Mathematics High School

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

hi can someone please answer my question. thank you ❤️​

Answers

hope this helps, have a great!!

How many tons are equal to 54,000 pounds?

Answers

Answer:

I think About 27 short ton

Figures A-G are all images of figure W. Which figures can you
not map figure Wonto using a single rotation around a vertex
translation, or reflection across the x-or y-axis? Select all
that apply
A figure A
B figure B
C figure
D figure D
E figure E
F figure F
G figure G

Answers

Answer:

figure d

Step-by-step explanation:

it is the smartes and most common answer

write the slope-intercept form of the equation (no space)

through: (-1, -2), parallel to y = -2x - 1

Answers

Answer:

slope=-2

y+2=(-2)(x+1)

This is the slope intercept form

What is the answer to 8x + 4( 4x - 3) = 4( 6x + 4) - 4

Answers

Answer:

x=24

Step-by-step explanation:

8x + 4(4x - 3) = 4(6x + 4) - 4

8x + 16x - 12 = 24x + 16 - 4

24x - 12 = 24x + 12

24x = 24x + 12 + 12

24x = 24x + 24

24x/24x = 24

x = 24

Answer:

0

Step-by-step explanation:

8x + 4(4x - 3) = 4(6x + 4) - 4

8x + 16x - 12 = 24x + 16 - 4

24x - 12 =  24x + 12

-24x                  -24x

      -12 = 12

      +12   +12

        0 = 24

Whats 9+10+823+636+0

Answers

Answer:

1478 is the answer

have a fang-tastic day <3

Step-by-step explanation:

Answer:

1478

Step-by-step explanation:

lol have a good day/night!!

Question 4 (5 points)
Determine the quotient of (22.8 x 10-3) = (5.7 x 10-6). Write your answer in
scientific notation.
A) 4 x 10-6
B) 4 x 10-9
C) 4 x 10-3
X
OD 4 x 10
X
Right answer will get brainlst

Answers

Answer:

b

Step-by-step explanation:

Find g(f(x)), given f(x)=3x2−x+1,g(x)=2x

Answers

Answer:

6x²-2x+2

Step-by-step explanation:

For g(f(x)), we have to first do f(x), and then substitute it into the "x" in g(x)

So, f(x) = 3x²-x+1

We need to substitute the "x" in g(x) with this entire thing

So, g(x) = 2x

When we substitute f(x) into it, it instead becomes 2(3x²-x+1)

Next, we have to expand the brackets, and doing so gives us the following:

6x²-2x+2

So that becomes our final answer!

Let me know if it makes sense! :)

y-6= -3(x-1) use integers A B C​

Answers

y=-3x+9 this should be the answer you are looking for

A bird was perched on a tree at a height of 12 feet. The bird then saw food on a branch below and
dropped down 4 feet. What is the current height of the bird?

Answers

Is it 8 feet? If a bird was 12 feet high than dropped 4 feet all you would need to do is 12-4 than add the feet bit. 12-4 equals 8 btw.

Multiply (-5)^3 (raised to the third power)

Answers

Answer:

- 125

Step-by-step explanation:

[tex](-5)^{3}[/tex]

= - 5 × - 5 × - 5

= 25 × - 5

= - 125

Answer:

-125

Step-by-step explanation:

-5^3= -5x-5x-5

-5^2=-5x-5= 25

25x-5=-125

What is the value of the expression 11 + (fraction 1 over 2)4 ⋅ 48?

Answers

Hello!

Answer:

107

Step-by-step explanation:

Hope this helps

Answer:

17

Step-by-step explanation:

d

the regular price for a bicycle is 210.19. the sale price is $43.48 less than the regular price. what is the sale price?

Answers

Answer:

$166.71

Step-by-step explanation:

210.19-43.48=166.71

The answer is 109.99 hope this helped u out

Marcos tem 44 carrinhos em sua coleção e comprou mais 13. Com quantos carrinhos Marcos ficará?​

Answers

Answer:

Marcos ficará com 57 carros.

Step-by-step explanation:

44+13=57

Aliás, 57 carros é muito carro!

12+17-3x2 rewrite this in perenthesis

Answers

Answer:

(12+17)-(3x2)

Step-by-step explanation:

Answer:

12+17-(3x2)

Step-by-step explanation:

You do multiblecation before addition so you put it in parenthesis

ABCD is a trapezium and D to C is 13 mm ,C to B 9 mm and D to A is 12 mm find A to B

Answers

Answer:

12 mmm

Step-by-step explanation:

Goo answer it Go Go Go

A cargo ship is 704 feet long. If 1.1 inch represents 13 feet. How long is the ship in the model? Round your answer to the nearest tenth if needed.

