Which three lengths could be the lengths of a triangle

Answer:

steps below

Step-by-step explanation:

((x²-2x-8)/(x²-3x-10)) - ((x²-2x-3)/(x²+7x+6))

= ((x+2)(x-4)/(x+2)(x-5)) - ((x+1)(x-3)/(x+1)(x+6))

= (x-4)/(x-5) - (x-3)/(x+6)

= (x-4)(x+6)/(x-5)(x+6) - (x-3)(x-5)/(x-5)(x+6)

= ((x-4)(x+6) - (x-3)(x-5))/(x-5)(x+6)

= ((x²+2x-24) - (x²-8x+15)) / (x-5)(x+6)

= (x²+2x-24-x²+8x-15) / (x-5)(x+6)

= (10x-39) / (x-5)(x+6)      ..... (10x-39) / (x²+x-30)

Step-by-step explanation:

We first need to simplify the quadratic numerators and denominators. We'll use the fact that any equation of form

[tex]ax^2 + bx + c = 0[/tex]

where it has solutions [tex]x_1[/tex] and [tex]x_2[/tex] can be written as

[tex]a(x-x_1)(x-x_2)[/tex]

Where [tex]b = -a(x_1 + x_2)[/tex] and [tex]c = ax_1x_2[/tex]

Fortunately, here a = 1 for all equations, so let's learn how to solve for a=1 because it's a bit simpler.

[tex]x^2 - 2x - 8 = 0\\x^2 - 2x + 1 - 9 = 0\\(x - 1)^2 - 9 = 0\\(x - 1)^2 = 9\\x - 1 = 3 \vee x - 1 = -3\\x = 4 \vee x = -2\\x^2 - 2x - 8 = (x - 4)(x + 2)\\~\\~\\x^2 - 3x - 10 = 0\\x^2 - 3x - 10 = 0\\\\x^2 - 3x + 2.25 - 12.25 = 0\\(x - 1.5)^2 - 12.25 = 0\\(x - 1.5)^2 = 12.25\\x - 1.5 = 3.5 \vee x - 1.5 = -3.5\\x = 5 \vee x = -2\\x^2 - 3x - 10 = (x - 5)(x + 2)\\~\\~\\\frac{x^2-2x-8}{x^2-3x-10} = \frac{(x-4)(x+2)}{(x-5)(x+2)} = \frac{x - 4}{x-5}[/tex]

See, we've simplified the first term of the subtraction. Now let's do the same with the right side:

[tex]x^2 - 2x - 3 = 0\\x^2 - 2x + 1 - 4 = 0\\(x - 1)^2 = 4\\x - 1 = 2 \vee x - 1 = -2\\x = 3 \vee x = -1\\x^2 - 2x - 3 = (x - 3)(x + 1)\\~\\~\\x^2 + 7x + 6 = 0\\x^2 + 7x + 12.25 - 6.25 = 0\\(x + 3.5)^2 = 6.25\\x + 3.5 = 2.5 \vee x + 3.5 = -2.5\\x = -1 \vee x = -6\\x^2 + 7x + 6 = (x + 1)(x + 6)\\~\\~\\\frac{x^2 - 2x - 3}{x^2 + 7x + 6} = \frac{(x-3)(x+1)}{(x+1)(x+6)} = \frac{x-3}{x+6}[/tex]

See, we've simplified the second term. Now we need to bring them to the common denominator:

[tex]\frac{x^2-2x-8}{x^2-3x-10} - \frac{x^2-2x-3}{x^2+7x+6} = \frac{x-4}{x-5} - \frac{x-3}{x+6} = \frac{(x-4)(x+6)}{(x-5)(x+6)} - \frac{(x-3)(x-5)}{(x+6)(x-5)} =\\~\\= \frac{(x-4)(x+6) - (x-3)(x-5)}{(x+6)(x-5)} = \frac{(x^2 + 2x - 24) - (x^2 - 8x + 15)}{(x+6)(x-5)} =\\~\\= \frac{10x-39}{(x+6)(x-5)}[/tex]

We could simplify even further if we can find some a and b so that

[tex]10x - 39 = a(x+6) + b(x-5)[/tex]

then

[tex]\frac{10x-39}{(x+6)(x-5)} = \frac{a}{x-5} + \frac{b}{x+6}[/tex]

So let's try!

[tex]a + b = 10\\6a - 5b = -39\\b = 10 - a\\6a - 5(10 - a) = -39\\6a - 50 + 5a = -39\\11a = 11\\a = 1\\b = 10 - 1 = 9\\~\\\frac{10x-39}{(x+6)(x-5)} = \frac{1}{x-5} + \frac{9}{x + 6}[/tex]

And that's the simplest form.

