Consider the circle of radius 10 centered at the origin. Find an equation of the line tangent to the circle at the point (6, 8)

Answer:

slope = [tex]\frac{5}{4}[/tex]

Step-by-step explanation:

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (4, 5)

m = [tex]\frac{5-0}{4-0}[/tex] = [tex]\frac{5}{4}[/tex]

Answer:

Step-by-step explanation:

Slope of a line is given by

where

m is the slope and

( x1 , y1) and (x2 , y2) are the points of the line

Slope of the line between the points

(0,0) and (4,5) is

Hope this helps you

Answer:

[tex]\sqrt[8]{197^{7} }[/tex]

Step-by-step explanation:

[tex]\sqrt[8]{197^{7} }[/tex]

Answer:

6x+2-1x+5=42

Step-by-step explanation:

Answer:

6x+2-x-5=42

Step-by-step explanation:

Answer:

7/12 is a rational

Step-by-step explanation:

because it is containing a quantity which are expressible

Answer:

4x²+14x-8 ( multiplying)

x=-4 , x=1/2 ( find solution)

Step-by-step explanation:

(2x+8)(2x-1)​

start :

2x*2x=4x²

2x*-1 = -2x

8*2x=16x

8*-1=-8

add the results  : 4x²-2x+16x-8 = 4x²+14x-8

(2x+8)(2x-1)​=0

2x+8=0

x=-8/2=-4

OR 2x-1=0

then x=1/2

Answer:

=4x2+14x−8

Step-by-step explanation:

(2x+8)(2x−1)

=(2x+8)(2x+−1)

=(2x)(2x)+(2x)(−1)+(8)(2x)+(8)(−1)

=4x2−2x+16x−8

=4x2+14x−8

I hope this helps! :]

Answer:

see below

Step-by-step explanation:

This is in slope intercept form

y = mx+ b  where m is the slope and b is the y intercept

32 is the slope

Parallel lines have the same slope so 32 would be the slope of  the parallel line

Perpendicular lines have slopes that multiply to -1

m*32 = -1

m = -1/32

The slope of the perpendicular line is -1/32

Answer:

12

Step-by-step explanation:

Hello, as the coefficient of the leading term is negative we know that the vertex of the parabola is a maximum. So we need to find the vertex.

This expression is maximum for

[tex]t=-\dfrac{b}{2a} \text{ where the parabola equation is}\\\\ax^2+bx+c=0[/tex]

So, here, it gives t = 8/2=4, and then, the maximum is

[tex]-4^2+8*4-4=-16+32-4=32-20=12[/tex]

So the answer is 12.

Thanks

Answer: When x=2 and z = 1, then the value of y =4.

Step-by-step explanation:

Given: y varies directly as x and z i.e. [tex]y\ \alpha \ xz[/tex]

[tex]y=k(xz)[/tex]      (i) , where k is the proportionality constant.

Put  Y=40 ,x =5 and z = 4, then we get

[tex]40=k(5\times4)\\\\\Rightarrow\ k=\dfrac{40}{20}\\\\\Rightarrow\ k=2[/tex]

Required equation: [tex]y=2(xz)[/tex]  [Put value of k in (i)]

Now put x=2 and z = 1, then we get

[tex]y=2(2\times1)=2(2)=4\\\\\Rightarrow\ y=4[/tex]

Hence, when x=2 and z = 1, then the value of y =4.

Answer:  70

Step-by-step explanation:

Antoine's elevation when he is halfway to the top is 70. You cut the diameter (120) in half which gets you 60 and you add the height of the stand holding the wheel (10) which gets you 70.

The his or her elevation should be 70.

Since the diameter is 120 And, elevation of Antoine should be halfway to the top so here we split the diameter into half i.e. half of 120 is 60 and there is the height for stand holding the wheel i.e. 10

So, the elevation should be

= 60 + 10

= 70

Therefore, The his or her elevation should be 70.

Learn more about elevation here: https://brainly.com/question/16616666

Answer:

Step-by-step explanation:

Given this expression 2(b+3c), its equivalent expression is derived by simply opening up the bracket as shown below;

Open the parenthesis by multiplying the constant outside the bracket with all the variables in parenthesis.

