A line passes through the ordered pairs (4,1) and (2,8) . What is the slope? Please help
Answers
Final answer:
The slope of the line that passes through the points (4,1) and (2,8) is calculated using the slope formula and results in a slope of -3.5.
Explanation:
To find the slope of a line passing through the ordered pairs (4,1) and (2,8), you can use the slope formula:
m = (y2 - y1) / (x2 - x1). Here, (x1, y1) is the first point (4,1) and (x2, y2) is the second point (2,8).Plugging in the values, we get:
m = (8 - 1) / (2 - 4) = 7 / (-2) = -3.5Therefore, the slope of the line that passes through the points (4,1) and (2,8) is -3.5.
The slope of the line passing through the given points is -3.5.
Let’s find the slope of the line passing through the points (4, 1) and (2, 8).
The slope of a line can be calculated using the following formula:
[tex]\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
where:
• [tex](x_1) and (y_1)[/tex] are the coordinates of the first point (in this case, (4, 1)).
• [tex](x_2) and (y_2)[/tex] are the coordinates of the second point (in this case, (2, 8)).
Let’s compute the slope:
1. Difference in (x)-coordinates: [tex](x_2 - x_1 = 2 - 4 = -2)[/tex]
2. Difference in (y)-coordinates:[tex](y_2 - y_1 = 8 - 1 = 7)[/tex]
Now, calculate the slope:
[tex]\text{slope} = \frac{7}{-2} = -3.5[/tex]
Therefore, the slope of the line passing through the given points is -3.5.
Related Questions
he table below shows 10 data values: What values of minimum, Q1, median, Q3, and maximum should be used to make a box plot for this data? (1 point) 301 345 305 394 328 317 361 325 310 362 Minimum = 300, Q1 = 345, median = 330, Q3 = 317, maximum = 362 Minimum = 300, Q1 = 317, median = 330, Q3 = 345, maximum = 362 Minimum = 301, Q1 = 310, median = 326.5, Q3 = 361, maximum = 394 Minimum = 301, Q1 =361, median = 326.5, Q3 = 310, maximum = 394
Answers
301 345 305 394 328 317 361 325 310 362
Re-arrange the data in ascending order:
301, 305, 310, 317,325, 328, 345, 361, 362, 394
from the above we see that:
Minimum value=301
Q1=310
median=(325+328)/2=326.5
Q3=361
Maximum value=394
Thus the box plot will be as follows:
Answer:
the third one its 100% verified
Step-by-step explanation:
how do you know if two lines are parallel?
Answers
Hope this helps/works.
Find the amount of annuity.
Amount of each deposit: $295
deposited: quarterly
Rate per year: 10%
Number of years: 6
Type of annuity: due
Answers
÷(0.1÷4))×(1+0.1÷4))
=9,781.54
We need to find the future value of annuity due with the following given values :-
Payment, Pm = 295 dollars.
N=4 (for quarterly)
Rate at 10%, r = 0.10/4 = .025
Time for 6 years, T = 6x4 = 24.
Future Value formula is :-
[tex]FV_{ad}=P_m*(1+r)*[\frac{(1+r)^T-1}{r} ] \\\\ FV_{ad}=295*(1+0.025)*[\frac{(1+0.025)^{24}-1}{0.025} ] \\\\ FV_{ad}=295*(1.025)*[\frac{(1.025)^{24}-1}{0.025} ] \\\\ FV_{ad}=295*(1.025)*[\frac{(1.80872595)-1}{0.025} ] \\\\ FV_{ad}=295*(1.025)*[\frac{0.80872595}{0.025} ] \\\\ FV_{ad}=295*(1.025)*(32.34903798) \\\\ FV_{ad}=9,781.54 \;dollars[/tex]
Hence, the final answer is 9,781.54 dollars.
Given z, find |z| -4+5i
Answers
|z| = √41
A marble is drawn at random from the bag. The bag contains 3 green, 4 yellow, 5 blue, and 8 pink marbles. What is the probability that the marble drawn is a green or blue? Type a numerical answer in the space provided. Use the / key to represent the fraction bar. Do not type spaces in your answer.
