Answer (assuming it can be in slope-intercept form):
[tex]y =2x[/tex]
Step-by-step explanation:
1) First, find the slope of the line. Use the slope formula, [tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]. Substitute the x and y values of the given points into the formula and solve:
[tex]m = \frac{(8)-(2)}{(4)-(1)} \\m = \frac{8-2}{4-1} \\m = \frac{6}{3} \\m = 2[/tex]
So, the slope is 2.
2) Now, use the point-slope formula [tex]y-y_1 = m (x-x_1)[/tex] to write the equation of the line in point-slope form. Substitute real values for [tex]m[/tex], [tex]x_1[/tex], and [tex]y_1[/tex].
Since [tex]m[/tex] represents the slope, substitute 2 in its place. Since [tex]x_1[/tex] and [tex]y_1[/tex] represent the x and y values of a point the line intersects, choose one of the given points (it doesn't matter which one, the results will equal the same thing) and substitute its x and y values into the formula as well. (I chose (1,2), as seen below.) Then, isolate y to put the equation in slope-intercept form ([tex]y = mx + b[/tex] format) and find the following answer:
[tex]y-(2) = 2 (x-(1))\\y-2 = 2(x-1)\\y -2 = 2x-2\\y = 2x+0\\y = 2x[/tex]
Solve the following inequalities and give the solutions in both set and interval notations.
-x/8 + 8/3 ≥ 3
Given:
The inequality is
[tex]-\dfrac{x}{8}+\dfrac{8}{3}\geq 3[/tex]
To find:
The solution for the given inequality in both set and interval notations.
Solution:
We have,
[tex]-\dfrac{x}{8}+\dfrac{8}{3}\geq 3[/tex]
It can be written as
[tex]-\dfrac{x}{8}\geq 3-\dfrac{8}{3}[/tex]
[tex]-\dfrac{x}{8}\geq \dfrac{9-8}{3}[/tex]
[tex]-\dfrac{x}{8}\geq \dfrac{1}{3}[/tex]
Multiply both sides by -8 and change the inequality sign.
[tex]x\leq -\dfrac{8}{3}[/tex]
It means all the values of [tex]x[/tex] which are less than or equal to [tex]-\dfrac{8}{3}[/tex] are included in the solution set.
Set notation is [tex]\{x|x\leq -\dfrac{8}{3}\}[/tex].
Interval notation is [tex]\left(-\infty,-\dfrac{8}{3}\right ][/tex].
During the two hours of the morning rush from 8 a.m. to 10 a.m., 80 customers per hour arrive at the coffee shop. The coffee shop has a capacity of 60 customers per hour. On average how long does a customer arriving during the morning rush wait to be served
Answer:
The average waiting time is 1/3 hours (or 20 minutes)
Step-by-step explanation:
Given
[tex]T = 2hours[/tex] --- Time
[tex]D = 80\ customers/hr[/tex] --- Arrivals
[tex]C = 60\ customers/hr[/tex] --- Capacity
Required
Determine the average waiting time
The average waiting time (AT) is calculated using the following formula:
[tex]AT = \frac{1}{2} * T * (\frac{D}{C} - 1)[/tex]
This gives:
[tex]AT = \frac{1}{2} * 2 * (\frac{80}{60} - 1)[/tex]
[tex]AT = 1*(\frac{80}{60} - 1)[/tex]
[tex]AT = (\frac{80}{60} - 1)[/tex]
Remove bracket
[tex]AT = \frac{80}{60} - 1[/tex]
Take LCM
[tex]AT = \frac{80-60}{60}[/tex]
[tex]AT = \frac{20}{60}[/tex]
[tex]AT = \frac{1}{3} hr[/tex]
or
[tex]AT = \frac{1}{3} * 60\ mins[/tex]
[tex]AT = 20\ mins[/tex]
Use the Binomial Theorem to expand (x + 1)^6
Answer:
Here is what i got x^2+6x^5+15x^4+6x+1
Step-by-step explanation:
^ that mark is for exponents btw. For anyone that is new to this
The Binomial Expansion of [tex](x+ 1)^6[/tex] is [tex]x^6[/tex] + 6[tex]x^5[/tex]y + 15[tex]x^4[/tex]y² + 20x³y³ + 15x²[tex]y^4[/tex] + 6x[tex]y^5[/tex] + [tex]y^6[/tex].
What is Binomial Expansion?An expression that has been raised to any finite power can be expanded using the binomial theorem. A useful expansion technique with applications in probability, probability theory, and algebra is the binomial theorem. A binomial expression is an algebraic expression with two terms that are not the same.
