Answer:
y=5x+4
Step-by-step explanation:
You would have to look up how to do the hadn written way of figuring out this but I just used my calculator. To do this with your TI-84 or newer calculator, press "stat" and go into "edit". You will see some columns with the names "L1, L2, L3, etc." which stand for lists. put your x values in "L1" and their corresponding y values next to them in "L2". When you're done press stat again and move right to the heading "Calc". Go down to number 4 which should say "LinReg(ax+b)" next to it and press enter. now you should see "Xlist" and "Ylist" with "L1" and "L2" beside them respectively. Once that is set, go down to "Calculate" and press enter and it should give you slope intercpet form and what "a" and "b" are. You're welcome.~ ;P
A health insurance policy requires that each
person covered pay the first $300 of a bill and
then 0.2 times the rest of the bill. Fran is
covered by this policy and had to pay $500.
What was her total bill?
Can anyone help me with this plzz?
===========================================================
Explanation:
Check out figure 1 in the attached images below. In this figure, I've plotted the function y = 6/(2x-3) on a 2D grid system. The function curve is in blue. Then I've plotted (2,0) and (3,0) on the x axis. Point A is somewhere between those endpoints. Point A is also on the x axis. Directly above A is point B such that B is on the blue function curve.
The distance from A to B is found by subtracting the y values of each point.
The y coordinate of A is y = 0. The y coordinate of B is y = 6/(2x-3)
Therefore, the distance from A to B is 6/(2x-3) units. This will form the radius of each cylindrical slice as figure 2 shows. Note the color coding to help see how the 2D view corresponds to the 3D view. The xy plane has been laid flat on the floor. So we're viewing the function curve at a downward angle now. Each of those gray cylinders combine to form an approximate 3D volume. The more cylinders we have, and the finer the cuts, the more accurate the total volume.
So it comes down to finding the volume of each cylindrical slice and adding up the volumes. This is effectively what integral calculus is all about.
------------------------------------
Since the radius of each cylinder is y = 6/(2x-3), this means r = 6/(2x-3) is plugged into the formula
V = pi*r^2*h
which is the volume of a cylinder formula
The height of each cylinder is delta x, which we'll use dx for short. So this is where the dx comes from in integrals.
This is what the integral will look like
[tex]\displaystyle V = \int_{2}^{3} \pi*\left(\frac{6}{2x-3}\right)^2dx[/tex]
which turns into
[tex]\displaystyle V = 36\pi\int_{2}^{3}\frac{1}{(2x-3)^2}dx[/tex]
after a bit of algebra. We're able to factor the 36pi out because it's a constant
From here we use u-substitution. Let u = 2x-3
This leads to du/dx = 2 which can be solved to dx = du/2
Since u = 2x-3, the lower endpoint x = 2 leads to
u = 2x-3 = 2*2-3 = 1
and x = 3 leads to
u = 2x-3 = 2*3-3 = 3
So the interval 2 < x < 3 turns into 1 < u < 3
After using u-sub, making the proper replacements, and integrating, we get
[tex]\displaystyle V = 36\pi\int_{2}^{3}\frac{1}{(2x-3)^2}dx\\\\\\\displaystyle V = 36\pi\int_{1}^{3}\frac{1}{u^2}\frac{du}{2}\\\\\\\displaystyle V = 36\pi*\frac{1}{2}\int_{1}^{3}\frac{1}{u^2}du\\\\\\\displaystyle V = 18\pi\int_{1}^{3}u^{-2}du\\\\\\\displaystyle V = 18\pi\left[-u^{-1}+C\right]_{1}^{3}\\\\\\\displaystyle V = 18\pi\left[-\frac{1}{u}+C\right]_{1}^{3}\\\\\\[/tex]
Let's evaluate that to get the following
[tex]\displaystyle V = 18\pi\left[-\frac{1}{u}+C\right]_{1}^{3}\\\\\\\displaystyle V = 18\pi\left[\left(-\frac{1}{3}+C\right)-\left(-\frac{1}{1}+C\right)\right]\\\\\\\displaystyle V = 18\pi\left(-\frac{1}{3}+1\right)\\\\\\\displaystyle V = 18\pi\left(\frac{2}{3}\right)\\\\\\\displaystyle V = 12\pi\\\\\\[/tex]
So the 3D volume formed by rotating that region (under the curve from x = 2 to x = 3) is exactly 12pi cubic units
PLEASE HELP I NEED THIS TODAY!!