Answers
Add green and blue: 5 + 3 = 8
8/20
Simplify this, and you will have 2/5
Hope I could help! Let me know if there is anything else you need!
p.s. Brainliest? I am trying to get to higher ranks and it would really help :)
Amber believes triangle ABC and triangle GFE are congruent. She has recorded the measures of some of the angles and the lengths of some of the sides in the triangles below.
What additional measurement would support Amber’s hypothesis?
a.The measure of c is 32
b.The measure of c is 40
c.The measure of c is 50
d.The measure of c is 90
Answers
b. The measure of c is 40.
_____
In actual fact, the triangles not only are not congruent, they cannot exist. The total of sides FG and FE (82 cm) is less than the length of side GE (38 in). 82 cm is about 32.3 inches, about 5.7 inches too short.
Even if you overlook the units problem, the sum of squares of the sides of the triangle is 32² +38² = 2468, somewhat short of 50² = 2500. That is, the largest angle is slightly more than 90°. It is closer to 90.754° ≈ 91°.
You can label a diagram any way you want, but that doesn't mean the numbers are consistent or sensible.
Answer:
B
Step-by-step explanation:
Which of the following comparisons is False
A..... 5.c is Warner than 5.F
B......15.c is cooler than 60.F
C........30.c is Warner than 90.F
D.......35.c is cooler than 100.F
Answers
The comparison that is FALSE is ...
C.....30 °C is warmer than 90 °F
_____
30 °C = 86 °F
32.2 °C ≈ 90 °F
PLEASE PLEASE HELP ASAP
Answers
2.40, 2.44, 2.48, 2.52, 2.56, ...
If we observe these terms, we'll see that the difference between two consecutive terms is the same i.e 0.04. Such a sequence is known as Arithmetic sequence.
We have to find the radius of 95th loop. This means we have to find the 95th term of the sequence.
Using the formula of Arithmetic Sequence, we can write:
[tex] a_{n} = a_{1}+(n-1)*d \\ \\ a_{95}=2.40+(95-1)*0.04 \\ \\ a_{95}=6.16 [/tex]
Thus, the radius of 95th loop of paper will be 6.16 centimeters.
So, the correct answer is option B
Hey can you please help me posted picture of question
Answers
So, the resulting function after these two translations will be:
[tex]G(x)= \frac{1}{x+3}+3 [/tex]
3 is added to x in denominator, and a 3 is added to the entire function value.
So, option D gives the correct answer
D. G(x)=(1/(x+3))+3
The explanation is the following:
1. You have the following function of the hyperbola given in the problem:
G(x)=1/x
2. When you plot the function above you obtain the graph shown in the first figure attached.
3. If you shifted the function of that hyperbola 3 units to the left and 3 units up, you obtain the graph shown in the second figure attached.
4. Therefore, as you can see, the correct answer is the option mentioned before.
What is the ratio of 5 gallons blue paint to 9 gallons of yellow paint?
Answers
This can be found by dividing 5 by 5 ( making the ratio say 1 to...) and dividing 9 by 5 giving you 1.8. Thus makin* the ratio 1:1.8 or 1 to 1.8.
I hope this helps!
Which solution to the equation (1/x-1)=(x-2/2x^2 -2) is extraneous?
a. x=1 and x=-4
b. nether x=1 or x=-4
c. x=1
d. x=-4
Answers
The appropriate choice is ...
c. x=1
_____
This can be solved without extraneous solutions by subtracting the right side.
(2(x +1) -(x -2))/(2(x -1)(x +1)) = 0
(x +4) = 0 . . . . . . . . . . . . . . . . . . . . . multiply by the denominator
x = -4 . . . . . . . . . . . . . . . . . . . . . . . . subtract 4
You have been asked to calculate the break-even point for a new line of souvenir t-shirts. the selling price will be $25 per shirt. the labor costs will be $5 per shirt. the administrative costs of operating the company are estimated to be $60,000 annually and the sales and marketing expenses are $20,000 a year. additionally, the cost of materials will be $10 per shirt. what is the break-even quantity?
