Perform the indicated operation and simplify the result. Leave your answer in factored form.

[tex]\frac{x}{x^{2} -9} +\frac{9}{x}[/tex]

The answer for the given expression, 17²-286 will be 3.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that,the expression is,

17²-286

The expression is solved by the arrthmetic operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

=17²-286

=289-286

=3

Thus, the answer for the given expression, 17²-286 will be 3.

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Answer:

Answer would be 22 km at southward direction.

Answer = 22km

Step-by-step explanation:

As it started from the point O.

* Goes 50 to East direction

* Goes 22 to North direction

* Goes 50 to West direction

* And the it travels back to the starting point when it turn to south direction. It traveled 22 km to southward direction.

> Total kilometers the train traveled is 144 kilometers.

I hope you get this right.

Answer:

Plane Y and CDB

Step-by-step explanation:

Plane Y and CDB

The equation y = -6x + 5 when rewritten is f(x) = -6x + 5

The equation is given as

y = -6 + 5

Rewrite the above equation properly

So, we have

y = -6x + 5

Express y as a function

So, we have

f (x) = -6x + 5

Hence, the equation y = -6x + 5 when rewritten is f(x) = -6x + 5

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Answer:

6ft

Step-by-step explanation:

180cm=5ft10in=70in

So it's closer to 6ft

Answer:

x + 3/7=2x-25/7 ​

X=4

Adam invested $350 at 6% and $450 at 10%

Amount invested by Adam = $800

Interest paid by one account = 6%

Interest paid by another account = 10%

Let the amount invested in one account be x and the other be y

The formula for simple interest is given by:

Simple interest = (P*R*T)/100

where P = Principal

R = rate of interest

T = number of years amount is invested

Substituting the value in the formula we get:

Simple interest in one account = (x*6*1)/100-------(1)

Simple interest in another account = (y*10*1)/100--------(2)

The question states that interest earned would be the same when $800 is invested at 8.25%, therefore

Simple interest = (800*8.25*1)/100

= 66----(3)

Equating (1), (2) and (3) we get:

x + y = 800-----(4)

6x/100 + 10y/100 = 66

6x + 10y = 6600-----(5)

Multiplying (4) with 6 and equating it with (5)

6x + 6y = 4800

6x + 10y = 6600

4y= 1800

y = 450

x = 350

So, Adam invested $350 at 6% and $450 at 10%

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The inequality of the number line is x > -1

A number line is a  vertical or horizontal line that has endpoints and it is used to represent numbers at a constant interval

From the number line in the question, we can see that:

From the question, we have

Point = -1

Assume the following

As a general rule, open circles implies that the number at that endpoint is not included part of the solution set.

This means that the inequality of the number line is x > -1

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Answer: x=24

Step-by-step explanation:

-1/3x+1= -7

you move the negative one to the other side of the equation to get x by itself and get -1/3x= -8

then you divide both sides by -1/3 and get 24

ΔFHE = ΔKHE, as the ∠FHE = ∠KHE. When two triangles contain the same two sides and include the same Angle, the remaining sides, Angle, and area are likewise identical, which means they're congruent.

∠FHE ≅ ∠KHE is an Identical part.

L(FE) = L(KE), as two Congruent angles have equal sides

L( FH) = L(KH)

L(EH)=L(EH),  Common part in a figure.

Congruent angles are two or more angles that are exactly the same. As a result, the lengths of these angles are identical.

hence, ΔFHE = ΔKHE, as the ∠FHE = ∠KHE. When two triangles contain the same two sides and include the same Angle, the remaining sides, Angle, and area are likewise identical, which means they're congruent.

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Expanding out the equation, we get

[tex]x^2 - ax - bx+ab+x^2 -bx-cx+bc+x^2 -ax-cx+ac=0 \\ \\ 3x^2 -x(2a+2b+2c)+(ab+bc+ac)=0[/tex]

Considering the discriminant,

[tex](2a+2b+2c)^2 - 4(3)(ab+bc+ac) \\ \\ =4a^2 + 4b^2 + 4c^2 + 8(ab+bc+ac)-12(ab+bc+ac) \\ \\ =4(a^2 + b^2 + c^2 - ab - bc - ac) \\ \\ =2((a-b)^2 + (b-c)^2 + (c-a)^2)[/tex]

This is always non-negative, meaning the roots are real.

The roots are equal if and only if the discriminant is 0, which is when a=b=c.

Answer: k=0,-5

Step-by-step explanation:

Your GCF is 5k, as you're able to take it out of both terms.

