Answers
Answer:
1/8.
Step-by-step explanation:
Use l'Hopitals rule - we find the derivative of top and bottom of the fraction.
Derivative of the numerator = 0 - 1/2 (16 - x)^-1/2 -1
= 1 / [ 2 * (16 - x)^1/2
Derivative of the denominator = 1
When x approaches 0 this is 1 / (2*4)
= 1/8.
Another way to do this is to multiply top and bottom by 4 + (16 - x)^1/2
This becomes 16 - (16 - x) / x(4 + (16-x)^1/2)
= 1 / (4 + (16 + x)^1/2
When x ---> 0
this = 1 /(4 + 4)
= 1/8.
Related Questions
Problem 1
Select all of the ordered pairs (x, y) that are solutions to
the linear equation 2x + 3y = 6.
(Select all that apply.)
(0,2)
(0,6)
(2,3)
(3,-2)
(3,0)
(6, -2)
Answers
I just plugged in the coordinates in the given equation and saw if it was true or not
Can you give brainleist
After substituting the given values of x and y in the equation, all that can apply are (0, 2), (3, 0), and (6, -2).
What is an equation?Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.
This relationship is illustrated by the left and right expressions being equal. The left-hand side equals the right-hand side is a basic, straightforward equation.
As per the given information in the question,
The given equation is,
2x + 3y = 6
Now, substitute the corresponding points and check,
1. For points (0, 2)
2(0) + 3(2) = 6
6 = 6, this is correct.
2. For points (0, 6)
2(0) + 3(6) = 18
6 ≠ 18, this is incorrect.
3. For points (2, 3)
2(2) + 3(3) = 6
13 ≠ 6, this is incorrect.
4. For point (3, -2)
2(3) + 3(-2) = 6
0 ≠ 6, this is incorrect.
5. For point (3, 0)
2(3) + 3(0) = 6
6 = 6, this is correct.
6. For point (6, -2)
2(6) + 3(-2) = 6
6 = 6, this is correct.
To know more about equation:
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Mark and Heather Starr are celebrating their 25th anniversary by having a reception at a local reception hall. They have budgeted $2,500 for their reception. If the reception hall charges a $60 cleanup fee plus $39 per person, find the greatest number of people that they may invite and still stay within their budget.
Answers
Answer:
62 personsStep-by-step explanation:
Step one:
given data
total budget=$2500
we are told that the hall charges $60 for cleanup, the amount is a fix charge
and per person is $39
let the number of persons be x
The model for the situation is described by y=mx+c
Step two:
2500=39x+60
solve for x
2500-60=39x
2440=39x
divide both sides by 39 we have
x=2440/39
x=62.56
The greatest number of people that they may invite and still stay within their budget. is 62
What is the length of the unknown side?
Answers
Answer:
20！
Step-by-step explanation:
Expand and simplify 6(2x - 3) – 2(2x + 1)
Answers
Answer 8x - 20
Step-by-step explanation:
6(2x - 3) - 2(2x + 1)
Distribute
6(2x) -6( 3) - 2(2x) -2( 1)
12x -18 -4x -2
Combine like terms
12x -4x -18 -2
8x-20
IF SET A={2,5,6} AND SET B={4,7,8}. THE FOLLOWING SET ARE DISJOINTS FOR.plsss
A.
{4,7,8}
B.
EMPTY SET
C.
{2,5,6,7,4,8}
D.
{2,5,6}
Answers
Answer:
C - {2,5,6,7,4,8}
Step-by-step explanation:
It's just because these are the numbers that they don't have in common.
You from irv guessing from your username?
Answer:
Step-by-step explanation:fhh
The amount that Ronnie earns, E, in terms of the number of hours that he works, h, is shown in the graph below.
What is the constant of proportionality,
E/H, for this situation?
+/-
.
Answers
Answer:
Pay Rate = Constant of Proportionality = E/h
Step-by-step explanation:
Recall this formula: Total Pay = (Hourly Pay Rate)*(Number of Hours Worked)
Apparently there was a graph associated with this problem; it's up to you to share all instructions and other info that comes with your question.
Rewriting Total Pay = (Hourly Pay Rate)*(Number of Hours Worked), using E for total earnings and h for the number of hours worked, we get:
E = (Hourly Pay Rate)*h
The relevant constant of proportionality is found by dividing E by h:
Pay Rate = Constant of Proportionality = E/h
A 1-litermbottle of orange juice used to cost $2.85 at a food market. its price has increased; the new price is 110 percent of the original price. What is the new price? Round your answer to the nearest cent
Answers
A bee flies at 9 feet per second directly to a flower bed from its hive. The bee stays at the flowerbed for 15 minutes, and then flies directly back to the hive at 6 feet per second. It is away from the hive for a total of 18 minutes
Answers
Complete question is;
A bee flies at 9 feet per second directly to a flower bed from its hive. The bee stays at the flowerbed for 15 minutes, and then flies directly back to the hive at 6 feet per second. It is away from the hive for a total of 18 minutes.
a. What equation can you use to find the distance of the flowerbed from the hive?
b. How far is the flowerbed from the hive?
