A line has equation 2x + y=20 and a curve has equation y=a+
18/x-3, where a is a constant.
Find the set of values of a for which the line does not intersect the curve

Answers

Answer 1

Answer:

we have two equations:

2*x + y = 20

y = a + 18/x - 3

We want to find the values of a such that the graphs of the equations do not intersect.

The first step is to isolate y in the first equation.

now we get:

y = 20 - 2*x

Then we have the system of equations:

y = 20 - 2*x

y = a + 18/x - 3

If the line intersects the curve at a point (x, y), then at that point both functions have the same value of y, then:

20 - 2*x = y = a + 18/x- 3

We want to find a value of such that this does not happen.

Let's solve that equation and see what we can find.

20 - 2*x =  a + 18/x - 3

20 + 3 = a + 18/x + 2*x

23 = a + 18/x + 2*x

(23 - a) = 18/x + 2*x

if we multiply all values by x, we get:

(23 - a)*x = 18 + 2*x^2

Then we have a quadratic equation, we can write this as:

2*x^2 - (23 - a)*x + 18 = 0

Now, remember that if the determinant of the quadratic function is smaller than zero, then the function does not have any real solution, then we need to find a such that the determinant of this quadratic equation is smaller than zero.

Remember that for a quadratic equation:

a*x^2 + b*x + c = 0 is:

b^2 - 4*a*c

In this case, the determinant is:

(-(23 - a))^2 - 4*2*18

(23 - a)^2 - 144

And this must be smaller than zero, then:

(23 - a)^2 - 144 < 0

23^2 - 2*23*a + a^2 - 144 < 0

529 - 46*a + a^2 - 144 < 0

a^2 - 46*a + 385 < 0

Notice that the function has a positive leading coefficient, then the arms of the function go upwards, then the region of the function that is smaller than zero is the values of a that are between both roots of a.

Then we need to solve:

a^2 - 46*a + 385 = 0

We can use the Bhaskara's equation to find the roots, the roots are given by:

[tex]a = \frac{-(-46) +- \sqrt{(-46)^2 - 4*1*385} }{2*1} = \frac{46 +-24}{2}[/tex]

Then the two roots are:

a₁ = (46 + 24)/2 = 35

a₂ = (46 - 24)/2 = 11

Then for all the values of a suc that:

11 < a < 35

The line does not intersect the curve.


Related Questions

Please please help asap!!! I will mark brainliest!!!

Answers

Answer:

The other angle is 63 if it is asking what I think it is asking

Step-by-step explanation:

If it is right can you mark brainliest

Answer:

63 or 72

Step-by-step explanation:

10 points possible. answer everything completely and I will mark brainliest

Answers

Answer: A is a function. B is not a function. C is a function. D is not a function. E is not a function. F is not a function. G is a function. H is a function. I is not a function.

Step-by-step explanation:

A light bulb manufacturer claims that the lifetime of the bulbs is normally distributed with a mean of 5000 hours and a standard deviation of 250 hours. If 20000 bulbs are produced on a particular day, what percentage of the bulbs will have a lifetime of between 4750 and 5500 hours?

Answers

Answer:

88

Step-by-step explanation:

A circular mirror has a diameter of 16.5 inches. What is the circumference of the mirror? Round to the nearest hundredth

Answers

Answer:

C≈51.84in

Step-by-step explanation:

C=2πr

d=2r

Solving for C

C= πd= π·16.5≈51.83628in

Enter the number that belongs in the green box

Answers

Answer: 60°

The reason for this is because the image shows that ALL the sides are EQUAL. Therefore, all the angles must be equal.
So, we know that a triangle equals a total of 180°. If we simply divide that total by 3 we get 60°.

Equilateral triangles are triangles whose all sides and angles are equal.

Since the above given triangle has 3 equal sides it is an equilateral triangle.

So, the three angles of this triangle can be 3x.

Which means :

[tex] =\tt 3x = 180[/tex]

[tex] =\tt x = \frac{180}{3} [/tex]

[tex]\hookrightarrow \tt \color{plum}x = 60°[/tex]

▪︎Therefore, x = 60°

Write an equation that models the linear relationship in the graph below

Answers

Answer:

y=-4/7x+4

Step-by-step explanation:

hope this helps

Answer:

4/7+4=y

Step-by-step explanation:

y=mx+b

The cereal box shown below is a rectangular prism. Find the surface area of the cereal box. ​

Answers

Answer:

580 cm^2

Step-by-step explanation:

First, find the area of the front and back. 20*10=200

There are 2 sides with 20*10 ( front and back) so we can multiply by 2. 200*2=400

Then, the sides. 3*20=60*2=120

Then, the top and bottom 10*3=30*2=60

400+120+60=580

Answer:

420

Step-by-step explanation:

60+60+30+30+120+120

hope this helped :)

Which number is equal to 100?

Answers

Answer:

10 square2

36 + 64 = 100. In other words, 6² + 8² = 10²

Answer:

C. 10^2

Step-by-step explanation:

When you have an exponent and the base is 10, the exponent is how many zeros there are total that come after the 1. There are 2 zeros after the 1 in 100, so 10^2 is the answer.

Emilio earns $15 per hour at one job and $18 per hour at a second job. He works for 3 hours at the first job and 90 minutes at the second. What is his average hourly pay rate?

Answers

answer: 16
explanation: i’m good at math

Solve for the value of p.
2 Xp=44

Answers

Answer:

p=22

sooooooooooooooooo ezzzzzzzzzzzzzzzzzzzzz

I NEED HELP ASAP PLEASE!!! I'LL GIVE BRAINLIEST FOR THE CORRECT ANSWER!!!

Answers

Answer:

x = 3

y = 4

Step-by-step explanation:

Please let me know if you want me to write an explanation for my answer :)

Angle A and angle B are supplementary angles. If the measure of angle A = (3x - 12) and the measure of angle B = (4x - 25), find the measure of angle B.

Answers

Answer:

what is x so I can help you.

one hundred twenty-three and thirty hundreths. in decimal form

Answers

Answer:

0.2330

Step-by-step explanation:

Solve the equation y – 5x = –7 for y.
A. y = 5x – 7
B. y = –5x – 7
C. y = 5x + 7
D. y = –5x + 7

Answers

Answer:

the answer is B

Step-by-step explanation:

Answer: A. y = 5x -7

Step-by-step explanation:

Y - 5x = -7

+ 5x + 5x

Y = 5x - 7

**you can’t subtract -5x to -5x because it’s already a negative. It should be a positive 5x so you can move it to the other side.

What is the answer for x?
-7=3.5+5x

Answers

Answer:

x=-2.1

Step-by-step explanation:

The answer is x = -2.1

A farmer bought three seeds ,the probability that each of them germination is 3/4.If he plant all of them,find the probability that only one of them germinate

Answers

Answer:

[tex]\frac{9}{64}[/tex]

Step-by-step explanation:

Probability refers to chance of occurrence of any event.

Probability that each of them is germinates [tex]=\frac{3}{4}[/tex]

So,

Probability that each of them is germinates won't germinate [tex]=1-\frac{3}{4}=\frac{1}{4}[/tex]

Probability that only one of them will germinate = [tex]=\frac{3}{4}(\frac{1}{4})^2=\frac{9}{64}[/tex]

HELPPP

The school that Ryan goes to is selling tickets to a play. You can buy 2 senior citizen tickets and 4 child tickets for a total of $70. You can also buy 2 senior citizen tickets and 1 child ticket for a total of $31. What is the price each of one senior citizen ticket and one child ticket?

A) senior citizen ticket: $13, child ticket: $9B) senior citizen ticket: $6, child ticket: $7C) senior citizen ticket: $9, child ticket: $13D) senior citizen ticket: $13, child ticket: $14

Answers

Answer:

6 for senior and 7c for child

Step-by-step explanation:

A seabird is 28 meters above the surface of the ocean. What is its elevation?

Answers

Answer:

The elevation is 28 meters.

Step-by-step explanation:

This is pretty obvious because it says that the bird is above the ocean, not below. So, it is positive.

Hope this helps! :)

Could you please help me? Thank you!

