A curve is given the equation xy=25 and the equation of a line y=mx+b.
i. Express m in terms of b given that the line and the curve have one and only one point of intersection.
ii. If the line intersects the curve in two distinct points, find the set of values of b, given m=-5

Answers

Answer 1

Answer:

Below in bold.

Step-by-step explanation:

i, This is a rectangular hyperbola with symmetry about the line y = -x

   If it touches the graph at one point only then

y = 25/x

y = mx + b so

25/x = mx + b

mx^2 + bx + 25 = 0

Using the quadratic formula:

x = (-b + sqrt(b^2 - 25*4*m)) / 2m

Now there's only one value of x so

b^2 - 25*4*m = 0

b^2 = 100m

m = b^2/100.

m = +/-b/10.

ii  In this case b^2 > 100m

If m = |-5|

b^2 > 500

b > +/-√500

So b > √500 or b < -√500.


Related Questions

how of find the area of a composite figure

Answers

Step-by-step explanation:

A composite figure is made up of simple geometric shapes. To find the area of a composite figure or other irregular-shaped figures, divide it into simple, nonoverlapping figures. Find the area of each simpler figure, and then add the areas together to find the total area of the composite figure. Formula = a(a=lw+bh)

How does the mean compare to the median? How do the values of 7 and 9 affect these measures of center?



Sorry I suck at taking pictures, and math apparently.

Answers

Answer:Bueno, normalmente en los artículos semanales intento transmitir dudas o cuestiones que están en el campo, los trending topics del sector porcino, y está claro que la estadística no es uno de ellos, pero precisamente ayer se dio una situación que me llevó a escribir ésta entrada.

Todos los que trabajamos en el sector porcino estamos acostumbrados a manejar y calcular un montón de datos que nos proporciona el programa de gestión, y en muchas ocasiones realizamos pequeñas (o grandes) pruebas, donde manejamos infinidad de números (pesos, GMD, IC etc…)

Lo que sí es cierto, es que la mayoría de nosotros usamos siempre la media como herramienta fundamental. Media de Nacidos vivos, Media de destetados, Media de peso al nacer, media de peso al destete…..media, media, media…y ¿qué tal si usáramos la Mediana?

Éste fue el debate que tuve ayer con un ingeniero agrónomo (si, si, y yo Veterinaria, diversión asegurada), y el que me ha inspirados para hoy.

Para el que, en estos momentos, esté rebuscando en los archivos de su cerebro, “yo esto lo sabía”, un pequeño recordatorio:

La media o promedio, Se interpreta como “punto de equilibrio” o “centro de masas  del conjunto de datos. Es un cálculo muy sencillo en el que intervienen todos los datos. Consiste en el sumatorio de todos los datos dividido por el número de valoresLa mediana, en cambio, es un valor de la variable que deja por debajo de sí a la mitad de los datos, y por encima, la otra mitad.( una vez que estos están ordenados de menor a mayor). Se sitúa, por lo tanto, en la mitad real de los datos.

Es mucho más difícil de calcular:

Con un ejemplo se entiende muchísimo mejor.

Imaginaos una empresa en la que la mayoría de los trabajadores tienen un sueldo de 1000 euros, excepto 2 encargados que cobran 2000 y el jefe que cobra 6000 euros mensuales.

¿Cuál es el salario medio de la empresa?

Si vemos la media sale casi 2000 euros, si miramos la mediana, nos da 1000.

¿Cuál se aproxima más a la realidad?

Cuando los datos son muy homogéneos la media nos da un valor representativo de la realidad, pero cuando los datos son muy heterogéneos no.

Un ejemplo más cercano a nosotros

Queremos saber el peso de los lechones a destete. Imaginemos que la camada A tiene los siguientes pesos:  (4-3-5-4.5-6.1-5-3-5.1-6.4-6-6.5-5.5-4.9).

Step-by-step explanatio

$9000.00 decreased by 0.5% make sure to show your work

Answers

Answer: 8550

Step-by-step explanation:

9000(1-0.5)

9000(0.95)

8550


Which inequality represents this situation?
The number of students, s, who ride in a bus is less than 30.
s< 30
s> 30
S 30
ss 30

Answers

Answer:

s<30

Step-by-step explanation:

s is the number of students. the staement says the number of students is less than 30

Please help :( I’ve been on this fit awhile

Answers

Okay think the answer b

What is the value of x in the diagram?
A right angled triangle with base 2x+2, altitude x and hypotenuse 2x+3.