Answer:
A) (d/9) + 900 + (d/6) = 1080
B) d = 648 ft
Step-by-step explanation:
A) We are told that A bee flies at 9 feet per second directly to a flower bed from its hive.
Time taken is given as;
t = distance/speed
If distance is d from the hive to the flower bird.
Then, t1 = d/9
The bee stays at the flowerbed for 15 minutes. Thus, time spent at the flowerbird in seconds is; t2 = 15 × 60 = 900 seconds.
We are told that the bee flew directly back to the hive at 6 feet per second.
Thus,time is;
t3 = d/6
Since total time spent away from hive is 18 minutes, then converting to seconds, we have; t = 18 × 60 = 1080 s
Thus;
(d/9) + 900 + (d/6) = 1080
B) Since we have derived;
(d/9) + 900 + (d/6) = 1080
Then we can find d.
Multiply through by 18 to get;
2d + (900 × 18) + 3d = 1080 × 18
2d + 16200 + 3d = 19440
5d = 19440 - 16200
5d = 3240
d = 3240/5
d = 648 ft
what is 5/2x-7=3/4x+14? help please
Answers
Answer:
x=12
Step-by-step explanation:
Question 8 of 10
If a point is on the bisector of an angle, then it is:
A. on one side of the angle.
B. the vertex of the angle.
C. equidistant from the two sides of the angle.
D. equidistant from the bisector and one side of the angle.
Pls and thank you
Answers
Answer:
yr point is A
Step-by-step explanation:
If a point is on the bisector of an Angle , then it is equidistant from two sides .
The Meaning of Bisector is to divide something or anything into two equal Halves.
The Meaning of Bisector of any Angle means to divide that Angle into two equal Parts.
Option A
equidistant from the two sides of the angle.
i jst taken the quiz
Answer:
equidistant from the two sides of the angle.
Step-by-step explanation:
E=RIGHT FOR AP-EX
The function y=f(x) is graphed below. Plot a line segment connecting the the points on f where x=5 and x=7. Use the line segment to determine the average rate of change of the function f(x) on the interval
Answers
Answer: average y = -8 average y =2
ARC : -4
Step-by-step explanation:
Average rate of change is the change in the function per unit in a given interval. The average rate of change from [tex]x = 5[/tex] to [tex]x = 7[/tex] is -4
Given
The graph of [tex]y = f(x)[/tex]
See attachment for the points on f(x) that links [tex]x = 5[/tex] to [tex]x = 7[/tex]
The line segment is represented by a green line
To determine the average rate of change using the line segment; we have the following values.
When [tex]x =5; y = 8[/tex]
When [tex]x =7; y = 0[/tex]
So, the average rate of change (m) is:
[tex]m = \frac{\Delta y}{\Delta x}[/tex]
Where:
[tex]\Delta y = y_2 - y_1[/tex]
[tex]\Delta y = 0-8[/tex]
[tex]\Delta y = -8[/tex]
[tex]\Delta x = x_2 - x_1[/tex]
[tex]\Delta x = 7 - 5[/tex]
[tex]\Delta x = 2[/tex]
So, we have:
[tex]m = \frac{\Delta y}{\Delta x}[/tex]
[tex]m = \frac{-8}{2}[/tex]
[tex]m = -4[/tex]
Hence, the average rate of change from [tex]x = 5[/tex] to [tex]x = 7[/tex] is -4
Read more about average rate of change at:
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Determine the equation of the line given by the graph.
A) y = 3x + 2
B y = 3x - 2
C y-1/3x+2
D y=1/3x-2
Answers
The table shows the height of water in las pool as it is
being filled
Height of Water in a Pool
Time
(min)
2
4
6
8
10
Height
(in.)
8
12
16
20
24
The slope of the line through the points is 2. Which
statement describes how the slope relates to the height
of the water in the pool?
O The height of the water increases 2 inches per
minute
O The height of the water decreases 2 inches per
minute.
O The height of the water was 2 inches before any
water was added
The height of the water will be 2 inches when the
pool is filled
Answers
Explanation: The height of the water increases 2 inches per minutes
Hope you have a good day:)
And please mark me brainiest
Which expression is equivalent to (xy)z?
