Write in slope-intercept form an equation of the line that passes through the points (-3, 2) and (1, -10).

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:

Of your choices, 87.5

Step-by-step explanation:

There may be a formula for figuring this out, but here's what I know how to do to solve this:

First we'll organize the data in ascending order:

3.9, 4.5, 5.7, 6.2, 7.4, 8.1, 8.4, 9.2  

The median is (6.2 + 7.4)/2 = 6.8

The first quartile is (4.5 + 5.7)/2 = 5.1

The third quartile is (8.1 + 8.4)/2 = 8.25

So the 75th percentile is 8.25

Since 9.2 is higher than that, I'd choose 87.5

Mildred's pie scored at the 87.5 percentile.

'A percentile is a measure used in statistics indicating the value below which a given percentage of observations in a group of observations fall.'

According to the given problem,

Organizing the data in ascending order:

3.9 < 4.5 < 5.7 < 6.2 < 7.4 < 8.1 < 8.4 < 9.2  

Median of the given data = [tex]\frac{6.2+7.4}{2}[/tex]

                                            = 6.8

First quartile = (4.5 + 5.7)/2

                      = 5.1

Third quartile = (8.1 + 8.4)/2

                       = 8.25

The third quartile is the 75th percentile,

⇒ 75th percentile = 8.25

Since, 9.2 > 8.25 , Mildred's pie scored at 87.5 percentile.

Hence, we can conclude, Mildred's pie scored at the 87.5 percentile.

Learn more about percentile here: https://brainly.com/question/1594020

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Answer:

njj

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

3^5 = 243

3^3 = 27

243 / 27 = 9

Hope this helps :)

Answer:

31

Step-by-step explanation:

1)32−3+14/7

2)29+14/7

3)29+2

4) 31

Answer:

p' (4,-2)

Step-by-step explanation:

P is at ( -1,5)

We are moving it 5 units to the right so add 5 to the x

We are moving it 7 units down so subtract 7 from the y

p'( -1+5, 5-7)

p' (4,-2)

Answer:

130°

Step-by-step explanation:

Angle 3 and 7 are the same so angle 7 is 50°

180° is the angle of a straight line so we take 50 away from 180 giving us 130°.

Hope this helps! :)

Answer:

[tex]Amount = 49 + 14.99k[/tex]

Step-by-step explanation:

Given

[tex]Books = 24[/tex]

[tex]Another\ Store = 25[/tex]

[tex]Model = k[/tex]

Cost of [tex]Model = 14.99[/tex] --- Missing from the question

Required

Represent the amount spent

The amount is calculated as:

[tex]Amount = Books + Another\ Store + Model * Cost[/tex]

[tex]Amount = 25 + 24 + k * 14.99[/tex]

[tex]Amount = 49 + 14.99k[/tex]

Answer:

The margin of error of his experiment is of 0.1074.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is of:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

30 M & M's from a bag, and 3 of them are green.

This means that [tex]n = 30, \pi = \frac{3}{30} = 0.1[/tex]

Standard 95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

Margin of error:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]M = 1.96\sqrt{\frac{0.1*0.9}{30}}[/tex]

[tex]M = 0.1074[/tex]

The margin of error of his experiment is of 0.1074.

Answer:

72 m^3

Step-by-step explanation:

volume of the kiosk = volume of cylinder + volume of cone

volume of a cylinder = nr^2h

n = 3.14

r = radius = 5/2 = 2.5

the diameter is the straight line that passes through the centre of a circle and touches the two edges of the circle.

A radius is half of the diameter

3.14 x (2.5^2) x 3 = 58.88  

Volume of a cone = 1/3(nr^2h)

3.14 x 1/3 x (2.5^2) x 2 = 13.08

13.08 + 58.88 = 71.96

To round off to the nearest cubic meter, look at the first number after the decimal, if it is less than 5, add zero to the units term, If it is equal or greater than 5, add 1 to the units term.

= 72 m^3

We need to solve this question using Algebraic expressions. The answer for the given question is x-6.

A mathematical expression with variables and/or numbers is called an algebraic expression. It can be simplified even if it cannot be solved since it lacks an equals sign (=). Algebraic equations, which have algebraic expressions divided by an equals sign, can be solved. Recognize the distinction between an algebraic equation and an algebraic expression. A mathematical expression called an algebraic expression can have variables or integers in it. be able to combine similar phrases. Adding up (or removing) the terms with the same degree is all that is required to combine related terms. All x2 terms can be mixed with other x2 terms, and all x3 terms can be coupled with x3 terms, according to this.

x students are trying in a chorus concert.

Only 6 students will be chosen.

        so the answer for the given question=x-6

We need to solve this question using Algebraic expressions. The answer for the given question is x-6.

To  refer more about Algebraic expressions, visit:

https://brainly.com/question/4344214

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Answer:

6.5cm)

Step-by-step explanation:

13.1 cm x 13.1 cm = 171.61

11.4 cm 11.4 cm = 129.96

171.61 - 129.96 = 41.65

Find the square root of 41.65.

41.65 = 6.4536811201050 x 6.4536811201050

Round 6.4536811201050.

x = 6.5cm

Note:

Pls let me know if my answer is incorrect, for the other users that will see this response. Thx!

-kiniwih426

Answer:

sdfgfgav

Step-by-step explanation:

Answer:

Step-by-step explanation:

The relationship between x and y is called a linear relationship because the points so plotted all lie on a single straight line. The number 95 in the equation y=95x+32 is the slope of the line, and measures its steepness.

