The line y = x + 3 has slope 1, so we look for points on the curve where the tangent line, whose slope is dy/dx, is equal to 1.
y² = x
Take the derivative of both sides with respect to x, assuming y = y(x) :
2y dy/dx = 1
dy/dx = 1/(2y)
Solve for y when dy/dx = 1 :
1 = 1/(2y)
2y = 1
y = 1/2
When y = 1/2, we have x = y² = (1/2)² = 1/4. However, for the given line, when y = 1/2, we have x = y - 3 = 1/2 - 3 = -5/2.
This means the line y = x + 3 is not a tangent to the curve y² = x. In fact, the line never even touches y² = x :
x = y² ⇒ y = y² + 3 ⇒ y² - y + 3 = 0
has no real solution for y.
An office manager budgeted $400 for
office supplies. The manager ordered
2 toner cartridges for $89 each and a
box of printer paper for $27. Each price
includes tax.
What is the greatest number of
additional boxes of printer paper the
manager can order with the money left
in the budget?
A. 2
B. 7
C. 8
D. 10
Answer:
B. 7
Step-by-step explanation:
To find this out, first, we multiply 89*2, which is 178, the amount already spent on toner.
Then, we add 27 to this to find the total amount spent so far. This comes out to $205 spent so far.
To find out how much we have left to spend, we subtract the amount spent from the original.
400-205 = $195, the amount of money left.
To find out how much paper we can buy, we divide the cost of one paper box, by the amount of money we have left.
195/27 = 7.222222222222222222222222222222
Since we cannot buy 7.222222222222222222222222 boxes, we can only buy 7. This is the answer.
Of the twenty-two students in a classroom, ten are transfer students, seven are nursing students, four are AAS students and one student is undecided:
If one student is chosen randomly, find the probability that the student is not an AAS student.
Answer:
What are all the ZEROS? Show all the work!
(2x+6)(x-4)
Answer:
4 and -3
Step-by-step explanation:
2x+6=0
2x=-6
-3
x-4=0
x=4
So its 4 and -3
Answer:
-3,4
Step-by-step explanation:
(2x+6)(x-4) = 0
Using the Zero Factor Principle: If ab =0 then a=0 or b=0
2x+6=0 or X-4=0
solve 2x+6=0:
2x+6=0
Subtract 6 from both sides
2x+6-6 0-6
Simplify
2x = -6
Divide both sides by 2
2x/2 = -6/2
Simplify
X=-3
then x-4 =0
add 4 from to both sides
x=4
zeros : -3,4
(-3,0),(4,0)
Ms. York gave a math quiz to each of her two classes. The quiz scores of each class are shown below. Find the mean, median, and mode for the afternoon class. Using this information, which class do you think did better on the quiz? Explain How you got your answer.
Morning Class Quiz Scores Afternoon Class Quiz Scores
Quiz Score 91, 80, 75, 80, 60, 87, 80 80, 87, 90, 70, 93, 80, 85, 90
88, 90, 87, 92, 98 95, 80
Mean 84
Median 87
Mode 80
The mean score of the class is: 84.5
The median score of the class is: 87
The modal score of the class is: 84.5
What is the Mean, Median, and Mode of a Data?Mean = sum of all data points divided by the number of data points.
Median = the middle value of the ordered data.
Mode = the data point with the highest frequency or that appears the most.
Thus:
Arrange the data in ordered form:
60, 70, 75, 80, 80, 80, 80, 80, 80, 85, 87, 87, 87, 88, 90, 90, 90, 91, 92, 93, 95, 98
Mean = 1858/22
Mean = 84.5
Median = (87 + 87)/2 = 87
Mode = 80
Thus:
The mean score of the class is: 84.5
The median score of the class is: 87
The modal score of the class is: 84.5
Learn more about mean, median, and mode of a data on:
https://brainly.com/question/542771
A Big Mac at McDonald’s costs $3.99. A 10pc. chicken nugget costs $4.49. How much would it cost if you bought (2) Big Mac’s and (2) 10pc chicken nuggets?
Answer: 16.96
Step-by-step explanation: 3.99 times 2 = 7.98 4.49 times 2 = 8.98
8.98 + 7.98 = 16.96
Proportion and give 6:8= n :12
Answer:
n = 9
Step-by-step explanation:
6/8 = n/12
(6/8)(12) = (n/12)(12)
n = 9
A sociologist was curious about how much smartphone access has changed for American teenagers. They obtained separate random samples of teenagers from
2017
20172017 and
2013
20132013. Here are their results:
Has access to smartphone?