Answers

Answer:

steak

Step-by-step explanation:

you can touch the steak

you can eat the steak

you can smell the steak

you can hear the steak sizzle

you watch the steak as it cooks

A computer store bought a program at $10 and sold it at a selling price of $12 find the percent makup

Answers

Answer:

20%

Step-by-step explanation:

12-10=2

changed ÷ original x 100

2 ÷ 10 x 100

=20%

PLZZ HELP ME IM DOING A TEST RNNNN.

Answers

Answer:

5(x)+5(y)=10

10(x)+2(y)=12

Step-by-step explanation:

i just got done with that same thing

2x-y+8z=13
3x+4y+52=18
5x-2y-72=20​

Answers

Answer:

Answer is above (In the image).

Step-by-step explanation:

I am not sure if that is what you were looking for. To convert it to decimals, just input the figures into your calculator.

In my opinion the best way to solve these equations are elimination, therefore I will be giving my answer in this way!

2x-y+8z=13 1️⃣

3x+4y+52=182️⃣

5x-2y-72=203️⃣

We first combine liked terms in equation 2 and 3.

2️⃣turns into 3x+4y=-34 let's call it 2️⃣'

3️⃣turns into 5x-2y=92 let's call it 3️⃣'

Then solve for x

3️⃣'*2

10x-4y=184

3️⃣+2️⃣

13x=150

x=150/13

Now substitute the x back into equation 2️⃣'

3*150/13+4y=-34

450/13+4y=-442/13

4y=-892/13

2y=-446/13

y=-223/13

Now we can substitute this back into 1️⃣ to solve for z

2*150/13- - 223/13+8z=169/13

523/13+8z=169/13

8z=-354/13

4z=-177/13

z=-177/52

This problem is kind of messy so let me restate my answer!

x=150/13

y=-223/13

z=-177/52

I really hoped this is correct and it helped, and would appreciate it if you give me brainlliest! If you have any more questions about my solution please ask me in the comments!

need help in this show working please​

Answers

this is what i got hope it helps

2) Add the following:

4a2 + b2 – 3ab, 3a2 – 7b2 + 8ab and a2 – b2 + 2ab



Answers

Answer:

8a2-8b2+7ab

Step-by-step explanation:

Putting together all of the a2 gets you to 8a2

Putting together all of the b2 gets you to -8b2

Putting together all of the ab gets you to 7ab

can someone help me pleaseee :)

u have to make the questions become y = mx + b

Answers

Answer:

3. 8y= -7x -12

4. -3y= 4x -12

5. 7y= -2x +4

Do you want me to do the rest?

did you got it??

The rest are:

6. -3y =6x +12

7. -10y= 5x+20

8. 4y=2x +12

Write the following inequality in slope-intercept form. –12x – 2y ≥ –42 y ≥ –6x – 21 y ≤ –6x – 21 y ≤ –6x + 21 y ≥ –6x + 21

Answers

Answer:

y ≤ –6x + 21

Step-by-step explanation:

Create an expression that is equivalent to 9(3x + 5 + x) without using
parentheses.

Answers

Answer:

27x + 45 + 9x

37x + 45

it's here

Convert the following to a percentage: $0.40 out of $2.50

Answers

Answer:

16%

Step-by-step explanation:

Solution for 0.40 is what percent of 2.50:

0.40:2.50*100 =

(0.40*100):2.50 =

40:2.50 = 16

Answer:

16%planation:

{y=5x-7
y=-2x+7 Solve the system by graphing.

Answers

Answer:

I love algebra anyways

The ans is in the picture with the  steps how i got it

(hope this helps can i plz have brainlist :D hehe)

Step-by-step explanation:

Answer: Put both equation into desmos and the crossing point will be (2,3) and the graph will be there.

Step-by-step explanation: 5x-7 = -2x+7                   y = 5(2) - 7

                                             5x = -2x + 7 + 7.              y = 3

                                             5x = -2x + 14

                                             5x + 2x = 14

                                             7x = 14

                                             x = 2

Which story shows 1/3 divided by 5?

Answers

I don’t know what you mean by “story” but 1/3 divided by 5 is 0.06
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