Answer: 201.06
Step-by-step explanation: The formula is pi times the radius squared.
D=
R=
Function?
Find the domain and range of each relation. Then, determine if the relation is a function.
Answer:
Step-by-step explanation:
D = { - 4 , 0 , 2 , 7 }
R = { - 8 , - 1 , 3 }
Yes the relation is a function.
Please help me!Find the slope of the line on the graph.
Write your answer as a fraction or a whole
number, not a mixed number or decimal.
Enter the correct answer
Answer:
[tex]m=-\frac{3}{2}[/tex]
Step-by-step explanation:
First, look at the graph and pick out two points that we can use for the slope equation. I see (0,2) and (-2,5) as two possibilities. Now, we just plug them into the slope equation. Remember that the slope equation is
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
(the '2' and '1' are subscripts, not exponents)
Let's call our first point (0,2) x1 and y1. (-2,5) can be the second point.
If we plug this into the equation:
[tex]m=\frac{5-2}{-2-0}[/tex]
Now we just simplify and get
[tex]m=\frac{3}{-2}[/tex]
Our slope is [tex]-\frac{3}{2}[/tex].
I hope this helps!
People with a brain in Health I need you
Why does my knee and hip keep popping out of its place as it hurts in the weirdest way i don't know if i should go to the hospital or not
and if I play basketball and football and track and volleyball it will pop out randomly but not soccer it is so weird and i donno whatta do
A Knee sleeve doesn't even work why? ughhhh I am bouta lose it
i will go to the gym and it will literally make me collapse....
Answer:
That ain't normal
Step-by-step explanation:
ASAP FOR BRAINLIEST!
Answer:
Slope is -1/4
Step-by-step explanation:
Goes down 1 and over 4 so -1/4
find the difference. (12m + 1) - (5m - 4)
Answer:
7m + 5
Step-by-step explanation:
1) Simplify.
(12m + 1) - 1 (5m - 4) -> (12m + 1) - 5m + 4
2) Eliminate unnecessary parenthesis.
(12m + 1) - 5m + 4 -> 12m + 1 - 5m + 4.
3) Combine like terms.
12m - 5m = 7m, 4 + 1 =5 -> 7m + 5
The solution is 7m + 5
if the cost of 8 mobile set is rs 40,000.how many mobile sets can be purchased for Rs 100,000
Answer:
20 mobile sets.
Step-by-step explanation:
Every mobile set costs:
40000 / 8
= 5000 Rs.
Therefore, for 100,000 Rs, the number of mobile sets that can be purchased is:
100,000 / 5000
= 20 mobile sets.
Hope this helped!
Answer correctly please !!!!!!!!!!!!!!!! Will mark brainliest !!!!!!!!!!!!!!!!!!!!!
can i have help i give you brainlest
Answer:
x = 12 or 12:204
Step-by-step explanation:
You have to set it up like this....
Just cross multiply.
[tex]\frac{3}{51}*\frac{x}{204}[/tex]
You'll multiply
3*204 = 612
51*x = 51x
612 = 51x (divide by 51 on both sides)
12 = x
12:204
Hope this helps!!!
The temperature has been dropping 2 degrees every hour and the current temperature is -15°F. How many hours ago was the temperature 0°F?
Answer: 6 1/2
Step-by-step explanation:
six and 1 half of a hour
what is the speed of a jet plane that travels 528 m in four seconds
Answer: 132 m/s
Step-by-step explanation:
Also known as "fast"
Answer: 132m/s
Step-by-step explanation:
Use the formula: speed = distance/time
Plug in your numbers: speed = 528/4
Solve: speed = 132m/s
hi i really need help!!