Answers
What is 40,630 written in scientific notation?
Answers
Always remember if the decimal is being moved to the left, the exponent will be positive.
Answer:
4.063 x 10*4
Step-by-step explanation:
take the big number and move it from the exponent then bwa
A teacher took a survey and found that 16 of 25 students liked a certain snack item best. Make a prediction of how many students liked the snack item best if there are 225 students.
Answers
We have then:
(16/25) * (100) = 64%
Then, for 225 students we have:
(0.64) * (225) = 144
Answer:
144 of 225 students liked a certain snack item best
Kim is a single woman in her mid-20s working while taking college credits to earn a bachelors degree. She is financing her education herself through both her income and taking out student loans. Her earnings in 2010 were $30,000 before taxes. She paid $5000 intuition and paid $350 interest on her student loan. In filing her state tax return form Kim takes a deduction for tuition paid and the interest paid on the loan. In taking these two deductions by how much did she lower taxable income? What is her taxable income now? What is her marginal tax rate? What will she owe in taxes for 2010?
Answers
Less: Deductions - 5,000 + 350 = 5,350
New taxable income - 24,650
Multiply: Marginal tax rate - 15%
Tax - 3,697.50
1.) She lowered her taxable income by 5,350.
2.) Her taxable income now is 24,650.
3.) Her taxable income falls under the income range of 8,375 - 34,000, so her marginal tax rate is 15%.
4.) She will have to pay 3,697.50 for her tax.
Hey can you please help me posted picture of question
Answers
While, in theoretical probability no experiment is performed, the results are drawn based on our knowledge of the event.
In the given case, we do not perform the experiment , rather we use our knowledge of alphabets to find the probability.
So, the correct answer is option A
10 POINTS
The graph below shows the price, y, in dollars, of different amounts of pounds of cheese, x: A graph titled Cheese Prices shows Number of Pounds on x axis and Price in dollars on y axis. The scale on the x axis shows numbers from 0 to 12 at increments of 2, and the scale on the y axis shows numbers from 0 to 72 at increments of 12. A straight line joins the ordered pairs 0, 0 and 12, 72 Which equation best represents the relationship between x and y? y = x + 6 y = 12x y = x + 12 y = 6x
Answers
y = kx
You are given the point (12, 72), so you know
72 = 12k
6 = k . . . . . . . divide by 12
Then the equation of the line is ...
y = 6x
The answer to the question is y=6x
Assume we have a calendrical system in which leap years happen every four years, no matter what. In a 150-year period, what is the maximum possible number of leap years?
Answers
In a calendrical system where leap years occur every four years without any exceptions, there would be 37 leap years in a 150-year period.
Explanation:In a calendrical system where leap years occur every four years without exception, the number of leap years in a 150-year period can be calculated with a simple division operation. This is because every 4 years there is a leap year consistent with the rules of this calendar system.
To calculate the maximum number of leap years in a 150-year period, you would divide 150 by 4 as this represents the frequency of leap years. This results in a total of 37.5. Given that a half year cannot be a leap year, we eliminate the fraction and we have 37 leap years.
While the Gregorian calendar also has a leap year every four years, there are exceptions for century years not divisible by 400. But since the question specified a system without such rule, there would be more leap years in this system compared to the Gregorian calendar for the same period of time.
Learn more about Leap Years here:https://brainly.com/question/25143066
#SPJ12
If prices increase at a monthly rate of 0.5%, by what percentage do they increase in a year?
What is the formula to solve?
Answers
We have been given that prices increase at a monthly rate of 0.5%.
Number of months in a year = 12
Let us suppose the item cost $1, then the percentage is given by
[tex]P=P_0(1+r)^n\\ \\ P=1(1+0.005)^{12}\\ \\ P=1.062[/tex]\\
Therefore, increase in a year is
[tex]1.062-1\\ =0.062[/tex]
Therefore, the required percentage in a year is 6.2%
Tom shoveled 12.5 yards of sand in 2.5 hours. At that rate how many yards did he shovel in one hour?