Answer:

D. y=3x+4

This is the correct answer

In the triangle in question, x has a value of √68. The triangle is right - angled triangle based on the dimensions provided. According to this, the neighboring angle will also be x°.

An angle is a shape made up of two rays that share a terminus and is designated by the name of the angle (the vertex).

The plane that contains the rays contains the angles created by two beams. The meeting of two planes might also result in an angle. These are referred to as dihedral angles.

An angle is created when two straight lines or rays intersect at the same point. The point where all points converge is known as an angle's vertex.

The Roman word angulus, which means "corner," is where the term "angle" comes from. In plane geometry, an angle is a shape made up of two rays or lines with the same termination.

In the triangle in question, x has a value of √68.

The triangle is right- angled triangle based on the dimensions provided. According to this, the neighboring angle will also be √68.

Therefore, a given triangle's angles will all be expressed mathematically as -

Using Pythagoras theorem,

[tex]x^{2} = 8^2 + 2^2\\x^{2} = 64 + 4\\x^{2} = 68\\x = \sqrt{68}[/tex]

As a result, the given triangle's x value is √68.

To learn more about the angle, refer to:

brainly.com/question/25716982

#SPJ1

Answer:

[tex]4 \times - 2 {}^{n - 1} [/tex]

Step-by-step explanation:

Use the formula.

[tex]f(n) = f(1) \times {r}^{n - 1} [/tex]

where f(1) is the first terms, r is the common ratio, and n is our undefined term.

4 is our first term. so

f(1)=4.

Our common ratio is -2 so

r=-2.

[tex]4 \times - 2 {}^{n - 1} [/tex]

Answer:

I'm willing to help you at the math problem

Answer:

Step-by-step explanation:

1) r = 6 m

Value of π = 3.14

Area of circle = πr²  

                      = 3.14 * 6 * 6

                     = 113.04

                     = 113 m²

3) r = 4 in

Area of circle = πr²

                      = 3.14 * 4 * 4

                      = 50.24

                      = 50 in²

Answer:

100.48. l hope i helped you well

Answer:  402.12

Step-by-step explanation:

V=πr^2h

=π·4^2·8

402.12386

402.12

Answer:

idc

Step-by-step explanation:

Answer:

17 + 23 = 40

23 - 17 = 6 the other person did it right.

Answer:

Here we have a math thinking case.

Usually when we add two numbers, we try to deconstruct the numbers in such a way that the sum is easier. One thing that we always try to do, is to make a 10.

For example, in;

4 + 9

We know that 9 = 6 + 3

Then we can write:

4 + (6 + 3)

And re do the sum as:

(4 + 6) + 3

10 + 3 = 13

Now, we want to apply the same principle, but this time we don't want to make a 10.

We also can, for example, make a 5, like in:

2 + 13

We know that 2 + 3 = 5

then:

2 + 13 = 2 + (10 + 3) = 2 + 3 + 10 = 5 + 10 = 15

Other similar example:

2 + 7

We know that we can rewrite 7 as 3 + 4

Then:

2 + (7) = 2 + (3 + 4) = 2 + 3 + 4 = 5 + 4 = 9

This is not exactly easier, but in some cases can be useful.

The equations that can be used to represent the addends are: 2 + 6 = 8 and 3 + 4 = 7

When a 10 is not needed to add, then the sum of the two numbers is less than 10, or the numbers in the expression are greater than 10.

Using the above highlight, the equations that can be used to represent the addends are:

2 + 6 = 8

3 + 4 = 7

Note that there are other equations that can represent this situation

Read more about addends at:

https://brainly.com/question/654494

Answer:

I believe the answer to be A

Step-by-step explanation:

First plug in 2 for x

next solve the equation/ 2 and 2 is 4 so 4 +1 is 5

next 3 of 2 is 6 and 6-1 is 5

so as a result both sides are b=5

Answer:

Step-by-step explanation:

Answer:

1 : 2

Step-by-step explanation:

Total = 150 + 250 + 400 = 800

Pennies : Total

400 : 800

Change into simplest form...