Answer:
GH = 12, JH = 8, GJ = 10.6, your answer is the first choice
Step-by-step explanation:
Mid-segment theorem basically means it's like cut in half so just apply that logic to the entire thing:
DG = GF and IH = HF
DI length, 24, divided by two, because half, equals 12 so 12 = GH
JH is DF divided by two so basically 16/2 which is 8 which also equals DG
GJ = IH because like I said half half theory
Essentially, all the parallel lines are halves of each other.
GH = 12, JH = 8, GJ = 10.6, your answer is the first choice
The speed of an object can be found by taking the distance it travels and dividing it by the time it takes to travel that distance. An object travels 100 feet in 2.5 seconds. Let the speed, , be measured in feet per second.
Write an equation to represent the relationship between the three quantities (speed, distance, and time).
speed = [tex]\frac{distance}{time}[/tex]
speed = [tex]\frac{100}{2.5}[/tex]
speed = 40 feet per second
A cuboid with a volume of 925cm^3 has dimensions.
4cm, (x + 1) cm and (x + 11) cm.
Show clearly that x^2 + 12x - 220 = 0
Solve the equation by factorising, making sure you show the factorisation.
State both values of x on the same line.
Finally, find the dimensions of the cuboid, writing all three on one line.
Answer:
Step-by-step explanation:
Volume of the cuboid = Length * Width * Height
Given
Length = 4cm
Width = (x+1)cm
Height = (x-11)cm
Volume of the cuboid = 4(x+1)(x+11)
Volume of the cuboid = 4(x^2+11x+x+11)
Volume of the cuboid = 4(x^2+12x+11)
Volume of the cuboid = 4x*2+48x+44
925 = 4x*2+48x+44
4x*2+48x+44-925 = 0
4x*2+48x-881 = 0
Divide through by 4
x^2 + 12x - 220.25 = 0
Factorize using the general formula;
x = -12±√12²-4(-220.25)/2
x = -12±√144+881/2
x = -12±√1025/2
x = -12±32/2
x = 12+32/2
x = 20/2
x = 10
Hence the dimension of the cuboid is 4cm, (10+1)cm and (10+11)cm
Dimension is 4cm by 11cm by 21cm
need help on 5 & 6 please !!!
Step-by-step explanation:
Q5. Let the cost of 28subscriptions be $s.
Words: 1subscription/28subscription = $21/$28
Numbers: 1/28 = 21/s
Cross multiply and solve: 1 x s = 21 x 28
s = 588
Answer with label: $588
Q6.
Words: 2inches/3.6inches = 2.5hours/bhours
Numbers: 2/3.6 = 2.5/b
Cross multiply and solve:
2 x b = 2.5 x 3.6
2b = 9
b = 4.5
Answer with label: 4.5hours
Anyone know the answer?
Answer:7
Step-by-step explanation: The range is the value of the difference of the highest and lowest numbers. As I can see here, the highest is 9, while the lowest is 2, so 9-2=7
please tell me the answer
Answer: D
Step-by-step explanation:
I solved it:)
Laura checked her outdoor thermometer and noticed that the temperature rose from 31 degrees in the morning to 45 degrees in the afternoon. What is the approximate percent increase for the day so far?
A. The percent increase is approximately 31%.
B. The percent increase is approximately 45%.
C. The percent increase is approximately 68%.
D. The percent increase is approximately 82%.
Answer:
C
Step-by-step explanation:
If you find the difference between 45 and 31, you find the increase. Take that and make it a percentage of 68. I hope this helped! Have a great day.
Is the relation in the mapping below a function? Explain.
Domain
1,3,5,7
Range
2,4,6
Answer: No
Step-by-step explanation:
The range and the Domain aren’t equal
The Great Pyramid of Egypt was built for Queen Cleopatra.
True
or
False
Answer:
False
Step-by-step explanation:
Answer:
False
that is the answer
Lines AB and MN intersect at P.
N
A
(3x + 24)
(9x - 54)
P
B
M
What is the value of x?
