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

The legend on a map states that 1 cm is 25 km. If you measure 8 cm on the map, how many kilometers would the actual distance be? Actual distance = [? ] km​

Answers

Answer:

200km

Step-by-step explanation:

Given

1cm = 25 km 8cm =?

Solve

if 1cm = 25,

then multiply 8 cm by 25.

Which is 200 km

URGENT PLEASE GET THIS QUICKLY PLEASE
If f(x)= 2x+7, find f(2)=

Answers

Answer:

21

Step-by-step explanation:

2(2) +7

14+7

21

Answer:

11

Step-by-step explanation:

show dis and i will mark you correcr

Answers

Answer:

A and D

Step-by-step explanation:

The area of the combined rectangle is:

t(5 + 4) = 5t + 4t = 9t

Incorrect choices are:

A. 4*5*tD. t + 5 + 4

Answer:

Solution :-

Second option is correct because t is the breadth and 5 and 4 are length. So, Option B is correct 5t + 4t

On adding both we get 9t. Option C is correct

We may also take t as common and may be written as

t(5 + 4)

Correct option are B,C,E

[tex] \\ [/tex]

WILL GIVE BRAINILEST!! 1. Al and Viola Speer were granted an $80,000 mortgage.
At the closing, they will have to pay the closings costs
shown plus real estate taxes of $1,230. What are the
total costs?

Answers

Answer:

81230

Step-by-step explanation:

The total cost for the mortgage and the real estate taxes is $81230.

What is a mortgage?

A mortgage is an agreement between an individual and an owner of a property that provides the owner the right to repossess your property if you fail to repay the loan plus interest at the agreed time.

Mortgage loans are used to purchase a property or to take loans upon the value of an existing home you already own.

From the information given:

Al and Viola Speer were granted an $80,000 mortgage.The real estate taxes on the mortgage = $1,230

Therefore, the total cost required by Al and Viola to pay for the mortgage is:

= $80000 + $1,230

= $81230

Learn more about mortgage here:

https://brainly.com/question/22598793

2 1/4 + 3 1/2 = ??? ​

Answers

Answer:

[tex]5\frac{3}{4}[/tex]

Step-by-step explanation:

You need to set bot denominators equal so multiply the second fraction by two for both the top and bottom.

[tex]2\frac{1}{4} +3\frac{1}{2} \\ =2\frac{1}{4} +3\frac{2}{4}\\\\ =5\frac{3}{4}[/tex]

helppp!!!!!! :(((((((((((((((((((((((((((((

Answers

Answer:

= <><=>=<>=<<

Here, is the answer of comparison

En una carrera participaron 7000 personas entre hombres y mujeres y 5000 personas entre mujeres y niños. Si han corrido 3000 mujeres ¿cuantas mujeres participaron en total?

Answers

Answer:

9000 personas en total participaron de la carrera.

Step-by-step explanation:

En este caso, planteo las siguientes variables:

x: cantidad de hombres que participaron de la carrera.y: cantidad de niños que participaron de la carrera.

En una carrera participaron 7000 personas entre hombres y mujeres. Si han corrido 3000 mujeres, entonces se puede interpretar mediante la siguiente expresión:

3000 + x= 7000

Entonces, resolviendo se obtiene que participaron la siguiente cantidad de hombres:

x= 7000 - 3000

x= 4000

En la carrera también participaron 5000 personas entre mujeres y niños. Entonces se puede interpretar mediante la siguiente expresión:

3000 + y= 5000

Resolviendo se obtiene que participaron la siguiente cantidad de niños:

y= 5000 - 3000

y= 2000

Para calcular la cantidad de personas en total que participaron de la carrera, debes sumar la cantidad de hombres, mujeres y niños. Esto es:

4000 hombres + 3000 mujeres + 2000 niños= 9000 participantes

9000 personas en total participaron de la carrera.

If apples are 6 for $2.70, how much is one apple?

