What is the slope of the line? Khan academy 15 points

Given:

The expression is:

[tex]\dfrac{1}{a+b}+\dfrac{2a}{a^2+b^2}+\dfrac{4a^7+4a^3b^4}{b^8-a^8}[/tex]

To find:

The simplified form of the given expression

Solution:

Formula used:

[tex]x^2-y^2=(x-y)(x+y)[/tex]

We have,

[tex]\dfrac{1}{a+b}+\dfrac{2a}{a^2+b^2}+\dfrac{4a^7+4a^3b^4}{b^8-a^8}[/tex]

It can be written as:

[tex]=\dfrac{1}{a+b}+\dfrac{2a}{a^2+b^2}+\dfrac{4a^3(a^4+b^4)}{(b^4)^2-(a^4)^2}[/tex]

[tex]=\dfrac{1}{a+b}+\dfrac{2a}{a^2+b^2}+\dfrac{4a^3(a^4+b^4)}{(b^4-a^4)(b^4+a^4)}[/tex]

[tex]=\dfrac{1}{a+b}+\dfrac{2a}{a^2+b^2}+\dfrac{4a^3}{(b^2-a^2)(b^2+a^2)}[/tex]

[tex]=\dfrac{1}{a+b}+\dfrac{2a}{a^2+b^2}+\dfrac{4a^3}{(b-a)(b+a)(b^2+a^2)}[/tex]

Taking LCM, we get

[tex]=\dfrac{1(b-a)(b^2+a^2)+2a(b-a)(b+a)+4a^3}{(b-a)(b+a)(b^2+a^2)}[/tex]

[tex]=\dfrac{b^3+a^2b-ab^2-a^3+2a(b^2-a^2)+4a^3}{(b-a)(b+a)(b^2+a^2)}[/tex]

[tex]=\dfrac{b^3+a^2b-ab^2-a^3+2ab^2-2a^3+4a^3}{(b-a)(b+a)(b^2+a^2)}[/tex]

[tex]=\dfrac{b^3+a^2b+ab^2+a^3}{(b-a)(b+a)(b^2+a^2)}[/tex]

Using the grouping method factories the numerator.

[tex]=\dfrac{b(b^2+a^2)+a(b^2+a^2)}{(b-a)(b+a)(b^2+a^2)}[/tex]

[tex]=\dfrac{(b+a)(b^2+a^2)}{(b-a)(b+a)(b^2+a^2)}[/tex]

Cancel out the common factors.

[tex]=\dfrac{1}{b-a}[/tex]

Therefore, the value of the given expression is [tex]\dfrac{1}{b-a}[/tex].

Answer:

$1.62

Step-by-step explanation:

Answer:

unbiased

Step-by-step explanation:

it would be biased if you lets say survey the history club kids

Answer:162 might be wrong tho so dont mark as brainlyest

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The slope is -1/2 and the y-intercept is 14

Answer:

B and C. if you got them wrong let me know :3

Answer:

F(x)=x^2 and G(x)=7x^2-2x-1

Step-by-step explanation:

I have to fill in characters for the step by step explanation so have fun reading the following Junk. KEEp wasting your time Dummy with

Answer:

i think A

Step-by-step explanation:

sorry if im wrong

Answer:

52

Step-by-step explanation:

13 divide 1/4 is the equivilent to 13 x 4

Answer:

52

Step-by-step explanation:

13/(1/4)

when a fraction is in the denominator you inverse the fraction and multiple by the numerator

so it would be 13*(4/1) = 13*4 = 52

Answer:

a = x² + 11x + 30

Step-by-step explanation:

a = (x + 5)(x + 6)

multiply each term in the first set of parenthesis by each term in the second

a = x(x + 6) + 5(x + 6)

a = (x² + 6x) + (5x + 30)

combine like terms

a = x² + 11x + 30

Answer:

x = 4

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define Systems

7x + y = 14

-2x - y = 6

Step 2: Solve for x

Elimination

Answer:

[tex]y = x + 7[/tex]

Step-by-step explanation:

[tex]y = gx + c[/tex]

[tex]gradient = \frac{y}{x} = \frac{1}{1} = 1[/tex]

[tex]where \: the \: line \: meet \: the \: y-axis = 7[/tex]

Answer:

y

=

3

2

x

Rewrite in slope-intercept form.

Tap for more steps...

y

=

3

2

x

Use the slope-intercept form to find the slope and y-intercept.

Tap for more steps...

Slope:  

3

2

y-intercept:  

(

0

,

0

)

Any line can be graphed using two points. Select two  

x

values, and plug them into the equation to find the corresponding  

y

values.

Tap for more steps...

x

y

0

0

2

3

Graph the line using the slope and the y-intercept, or the points.

Slope:  

3

2

y-intercept:  

(

0

,

0

)

x

y

0

0

2

3

image of graph

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

I have to write more but its true

Answer:

Hello,

Please, see the attached file.

Thanks.

Step-by-step explanation:

The remaining steps can be ∆ABC ∼ ∆DBA AA criterion for similarity Corresponding sides of similar triangles are proportional, AB/AC = AD/AB, and AB2 = AC × AD.

Triangles are closed two-dimensional geometric figures with three straight sides and three angles. The sum of the three angles in any triangle is always 180 degrees.

The first 10 steps to prove that AB2 + BC2 = AC2 are given in the table. The remaining steps to their correct sequence in the proof are:

These steps follow logically from the previous statements in the proof. In step 11, the Pythagorean Theorem is applied to the right triangle ADB.

Thus, this can be the match for the given scenario.

For more details regarding triangles, visit:

https://brainly.com/question/2773823

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Answer:

100 meters per hour.