Answers

Answer:

x = 5

Step-by-step explanation:

x² + (2x+2)² = (2x+3)²

x² + 4x² + 8x + 4 = 4x² + 12x + 9

x² - 4x - 5 = 0

(x - 5)(x + 1) = 0

x = -1  This can be discounted as the answer because you cannot have a negative length

answer: x = 5

Which of the following is a prime number between 50 and 60?
A.
55
B.
53
C.
57
D.
51

Answers

Answer: B, 53

53 is the only prime number between 50 and 60

Remove the brackets using the distributive law for the following: -7(2x - 5y)

Answers

the answer is -14x+35

Find the value of y.
120°

Answers

Answer:

y = 60°

Step-by-step explanation:

The tangent- chord angle y is half the measure of its intercepted arc , then

y = [tex]\frac{1}{2}[/tex] × 120° = 60°

The value of y is 60 °

What is the tangent- chord angle theorem?"The angle generated by a tangent to a circle and a chord is equal to half the angle measure of the intercepted arc," is another way to state the Tangent-Chord theorem. Since the angle measure of an intercepted arc is double that of the inscribed angle that subtends it, this is equivalent to what we have demonstrated.The measure of an angle formed by a tangent and a chord meeting at the point of tangency is half the measure of the intercepted arc.

Given , the angle is 120°

Now apply the  tangent- chord angle theorem, " a chord meeting at the point of tangency is half the measure of the intercepted "

y = 1/2 × 120°

y = 1/2 × 120° = 60°

Therefore, the value of angle y is 60°.

Learn more about the Tangent-Chord theorem brainly.com/question/2193714

#SPJ2

a) Write down the mathematical name of this shape?

Answers

Answer

this is a Parallelogram or a Polygon

Step-by-step explanation:

most likey the polygon

as i see it, it looks like a polygon

Alan has read 70% of a book. He has 15 more pages to finish. How many pages are there in the
book?

Answers

50 pages. See the details in the attached picture.

There is a 3 out of 20 chance that you can win a game. How many "wins" would you predict if you played the game 50 times?

Answers

Answer:

7.5

Step-by-step explanation:

The probability of winning = 3 out of 20 ;

P(winning) = 3/20

Predicted Number of winnings if game is played 50 times ;

P(winning) * number of games played

(3 /20) * 50

0.15 * 50

= 7.5

Predicted Number of winnings = 7.5

Answer:7.5

Step-by-step explanation:

first you want to clarify the numbers which is 3 and 20 and your chance is 3/20 which equals 7.5 but round to the nearest whole number so 8,

Written Response: Sally believes that 1/2% is equivalent to 50%. Is she correct? Why or why not?​

Answers

Answer:

She is correct.

Step-by-step explanation:

1/2 and 50% is the same thing

50%  is 1/2 of 100

She is indeed correct I agree with the other person

In the diagram, x is a negative number and y is a positive number. Select the expression that is a positive.

Answer choices:
x(y)

x - y

y/x

y - x

Answers

Answer:

Option 4: y -x

Step-by-step explanation:

Option 1

Multiplying a positive and a negative number will result in a negative number.

For example, if x= -1 and y=5,

x(y)= -1(5)= -5 (a negative number)

Thus, option 1 is incorrect.

Option 2

In this option, we are essentially multiplying -1 to y, a positive number, before adding the result with x.

Since y is a positive number, -y is a negative number and hence x -y (when x is a negative number) will result in a negative number. Let's plug in values into x and y to check this.

For example, x= -2 and y=3.

x -y= -2 -3= -5

Option 2 is thus incorrect.

Option 3

Dividing a positive number with a negative number will result in a negative number.

For example: 6÷(-2)= -3

Option 3 is also incorrect.

Option 4

Subtracting a negative number from a positive number will result in a positive number.

For example: x= -1, y= 8

y -x= 8 -(-1)= 8 +1= 9

As seen from the example above, when the negative number is multiplied to negative 1, a positive sign results.

In summary, when a positive number is multiplied to a positive number, the resulting number is positive.

When a negative number is multiplied to a negative number, the resulting number is positive.

When a positive number is multiplied to a negative number, the resulting number is negative.

+(+)= +

-(-)= +

+(-)= -

This applies to division too.