Given:
We have to expand [tex](x+ 1)^6[/tex]
We know the general form of Binomial Expansion
(x + y[tex])^n[/tex] = C(n, 0) [tex]x^ny^0[/tex] + C(n, 1) [tex]x^{n-1}y^1[/tex] +.........+ C(n, n) [tex]x^0y^n[/tex]
Here n= 6
So, the expansion of [tex](x+ 1)^6[/tex] is
= C(6, 0) [tex]x^6y^0[/tex] + C(6, 1)[tex]x^5y^1[/tex] + C(6, 2) [tex]x^4y^2[/tex] + C(6, 3) x³y³ + C(6, 4) x²[tex]y^4[/tex] +
C(6, 5) x[tex]y^6[/tex] + C(6, 6) [tex]x^0y^6[/tex]
= [tex]x^6[/tex] + 6[tex]x^5[/tex]y + 15[tex]x^4[/tex]y² + 20x³y³ + 15x²[tex]y^4[/tex] + 6x[tex]y^5[/tex] + [tex]y^6[/tex]
Learn more about Binomial Expansion here:
https://brainly.com/question/28983418
#SPJ5
What percent of a dollar is a nickel and a penny?
It is ______% of a dollar.
Answer:
6 %
Step-by-step explana
100 pennies makes a dollar... you just add 5 for the nickel and 1 fo the penny and it makes 6
Please help answer this question!!
Answer:
The answer of this question is 265 feet.
100 POINTS!!! Orthographic projection and isometric projection are two ways to show three-dimensional objects in a two-dimensional space, such as on a piece of paper or a computer screen. Each method gives a different perspective. Do some research and then compare and contrast the two methods for displaying three-dimensional shapes. Then try your hand at creating both types of projections for a simple geometric shape using paper, pencil, and a ruler.
In your opinion, what are the pros and cons of each projection? What are the limitations? In which circumstances, environments, or occupations is one type of projection likely preferred over the other? Describe any special tools that might be needed to create the projection. Which projection is easiest for you to interpret visually? Why?
Example 1:
The pros of Orthographic is that they can show hidden details and all of the connecting parts, they can be annotated to display material and finishes. The pros of Isometric projection is that they dont need many views and it gives accuracy, cons are is created a unorginized apperance by the lack of foreshortening, I would choose Isometric projection because it shows the size of the figure.
Example 2:
Orthographic projection is a good option for showing lots of detail and small things. The limitation is that with all of that detail, they can become quite messy and hard to understand to someone new to them. However, that is one of the pros of Isometric projection. It gives easy detail and is just as good as an Orthographic. Personally, I find Isometric projections easier to interpret.
What are terms in a polynomial separated by ?
Answer:
Terms are separated by addition signs and subtraction signs, but never by multiplication sign
Step-by-step explanation:
A polynomial with one term is called a monomial. A polynomial with two terms is called a binomial. A polynomial with three terms is called a trinomial.
I need help ASAP will mark the brainliest
Answer:
so it's difficult to do
i try
I need to help u
7. How do you write a deposit of $15?
You would need to generate a deposit slip or utilize an electronic banking system to send the funds into your account to deposit $15.
What is a deposit slip?A deposit slip is a little paper form that is included by a bank customer when depositing payments into a bank account.
To write a deposit of $15, you would need to create a deposit slip or use an electronic banking system to transfer the money into your account.
To write a deposit slip, you would need to follow these steps:
Obtain a deposit slip from your bank or financial institution, or use a deposit slip provided by your bank's mobile app.
Fill in your personal and account information, including your name, account number, and any other required information.
Indicate the amount of the deposit, in this case $15, in the designated area on the deposit slip.
If you are depositing checks or other negotiable instruments, list the details of each item in the designated area on the deposit slip, including the payee, check number, and amount.
Review the deposit slip for accuracy and completeness, and make any necessary corrections.
Submit the deposit slip and any accompanying cash or checks to a bank teller or use an ATM or mobile app to complete the deposit.