Step-by-step explanation:

7,200 seconds / 60 = 120 minutes

120 minutes / 60 = 2 hours

200 meters / 2 hours = 100 meters

Since the squirrel moved 200 meters in 2 hours, the squirrel moved 100 metres per hour.

Answer:

18 ft

Step-by-step explanation:

We are to determine the base given the hypotenuse and length.

The Pythagoras theorem : a² + b² = c²

where a = length

b = base

c =  hypotenuse

30²  = 24² + b²

900 = 576 + b²

b² = 900 - 576

b²  = 324

square root = 18

Answer:

64cm² I think :) if u get it wrong dont blame it on me.

Answer:

64 cm^2

Step-by-step explanation:

The area of a square can be calculated by A = s^2 (Area = side squared aka the side multiplied by itself)

A = s^2

= 8^2 (8 x 8)

= 64 cm^2

Answer:

Parallelogram

Result

Area = b × h

= 5.5 × 11

Answer:

x = 15 and y = 7

Step-by-step explanation:

x = 2y + 1

x + y - 8 = 14

Let's substitute the value of x in the second equation:

(2y + 1) + y - 8 = 14

3y -7 = 14

3y = 14 + 7

3y = 21

y = 21/3

y = 7

And now you substitute the value of y in the first equation:

x = 2•7 + 1

x = 14 + 1

x = 15

Answer:

2 1/2

Step-by-step explanation:

divide in 5 then divide half in 5 also

Answer:

2,5

Step-by-step explanation:

The length of a piece of wood is:

12 ½ : 5 = 5/2 = 2,5

⭐Answer:

✰According to angle property between tangent and secant✰

[tex](4x-8)=1/2(80)[/tex]

[tex]4x-8=40[/tex]

[tex]4x=40+8[/tex]

[tex]4x=48[/tex]

[tex]x=48/4[/tex]

[tex]x=12[/tex]

〖D) 12〗

☁☁☁☁☁☁☁

hope it helps...

The value of x is 12

Circle is the collection of all points in a plane at a constant distance from a fixed point. The fixed point is known as the centre, and the constant distance is the circle’s radius. A line that intersects a circle in two distinct points is called a secant to the circle.

A line meeting a circle only in one point is called a tangent to the circle at that point. In this article, we will talk about the relative position of the circle and a line in the same plane. We will also examine the existence of tangents to a circle and their properties.

Using angle property between tangent and secant

(4x - 8) = 1/2*80

4x- 8 = 40

4x= 48

x= 12

Learn more about tangent here:

https://brainly.com/question/19064965

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Answer:

The speed from A to B is 40 km/h.

Step-by-step explanation:

Distance from A to B = 40 km

Distance from B to C = 30 km

Speed from A to B is v km/h

Speed fro B to C is v + 5 .

total time, t = 2 hours

Stopping time at B = 20 minutes

Let the time from A to B is t'.

[tex]t'=\frac{40}{v}[/tex]

Let the time from B to C is t''.

[tex]t''= \frac{30}{v+5}[/tex]

The total time is

[tex]\frac{40}{v}+\frac{30}{v+5}+\frac{20}{60}=2\\\\\frac{40 v + 200 + 30 v}{v^2 + 5 v}=\frac{10}{6}\\\\420 v + 1200 = 10 v^2 + 50 v\\\\10 v^2 -370 v - 1200 = 0 \\\\v^2 - 37v - 120 = 0 \\\\v^2 - 40 v + 3 v - 120 = 0 \\\\v(v - 40) + 3 (v - 40) = 0\\\\(v - 4)(v + 3) = 0\\\\v = 40 km/h or - 3 km/h[/tex]

Speed cannot be negative so the speed from A to B is 450 km/h.

Answer: its 180 , because it dont matter if its up or side .

Answer:

13°

Step-by-step explanation:

the lines are parallel so

82 + 85 = 167

167 - 180 = 13

x = 13°

==========================================

Work Shown:

(tangent)^2 = (whole secant)*(external secant)

(TU)^2 = (RT)*(ST)

(TU)^2 = (RS+ST)*(ST)

(TU)^2 = (8+4)*(4)

(TU)^2 = 48

TU = sqrt(48)

TU = 6.928203

TU = 6.9

For more info, you can search out "secant tangent chord", or something similar, and you should get to a page that describes the formula of what's going on here. This should match up fairly similarly to what lesson 3.09 is talking about.

Answer: 9.8

TU^2= TS x TR

TU^2= 8 x 12

TU= sqrt(96) = 9.79

Answer:

Step-by-step explanation:

If the minor arc is 133, the major arc is going to be

Major arc = 360 - Minor arc

Minor arc = 133

Major arc = 360 - 133

Major arc = 227

Does this make sense? It should. If you put a line from C to A then extend it until it hit the circumference, you would get a diameter which is a 180o angle. The major arc through D is greater than 180. So 227 is a reasonable answer.

Answer:

hope it is helpful to you

Answer:

4(7a+3)

Step-by-step explanation:

28a+12

take common

4 is the common number for both the terms because it divides 28 and 12 exactly.

4(7a+3)

Answer:

Option A

Step-by-step explanation:

[tex] \frac{12}{25} \times \frac{11}{24} \times \frac{10}{23} \times \frac{9}{22} [/tex]

we start with 12 red marbles out of 25 marbles, that's the probability for the first.

in the second step we have one red marble less, wich also means one marble less overall

and so on

[tex] \frac{12 \times 11 \times 10 \times 9}{25 \times 24 \times 23 \times 22} [/tex]

[tex] = \frac{11880}{303600} [/tex]

can be reduced by 1320 (step by step) to

[tex] \frac{9}{230} [/tex]