Answer:

√85

Step-by-step explanation:

A (-3 , 4)    B (4 , -2)

AB² = (4 - -3)² + (-2 -4)² = 49 + 36 = 85

AB = √85

Answer:

Given- O is the centre of a circle in which an equilateral ΔPQR has been inscribed.

To find out- ∠QOR=?

Solution- The points P, Q & R are on the circumference of the circle since ΔPQR has been inscribed in the circle. Now the chord QR subtends ∠QOR to the centre O and ∠QPR to the circumference at P.

∴ By rule, ∠QOR=2∠QPR.........(i).

Now PQR is an equilateral Δ. Each of its angle is 60

o

. i.e ∠QPR=60

o

.

So, from (i), ∠QOR=2∠QPR=2×60

o

=120

o

.

Ans- Option B.

solution

Answer:

Step-by-step explanation:

If we draw radii from the center of this 18-gon to each vertex, we end up with 18 triangles that are all congruent to each other. If we divide 360 by 18 we get the measure of the vertex angle of each of these 18 triangles. 360/18 = 20. So we take one of these triangles and pull it out and use it as a representative triangle from which we use trig to find its height and its base length.

The formula for the area for a regular polygon is

[tex]A=\frac{1}{2}ap[/tex] where a is the apothem (the height of our triangle) and p is the perimeter (found from the base of our triangle).

If we split this triangle we extracted right down the center vertically, we get 2 right triangles. Pull one of those out and this is the triangle we work with. The vertex angle is split in half and it now measures 10. The one base angle is the right angle and, by the Triangle Angle-Sum Theorem, the other base angle is 80. To find the height (or the apothem) of this right triangle that has a hypotenuse of 1 (the radius of the polygon is the hypotenuse of the right triangle), we use the sin or cos ratio. I used cos:

[tex]cos10=\frac{a}{1}[/tex] so

a = .9848

To find the base of this right triangle, I used the sin ratio:

[tex]sin10=\frac{p}{1}[/tex] so

p = .1736. But this is only half the length of one of the sides of the polygon, so multiply it by 2 to get the length of the whole side.

.1736 * 2 = .3473

Now, in order to find the perimeter, we multiply that one side by 18 to get

p = 6.2514

Now we're ready to find the area:

[tex]A=\frac{1}{2}(.9848)(6.2514)[/tex] so

A = 3.078 square feet

Answer:

J >= 1 or j is greater than or equal to 1

Step-by-step explanation:

Write equation:

2(j-4)>= -6

1. Distribute:

2j - 8 >= -6

2. Add 8 on both sides:

2j -8 +8 >= -6 + 8

2j >= 2

3. Divide 2 on both sides:

2j/2 >= 2/2

j >= 1

There ya go! Hope this helps, have a good night or day! ;)

Answer:

translated 5 units to the right

Step-by-step explanation:

Answer:

I hope the above attachment helps you mate

Have a great day

[tex]#Liliflim[/tex]

Answer:

Solution given;

a⁴-23a²b²+b⁴

making in the form of a²+2ab+b²

a⁴+2a²b²+b⁴-2a²b²-23a²b²

(a²+b²)²-(5ab)²

factoring by using formula

x²-y²=(x+y)(x-y)

(a²+5ab+b²)(a²-5ab+b²)

Answer:

0.25 (or [tex]\frac{1}{4}[/tex])

Step-by-step explanation:

As the coin is fair, there is an equal chance the coin lands on heads or tails, therefore:

Probability of heads = 0.5 (or [tex]\frac{1}{2}[/tex])

Probability of tails = 0.5 (or [tex]\frac{1}{2}[/tex])

For Bob to win, the coin must land on heads twice, To work this out, we multiply the two events together.

Probability of 2 heads = 0.5 (probability of landing heads up) x 0.5 (probability of landing heads up) = 0.25 (or [tex]\frac{1}{4}[/tex])

Answer:

The input for the method is a continuous function f, an interval [a, b], and the function values f(a) and f(b). The function values are of opposite sign (there is at least one zero crossing within the interval). Each iteration performs these steps: Calculate c, the midpoint of the interval, c = a + b2.

Step-by-step explanation:

---------------------------

Answer:

60 bacteria

Step-by-step explanation:

c on edge 2022

Answer:

s + 178 = Abha's Can's

Step-by-step explanation:

Well since Abha collected 178 more cans than Shane, it would be Shane's amount of cans they collected AND 178 cans on top of that.

(i didnt know if you wanted the solution of s or just the equation on how to find s)

Answer:

3/4

Step-by-step explanation:

2 problems consist 8 choices of answers.

the events for the correct answer are 2

and the events for incorrect answer are 6

so, the probability that she answered neither of the problems correctly = 6/8 = 3/4

Answer:

hello

3x = 1/81

x = 1/ 81*3

x = 1/243

Step-by-step explanation:

Answer:

x=(1/81)/3

x=1/243

Step-by-step explanation:

C, 3 units translated to the left due to the +3 inside the bracket, vertically reflected on the x-axis as it is negative outside the bracket and translation 1 unit up because of the +1 outside the brackets.

Answer:

C

Step-by-step explanation:

f(-2) = 4(-2) + 5

f(-2) = -8 + 5

f(-2) = -3

Answer:

-3

Step-by-step explanation:

f(x) = 4x + 5

Let x = -2

f(-2) = 4(-2) + 5

        =-8+5

           -3