Learn more about the deposit slip here:
https://brainly.com/question/30081338
#SPJ2
A candy shop puts together two prepackaged assortments to be given to trick-or-treaters on Halloween. The feasible set for producing x packages of assortment A and y packages of assortment B has been graphed to the right. For the earnings function Earningsxy, where Earnings is in cents, how many of each assortment should be prepared in order to maximize profits? What is the maximum profit? 0 600 0 600 x y A coordinate system has a horizontal x-axis labeled from 0 to 600 in increments of 120 and a vertical y-axis labeled from 0 to 600 in increments of 120. A four-sided polygon labeled as the feasible set is formed by a series of line segments and their intersection with the x-axis and y-axis. The line segments are labeled as follows: y equals negative 2 x plus 600; y equals negative x plus 350. The shop should prepare nothing packages of assortment A and nothing packages of assortment B to maximize profit. (Type whole numbers.) The maximum profit is $ nothing. (Round to the nearest cent as needed.)
Answer:
Step-by-step explanation:
The correct question is attached in the image below;
From there, given that: the earnings = 60x + 50 y ------ (1)
y = -x + 175
for x = 0 ⇒ y = 175 ; Then Point A (0, 175)
y = -2x + 300
for y = 0 ⇒ x = 150 ; Then Point C (150, 0)
For Point B;
y = -x + 175 ---- (a)
y = -2x + 300 ---- (b)
Equating both (a) and (b) from above together; then:
⇒ -x + 175 = -2x + 300
⇒ x = 125
∴
From y = -x + 175
y = -125 + 175
y = 50
So point B ( 125, 50)
Now, the points are O(0, 0), A(0, 175), B(125, 50), C(150, 0)
As such, profit at these points are:
O(0, 0), Profit = 60 × 0 + 50 × 0 = 0
A(0, 175), Profit = 60 × 0 + 50 × 175 = 8750
B(125, 5), Profit = 60 × 125 + 50 × 50 = 10,000
C(150, 0), Profit = 60 × 150 + 50 × 0 = 9000
Hence, maximum profit takes place at B(125, 50) which is = $10,000
Finally, we can conclude that the shop should prepare 125 packages of assortment A and 50 packages of assortment B to maximize profit.
The maximum profit is $10,000
Find a solution to the following system of equations by graphing
y= 7x + 3
y= 3x -0.5
Answer: (-7/8, -3 1/8)
Step-by-step explanation:
To find the solution to a system of equations by graphing, you graph the two equations and the solution is where the two lines intersect. Attached is the graph.
Answer:
the answer is (-0.875, -3.125)
Which rule should be applied to reflect f(x)=x^3 over the line y=x?
NEED HELP NOW!!!!! 12 points!!!!!
Answer:
A. Substitute -x for x and simplify f(-x)
Step-by-step explanation:
i just did this
Answer:
I just did this
There are four people in a family-a father, a mother and two children-and they have won two tickets to go to Disneyland for a week. They decide to select a sample of two people for the trip as follows: the mother and father flip a coin to see which of the two of them will go, and they then flip a coin to see which of the two children will go. Which of the following is true?
Okay I know this is a crazy thing to ask on brainly but would anyone be interested in finishing my Math 4 class for $100 dollars?? my word is good I promise! I just need to pass!!! PLS HELP
Answer:
ok but I know this is a lie I'm just willing to help
15 L is approximately
Answer:
Rounding out we have that 15 liters equals 3.96 gallons
Step-by-step explanation:
I hope this halp
I WILL GIVE BRAINLIST!! The perimeter of ABCD is 140. Solve for x, y, and z
* there is picture down below*
Answer:
ABCD is a kiteProperties:
AB = AD, CB = CD, AC⊥DB, AC is angle bisector of DAB and DCBFind x:
P = 140 2(2x + 7 + 4x +3) = 1406x + 10 = 706x = 60x = 10Find y:
3y - 1 and 28° are complementary3y - 1 = 90° - 28°3y - 1 = 62°3y = 63°y = 21°Find z:
4z and 58° are complementary4z = 90° - 584z = 32°z = 8°Answer:
x=10
y = 21°
z=8°
Step-by-step explanation:
we have
AB = AD, CB = CD,
AC perpendicular to DB, AC is angle bisector of DAB and DCB
Perimeter = 140
2(2x + 7 + 4x +3) = 140
6x + 10 = 70
6x = 60
x = 60/6=10
x=10
again
3y - 1 +28° =90
3y - 1 = 90° - 28°
3y - 1 = 62°
3y = 63°
y = 21°
again
4z+58°=90
4z = 90° - 58
4z = 32°
z=32/4
z=8°
Measurement of missing angle?