Answers

Answer:

59.57

Step-by-step explanation:

704 / 13

= 54.1538461538

54.1538461538 x 1.1

= 59.5692307692

Solve:
1 < ( x + 5.5 ) / 2

Full working out please

Also does X have to be on the Left side always?​

Answers

Answer:

x > -3.4

Step-by-step explanation:

1 < (x + 5.5) / 2

first multiply each side by 2

2 < x + 5.5

Then subtract 5.5 from each side

-3.4 < x

x has to be on the left so you switch the hole equation around to get

x > -3.4

The formula used to convert degrees Celsius to degrees Fahrenheit is

F = C +32

Convert 68°F to degrees Celsius. Solve the formula for C, and then use it to

convert the temperature.

Which is the correct formula and conversion?


A. C= F-32; conversion: 68°F = 180°C

B. C = (F- 32); conversion: 68°F = 122°C

C. C= 5(F- 32); conversion: 68°F = 20°C

D. CE F-32; conversion: 68°F = 20°C

O

O

Answers

Answer:

C.

Step-by-step explanation:

The formula to convert C° to F° is C = 5(F-32)

Can a quadrilateral have no obtuse angles? Explain.

Answers

A ǫᴜᴀᴅʀɪʟᴀᴛᴇʀᴀʟ ʜᴀᴠᴇ 4 ᴏʙᴛᴜsᴇ ᴀɴɢʟᴇs

A quadrilateral is a four-sided closed figure with straight sides. The sum of the interior angles of a quadrilateral is

A quadrilateral is a four-sided closed figure with straight sides. The sum of the interior angles of a quadrilateral is 360

A quadrilateral is a four-sided closed figure with straight sides. The sum of the interior angles of a quadrilateral is 360∘

A quadrilateral is a four-sided closed figure with straight sides. The sum of the interior angles of a quadrilateral is 360∘360∘. Common quadrilaterals include parallelograms, rectangles, squares, kites, and trapezoids.

1. Determine el valor de W en las proporciones siguientes:
a) (12/w) = (4/3); w =

Answers

Aplicando multiplicación cruzada, tiene-se que el valor de w es w = 9.

Cuando una proporción es dada, con una igualdade de duas proporciones, puede-se aplicar multiplicación cruzada entre ellas.

En este problema, la ecuación que relaciona las proporciones es dada por:

[tex]\frac{12}{w} = \frac{4}{3}[/tex]

Aplicando multiplicación cruzada:

[tex]4w = 12(3)[/tex]

[tex]4w = 36[/tex]

[tex]w = \frac{36}{4}[/tex]

[tex]w = 9[/tex]

El valor de w es w = 9.

Un problema similar es dado en https://brainly.com/question/24615636

Which choices are equivalent to the expression below? Check all that apply

Answers

Answer:

f son similares por defecto

what's A ∩ B' in its simplest form?

Answers

Answer:

 

Step-by-step explanation:

please helpppppppppppppppppppppppp

Answers

Answer:

12,000

Step-by-step explanation:

1,306+ 7,247 + 3,418 = 11,971

11,971 rounds up to 12,000

I don't understand this question can someone help me with this please, please explain!! and thank you for the help!!

Answers

Answer:

a. 35 people participated in the walk.

b. About 16 people traveled more than 14 kilometers.

Step-by-step explanation:

(Warning: This may be wrong)

1 3/8 x 3 =

3 2/8 x 3 =

Answers

Answer:

1. 4.125

2. 9.75

Step-by-step explanation:

ALRIGHTY, HELP AGAIN! YOU'LL GET BRAINLIEST IF YOU'RE RIGHT! HERE'S THE PICTURE!

Answers

Option B (2,-6)How??

As we can see on grid point K is on 2,6 and when we mirror it we get the points 2,-6. They have said across x axis which means the reflection is below x-axis not parallel to it.

You can check the attachment for better understanding...

Answer:

B. (2, -6)

Sorry if you don't need this anymore...


There were 45 runners to start a race. In the first half of the race,2/3 of them dropped out. How many runners finished the race?

Answers

45 / 3 = 15
15 x 2 = 30

So 30 runners dropped out and 15 runners finished the race
30 and 15

I’m to lazy to explain

Find real numbers a and b such that the equation is true.

a + bi = 7 + 6i

Answers

The A=7 and the B=6 tell me if it’s wrong

To mix a particular shade of purple paint, red paint and blue paint are mixed in the ratio 5:3. To make 20 gallons of this shade of purple paint, how many gallons of red and blue paint should be used?

Type the correct answers into the boxes below.

red paint:
gallons
blue paint
gallons

Answers

100 gallons of red 60 gallons of blue (20x5):(20x3)
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