Answers

Answer:

0.45

Step-by-step explanation:

2.70 / 6 = 0.45

Answer:

1 apple is 2.2

Step-by-step explanation:

The area of a parallelogram can be found by the equation area = (b)(h)

Find the height of a parallelogram that has an area of 10
1
2
in² and a base of
3
4
in.

The height of the parallelogram is
inches.

Answers

Answer:

14

Step-by-step explanation:

Answer:

answer: 14

Step-by-step explanation:

got it right

which equation can be used to solve x in the diagram??

a) 13x - 5x = 180

b) 5x + 13x = 90

c) 5x + 13x = 180

d) 5x = 13x

no links

Answers

Answer:

[tex]5x \: + \: 13x \: = 180[/tex]

Find the domain of the relation:
{(-5, -4), (-2, -1), (1, 0), (2, 2), (4,3)}
O {-5, -4, -2, -1, 0, 1, 2, 3, 4}
O {-5.-2. 1. 2. 43
(-4,-1.0.2, 3)
-4.-1.2.3)

Answers

the domain is -5, -4, 1, 2, 4

Somebody help please!<333

Answers

Answer:

C is correct I think.

Step-by-step explanation:

Tell me if I am right.

Have a nice day!

Describe an Angle Bisector

Answers

Answer:

An angle bisector is a straight line that divides the angle into two equal parts.

Step-by-step explanation:

Answer:

The (interior) bisector of an angle, also called the internal angle bisector (Kimberling 1998, pp. 11-12), is the line or line segment that divides the angle into two equal parts. The angle bisectors meet at the incenter.

Step-by-step explanation:

please mark me as brainlest

Someone help please! D:

Answers

Answer:

D) (10,22)

Step-by-step explanation:

based on given slope and point, the linear equation is y = 9/5x + 2

plugging in x-and-y values only results in a true statement for option D

example:

22 = 9/5(10) + 2

Does 22 = 18 + 2?  Yes


Identify all integers less than -14.

Answers

Answer:

An integer is a whole number that can be either greater than 0, called positive, or less than 0, called negative.

Step-by-step explanation:

Answer:

-28, -19, -18, -15,

Step-by-step explanation Cause -14 is more closer to 0 then all 4 of those negative numbers so that mean all 4 of these negative numbers are greater than -14 :) if that makes sense

An altitude is drawn forming a right angle and two congruent triangles. The length of the altitude is 18 inches, and the length of the base is 17 inches. Find the triangle’s perimeter. Round to the nearest tenth of an inch.

Answers

Answer:

56.8

Step-by-step explanation:

Base: 17/2=8.5

8.5^2+18^2=x^2

72.25+324=x^2

x^2=396.25

Perimeter: 19.9+19.9+17=56.81

The area of a rectangular patio is 3x2 + 17x + 20 ft
Which of the following could be dimensions of the patio?
O A. X+ 5 ft by 3x + 4 ft
B. 3x + 5 ft by x + 4 ft
O
C. X + 5 ft by x + 4 ft
O D. 3x + 5 ft by 3x + 4 ft

Answers

Answer:

a

Step-by-step explanation:

Last question!!!!!
explain if posible ​

Answers

Answer:

<ABT = 43°<TBC = 43°

Step-by-step explanation:

Given,

Line BT is the bisector of <ABC

So,

3x + 13 = 5x - 7

=> 13 + 7 = 5x - 3x

=> 20 = 2x

[tex] = > x = \frac{20}{2} [/tex]

=> x = 10

As,

We got the value of x = 10

Therefore,

<ABT = 3x + 13 °

= 3×10 + 13 °

= 30 + 13°

= 43°

<TBC = 5x - 7°

= 5 × 10 - 7°

= 50 - 7°

= 43°

Hence,

Value of <ABT = 43° and value of <TBC = 43° (Ans)

can any one help me i do not get it

Answers

Answer:

x=30

Step-by-step explanation:

The figure on the right has 12 in. on one side and 10 on the other and the figure on the left is 3 times the number that the figure on the left has. When you multiply 3 and 12 you get 36. From there on you can infer that you multiply 10 by 3. Your solution to x is 30.

