Suppose A and B are points. How many distinct lines contain both A and B?
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1
2
3
infinitely many

Answer:

[tex]\left (-\dfrac{4}{\sqrt{5}},\dfrac{8}{\sqrt{5}}\right )\text{ and }\left (\dfrac{4}{\sqrt{5}},-\dfrac{8}{\sqrt{5}}\right )[/tex].

Step-by-step explanation:

We need to find all the points on the curve x=4cos(t),y=4sin(t) that have the slope of 1/2.

[tex]x=4cos (t)[/tex]

[tex]\dfrac{dx}{dt}=-4sin (t)[/tex]

[tex]y=4sin (t)[/tex]

[tex]\dfrac{dy}{dt}=4cos (t)[/tex]

Now,

[tex]\dfrac{dy}{dx}=\dfrac{dy}{dt}\times \dfrac{dt}{dx}[/tex]

[tex]\dfrac{dy}{dx}=4cos (t)\times \dfrac{1}{-4sin (t)}[/tex]

[tex]\dfrac{dy}{dx}=-\cot t[/tex]

So, slope of the curve is [tex]-\cot t[/tex].

[tex]-\cot t=\dfrac{1}{2}[/tex]

[tex]-\tan t=2[/tex]

[tex]\tan t=-2[/tex]            ...(1)

Using [tex]\sec^2t=1+\tan^2t[/tex], we get

[tex]\sec^2t=1+(-2)^2[/tex]

[tex]\sec^2t=1+4[/tex]

[tex]\sec t=\pm \sqrt{5}[/tex]

[tex]\cos t=\pm \dfrac{1}{\sqrt{5}}[/tex]

Now,

[tex]\sin^2t=1-cos^2t[/tex]

[tex]\sin t=\pm \sqrt{1-\dfrac{1}{5}}[/tex]

[tex]\sin t=\pm \sqrt{\dfrac{4}{5}}[/tex]

[tex]\sin t=\pm \dfrac{2}{\sqrt{5}}[/tex]

It equation (1), tan(t) is negative. So, sin and cos have different signs.

If [tex]\sin t= \dfrac{2}{\sqrt{5}}[/tex], then [tex]\cos t=- \dfrac{1}{\sqrt{5}}[/tex].

[tex]x=4cos (t)=-\dfrac{4}{\sqrt{5}}[/tex]

[tex]y=4sin (t)=\dfrac{8}{\sqrt{5}}[/tex]

If [tex]\sin t=- \dfrac{2}{\sqrt{5}}[/tex], then [tex]\cos t= \dfrac{1}{\sqrt{5}}[/tex].

[tex]x=4cos (t)=\dfrac{4}{\sqrt{5}}[/tex]

[tex]y=4sin (t)=-\dfrac{8}{\sqrt{5}}[/tex]

Therefore, the two points are [tex]\left (-\dfrac{4}{\sqrt{5}},\dfrac{8}{\sqrt{5}}\right )\text{ and }\left (\dfrac{4}{\sqrt{5}},-\dfrac{8}{\sqrt{5}}\right )[/tex].

Answer: The answer is 28. Hope this helps:)

Answer:

-1

hope this helps

plz mark brainleist

Answer:

12x

Step-by-step explanation:

Answer: x = 35°

Step-by-step explanation:

Answer

14

you have to simplify

8+1/2(12)

14

Answer:

p = 26

Step-by-step explanation:

(p+4)/6 = 5

Multiply each side by 6

(p+4)/6 *6 = 5*6

p+4 = 30

Subtract 4 from each side

p+4-4 = 30-4

p = 26

Answer:

20

Step-by-step explanation:

12 (2 + ) − (4 + )

24-4

=20

Answer:

20

Step-by-step explanation:

Step-by-step explanation:

F(g(x)) = -10x-13

First blank: -10

Second blank: -13

Answer:

21

Step-by-step explanation:

Answer:

21

Step-by-step explanation:

Answer:

B. -5

Step-by-step explanation:

3x-1 > 4x-6

   +1

3x>4x-5

     -4x

-x>-5

/-1   /-1

x>-5

Answer:

5h-6e

Step-by-step explanation:

3h - e + 2h - 5e =

= 3h + 2h - e - 5e

= 5h-6e

Answer:

5h - 4e

Step-by-step explanation:

Add 3h and 2h to get 5h then subtract e from 5e which equals 4e

Hope this helps!

Answer:

y = 1874.25

Step-by-step explanation:

2(4y - 5) = 14 983

2*4y + 2*-5 = 14983

8y - 10 = 14983

8y = 14983 + 10

8y = 14993

y = 14993/8

y = 1874.25

Answer:

Step-by-step explanation:

2(4y - 5) = 14

8y - 10 = 14

8y = 24

y = 3

Answer:

11.66 meters

Step-by-step explanation:

First draw a diagram. See attachment.