2017
20172017
2013
20132013
Yes
450
450450
120
120120
No
150
150150
280
280280
Total
600
600600
400
400400
They want to use these results to construct a
95
%
95%95, percent confidence interval to estimate the difference in the proportion of teens each year who had access to a smartphone
(
p
2017
−
p
2013
)
(p
2017
−p
2013
)left parenthesis, p, start subscript, 2017, end subscript, minus, p, start subscript, 2013, end subscript, right parenthesis. Assume that all of the conditions for inference have been met.
Which of the following is a correct
95
%
95%95, percent confidence interval based on their data?
Using the z-distribution, as we are working with a proportion, it is found that the 95% confidence interval for the difference in the proportions of teenagers with access to smartphones in 2017 and in 2013 is of (0.393, 0.507).
What is the mean and the standard error of the distribution of differences?In 2017, 450 out of 600 students had access, hence:
[tex]p_1 = \frac{450}{600} = 0.75, s_1 = \sqrt{\frac{0.75(0.25)}{600}} = 0.0177[/tex]
In 2013, 120 out of 400 students had access, hence:
[tex]p_2 = \frac{120}{400} = 0.3, s_2 = \sqrt{\frac{0.3(0.7)}{400}} = 0.0229[/tex]
For the distribution of differences, we have that the mean and the standard error are, respectively, given by:
[tex]p = p_1 - p_2 = 0.75 - 0.3 = 0.45[/tex]
[tex]s = \sqrt{s_1^2 + s_2^2} = \sqrt{0.0177^2 + 0.0229^2} = 0.0289[/tex]
What is the confidence interval?It is given by:
[tex]p \pm zs[/tex]
95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so [tex]z = 1.96[/tex].
Then:
[tex]p - zs = 0.45 - 1.96(0.0289) = 0.393[/tex]
[tex]p + zs = 0.45 + 1.96(0.0289) = 0.507[/tex]
The 95% confidence interval for the difference in the proportions of teenagers with access to smartphones in 2017 and in 2013 is of (0.393, 0.507).
More can be learned about the z-distribution at https://brainly.com/question/25890103
Answer:
0.45+-0.057
Step-by-step explanation:
What is the perimeter of the figure to the nearest tenth of a millimeter?
A. 9.4 millimeters
B. 12.0 millimeters
C. 21.4 millimeters
D. 30.8 millimeters
Answer:
i think the answer is C
Step-by-step explanation:
i normally just do length divided by width to figure this out
bettie bought are reel of thread for sowing that is 14.5 meters long. Bettie uses 425 centimeters for a project. How many meters are left on the reel?
The phantoms won 8 more games than the Aztecs last year. Their combined wins were 32. Finds the
number of games won by each team last year,
Step-by-step explanation:
let aztecs = x
since the phantoms won 8 more than the aztecs
then, the phantoms = x + 8
and their combined win was 32
therefore
x + x + 8 = 32
2x + 8 =32
2x = 32 - 8
2x = 24 , x = 12
so , aztecs won 12 games and the phantoms won 20 games.
If this helped pls give brainliest
The graph shows the distance $y$ (in miles) that a bus travels in $x$ hours. Find and interpret the slope of the line.
The slope of the line is (Answer here)
. The bus is traveling at a speed of (Answer here)
miles per hour.
Answer:
Slope is 60/1 or simply 60. Miles per hours is also 60
Step-by-step explanation:Rise/Run Up60 Over1 which is why slope =60, mph is same as slope or just calculate how many miles car goes in one hour by reading the graph.
Find the value of x. Please help me with this?
The interior angles of any triangle sum to 180° in measure, and in ∆ABC, the angles at vertices A and C are congruent. If we call their measure a, then
24° + 2a = 180° ⇒ 2a = 156° ⇒ a = 78°
The angle at vertex C and the angle with measure (2x - 18)° are supplementary, meaning they add up to 180° :
a + (2x - 18)° = 180°
Solve for x :
78° + (2x - 18)° = 180°
(2x - 18)° = 102°
2x = 120
x = 60
Melissa made $221 for 17 hours of work. At the same rate, how much would she make for 13 hours of work?
Answer:
$169 Is correct.
Step-by-step explanation:
We know that Melissa made $221 for 17 hours, so using this ratio, we can calculate how much she made for 13 hours as follows
13 hours× [tex]\frac{221}{17~hours} =[/tex] $169
Therefore, the answer is $169
444444r54drtfjfftddtcghgcgvvvvbvgiygygvvvvuygyv8uu8yut
Answer:
l
Step-by-step explanation:
l
Jia wishes to briskly walk 150 minutes per week. When briskly walking, Jia takes 100 steps per minute. Approximately how many briskly-walked steps should Jia take per day to achieve the 150 minutes weekly goal?
Group of answer choices
250
2,100
15,000
105,000
Answer:
15000
Step-by-step explanation:
150x100
15000
Mario has $50, which is $8 more than twice the amount of money that Kevin has. How much money does Kevin have?
Answer:
21
Step-by-step explanation:
First you would subtract 8 from 50 (50 - 8). Once you have that answer, 42, you divide it in half (42/2). Your final answer is 21. The full equation is:
(50 - 8)/2
According to the number line, what is the distance between points A and B?
A
B
SARE
+++
-16-14-12-10 -8 -6 -4 -2
02
4
6
8 10 12 14 16
O 6 units
O 7 units
O 12 units
0 14 units
Answer:
14 units
Step-by-step explanation:
i think you just need to minus it to get the distance between it
like :
=point B - point A
=12 - (-2)
=12 +2
=14
so it 14 units
According to the number line the distance between points A and B is 14 units.
What is Number system?A number system is defined as a system of writing to express numbers.
We need to find the distance between points A and B.
The length along a line or line segment between two points on the line or line segment.
A number line is a picture of a graduated straight line that serves as visual representation of the real numbers.
The point A is at -2
The point B is at 12 on the number line
AB=OB-OA
=12-(-2)
=12+2
=14 units.
Hence, According to the number line the distance between points A and B is 14 units.
To learn more on Number system click:
https://brainly.com/question/22046046
#SPJ7
5. Solve the differential equations using Laplace transforms
y'' − 3y' + 2y = 1, y(0) = 1, y'(0) = 0
y'' + y' − 2y = x², y(0) = 0 and y'(0) = 0
y'' + y' − 2y = e⁻³ˣ, y(0) = 0 and y'(0) = 0
Answer:
First problem: [tex]y(x)=\frac{1}{2}+e^x-\frac{1}{2}e^{2x}[/tex]
Step-by-step explanation:
Solve for Y(s) by taking the transform of every term
[tex]y''-3y'+2y=1,\:y(0)=1,\:y'(0)=0\\\\\mathcal{L}\{y''\}-3\mathcal{L}\{y'\}+2\mathcal{L}\{y\}=\mathcal{L}\{1\}\\\\s^2Y(s)-sy(0)-y'(0)-3[sY(s)-y(0)]+2Y(s)=\frac{1}{s}\\\\s^2Y(s)-s-3[sY(s)-1]+2Y(s)=\frac{1}{s}\\\\s^2Y(s)-s-3sY(s)+3+2Y(s)=\frac{1}{s}\\\\(s^2-3s+2)Y(s)-s+3=\frac{1}{s}\\\\(s-1)(s-2)Y(s)=\frac{1}{s}-3+s\\\\Y(s)=\frac{1}{s(s-1)(s-2)}-\frac{3+s}{(s-1)(s-2)}[/tex]
Perform partial fraction decomposition
[tex]Y(s)=\frac{1-3s+s^2}{s(s-1)(s-2)}\\\\Y(s)=\frac{s^2-3s+1}{s(s-1)(s-2)}\\ \\\frac{s^2-3s+1}{s(s-1)(s-2)}=\frac{A}{s}+\frac{B}{s-1}+\frac{C}{s-2}\\\\s^2-3s+1=A(s-1)(s-2)+B(s)(s-2)+C(s)(s-1)[/tex]
Solve for each constant
[tex]s^2-3s+1=A(s-1)(s-2)+B(s)(s-2)+C(s)(s-1)\\\\(2)^2-3(2)+1=A(2-1)(2-2)+B(2)(2-2)+C(2)(2-1)\\\\-1=2C\\\\-\frac{1}{2}=C[/tex]
[tex]s^2-3s+1=A(s-1)(s-2)+B(s)(s-2)+C(s)(s-1)\\\\(1)^2-3(1)+1=A(1-1)(1-2)+B(1)(1-2)+C(1)(1-1)\\\\-1=-B\\\\1=B[/tex]
[tex]s^2-3s+1=A(s-1)(s-2)+B(s)(s-2)+C(s)(s-1)\\\\(0)^2-3(0)+1=A(0-1)(0-2)+B(0)(0-2)+C(0)(0-1)\\\\1=2A\\\\\frac{1}{2}=A[/tex]
Take the inverse transform to solve the IVP
[tex]Y(s)=\frac{\frac{1}{2}}{s}+\frac{1}{s-1}+\frac{-\frac{1}{2}}{s-2}\\ \\y(x)=\frac{1}{2}+e^x-\frac{1}{2}e^{2x}[/tex]
The scatterplot shows the relationship of scores for students who took a math test and history test. Based on a line of best fit, what score would be the BEST prediction for a student's history test if they made a 60 on their math test?
A) 50
B) 60
C) 70
D) 75
Answer:
c
Step-by-step explanation:
lucky guess
NO LINKS!!! Please help me with this problem. Part 14
Explanation:
The Law of Cosines can be used to write a quadratic in x. The desired form corresponds to its solution using the quadratic formula.