A (x+y)+z
B 2z(xy)
C x(yz)
D x(y+z)
Answers
Answer:
c
Step-by-step explanation:
Answer:
It's C Aka x(yz)
Step-by-step explanation:
I Just Got A lOO% When I Put That As My Answer On My Quiz On Edge. :)
calculeaza,grupand convenabil factori
8x7x0 3x7x2 5x8x2
7x4x2 5x10x5 4x9x2
2x9x5 10x9x9 2x3x7
Answers
Step-by-step explanation:
1. 0
2. 42
3. 80
4. 48
5. 250
6.64
7. 90
8. 180
9. 42
is that answer able?
Step-by-step explanation:
do you want the answer to those questions or is it just one question built in with those
Wassup peeps!!! I need help cuz im kinda stupid.
A line that includes the points (10,–3) and (9,t) has a slope of –7. What is the value of t?
Pls, help me?
Answers
Desde la parte más alta de un edificio a 25 m una persona lanza hacia la base un objeto de 150 g con una velocidad de 0.8 m por segundo calcula la energía mecanica total
Answers
Answer:
[tex] E_{T} = 36.84 J [/tex]
Step-by-step explanation:
La energía mecánica total está dada por:
[tex] E_{T} = E_{c} + E_{p} [/tex]
[tex] E_{T} = \frac{1}{2}mv^{2} + mgh [/tex]
En donde:
m: es la masa = 150 g
v: es la velocidad = 0.8 m/s
h: es la altura = 25 m
g: es la gravedad = 9.81 m/s²
[tex] E_{T} = \frac{1}{2}mv^{2} + mgh = \frac{1}{2}0.15 kg*(0.8 m/s)^{2} + 0.15 kg*9.81 m/s^{2}*25 m = 36.84 J [/tex]
Por lo tanto, la energía mecánica total es 36.84 J.
Espero que te sea de utilidad!
H shows the ratio of pencils to pens sold at the school bookstore. If the bookstore sells 15 pencils, what is the ratio of pencils to pens sold written as a fraction?
Answers
Answer:
[tex]Ratio = \frac{3}{2}[/tex]
Step-by-step explanation:
See attachment for complete question.
We start by solving for the equation of the graph (The graph shows a linear equation)
Represent pencils with x and pen with y
From the graph, we have that:
[tex](x_1,y_1) = (6,4)[/tex]
[tex](x_2,y_2) = (12,8)[/tex]
Solve for slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{8 - 4}{12- 6}[/tex]
[tex]m = \frac{4}{6}[/tex]
[tex]m = \frac{2}{3}[/tex]
The equation is calculated using:
[tex]y - y_1 = m(x - x_1)[/tex]
Where
[tex]m = \frac{2}{3}[/tex]
[tex](x_1,y_1) = (6,4)[/tex]
[tex]y - 4 = \frac{2}{3}(x - 6)[/tex]
[tex]y - 4 = \frac{2}{3}x - \frac{2}{3} * 6[/tex]
[tex]y - 4 = \frac{2}{3}x - \frac{2 * 6}{3}[/tex]
[tex]y - 4 = \frac{2}{3}x - \frac{12}{3}[/tex]
[tex]y - 4 = \frac{2}{3}x - 4[/tex]
Add 4 to both sides
[tex]y - 4 +4= \frac{2}{3}x - 4 + 4[/tex]
[tex]y= \frac{2}{3}x[/tex]
Now, to the question.
When pencils is 15 implies that
[tex]x = 15[/tex]
Solving for x, we have:
[tex]y= \frac{2}{3}x[/tex]
[tex]y= \frac{2}{3} * 15[/tex]
[tex]y= \frac{2* 15}{3}[/tex]
[tex]y= \frac{30}{3}[/tex]
[tex]y= 10[/tex]
i.e. Pen = 10
Ratio = x ; y
[tex]x : y = 15 : 10[/tex]
Convert to fraction
[tex]\frac{x}{y} = \frac{15}{10}[/tex]
Simplify
[tex]\frac{x}{y} = \frac{3}{2}[/tex]
Hence,
[tex]Ratio = \frac{3}{2}[/tex]
Answer:
3/2 :)
Step-by-step explanation:
solve: -3 |x-3| = -6
how do i solve absoulute value ?
Answers
Answer:
x=5,1
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
PLSSS HELPPPPP MEEEE I WILLL GIVVVEEE BRAINLIESTTTT!!!!!!
PLSSS HELPPPPP MEEEE I WILLL GIVVVEEE BRAINLIESTTTT!!!!!!
PLSSS HELPPPPP MEEEE I WILLL GIVVVEEE BRAINLIESTTTT!!!!!!