1 : 2

Answer:

Step-by-step explanation:

1

Answer:

[tex]f(8) = 81[/tex]

[tex](g\ o\ f)(x) = x^2 + 2x -4[/tex]

Step-by-step explanation:

Solving (a):

[tex]f(x) = x^2 + 2x +1[/tex]

[tex]g(x) = x - 5[/tex]

Solve for f(8)

We have:

[tex]f(x) = x^2 + 2x +1[/tex]

Substitute 8 for x

[tex]f(8) = 8^2 + 2*8 +1[/tex]

Solve

[tex]f(8) = 64 + 16 +1[/tex]

[tex]f(8) = 81[/tex]

Solving (b):

[tex](g\ o\ f)(x)[/tex]

This is solved by:

[tex](g\ o\ f)(x) = g(f(x))[/tex]

So, we have:

[tex]g(x) = x - 5[/tex]

[tex]g(f(x)) = f(x) - 5[/tex]

Substitute: [tex]f(x) = x^2 + 2x +1[/tex]

[tex]g(f(x)) = x^2 + 2x + 1 - 5[/tex]

[tex]g(f(x)) = x^2 + 2x -4[/tex]

Hence:

[tex](g\ o\ f)(x) = x^2 + 2x -4[/tex]

Answer:

Volume = lwh

V = 1.6 x 2.8 x 3.2

V = 14.336

V = 14.3 cubed

Yellow is the right answer.

Answer:

A

Step-by-step explanation:

you get the numbers then divide after you have multiplied and then just find the distribution of the subtracted number :)

Answer:

a

Step-by-step explanation:

made a 100

Answer:

a = 38%, b = 3%

Step-by-step explanation:

got it correct.

Answer:

1372/3

Step-by-step explanation:

Answer:

x = 3

Step-by-step explanation:

we can use the Pythagorean theorem to solve this problem

x^2 + 4^2 = 5^2

x^2 + 16 = 25

x^2 = 9

x = +/- 3

we take only the positive value because a length can‘t be negative

x = 3

Answer:

the probability that this employee belongs to group I is 0.2118

Step-by-step explanation:

Given the data in the question;

P( group 1 )  = 0.20

P( group 11 ) = 0.60

P( group 111 ) = 0.20

now

[tex]P( \frac{certified}{Group1} )[/tex]         = 0.10

[tex]P( \frac{Not-certified}{Group1} )[/tex] = 0.90

[tex]P( \frac{certified}{Group11} )[/tex]        = 0.20

[tex]P( \frac{Not-certified}{Group11} )[/tex] = 0.80

[tex]P( \frac{certified}{Group111} )[/tex]        = 0.05

[tex]P( \frac{Not-certified}{Group111} )[/tex] = 0.95

so

[tex]P( \frac{group1}{Not-certisfied} )[/tex] = [ [tex]P( \frac{Not-certified}{Group1} )[/tex] × P( group 1 ) ] / [ [tex]P( \frac{Not-certified}{Group1} )[/tex] × P( group 1 ) + [tex]P( \frac{Not-certified}{Group11} )[/tex] × P( group 11 ) + [tex]P( \frac{Not-certified}{Group111} )[/tex] × P( group 111 ) ]

we substitute

[tex]P( \frac{group1}{Not-certisfied} )[/tex] = [ 0.90×0.20 ] / [ 0.90×0.20 + 0.80×0.60 + 0.95×0.20

[tex]P( \frac{group1}{Not-certisfied} )[/tex] = 0.18 / [ 0.18 + 0.48 + 0.19 ]

[tex]P( \frac{group1}{Not-certisfied} )[/tex] = 0.18 / 0.85

[tex]P( \frac{group1}{Not-certisfied} )[/tex] = 0.2118

Therefore, the probability that this employee belongs to group I is 0.2118

Answer:

Two independent sample t test

Step-by-step explanation:

The research described describes the statistics of two different samples which are also independent,

Sample 1 :

Sample size, n1 = 16

Mean, xbar = 4.75

Standard deviation s2 = 2.8

Sample 1 :

Sample size, n1 = 15

Mean, xbar = 3.93

Standard deviation s2 = 2.4

The hypothesis :

H0 : μ1 = μ2

H1 : μ1 ≠ μ2

The t statistic :

(xbar1 - xbar 2) ÷ sqrt[(s1²/n1 + s2²/n2)

From on the test statistic, obtain the p value and compare with Given α - value to make and conclude in a decision.

Answer:

A. u just asked if he or she tracks profile daily. 220 lines up with daily

Answer:

[tex] y + 6 = -2(x - 4) [/tex]

Step-by-step explanation:

Given:

Slope (m) = -2

Point on the line = (4, -6)

Required:

Point-slope equation of the line

Solution:

Point-slope equation takes the following form:

[tex] y - b = m(x - a) [/tex],

Where,

m = slope of the line = -2

(a, b) = coordinates of the point on the line. = (4, -6)

Plug in the values into the slope-point equation

[tex] y - (-6) = -2(x - 4) [/tex]

[tex] y + 6 = -2(x - 4) [/tex]

Answer:

I believe the value would be 9.

Answer:

9

Step-by-step explanation:

3 x 3 = 9

Mark me Brainllest

Answer:nonononononnj

Step-by-step explanation: