The equations of the lines in the form y=mx+b are-
Tangent line: y = 240x - 215994Normal line: y = - 0.00417x + 9.75What is slope?A line's slope is described like the change in y coordinate to the change in x coordinate. The net y coordinate change is y, whereas the net x coordinate change is x.
Therefore the variation in y coordinate in relation to the variation in x coordinate is written as, dy/dx.
Now, as per the given conditions;
The equation of the line is y = (6 + 4x)²
Simplifying the equation;
y = (6 + 4x)²
= 36 + 48x + 16x²
y = 16x² + 48x + 36
Now, differentiate the equation to find the tangent slope;
dy/dx = 32x + 48
At the point (6,900),
dy/dx = 32(6) + 48 = 240
Let equation of the tangent at point (a,b) is;
(y - b) = m(x - a)
a = 6, b = 900, m = 240
y - 6 = 240(x - 900)
Write this in y = mx + b form,
y - 6 = 240x - 216000
y = 240x - 215994 (Equation of Tangent line)
The slope of the normal line = -(1/slope of the tangent line) (since they're both perpendicular to each other)
Slope of the normal line = -1/240
The, equation of the normal will become;
y - 6 = (-1/240)(x - 900)
y - 6 = (-x/240) + 3.75
y = (-1/240)x + 9.75
y = - 0.00417x + 9.75 (Equation of Normal line)
Thus, the equation for the normal and tangent has be found.
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The complete question is-
Find the equation of the tangent line and normal line to the curve y = (6 + 4x)² at the point (6,900). Write the equations of the lines in the form y=mx+b. Tangent line: y=
Normal line: y=
there is a bot located at a pair of integer coordinates it must be moved to a location with another set
Unknown or unidentified numbers are denoted in mathematical equations by lowercase, italicized letters from the "late middle" of the alphabet. P, q, r, and s are the most prevalent.
Denumerable sets include the set Z. Denumerability is the property that even if a set may include an endless number of members, any element in the set may be represented by a list that implies its identity.
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Use the following statement to answer questions 10-16.
If a number is greater than -500, then the number is greater than 500.
Determine the truth value of the conditional statement. Explain.
The truth value of the conditional statement is false
How to determine the truth value of the conditional statement?
The conditional statement is given as
“If a number is greater than -500, then the number is greater than 500.”
The above conditional statement is false
This is because not all numbers greater than -500 are greater than 500
for example 450 is greater than -500, but less than 500 that is the number between -500 and 500 will not satisfy the above statement.
Hence, the truth value of the conditional statement is false
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The empty gas tank of a motor boat is to be fllled. The tank is shaped like a rectangular prism with length 30cm, width 24cm, and height 18cm. Suppose gas Is pumped into the tank at a rate of 864cm^(3) per minute. How many minutes does it take to fill the empty tank?
Answer:
Step-by-step explanation:
volume of the tank:
30cm*24cm*18cm
12960cm^3
rate=amount/time
time=amount/rate
time=12960cm^3/864cm^3/min
time=12960/864 min
time=15min
What kind of taxes are likely to pay for universities and police? a. local taxes b. state taxes c. federal taxes d. income taxes Please select the best answer from the choices provided A B C D Mark this and return
Answer:
B
Step-by-step explanation:
Given directed line segment cd, if point e divides cd three-fourths of the way from c to d, find the coordinates of e.
The coordinates of point E is (-2, -1.5)
How to determine the coordinates of point E?
see in the file attached below
The given parameters are
C = (1, 6)
D = (-3, -4)
The ratio 3/4 can be represented as:
m : n = 3 : 1
So, the coordinate of point E is
E = 1/(m + n) * (mx2 + nx1, my2 + ny1)
So, we have:
E = 1/(3 + 1) * (3 * -3 + 1 * 1, 3 * -4 + 1 * 6)
Evaluate
E = 1/(4) * (-8, -6)
This gives
E = (-2, -1.5)
Hence, the coordinates of point E is (-2, -1.5 )
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[tex]x(2x + 5) = 3 \\ 2x {}^{2} + 5x = 3[/tex]
can somoeone help me ..urgent
x(2x+5) = 3 and 2x²+5x = 3 are equivalent algebraic expression.
Equivalent expressions are those expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value(s) for the variable(s). They are same but looks different.
Given that, x(2x+5) = 3 and 2x²+5x = 3 and we have to conclude how both expressions are related to each other.
Let's procced to solve this.
x(2x+5) = 3 ..............(1)
2x²+5x = 3 ...............(2)
Now, solving equation (1), we get
x(2x+5) = 3 ⇒2x²+5x = 3, which is equation (2)
So, when we solve equation (1), we get equation (2) and vice-versa.
Hence, x(2x+5) = 3 and 2x²+5x = 3 are equivalent algebraic expression.
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HELP ASAP PLEASE
Which of the following properties could you use to solve 3/4t < 4 for t in one step? Select all that apply.
subtraction property of inequality
addition property of inequality
division property of inequality
multiplication property of inequality
Answer: t = 1.33333
Step-by-step explanation:
Answer: division property of inequality
Step-by-step explanation:
you would devide 3 by 4 which is 0.75 then add you varible. Thats 0.75t that means that 0.75t is less than 4
slope intercept form of -5/6x+4
The slope of equation y = -5/6 x + 4 is -5/6 and the slope-intercept form of -5/6x+4 is y = -5/6 x + 4
The slope of a function y = f(x) is given by a formula
slope = y2-y1 / x2- x1
where ( x1 , y1) and (x2, y2) are coordinates of any two points on the line of graph representing y = f(x)
Or we can simply use the slope-intercept form
y = mx+ c
where m is the slope of the given equation and c is the constant
so, in the given equation y = -5/6 x + 4
slope of the equation is -5/6
Hence, The slope of equation y = -5/6 x + 4 simply is -5/6 and the slope intercept form of -5/6x+4 is y = -5/6 x + 4
When you know the slope of the line to be investigated and the point given is also the y intercept, you can utilize the slope intercept formula y = mx + b. (0, b). The y value of the y intercept point is represented by b in the formula.
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nuss: a tool for propagating multigroup nuclear data covariances in pointwise ace-formatted nuclear data using stochastic sampling method
NUSS is a device for propagating multigroup nuclear information covariances in pointwise ace-formatted nuclear information the use of stochastic sampling method.
Stochastic sampling (SS) method for quantifying nuclear facts uncertainties is finished with the resource of the use of the use of perturbed nuclear facts in recurring neutronics calculations and identifying the variance of output parameters due to the input nuclear facts uncertainties. In this work, an SS-based absolutely device, called NUSS is carried out which perturbs pointwise ACE-formatted nuclear facts the use of multigroup nuclear facts covariance. The use of pointwise ACE-formatted nuclear facts in NUSS can accommodate flexible multigroup covariance structures and allows for nuclear facts uncertainty propagation through the continuous/pointwise-energy delivery code MCNPX. Next, Light Water Reactor (LWR) pin mobileular models from the OECD/NEA UAM Phase-1 benchmark were analyzed. Results of pass section and uncertainties in interest of numerous nuclear facts covariance libraries are presented.
Therefore, NUSS is a device for propagating multigroup nuclear information covariances in pointwise ace-formatted nuclear information the use of stochastic sampling method.
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?
Levi earned a score of 710 on Exam A that had a mean of 700 and a standard
deviation of 25. He is about to take Exam B that has a mean of 200 and a standard
deviation of 50. How well must Levi score on Exam B in order to do equivalently well
as he did on Exam A? Assume that scores on each exam are normally distributed.
Normal Distribution - Equivalent Scores
Sep 16, 8:06:22 AM
Levi must score 220 in Exam B in order to do equivalently well as he did in Exam A
How well must Levi score on Exam B in order to do equivalently well as he did on Exam A?The given parameters are:
Exam A
Score = 710
Mean = 700
Standard deviation = 25
Exam B
Mean = 200
Standard deviation = 50
The z-score is calculated as
z = (Score - Mean)/Standard deviation
For exam A, we have
z = (710 - 700)/25
z = 0.4
For exam B, we have
z = (Score - 200)/50
Substitute z = 0.4 in z = (Score - 200)/50
0.4 = (Score - 200)/50
This gives
Score - 200 = 20
Add 200 to both sides
Score = 220
Hence, Levi must score 220 in Exam B in order to do equivalently well as he did in Exam A
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61= -9c +7
its asking to solve c please help :)
Answer:
c = -6
Step-by-step explanation:
add 9c to both sides to get 61 + 9c = 7
subtract 61 from both sides to get 9c = -54
divide by 9 to get c = -6
50 points if you answer! + brainliest
Answer:
8/3
Step-by-step explanation:
Divide 8/3
Answer:
Option D: 8/3
Step-by-step explanation:
(2 x 3 + 2)/3 = 2 2/3
(6 + 2)/3 = 2 2/3
8/3 = 2 2/3
5^4 times 3^3/5^2 times 3^2
Power is the result of multiplying same number for n number of times. The value of the given expression when simplified is equal to 75.
What is power?Power is the result of multiplying same number for n number of times. Power is typically expressed by a base number and an exponent. The base number indicates the number being multiplied. The exponent, which is a little number printed above and to the right of the base number, indicates the number of times the base number is multiplied.
The given expression can be simplified as shown below.
(5⁴ × 3³) / (5² × 3²)
= (625 × 27) / (25 × 9)
= 16,875 / 225
= 75
Hence, the value of the given expression when simplified is equal to 75.
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a rectangle’s length is 5 inches more than twice its width. its area is 50 square inches. which equation can be used to find its width, w? 2w(2w 5)
The equation used is 50 = (2w + 5) × w which can be used to find its width, w.
According to the question we are Given,
Length of rectangle = 5 inches more than its width
Area of rectangle = 50sq. inches
Let width of rectangle = w
So, According to the question,
length = 2w + 5
Area of rectangle = Length × Breadth
50 = (2w + 5) × w
So, our required equation is 50 = (2w + 5) × w
How can we describe the area of rectangle as?The quantity of space occupied by a flat surface with a specific form is referred to as the area. It is calculated as a "number of" square units (square centimeters, square inches, square feet, etc.) The quantity of unit squares that may fit within a rectangle called its area. The flat surfaces of laptop monitors, blackboards, painting canvases, etc. are a few instances of rectangular forms.
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sally paid $3.50 for 7 apples. write an equation to represent the total cost y of buying x apples
Answer:
24.5 = 3.50 * 7
Step-by-step explanation:
I used multiplication.
Answer:
y=x+b
3.50=7x
Step-by-step explanation:
7 is how many apples sally bought
it is $3.50 for 7 apple so $3.50 is y
7 times the price for one apple is $3.50
which also means each apple is $0.50
Michael downloaded 16 apps on his iPhone in 12 seconds? At this rate, how many apps can he download in one minute? (12 seconds = 1/5 minute)
What is the measure of ∠ADB? WILL CHOOSE THE BRAINLIEST ANSWER!
Answer: A
Step-by-step explanation:
Angles on a straight line must add up to 180 so angle BCA is 180-132=48
Because the triangle BAC is an isosoles angle BCA and ABC must be the same so 48
We can now use the angle on a straight line rule to figure out angle DBA 180-48=132
We know that triangle DBA is an isosoles trianlge so and x and DAB must be the same and both be x, and we know that angles in a triangle add up to 180 so the equation can be written as:
180=2x+132
48=2x
x=24
The study participants were divided into four groups-two groups received the Power Pill
(Group A and Group B) and two groups received a placebo (Group C and Group D). The effects
of the Power Pill were measured. One group that received the Power Pill (Group A) and one
group that received the placebo (Group C) were told of the anticipated effects of the Power
Pill-accelerated hair growthwhile the other two groups (Group B and Group D) were not
provided with this information. All four groups were told to monitor and report any physical
changes during the study.