Answers
Answer:
50
Step-by-step explanation:
5 times 5 =25
25 times 2 =50
which situation can be represented by the expression -27 4/5+50?
Answers
Answer:
22.2
Step-by-step explanation:
Answer:
Answer A
Step-by-step explanation:
Below sea level = -x
Above sea level = x
Just read it carefully
Anyone in 10th grade geometry I could really use a partner to help me with it please?! :)
Answers
Answer:
I can help
Step-by-step explanation:
I'm in honors classes
LAST ONE I NEED HELP ON PLEASE
Answers
Answer:
A
Step-by-step explanation:
First you find the volume of the cube which is 512. Then you find the volume of the cone which is 133.97333333 and so on. Lastly you subtract 512 by 133.973333333 (and so on) which is 378.026667. Rounded the answer would be 378.0 which is answer A.
Plz mark brainliest!!! I spent lot of time on this.
Suponga que le piden averiguar cuán alto es un poste de luz, su mejor
momento es durante la tarde en un día soleado, si la única herramienta
que tiene es una cinta métrica de 5m ¿cómo haría para saber con la
mayor exactitud posible el tamaño del poste?
Answers
Answer:
gtdnuf fjgdyj gudchu hfvhd gjsjck
grixbedfb hvdb kgtd kggyan samera hhgv bcc
After some snacks at McDonalds at Lower Bonifacio Street, Kristina drove 145 meters towards the three-way junction and turns right to reach a nearby church around Rimando Road. If the displacement between the church and McDonalds is 191.442 meters, how far did Kristina travel from the three-way junction to the church?
Answers
Answer:
125 m
Step-by-step explanation:
The path of Kristina is in the shape of a right triangle where, the perpendicular is the path from the McDonalds to the three-way junction which is 145 m and the shortest distance between the McDonalds and the church is 191.442 m.
By Pythagoras theorem
[tex]145^2+x^2=191.442^2\\\Rightarrow x=\sqrt{191.442^2-145^2}\\\Rightarrow x=125\ \text{m}[/tex]
Christina had to travel 125 m from the three-way junction to the church.
The distance Kristina travelled from the three-way junction to the church is; x = 125 meters
We are told that she drove 145 meters towards the three way junction. She now turned right to reach a nearby church around rimando road.
This means that if the distance at which she turned right is x, then x is perpendicular to 145 m.
Now, we are told that the displacement between the church and McDonalds is 191.442 meters.
The displacement means the distance from the final position to the initial position. Thus, there will form a right angled triangle with 191.442 as the hypotenuse.
Using Pythagoras theorem, we have;
x² + 145² = 191.442²
x² = 191.442² - 145²
x² = 15625.039364
x = √15625.039364
x = 125 meters
Read more at; https://brainly.com/question/20530468
Find the slope and the y-intercept of the line.
y = 8x - 1
Answers
Answer:
y = - 1
you basically replace with a 0 and multiply 8 and 0 which leaves you with y = -1
Brian bought a jacket that cost d dollars. He paid the clerk $60,00 He received $7.39
in change. How much did Brian pay for the jacket?
Answers
Answer:
52.61 is what Brian payed for the Jacket.
Step-by-step explanation:
52.61 + 7.39 = 60$ in total.
Answer:
ok so a jacket would never cost 60,00 i think you meant 60.00 so it would be $52.61 for the jacket
Step-by-step explanation:
Subtract 7.39 from 60
if you really did mean 60000 the answer would be 5992.61
The solution to the system of equation below is (−2, −1).
2x − 3y = −1
11x − 9y = −13
When the first equation is multiplied by −3, the sum of the two equations is equivalent to 5x = −10.
Which system of equations will also have a solution of (−2, −1)?
5x = −10
11x − 9y = −13
2x + 9y = −1
11x − 9y = −13
−6x + 9y = −1
11x − 9y = −13
−6x + 3y = −1
5x = −10
Which system of equations will also have a solution of (−2, −1)?
Answers
Answer:
I'm pretty sure it's 5x= -10
Answer:
5x = −10
11x − 9y = −13
took test edg 2021
3. During a particular year, 42 graduating boys chose to attend a 4-year college,
while 58 boys attended a 2-year college; 84 girls chose a 4-year college, and 16
attended a 2-year college. What conclusion can be drawn about how gender and
choice of college are related?
Answers
Answer:
girls are more likely to choose a 4-year college, while boys are more likely to choose a 2-year college
Step-by-step explanation:
hope this helps :]
Find the 81st term of the arithmetic sequence 24, 11, -2, ...24,11,−2,
Answers
Answer:
-1029
Step-by-step explanation:
24, 11, -2...
f(n) = 24 - 13n
f(81) = 24 - 13(81) = 24 - 1053 = -1029