Answer: 30

Step-by-step explanation:

36/3=12, 30/3=10

who here dose not like edg

Answers

Answer:

Step-by-step explanation:

i dont have edg but i use ap'ex and i hate it so much

Answer:

MEE I am so behind. Latterly why do they give us so many lessons a day. I am just doing well I am online. I can't what until I go back to my normal school

Step-by-step explanation:

What are the numerical measures of each angle in the diagram? ∠1 and ∠3 measure degrees. ∠2 and ∠4 measure degrees.

Answers

A⁣⁣⁣⁣nswer i⁣⁣⁣s i⁣⁣⁣n a p⁣⁣⁣hoto. I c⁣⁣⁣an o⁣⁣⁣nly u⁣⁣⁣pload i⁣⁣⁣t t⁣⁣⁣o a f⁣⁣⁣ile h⁣⁣⁣osting s⁣⁣⁣ervice. l⁣⁣⁣ink b⁣⁣⁣elow!

bit.[tex]^{}[/tex]ly/3a8Nt8n

Answer:

29 degrees and 151 degrees!

Step-by-step explanation:

I need the Answers to this giving brainliest to the person who does not send me a unknown link and actually does the work

Answers

which question do you need to be answered? do you want all of them?

Answer: Look below!

Step-by-step explanation:You can use the Calc below in the pictures

1. √2/2

2. -√2/2

Proof it works!

Graph y= - |x-3| +4

Answers

Answer:

x-1 y-2

x-2 y-2

x-3 y-4

Step-by-step explanation:

graph the points. It should look like a triangle without the bottom.

Tell if the Ratio is Part-to-part or part-to-whole

4 apples to 3 oranges

Answers

Answer: Part-to-part

Step-by-step explanation:

This is a part-to-part, because they show part of apples, and part of oranges. This ratio when set up is 4:3. If the ratio was part-to-whole, then the apples would be compared to the total amount of oranges and apples. The ratio for part-to-whole would be 4:7.

Hope this helps!

pls help help help help​

Answers

Answer:

14

Step-by-step explanation:

If x is -18, then we can change the equation to this:

17 + -18/6

14

THIS IS VERY IMPORTANT I WILL GIVE BRAINLIEST TO THE PERSON WHO DOES ALL 5 QUESTIONS FOR ME.

Answers

Answer:

Step-by-step explanation:

406525%

Answer:

Q1; 40

Q2; 65

Q3; B (25)

Q4; A (?)

Q5;  63

Step-by-step explanation:

I believe

Resolva os problemas:
a) x^2 - 10x + 25 = 0
b) x^2 - 4x - 5 = 0

(preciso da montagem da conta, junto com o resultado)

Answers

Answer:

Step-by-step explanation:

a) x² - 10x + 25 = 0

(x-5)²=0

x-5=0

x=5

b) x² - 4x - 5 = 0

⇒ ( x 2 − 4 x + 4 ) − 5 − 4 = 0

⇒ ( x 2 − 4 x + 4 ) − 9 = 0

( x − 2 ) 2 − 9 = 0 ⇒

( x − 2 ) 2 = 9 ⇒

( x − 2 ) = ± √ 9 (don't forget the ± !) ⇒

x= − 1   x = 5

solve for t
-18 = -3t
t = (_)

Answers

Answer:

3×6=18 t= (6)

I hope this helps by using division

Answer:

t = 6

Step-by-step explanation:

you want (t) by itself so you would divide both sides by -3. A negative divided by a negative is a positive. same goes for multiplying two negative numbers. The answer would be positive

Need help ASAP pleaseeeeee

Answers

Answer:

If she downloaded 40 songs she would pay $36 per month.

If she downloaded s songs she would pay 0.75(s)+6 per month.

Step-by-step explanation:

Find the surface area of each prism or pyramid. Round to the nearest tenth if necessary. Can someone help me with 17-19 for 30 points

Answers

17) 388 in^2
18) 585 in^2
19) 960 ft^2
*fyi- ^2 means squared just in case you didn’t know also hope the picture helps!
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