= 2(b+3c)

=  2(b)+ 2(3c)

= 2b +2*3*c

= 2b +6c

It can also be written as sum of b+3c in 2 places i.e (b+3c)+(b+3c) because multiplying the function b+3c by 2 means we are to add the function by itself in two places.

Hence the equivalent expression are (b+3c)+(b+3c) and 2(b)+2(3c) or 2b+6c

Answer:

-7/2

Step-by-step explanation:

cuz thats right

Answer:

The ratio of the area of ABCD to the area of EFGH is 9:1.

Step-by-step explanation:

Let us assume that the shapes are rectangles and they are similar. If the two shapes are similar then their sides are in the same proportion. Therefore the ratio of the sides are in the same proportion.

[tex]\frac{AB}{BC}=\frac{EF}{FG}\\ \\\frac{18}{24}=\frac{6}{x}\\\\18x=24*6\\ \\x=\frac{24*6}{18}=8[/tex]

The area of ABCD = AB × BC = 18 × 24 = 432

The area of EFGH = EF × FG = 6 × 8 = 48

The ratio of the area of ABCD to the area of EFGH = Area of ABCD / Area of EFGH = 432 / 48 = 9/1 = 9 : 1

Answer:

y= 2x+1

hope it helps...........

Answer:

=2ab +abk -2m- mk

= ab(2+k) -m(2+k)

=(2+k)(ab-m)

Step-by-step explanation:

Answer:

See below.

Step-by-step explanation:

So we have the two functions:

[tex]f(x)=5x+4\text{ and } g(x)=-2x+1[/tex]

1)

First, find the values of each function:

[tex]f(x)=5x+4\\f(6)=5(6)+4\\f(6)=30+4=34[/tex]

[tex]g(x)=-2x+1\\g(-8)=-2(-8)+1\\g(-8)=16+1=17[/tex]

Therefore:

[tex]f(6)+g(-8)\\=(34)+(17)=51[/tex]

2)

Plug in the number into the function:

[tex]g(x)=-2x+1\\g(4)=-2(4)+1=-8+1=-7[/tex]

3)

Like the last one:

[tex]f(x)=5x+4\\f(-2)=5(-2)+4=-10+4=-6[/tex]

Answer:

what number must be added to sum of two angles that the sum of three angles become 180.

Since sum of two angles is 100 , 80 must be added to 100 to make it equal to 180.

Step-by-step explanation:

Given

sum of measure of angle of triangle = 180°

given two angles 40°and  60°

Let the third angle be x°

thus

40°+  60°+x° = 180°

100°+x° = 180°

x° =  180°- 100° =  80°

Thus, third angle measure 80°

She must have sum the first two known angles.

as given sum of three angles are 180

she must have assumed other angle to be x

then sum of all three angles must be 180

now to find third angle she subtracted sum of two known angles to find third angle.

other way can what number must be added to sum of two angles that the sum of three angles become 180.

Since sum of two angles is 100 , 80 must be added to 100 to make it equal to 180.

Answer:

[tex](- \infty, 2), (2, \infty)[/tex]

Step-by-step explanation:

Given the function:

[tex]f(x) = \dfrac{x+1}{x-2}[/tex]

To find:

Domain of the function.

Solution:

First of all, let us learn about definition of  domain of a function.

Domain of a function is the valid input values that can be provided to the function for which output is defined.

OR

Domain of a function [tex]f(x)[/tex] are the values of [tex]x[/tex] for which the output [tex]f(x)[/tex] is a valid value.

i.e. The function does not tend to [tex]\infty[/tex] or does not have [tex]\frac{0}0[/tex] form.

So, we will check for the values of [tex]x[/tex] for which [tex]f(x)[/tex] is not defined.

For value to tend to [tex]\infty[/tex], denominator will be 0.

[tex]x-2\neq 0 \\\Rightarrow x \neq 2[/tex]

So, the domain can not have x = 2

Any other value of x does not have any undefined value for the function [tex]f(x)[/tex].

Hence, the answer is:

[tex]\bold{(- \infty, 2), (2, \infty)}[/tex]     [2 is not included in the domain].

Hello There!!

Your best answer choice will be is A.

(2x + 7) feet.