13 ft 10 ft 18 ft Find the area of the trapezoid. [?] square feet​

Answers

Step-by-step explanation:

A=a+b

2h=13+10

2×18=207

formula a=a+b/2×18

Tara has five 10p coins and four 20p coins in her purse. She takes out two
coins at random. What is the probability that she takes out at least 30p?

Answers

Answer:

4/9

Step-by-step explanation:

9 coins in total

Amount of combinations to get 30p is 4 ways

so 4/9

A trapezoid has a height of 3 meters, a base length of 8 meters, and an area of 30 square meters. What is the length of the base?

Answers

Answer:

Length of the second base will be 12 meters.

Step-by-step explanation:

Area of a trapezoid is given by the formula,

Area = [tex]\frac{1}{2}(b_1+b_2)h[/tex]

Here, b₁ and b₂ are the bases of the trapezoid and 'h' is the vertical distance between the bases.

By substituting the values in the formula,

[tex]30=\frac{1}{2}(8+b_2)3[/tex]

[tex]60=3(8+b_2)[/tex]

[tex]20=8+b_2[/tex]

[tex]b_2=12[/tex]

Therefore, length of the second base will be 12 meters.

One number is 60 more than another. If the larger number is divided by the smaller number, the quotient is 4.
What are the numbers?​

Answers

Answer:

80 and 20

Step-by-step explanation:

Let the 1st no. be 'x'.

2nd no. should be 'x + 60'.

If the larger no.(x + 60) is divided by the smaller number(x), the quotient is 4.

=> (x + 60)/x = 4

=> x + 60 = 4x

=> 60=4x-x

=> 60=3x

=> 60/3 = x

=> 20 = x

No. are x = 20 and x+60 = 20+60= 80

A city planner knows that the number of daily riders on the subway is expected to increase by 12% over the next year. If the current number of daily riders is represented by d,
which expression does NOT represent the expected number of daily riders next year?

A.d+0.12d
B. 1.12d
C. (1 + 0.12)d
D.0.12d

Answers

Answer:

Step-by-step explanation:

B

because it doesn’t start off or have 0.12 in the equation.

(-9)5 ∙ (-9)7
what's the answer

Answers

Answer:

2835

Step-by-step explanation:

-9×5= -45

-9×7= -63

-45×(-63)=2835

An aluminum can has a capacity of 2.37 L. What is the capacity of the can in milliliters?
(1 L = 1,000 mL)

Answers

Answer:

2,370 mL

Step-by-step explanation:

1000mL = 1 L, so I multiplied 1000 by 2.37

If they ask for it to be set up as a proportion, I would write 1/1000 = 2.37/x and cross multiply. x = 2,370

A banana split costs $2.50. A milkshake costs $1.70. Bobby,Jack, and Ted ordered one of each and split the cost. How much does each boy owe?

Answers

Answer:

$4.20

2.50+1.70=4.20

Answer:

Jack= $4.20

Bobby=$4.20

Ted=$4.20

Step-by-step explanation: This is the answer because if you add up all the drinks the total they payed is $12.60 so you just divided that by how many people there are and get $4.20

Rob's office recycled a total of 12 kilograms of paper over 2 weeks. How many weeks will it
take Rob's office to recycle a total of 18 kilograms of paper? Assume the relationship is
directly proportional.
weeks
Submit

Answers

Answer:

Weeks thats easy man

Step-by-step explanation:

ASAP HELP NEEDED, TAKING A TEST

Question: Based on the data set above for the hours per day sixth graders spend using an electronic device, what is the mean number of hours sixth graders use an electronic device?
No links, useless words, or anything like that. I will report you.

Answers

Answer:

Step-by-step explanation:

The mean is the average of the numbers. It is easy to calculate: add up all the numbers, then divide by how many numbers there are. In other words it is the sum divided by the count.

1+1+1+1+2+3=9

2+4+4+5+6+6+7+8+8=50

50/9=5.55555555556

or

9/50=0.18

If u know ,
Help me please .

Answers

Answer:

50cm³

Step-by-step explanation:

Multiply the dimensions then divide by three to get the volume of the pyramid

10 Please! HELP! very easy! will give brainliest!

Answers

4 x 11 = 44
13 x 6 = 78
78 - 44 = 34
The answer is 34 ft
It’s 34 ft.
Hope this helps!