Once you've taken out a 5k, this will leave you with an equation that looks like this;5k(k+5)=0.

Set your 5k equal to 0 and divide to get k=0

Set your k+5 equal to 0 and subtract on both sides to get k=-5

Hope this helps you, dawg.

Answer:

5,609

55,209

56,209

562,009

Answer:

£980

Step-by-step explanation:

3 portions = 210

1 portion = 70

so 70

70 × 4 = would be 280

70 × 7 = 490

490 + 280 + 210 = 980

hope this works : )

The coordinates of the resulting point after the reflection are (-5, -5)

When we do a reflection over a given line, the perpendicular distancee between the line and the point is invariant.

In this case, we want to reflect the point (-5, -1) over the line y = -3

The distance between the y-value of the point and the line is:

D = |-1 - (-3)| = | -1 + 3| = 2

The point is at 2 units (above) from the line, then after the reflection, the point will be 2 units below the line.

So the new y-value is:

y = -3 - D = -3 - 2 = -5

The coordinates of the resulting point are (-5, -5).

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Answer:

1, 2, 3, 6, 13, 26, 39, and 78

Step-by-step explanation:

:)

Answer:

A. 0

Step-by-step explanation:

[tex]2 \frac{3}{4} + ( - 2 \frac{3}{4}) \\ = \frac{11}{4} - \frac{11}{4} \\ = \frac{11 - 11}{4} \\ = \frac{0}{4} = 0 \\ hope \: this \: would \: help[/tex]

Answer:

A. 0

Explanation:

Given:

[tex]2\dfrac{3}{4} +(-2\dfrac{3}{4} )[/tex]

In improper fractions:

[tex]\dfrac{11}{4} +(\dfrac{-11}{4} )[/tex]

Simplify:

[tex]\dfrac{11}{4} -\dfrac{11}{4}[/tex]

Evaluate:

[tex]0[/tex]

Tip:

As the integers are alike, when subtracted they simplify to zero as a result.

Answer: can u finish the question

Step-by-step explanation:

Answer:

$866.13

Step-by-step explanation:

to get an average, you add up all the factors then divide them by how many there are. I added 500 12 times to 1250 12 times to 1150 3 times and 600 4 times.

aka (500*12)+(1250*12)+1150+1150+1150+600+600+600

then i divided by 31 because 12+12+3+4=31. giving the average $866.13.

Step-by-step explanation:

but please where is the question I'm eager to answer and win the pizza

Answer:

Step-by-step explanation:

( g ° f )(x) = ( x + 7 )² = x² + 14x + 49

20 + 3(x² + 14x + 49) = - 34

20 + 3x² + 42x + 147 = - 34

3x² + 42x + 201 = 0 ⇔ x² + 14x + 67 = 0

D = 196 - 268 = - 72 < 0

There is no any roots in set of real numbers.

The values of x in set of complex numbers are:

[tex]x_{12}[/tex] = [tex]\frac{- 14 }{2}[/tex] ± [tex]\frac{6\sqrt{2}i }{2}[/tex]

[tex]x_{12}[/tex]  = - 7 ± 3√2 i  

The line skewed to AT is HB

As a general rule, skew lines are nonparallel lines that do not intersect

This means that the lines are in different planes

From the given figure, we can see that lines HB and AT do not intersect and they are not parallel

Hence, the line skewed to AT is HB

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Based on the results shown in the dot plot on the number of pets owned by students in Ileana's grade, the mean number of pets owned by students is 2.5 pets

The number of pets owned per student home according to the dot plot is:

= 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 8

The total number of pets owned is:

= 0 + 0 + 0 +1 + 1 + 1 + 1 + 1 + 2 + 2 + 2 + 3 + 3 + 3 + 4 + 4 + 4 + 5 + 5 +8

= 50 pets

The mean number of pets owned is:

= 50 / 20 students

= 2.5 pets

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The function notation of the coordinate point where the coordinate point is given as (-5, 18) is f(-5) = 18

Coordinate points are mathematical statements that are used to represent the location of points on a coordinate plane

The coordinate point is given as

(-5, 18)

The above coordinate point can be represented as

(x, y) = (-5, 18)

The above coordinate point can further be rewritten as

(x, f(x)) = (-5, 18)

So, we have

x = -5

f(x) = 18

Substitute x = -5 in the equation f(x) = 18

f(-5) = 18

Hence, the function notation of the coordinate point where the coordinate point is given as (-5, 18) is f(-5) = 18

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The mean absolute deviation is 5.4.

The mean absolute deviation tells us that the variance of each data set is 5.4.