Results were reported and participants were grouped as to either "Saw Results," meaning that
participants reported increased hair growth as part of physical changes during the study, or "No of
Results," meaning that increased hair growth was not mentioned as part of physical changes
during study.
Results are as follows:
6 in Group A saw results.
7 in Group B saw results.
5 in Group C saw results.
4 in Group D saw results.
Part 1:
Create a two-way table for the data and find the probabilities for each group. Describe results
in
terms of the study.
Answer: L
Step-by-step explanation:
in a balloon it was notices that the pressure, in atmosphere (atm), was inversely proportional to the square root of the height, in metres. when the balloon was at the height of 25m,tge pressure was 1.44atm. what was the pressure at a height of 9m?
It was discovered that the pressure in atmospheres (atm), when applied to a balloon, was inversely related to the height in meters, squared root. The pressure was 1.44 atm when the balloon was 25 meters height in the air. What was the pressure like at a 9-meter height?
The pressure is 2.4 atm when the height is 9m.
Inversely proportion means when one variable is directly proportional to the reciprocal of the other, there is an inverse fluctuation between the two variables. In other words, the two variables' product has a fixed value. Therefore, as one variable rises, the other falls.
Here, We take pressure of atmosphere as P and the height of the balloon as H.
Given that, The pressure of atmosphere was inversely proportional to the square root of the height.
We write this as [tex]P[/tex]∝[tex]\frac{1}{\sqrt{H} }[/tex].
Taking constant of the proportionality as k.
[tex]P[/tex]=[tex]\frac{k}{\sqrt{H} }[/tex].
We have, The pressure was 1.44 atm when the balloon was 25 meters height in the air.
P=1.44 and H=25
[tex]1.44=\frac{k}{\sqrt{25} }[/tex].
[tex]1.44=\frac{k}{5}[/tex]
[tex]k=5\times1.44[/tex]
[tex]k=7.2[/tex]
Now [tex]P=\frac{7.2}{H}[/tex]
We have to find If H is 9m then what is P?
[tex]P=\frac{7.2}{\sqrt{9} }[/tex]
[tex]P=\frac{7.2}{3}[/tex]
[tex]P=2.4\\[/tex]
Therefore, The pressure is 2.4 atm when the height is 9m.
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The endpoints of CD are C(3,
5) and D(7, 9).
The coordinates of the
midpoint M of CD are
Answer: M(5,7)
Step-by-step explanation:
[tex]\displaystyle\\C(3,5)\ \ \ \ \ D(7,9)\ \ \ \ \ M(x_M,y_M)=?\\\\M(x_M,y_M)=(\frac{3+7}{2},\frac{9+5}{2})\\\\ M(x_M,y_M)=(\frac{10}{2},\frac{14}{2} )\\\\ M(x_M,y_M)=(5,7)[/tex]
Construct a relative frequency histogram for tuition and fees for students at public four-year colleges. write a few sentences describing the distribution of tuition and fees, commenting on center, spread, and shape.
Hi, please answer
is 1/24 and 7/19 equivalent????
please thank yoooouuuu
Answer:No this is not equivalent.
Answer:
No
Step-by-step explanation:
Both fractions have been simplified as much as possible and aren't the same. They are not equivalent for this reason.
I wasn't entirely sure how to explain this but I hope this helps!
| 5)
order
22, 37, 19, 25, 37, 51, 82
Mean
Mode
Median
Range
Answer:
Mean:39
Mode:37
Median:37
Range:82-19=63
Please help with problem 20
Algebra 1
The solutions to the given absolute value equations are given as follows:
A. t = -1, t = 1.4.
B.
The graph of item A is given at the end of the answer.
What is the absolute value function?The absolute function is defined by:
|x| = x, x ≥ 0.|x| = -x, x < 0.It measures the distance of a point x to the origin, hence, for example, |-2| = |2| = 0.