Solve for missing value

Answers

Your missing value would be 47
The missing value is 47 degrees

You have $210 and save $5 a week. Your friend has $265, saves nothing, and spends $10 a week. Determine how many weeks it will take before you have more money than your friend.

a. 4 weeks

b. 3 weeks

c. 2 weeks

d. 6 weeks

Answers

Answer:

This answer is A

Step-by-step explanation:

Im fast to answer :)

Please help with this question

Answers

Answer:

Point G and Point B

Step-by-step explanation:

The quadrant on the top right is quadrant 1 and the quadrant on the top left is quadrant 2. The quadrant on the bottom right is quadrant 4 and the quadrant on the bottom left is quadrant 3.

45 minutes ago
Share
Background
Layout
Theme
Transition
4.
P:
Caleb invests $10,000 in a savings
account that pays 3% simple interest.
How many years will it take the account
to grow to $12,700, if he does not make
any withdrawals or deposits?
A 7 years
B 12 years
C 9 years
22 years
r:
t:
D
k to add speaker notes

Answers

Answer:

876889068

Step-by-step explanation:

Other Questions
You're a quality control manager in a fruit juice company. You want to choosea sample size for a quality check on the cans used to package the juice. Froma batch of 30,000 cans, you want a sample size that will allow you to closelyapproximate the population parameters for the entire batch. Which samplesize will most likely produce the least variability among different samples? Whats the answer? PLEASE ! NO LINKS. thanks ! Was American cowboy music influenced by vaquero culture from Mexico? True or false ANYONE PLEASE HELP ME DONT SEND ME A LINK PLEASE I REALLY NEED HELP. Which of the the following is a tool of remote sensing?A.TripodB.CompassC.LandsatD.Theodolite Mr. K was able to spot quite a few window washers on the skyscrapers there. He asked them how long it took to wash windows on such a building. They said that each person could wash 50 windows in 1 hour. (How long would it take the 3 workers to wash all 1000 windows on one of the skyscrapers?) Amanda completes 18 assignments in 3 days. At that rate, how many assignments would she complete in 7 days? Theo rolls a dice 306 times.Work out an estimate for the number of times Theo rolls an even number How was the expedition of Daniel Boone different from the expeditions of Zebulon Pike and John Frmont? Help me out, math is irritating Read the excerpt from The Wind in the Willows by Kenneth Grahame. The Mole had been working very hard all the morning, spring-cleaning his little home. First with brooms, then with dusters; then on ladders and steps and chairs, with a brush and a pail of whitewash; till he had dust in his throat and eyes, and splashes of whitewash all over his black fur, and an aching back and weary arms. How does the authors word choice help express the tone of the excerpt? The negative connotations of the words dust, aching, and weary give the excerpt a tone of relaxation. The negative connotations of the words dust, aching, and weary give the excerpt a tone of tiredness. The positive connotations of the words home, morning, and splashes give the excerpt a tone of relaxation. The positive connotations of the words home, morning, and splashes give the excerpt a tone of tiredness. A new shopping mall is considering setting up an information desk manned by one employee. Based upon information obtained from similar information desks, it is believed that people will arrive at the desk at a rate of 20 per hour. It takes an average of 2 minutes to answer a question. It is assumed that the arrivals follow a Poisson distribution and answer times are exponentially distributed. Assume that the information desk employee in Problem 1 earns $10 per hour. The cost of waiting time, in terms of customer unhappiness with the mall, is $12 per hour of time spent waiting in line. Find the total expected costs over an 8-hour day Help.me please!!!!!! All of the following have been accomplished by space programs except-A. placing semi-permanent structures in earths orbitB. landing spacecraft on planets other than our ownC. sending spacecraft into orbit that allow us to study the universe in greater detailD. develop technology and resources capable of sending the general population into space on a regular basis 2 yResponde por escrito estas preguntas y, con esos argumentos, realicenen el curso un debatea Consideran que los mitos contribuyen a la cohesin y unidad cultural de las comu-nidades? Por qu?b. Qu sucede si una cultura olvida sus mitos?BOSS On a graph, when demand , the demand curve shifts to the left. Hayden built a wooden sculpture with the dimensionsshown. Now he wants to paint it.How much paint does he need?64 in.296 in 28 in.192 in.2256 in.28 in8 in. Plss I need this rnnn help please, asap. i need this done A 4.00g sample of gas is found to exert a pressure of 1.71 atm when confined in 3.60L container at a temperature of 24 On the map, Winton ,California is located at( (2,10.5) in Lake Tahoe is located at (14,16). Each unit on the map equals 16.5 miles what is the approximate distance between the cities round to the nearest mile.