The mean absolute deviation is a measure of variance that determines the average distance between each data point in the dataset and its mean.

The mean absolute deviation = 1/n ∑ l x - m(x) l

The first step is to determine the mean of the data set: (18 + 15 + 25 + 17 + 13 + 15 +  23 + 27 + 30 +  27) / 10

= 210 / 10

= 21

The second step is to determine the absolute difference between the mean and each data point. Then add the result together.

|(18 - 21) + (15 - 21)+ (25- 21) + (17- 21) + (13- 21) + (15- 21) +  (23- 21) + (27- 21) + (30- 21) +  (27- 21)| = 54

Now, divide the sum by the total numbers in the data set : 54 / 10 = 5.4

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Answer:

Step-by-step explanation:

Answer:

$5,298.48

Step-by-step explanation:

Given vertices:

As points A and B, and points C and D, have the same y-coordinates, AB is parallel to CD.

As there is a difference of 5 units between points A and B, and C and D, AB = CD.

As AB is parallel to CD and AB = CD ⇒ AD = BD and AD is parallel to BD.

Therefore, the quadrilateral ABCD is a parallelogram (see attachment).

To find the perimeter of ABCD, calculate the side lengths of AB and AD using the Distance Formula.

[tex]\boxed{\begin{minipage}{4.7 cm}\underline{Distance Formula}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two endpoints.\end{minipage}}[/tex]

[tex]\begin{aligned}AB & =\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\& =\sqrt{(10-5)^2+(-3-(-3))^2}\\& =\sqrt{(5)^2+(0)^2}\\& =\sqrt{25}\\& =5\:\:\sf units\end{aligned}[/tex]

[tex]\begin{aligned}AD & =\sqrt{(x_D-x_A)^2+(y_D-y_A)^2}\\& =\sqrt{(7-5)^2+(-11-(-3))^2}\\& =\sqrt{(2)^2+(-8)^2}\\& =\sqrt{4+64}\\& =\sqrt{68}\:\:\sf units\end{aligned}[/tex]

The perimeter of a two-dimensional shape is the distance all the way around the outside.

[tex]\begin{aligned}\textsf{Perimeter of $ABCD$} & = AB + CD + AD + BC\\& = 2\:AB + 2\:AD\\& = 2 \cdot 5+2 \cdot \sqrt{68}\\& = 10+2 \sqrt{68}\\& = 10+2\sqrt{4 \cdot 17}\\& = 10+2\sqrt{4}\sqrt{17}\\& = 10+2 \cdot2\sqrt{17}\\& = 10+4\sqrt{17}\:\:\sf units\end{aligned}[/tex]

As 1 unit = 1 meter, the perimeter of the fence is (10 + 4√17) m.

If fencing costs $200 per meter:

[tex]\begin{aligned}\sf \implies Cost \:of\:fencing& = 200(10 + 4 \sqrt{17})\\& = 2000+800 \sqrt{17}\\& = 5298.4845\\ & = \$5298.48\end{aligned}[/tex]

Therefore, it will cost Maya $5,298.48 to fence her yard.

Answer:

4

Step-by-step explanation:

9x+6y=42

solution

Balancing Method :

subtract both sides by 6

9x-6y+6y=42-6=

9x=42-6=36

divide both by 6

9 ÷9=36÷9=4

Roman should invest $18,223.97 in order to withdraw $22450.15 in exactly 3.7 years from now if interest rate is 5.65 % compounded monthly.

First, convert R as a percent to r as a decimal

r = R/100

r = 5.65/100

r = 0.0565 per year,

Then, solve the equation for P

P = A / (1 + r/n)^(nt)

P = 22,450.15 / (1 + 0.0565/12)^{(12)(3.7)}

P = 22,450.15 / (1 + 0.0047)(44.4)

P = $18,223.97

The principal investment required to get a total amount of $22,450.15 from compound interest at a rate of 5.65% per year compounded 12 times per year over 3.7 years is $18,223.97.

Therefore, Roman should invest $18,223.97 in order to withdraw $22450.15 in exactly 3.7 years from now if interest rate is 5.65 % compounded monthly.

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(0,5) is that equations y intercept so it WILL pad through that point.

[tex]Answer:\ y=3x+5\ pass\ throught\ the\ (0,5)[/tex]

Step-by-step explanation:

[tex]y=3x+5\ \ \ \ \ (0,5)\\5=3*0+5\\5=0+5\\5\equiv5\\Hence,\\y=3x+5\ pass\ throught\ the\ (0,5)[/tex]