Because, All you have to do for this problem is factor the equation. I would be hard to explain on this so I recomment you watch a video on it. If you did not know how to factor, you could have muliplied each of the answers by themselves to determine the correct answer because it is a square.

Hope This Helps!!

Answer:

(2x+7)

Step-by-step explanation:

4x^2 + 28x + 49

This is a perfect square trimonial

a^2 + 2ab + b^2 =  (a+b)^2

(2x)^2 + 2 * 2x*7 + 7^2

( 2x+7)^2

Answer: (-1, -2)

Step-by-step explanation:

so at first you have (1, 2)

then you were asked to reflect about y=x which is (x, y) = (y, -x)

(1, 2) = (2, -1)

then followed by y=-x which is (x, y) = (-y, -x)

(2, -1) = (-1, -2)

I hope this helps!

Answer:

8 hours

Step-by-step explanation:

Given:

Sheyna drives to the lake with average speed of 60 mph and

[tex]v_1 = 60\ mph[/tex]

Sheyna drives back from the lake with average speed of 36 mph

[tex]v_2 = 36\ mph[/tex]

It took 2 hours less time to get there than it did to get back.

Let [tex]t_1[/tex] be the time taken to drive to lake.

Let [tex]t_2[/tex] be the time taken to drive back from lake.

[tex]t_2-t_1 = 2[/tex] hrs ..... (1)

To find:

Total time taken = ?

[tex]t_1+t_2 = ?[/tex]

Solution:

Let D be the distance to lake.

Formula for time is given as:

[tex]Time =\dfrac{Distance}{Speed }[/tex]

[tex]t_1 = \dfrac{D}{60}\ hrs[/tex]

[tex]t_2 = \dfrac{D}{36}\ hrs[/tex]

Putting in equation (1):

[tex]\dfrac{D}{36}-\dfrac{D}{60} = 2\\\Rightarrow \dfrac{5D-3D}{180} = 2\\\Rightarrow \dfrac{2D}{180} = 2\\\Rightarrow D = 180\ miles[/tex]

So,

[tex]t_1 = \dfrac{180}{60}\ hrs = 3 \ hrs[/tex]

[tex]t_2 = \dfrac{180}{36}\ hrs = 5\ hrs[/tex]

So, the answer is:

[tex]t_1+t_2 = \bold{8\ hrs}[/tex]

Answer:

x = 20

Step-by-step explanation:

Intersecting Chords Theorem: ab = cd

Step 1: Label our variables

a = x

b = x - 11

c = x - 8

d = x - 5

Step 2: Plug into theorem

x(x - 11) = (x - 5)(x - 8)

Step 3: Solve for x

x² - 11x = x² - 8x - 5x + 40

x² - 11x = x² - 13x + 40

-11x = -13x + 40

2x = 40

x = 20

Answer: x=20

Step-by-step explanation:

[tex]ab=cd[/tex]

[tex]x(x - 11) = (x - 5)(x - 8)[/tex]

[tex]x^2 - 11x = x^2 - 13x + 40[/tex]

[tex]x^2 - 11x = x^2 - 8x - 5x + 40[/tex]

[tex]-11x = -13x + 40\\2x = 40\\x = 20[/tex]

Answer:

Step-by-step explanation:

North-east has a bearing of 45 degrees

South-west has a bearing of 225 degrees.

Taken anticlockwise,

angle = south-west - north-east

=  (225-45)

= 180 degrees

answer

hope this helps....

Answer:

Step-by-step explanation:

23x +2 = 15x+48x+6

To solve for x group like terms

That's

Send the constants to the right side of the equation and those with variables to the left side

We have

23x - 15x - 48x = 6 - 2

Simplify

- 40x = 4

Divide both sides by -40

We have the final answer as

Hope this helps you

Answer:

C

Step-by-step explanation:

Not all real numbers are irrational.

Answer:

D

Step-by-step explanation:

Answer:

3 and and half minutes--> 7ft

Step-by-step explanation:

If it travels 24 inches aka 2ft per minute

then it has to travel 12 inches aka 1ft in 30secs

SO

3mins and 30secs to travel 7ft

24inches--- 2ft---- per minute

4ft--- 2 mins

6ft---- 3mins

7ft--- 3minutes and 30 seconds