic equation with the second degree of the variable is called an Quadratic equation.
We have to given that;
The height of a ball in feet is modeled by the equation,
y = - 16x² + 72x
where, x is the time in seconds after the ball is hit.
Hence, For time of the ball in the air, we can plug y = 0 in above equation.
y = - 16x² + 72x
0 = - 16x² + 72x
Solve for x;
- 16x² + 72x = 0
- 4x (4x - 18) = 0
This gives,
4x = 18
x = 18/4
x = 4.5 seconds
Thus, The value of time of the ball in the air is,
⇒ 4.5 seconds
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Need help please....
Answers
When setting up a proportion, it doesn't really matter which numbers go where, as long as you are consistent.
A is the correct answer because it is set up as width/length = width/length. So when you solve for the missing length, you are finding what value of x will make 9/x the same ratio as 10/12.
Hope this helps!