[tex]L^2=r^2 +x^2 -2rx\cdot\cos{\theta}\\\\x^2-2rx\cdot\cos{\theta}+(r^2-L^2)=0[/tex]
Using the quadratic formula gives the positive value of x as ...
[tex]x=\dfrac{-(-2r\cdot\cos{\theta})+\sqrt{(-2r\cdot\cos{\theta})^2-4(1)(r^2-L^2)}}{2(1)}\\\\\boxed{x=r\cos{\theta}+\sqrt{r^2\cos^2\theta+L^2-r^2}}[/tex]
What’s the answer to this ?
Answer:
It would be the first option 8x-8y=32
Rachel weighed her two cats, Tiger and Mittens. Tiger weighed 10.91 pounds, and Mittens weighed 178.08 ounces. Which cat is heavier, and how many pounds heavier is she?
a.
Tiger is 1.02 pounds heavier than Mittens.
b.
Tiger is 3.49 pounds heavier than Mittens.
c.
Mittens is 0.22 pounds heavier than Tiger.
d.
Mittens is 3.93 pounds heavier than Tiger.
ANSWER IS C
Answer:
answer is c
Step-by-step explanation:
178.08 oz = 11.13 lb
11.13-10.91 = 0.22 lb
Mittens is heavier than Tiger by 0.22 pounds.
What is mean by subtraction?Subtraction is a mathematic operation. Which is used to remove terms or objects in an expression.
Given that;
Rachel weighed her two cats, Tiger and Mittens.
Tiger weighed 10.91 pounds,
And, Mittens weighed 178.08 ounces.
Now, To compare the weights:
First, we convert the weights into ounces.
1 pound = 16 ounces.
Tiger weighed 10.91 pounds.
That means,
= 178.08 / 16
= 11.13 pounds.
And 11.13 > 10.91
Now, Subtracting the weights,
11.13 - 10.91 = 0.22 pounds
Therefore, Mittens is heavier by 0.22 pounds.
Learn more about the subtraction visit;
brainly.com/question/2346316
#SPJ7
Meaning of Constituted Authority
Answer:
ENGLISH:CONSTITUTED AUTHORITIES. Those powers which the constitution of each people has established to govern them, to cause their rights to be respected, and to maintain those of each of its members.SPANISH:AUTORIDADES CONSTITUIDAS. Los poderes que la constitución de cada pueblo ha establecido para regirlos, hacer respetar sus derechos y mantener los de cada uno de sus miembros.Explain why the initial value of any function of the form
f(x) = a(bº) is equal to a.
Anna made her uncle a garden. The width is 7 2 5 ft and the length is 5 1 2 ft. What is the area of the garden?
Answer:
The answer to that is 371200ft2
Step-by-step explanation:
725 x 512 = 371200ft2
Answer:
the answer is 40 7\10
Step-by-step explanation:
7 2\5 x 5 1\2= 407\10 = 40 7\10
Question 1 (1 point)
Train X travels 20 km/hr faster than train P. If train X travels 50 km in the same time
that train P travels 40 km. How long would it take Train X to travel 500 km?
Approximate you answer to 2 decimal places, and input your answer in hours.
By solving a system of equations, we will see that Train X travels 500km in 5 hours.
How to get the speeds of the trains?
Remember the relation:
distance = speed*time.
First, if Sx is the speed of the train X and Sp is the speed of the train P, we know that:
Sx - 20 km/hr. = Sp
Then, we know that in the time T in which X travels 50 km, P travels 40km, we can write that as:
50km = Sx*T
40km = (Sx - 20km/hr)*T
So we have a system of equations.
Now we can solve this to find the speed Sx, to do it, we need to isolate T on one equation.
T = 50km/Sx.
Now we can replace that with the other equation:
40km = (Sx - 20km/hr)*50km/Sx.
Now we can solve this for Sx.
40km*Sx = (Sx - 20km/hr)*50km
40km*Sx = Sx*50km - 1,000 km^2/hr
40km*Sx - Sx*50km = -1,000 km^2/hr
-Sx*10km = -1,000 km^2/hr
Sx = (-1,000 km^2/hr)/(-10 km) = 100km/h
Now we want to know how long the train X takes to travel 500km, so we need to solve:
500km = 100km/h*T
500km/(100km/h) = 5h = T.
The train will travel 500km in 5 hours.
If you want to learn more about systems of equations, you can read:
https://brainly.com/question/13729904
Hello. Can someone please help me with this probability math homework? Appreciated
hope it's helpful at you all
If the answer is 5 why isn't 5 an option?
Answer:
because they made a mistake
can someone pls answer both of these ?'s i WILL mark BRAILIEST
How many times greater is 10,000 than 100?
Show the solution and a proper answer, please.