We notice that if we draw everything out, we get a right triangle.

The flag pole and its shadow are the two legs, with lengths 10 and 6 meters. We want to find the distance from the top of the pole to the end of the shadow, so we need to use the Pythagorean Theorem, which states that for a right triangle with legs a and b and hypotenuse c:

a² + b² = c²

Here, a = 10 and b = 6, and we want to find c:

a² + b² = c²

10² + 6² = c²

100 + 36 = c²

136 = c²

c = √136 = 2√34 ≈ 11.66 meters

~ an aesthetics lover

Answer:

11.7

Step-by-step explanation:

Answer:

A3=44 56-7

Step-by-step explanation:

Answer:

2.37

I hope this helps, also next time make sure your question makes sense

Answer:

DE= 7.3

Step-by-step explanation:

you subtract the length if CE - CD to get DE

13.8 - 6.5 = 7.3

Answer:

Salary after 5 years: 60000+(5000)5= 85000

Salary after T years: 6000+(5000)t

Step-by-step explanation:

The way that you would find the amount of money needed after 5 years is by multiplying the 5000, since that is William's raise per year, and then adding 60000, which is the original salary.

In order to find William's salary after t years, since you do not have a number, but have t, you would want to multiply 5000, which is the yearly raise, and t, hich can be any amount of years. After that, you would want to add William's original income to find an answer.

Answer:

The answer would be 18 years

Step-by-step explanation:

hope this helps:)

Answer:

0.84, 1.17, 2.25

Step-by-step explanation:

Answer:

.84, 1.17, 2.25

Step-by-step explanation:

You can answer this on your own by finding which numbers are farther away from zero. So the farther you get from zero, the more you have.

Answer:

yes, ordinary netizens have a right to do what they want or what opinion they want to say. Declaration of Indepence is not just for powerful people but also for ordinary netizens in order for them to spek the truth

Answer:

x= k/a-b

Step-by-step explanation:

Move all terms to the left side and set equal to zero as well as each factor.

Hope this helps.

The value of x is k/ (a-b).

algebra is the branch of mathematics that helps in the representation of problems or situations in the form of mathematical expressions. it involves variables like x, y, z, and mathematical operations like addition, subtraction, multiplication, and division to form a meaningful mathematical expression.

Given:

ax-bx=k​

x(a-b)=k

x= k/ (a-b)

Hence, the value  x is k/(a-b)

Learn more about algebra here:

https://brainly.com/question/24875240

#SPJ2

Step-by-step explanation:

A piecewise function is a function built from pieces of different functions over different intervals. For example, we can make a piecewise function f(x) where f(x) = -9 when -9 < x ≤ -5, f(x) = 6 when -5 < x ≤ -1, and f(x) = -7 when -1 <x ≤ 9.

Hey there!

[tex]6 \frac{7}{20}[/tex] as a decimal

The percentage for 6 7/20 is 35%. So if that was the percent, then the decimal would be 0.35.

[tex]0.35(ANSWER)[/tex]

Hope this helps!

[tex]\text {-TestedHyperr}[/tex]

Answer:

Perimeter of the given triangle = [tex]\frac{7x+38}{(x+8)(x+5)}[/tex] units

Step-by-step explanation:

Perimeter of a polygon = Sum of the measures of all sides of the polygon

From the picture attached,

Perimeter of the given isosceles triangle = Measures of two equal sides + remaining side

P = [tex]2(\frac{3}{x+8})+\frac{x}{x+5}[/tex]

  = [tex]\frac{6}{(x+8)}+\frac{x}{(x+5)}[/tex]

  = [tex]\frac{6(x+5)+(x+8)}{(x+8)(x+5)}[/tex]

  = [tex]\frac{6x+30+x+8}{(x+8)(x+5)}[/tex]

  = [tex]\frac{7x+38}{(x+8)(x+5)}[/tex] units

Therefore, perimeter of the given triangle is [tex]\frac{7x+38}{(x+8)(x+5)}[/tex] units

Answer:

Hope this helps;))

Step-by-step explanation:

-3ab+6ab=3ab

2a-4a+3a=1a

7+5=12

12+3ab+1a

Answer:

-2+2ab-a

Step-by-step explanation:

Never combine unlike terms

Ex. Never combine a and ab

By following those rules, you will get -2+2ab-a as your answer.

Answer:

XW since it matches the same as IH  

Step-by-step explanation:

example if it asked another question saying what corresponds with XY. XY is on the last part of the statement so it would  correspond with IJ

Answer:

yes

Step-by-step explanation:

um ok.........................