Answer:
79 degrees
Step-by-step explanation:
180 - 73 - 28 = 79
Because a line is 180 degrees
FIND THE AREA OF A TRIANGLE
Answer:
80
So, the area A of a triangle is given by the formula A=12bh where b is the base and h is the height of the triangle. Example: Find the area of the triangle. The area A of a triangle is given by the formula A=12bh where b is the base and h is the height of the triangle.
a school is having a competition to see who can read the most books in one month (30 days). In the first 5 days, Jake reads 4 books. Meanwhile, Amy reads 5 books over 6 days. If they continue at these rates, who will win? By how many books?
Answer:
Amy will winStep-by-step explanation:
Jake
4 books ⇔ 5 days
x books ⇔ 30 days
5x = 4*30x = 120/5x = 24 booksAmy
5 books ⇔ 6 days
x books ⇔ 30 days
6x = 5*30x = 150/6x = 25 booksAmy will win by 25 - 24 = 1 book
A manufacturer of flashlight batteries took a sample of 15 batteries from a day's production and used them
continuously until they failed to work. The life lengths of the batteries, in hours, until they failed.
426
317
545
264
1049
631
512
366
592
562
298
421
678
345
987
At the .05 level of significance, is there evidence to suggest that the mean life length of the batteries produced by this manufacturer is more than 500 hours?
A jug contains 4 gallons of water. How many quarts of water does the jug contain? The jug contains quarts of water.
Answer:
It contains 16 quarts of water
Step-by-step explanation:
Just do 4 gallons by the 4 quarts in one gallon and youll get 16
Answer:
One gallon is equivalent to four quarts. so 4 gallons equal 4×4=16 quarts.
a stack of 150 pieces of paper is 2.5 cm thick how many pieces of paper are in a pile 6.5 CM thick
Find the scale factor of the height:
6.5cm / 2.5cm = 2.6
Multiply the known pages by the scale factor:
150 x 2.6 = 390 pieces of paper.
a triangle has one angle that measures 32 degrees and one angle that measures 102degrees. the measure of the triangle's thrid angle is what degrees?
46
Step-by-step explanation:
all angles must add to 180
32+102= 134
180-134= 46
correct me if im wrong:)
ok soo i am having trouble with this question lol what is 0 divided by 0
Answer:
0 because 0 is 0 and divided it's 0
norma made the graph below to show the relationship between the age and value of 12 cars. Which value, when removed from the graph, would result in the relationship being a function?
A carpenter cuts a board 3 3/8 feet off the end of a board that is 6 1/2 feet long. How long is the remaining piece of board?
Answer:
[tex]6 \times \frac{1}{2} - 3 \times \frac{3}{8} = 1 \times \frac{7}{8} [/tex]
A fraction is written in the form of a numerator and a denominator where the denominator is greater than the numerator.
The remaining piece of the board when [tex]3\frac{3}{8}[/tex] feet is cut off from the end of the board of [tex]6\frac{1}{2}[/tex] feet is
[tex]3\frac{1}{8}[/tex] feet
What is a fraction?A fraction is written in the form of a numerator and a denominator where the denominator is greater than the numerator.
Example:
1/2, 1/3 is a fraction.
1/2 of 4 is 2.
1/4 of 20 is 5.
We have,
Length of the board = [tex]6\frac{1}{2}[/tex] feet.
The length cut off from the board = [tex]3\frac{3}{8}[/tex] feet.
The remaining length of the board:
= [tex]6\frac{1}{2}[/tex] - [tex]3\frac{3}{8}[/tex]
= 13/2 - 27/8
Find the Lcm of 2 and 8.
The Lcm of 2 and 8 is 8.
= (13x4 - 27) / 8
= (52 - 27) / 8
= 25/8
Write it in a mixed fraction.
= [tex]3\frac{1}{8}[/tex] feet
Thus,
The remaining piece of the board when [tex]3\frac{3}{8}[/tex] feet is cut off from the end of the board of [tex]6\frac{1}{2}[/tex] feet is [tex]3\frac{1}{8}[/tex] feet.
Learn more about fractions here:
https://brainly.com/question/24370499
#SPJ2
can someone help me with this please
Answer:
I': (-1, 4)
J': (3, 5)
K': (3, 2)
Step-by-step explanation:
to find the new 'x' values, add 2 to original 'x' values
to find the new 'y' values, add 6 to original 'y' values
find the product 240 * 5.07
Answer:
1216.8
Step-by-step explanation:
Multiply 240 by 5.07 . 1216.8
Pls help me with the question
solve the systems by elimination
-x+5y=17
x + 2y =11
they are both different equations but they are the same question
Please ASAP someone help with this Math It's a missing assignment and it needs to be done and I don't know!!!!!!!!!!!!!!