Answers
Find a cartesian equation for the curve. r = 9 sin(θ)
Answers
r = 9 sin (θ)
In addition, we have the following change of variables:
y = r * sine (θ)
Rewriting the equation we have:
r = 9 sin (θ)
r = 9 (y / r)
r ^ 2 = 9y
On the other hand:
r ^ 2 = x ^ 2 + y ^ 2
Substituting values:
x ^ 2 + y ^ 2 = 9y
Rewriting:
x ^ 2 + y ^ 2 - 9y = 0
Completing squares:
x ^ 2 + y ^ 2 - 9y + (-9/2) ^ 2 = (-9/2) ^ 2
Rewriting:
x ^ 2 + 1/4 (2y-9) ^ 2 = 81/4
4x ^ 2 + (2y-9) ^ 2 = 81
Answer:
The Cartesian equation is:
4x ^ 2 + (2y-9) ^ 2 = 81
Jenna bought n notebooks which cost 5 dollars each, and 3 pens which cost r dollars each. How much money did she spend?
Answers
5n (this is the amount she spent on notebooks) + (and) 3r (this is the amount she spent on pens)
5n + 3r would show how much money she spent. If you know how many notebooks she bought and how much each pen costs, you would multiply these numbers by the 5 and the 3 and add them.
Solve the equation by completing the square x^2-18x+58=0. is it
A. x= -9+-√23
B. x= -9+-√139
C. x= 9+-√139
D. x= 9+-√23
Answers
x² -18x +58 +23 = 23
(x -9)² = 23 . . . . . . . . . . . rewrite the left side as a square
x -9 = ±√23 . . . . . . . . . . . take the square root
x = 9 ±√23 . . . . . . . . . . . .add 9
The answer corresponds to selection ...
D. x = 9 ±√23
Answer:
x = 9 ±√23
Step-by-step explanation:
please answer the question in the picture above
Answers
4.55·10¹³ kg -1.78·10¹² kg
= 4.55·10¹³ kg - 0.178·10¹³ kg
= (4.55 -0.178)·10¹³ kg
= 4.372·10¹³ kg
Rounded to the appropriate precision, the mass of the Antarctic iceberg exceeds that of the Rock of Gibraltar by ...
4.37·10¹³ kg
Zachary used the calculations shown to find how much he would spend on 16 ounces of pistachios. 6 ounces of pistachios cost $7.50 mc022-1.jpg Unit price = $0.80 per ounce mc022-2.jpg What was his first error? The price per ounce should have been $45.00 per ounce. The price per ounce should have been $1.25 per ounce. The final cost should have been $20.00. The final cost should have been $16.80.
Answers
A factory's worker productivity is normally distributed. one worker produces an average of 77 units per day with a standard deviation of 22. another worker produces at an average rate of 66 units per day with a standard deviation of 19.
a. what is the probability that in a single day worker 1 will outproduce worker 2?
Answers
The probability that worker 1 will outproduce worker 2 in a single day is approximately 0.352 or 35.2%.
To find the probability that worker 1 will outproduce worker 2 in a single day, we need to compare their production rates using their respective means and standard deviations.
Let X be the production of worker 1 and Y be the production of worker 2. We are interested in finding P(X > Y).
Given:
Worker 1: X ~ N(77, 22^2)
Worker 2: Y ~ N(66, 19^2)
First, we standardize the variables:
Z1 = (X - 77) / 22
Z2 = (Y - 66) / 19
Now, we find P(X > Y) = P(X - Y > 0):
= P((X - 77) - (Y - 66) > 0)
= P((X - Y) > (77 - 66))
Now, we find the mean and standard deviation of the difference:
Mean of (X - Y) = 77 - 66 = 11
Standard deviation of (X - Y) = sqrt(22^2 + 19^2) = sqrt(484 + 361) = sqrt(845) ≈ 29.07
Now we standardize the difference:
Z = (11 - 0) / 29.07 ≈ 0.378
Finally, we find the probability using the standardized normal distribution table:
P(Z > 0.378) ≈ 0.352
So, the probability that worker 1 will outproduce worker 2 in a single day is approximately 0.352 or 35.2%.
the probability that Worker 1 will outproduce Worker 2 in a single day is approximately 0.7202 or 72.02%.