For item a, we have that two possibilites, as follows:
5t - 1 = 6 -> 5t = 7 -> t = 7/5 -> t = 1.4. (between 1 and 2).5t - 1 = -6 -> 5t = -5 -> t = -1.The graph is given at the end of the answer(correct solutions dashed in blue).
For item b, following the same procedure, the solutions are:
2a + 1 = 1 -> 2a = 0 -> a = 0.2a + 1 = -1 -> 2a = -2 -> a = -1.The graph is also given at the end of the answer, with the -1 marked in blue. (you have to remove the marking from 1).
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Sorry I couldn’t type it out it came with the image
Check the picture below.
351.92 in scientific notations
A cuboid has a length of 6 cm, a width of 7 cm
and a height of 5 cm.
a) Work out the surface area of this cuboid.
b) Three of these cuboids are stacked on top
of each other to form a cuboid-shaped tower.
The height of this tower is 15 cm.
What is the surface area of this tower?
Give your answers in cm².
a) Surface area of this cuboid = 214 cm²
b) Surface area of the tower = 474 cm²
Dimensions of cuboid :
Length (l) = 6 cm
Width (w) = 7 cm
Height (h) = 5 cm
The Surface Area of Cuboid (SA) = 2(lw + lh + hw)
SA = 2(6×7 + 6×5 + 5×7)
= 2(42 + 30 + 35)
= 2×107
The Surface Area of Cuboid = 214 cm²
Dimensions of tower :
Length (l) = 6 cm
Width (w) = 7 cm
Height (h) = 15 cm
The Surface Area of Tower = 2(lw + lh + hw)
= 2(6×7 + 6×15 + 15×7)
= 2(42 + 90 + 105)
= 2 × 237
The Surface Area of Tower = 474 cm²
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The sum of the angle measures of a quadrilateral is 360 degree. Write and solve an equation to find the value of x.
Answer: 115+85+60+x=360
x=100 degrees
Step-by-step explanation:
115+85+60+x=360==> 115, 85, 60, and x are all 4 angles in the quadrilateral
200+60+x=360
260+x=360
260-260+x=360-260
x=360-260
x=100 degrees
ALGEBRA!!!!
Determine whether each relation represents a
function. For those that are functions, state the
domain and range.
a. {(1,4), (2,5), (3,6), (4,7))
b. {(1,4), (2,4), (3,5), (6,10))
c. {(-3,9), (-2,4), (0,0), (1,1), (-3,8)}
Among the given relations {(1,4),(2,5), (3,6), (4,7)} represents a function.
Given three options as under:
1) {(1,4), (2,5), (3,6), (4,7)}
2) {(1,4), (2,4), (3,5), (6,10)}
3) {(-3,9), (-2,4), (0,0), (1,1), (-3,8)}
We are required to choose the relation which represents a function.
Function is basically from a set X to a set Y assigns to each element of X exactly one element of Y.
Among the given options the relation which is a function is
{(1,4),(2,5), (3,6), (4,7)} because the other options have two values for one value of x or one value is giving two values of y which is opposite to the characteristics of a relation to be a function.
Hence among the given relations {(1,4),(2,5), (3,6), (4,7)} represents a function.
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Keilantra wants to ride her bicycle 28.8 miles this week. She has already ridden 4
miles. If she rides for 4 more days, write and solve an equation which can be used to
determine m, the average number of miles she would have to ride each day to meet
her goal.
Equation:
Answer: m =
Submit Answer
attempt 1 out of 2
To meet her goal of riding a total of 28.8 miles, Keilantra needs to ride an average of 6.2 miles.
How to find the average number of miles that she needs to ride each day?Here we know that Keilantra wants to rude her bicycle for a total of 28.8 miles.
We know that she has already ridden 4 miles, so the distance left to meet her goal is:
D = 28.8mi - 4mi = 24.8mi
Now we know that she wants to meet her goal in 4 days, so the average that she needs to ride in each of these 4 days is given by the quotient:
24.8mi/4 = 6.2 mi
To meet her goal, Keilantra needs to ride an average of 6.2 miles.
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