Answer:
x = 13
Step-by-step explanation:
To solve for x, we set equations (9x - 54) and (3x + 24) equal to each other because the angles are equal
(9x - 54) = (3x + 24); add 54 to both sides
9x = 3x + 78; subtract 3x from both sides
6x = 78; now divide by 6
x = 13
Write the equation of a line that passes through (-4, 5) and (-4, 11)
Answer:
x=-4
Step-by-step explanation:
Both points are on same line x=-4
A small town has two local high schools. High School A currently has 850 students and is projected to grow by 35 students each year. High School B currently has 700 students and is projected to grow by 60 students each year. Let AA represent the number of students in High School A in tt years, and let BB represent the number of students in High School B after tt years. Write an equation for each situation, in terms of t,t, and determine after how many years, t,t, the number of students in both high schools would be the same.
An equation for each situation, in terms of t, is y = 850e^35t and
y = 700e^70t
The required equation will be in the form y = Ae^kt
where:
k is the growth constantA represents the number of students in High School A in t years.B represents the number of students in High School B after t years.If High School A currently has 850 students and is projected to grow by 35 students each year, hence;
A = 850k = 35 (growth factor)Substituting into the formula, we will have:
y = 850e^35t
If High School B currently has 700 students and is projected to grow by 60 students each year, hence;
A = 700k = 60 (growth factor)Substituting into the formula, we will have:
y = 700e^70t
An equation for each situation, in terms of t, is y = 850e^35t and
y = 700e^70t
Learn more on exponential function here: https://brainly.com/question/12940982
180 in the ratio 1:3:4
Answer:
let 1:3:4 be written as x:3x:4x
therefore, x+3x+4x = 180
8x = 180
x = 180/8
x = 22.5
therefore, x = 22.5
3x = 22.5 * 3 = 67.5
4x = 22.5 * 4 = 90
Hope it helped u,
pls mark this as brainliest
and put thanks
^_^
The points in each table lie on a line. Find the slope of the line.
O 1/2
O 1
O 2
O None of the above
Answer:
1
Step-by-step explanation:
Given table:
x -1 1 3 5
y -2 0 2 4
Unknown:
Slope of the line = ?
Solution:
Each x and y pair on the table lies on the line. Therefore, we can use them to find the slope;
Slope = [tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]
let us take;
x₁ = -1 x₂ = 3
y₁ = -2 y₂ = 2
Insert the parameters and solve;
Slope = [tex]\frac{2 - (-2)}{3- (-1)}[/tex] = [tex]\frac{4}{4}[/tex] = 1
The slope of the line is 1
A tanning salon opens with 50 members. Each month the membership increases by 10 members. Write an equation that represents the relationship between the number of months the salon has been opened, x, and the total salon memberships, y?
Answer:
y= 10x+50
Step-by-step explanation:
x is an increasing variable so, if 10 members are joining each month, x equals 10. 50 is a non increasing number so it has no variable. and y equals all members in total, so y= 10x+50
Prasitha has two buildings A and B. A is 10 feet shorter than the twice the height of B. The distance between the buildings is 120 feet and the height of B is 60 feet. Find the distance between their tops.
Answer:
The distance between their tops is 130 feet
Step-by-step explanation:
The given parameters are;
The height of A, [tex]h_A[/tex] = 2 × The height of B - 10
The distance between the two buildings, d = 120 feet
The height of B, [tex]h_B[/tex] = 60 feet
Therefore, we have;
The height of A, [tex]h_A[/tex] = 2 × The height of B - 10 = 2 × 60 - 10 = 110 feet
The height of A, [tex]h_A[/tex] = 110 feet
By Pythagoras theorem, the distance between their tops = √(([tex]h_A[/tex] - [tex]h_B[/tex])² + d²)
Substituting the values gives;
The distance between their tops = √((110 - 60)² + 120²) = 130
The distance between their tops = 130 feet.
If m <2 = 120', what is m<7?
m<7=120'
Step-by-step explanation:
m<2 = m<6 because m and l are parallel and m<6 =m<7 because they are vertically opposite angles (v.o.a)
Answer:
m<7=120
Step-by-step explanation:
2 and 7 are alternate exterior angles and because l and m are parallel lines then m<2=m<7