To find the probability that Worker 1 will outproduce Worker 2 in a single day, we can use the z-score formula for normal distributions.
The z-score formula is given by:
[tex]\[ z = \frac{{X - \mu}}{{\sigma}} \][/tex]
Where:
- ( X ) is the value we want to find the z-score for (in this case, Worker 1's productivity).
- [tex]\( \mu \)[/tex]is the mean (average) productivity.
- [tex]\( \sigma \)[/tex] is the standard deviation.
For Worker 1:
- [tex]\( X_1 = 77 \)[/tex] units per day (average productivity)
- [tex]\( \mu_1 = 77 \)[/tex]units per day (average productivity)
- [tex]\( \sigma_1 = 22 \)[/tex] units per day (standard deviation)
For Worker 2:
-[tex]\( X_2 = 66 \)[/tex]units per day (average productivity)
- [tex]\( \mu_2 = 66 \)[/tex]units per day (average productivity)
- [tex]\( \sigma_2 = 19 \)[/tex] units per day (standard deviation)
First, we find the z-score for Worker 1's productivity relative to Worker 2's productivity:
[tex]\[ z = \frac{{X_1 - \mu_2}}{{\sigma_2}} = \frac{{77 - 66}}{{19}} = \frac{{11}}{{19}} \approx 0.579 \][/tex]
Next, we look up the z-score in the standard normal distribution table or use a calculator/tool that can calculate probabilities from the standard normal distribution. The z-score of 0.579 corresponds to a probability of approximately 0.7202.
Therefore, the probability that Worker 1 will outproduce Worker 2 in a single day is approximately 0.7202 or 72.02%.
Which algebraic expression represents “the bagels were divided equally into fifteen bags”?
15 + b
157b
Which algebraic expression represents “the bagels were divided equally into fifteen bags”?
a. 15 + b
b. 157b
c. 15/b
d. b/15
Answers
Answer:
Option D [tex]\frac{b}{15}[/tex]
Step-by-step explanation:
Let
b-----> the number of bagels
we know that
To find the algebraic expression of "the bagels were divided equally into fifteen bags" , divided the number of bagels by fifteen
so
[tex]\frac{b}{15}[/tex]
*Please help, will thank and award brainliest*
Which costs are paid by the origination fee?
A. Title search
B. Attorney and notary fees
C. Credit check and administrative costs associated with loan processing
D. Property appraisal
Answers
for apex!!
Answer:
The answer "attorney and notary fees" made me get the question wrong on brainly. The correct answer it showed me after I got it wrong was C. Credit check and administrative costs associated with loan processing
Step-by-step explanation:
When flying at an altitude of 5 miles, the lines of sight to the horizon looking north and south make about a 173.7 degree angle. how much of the longitude line directly under the plane is visible from 5 miles high?
Answers
Final answer:
The visible portion of the longitude line under the plane from an altitude of 5 miles is approximately 320.38 kilometers, using the formula D = 112.88 km √h where h is the altitude in kilometers.
Explanation:
The question asks how much of the longitude line directly under the plane is visible from an altitude of 5 miles high. To find this distance, we can use the formula given for horizon distance: D = 112.88 km √h, where h is the altitude in kilometers. Since 5 miles is approximately 8.05 kilometers, we can calculate the distance to the horizon by taking the square root of the altitude and multiplying by 112.88 kilometers.
First, calculate the square root of the altitude:
√8.05 ≈ 2.838.
Then, we multiply by the constant:
D ≈ 112.88 km × 2.838 ≈ 320.38 km.
Therefore, from an altitude of 5 miles, the visible portion of the longitude line directly under the plane is approximately 320.38 kilometers long.
Find the x-intercepts of the parabola with vertex (1, -9) and y intercept at (0, -6).
Answers
(-0.73, 0, (2.73, 0)